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eijah
20th April 2010, 07:04 PM
I was wondering if "In the beginning was the word" might have anything to do with formal grammars? Or cognitive grammars? Or, even better, cognitive formal grammars? Does anyone here know much about any of that stuff? Especially the cognitive formal grammar one which would seem to me to have combination formation/transformation rules.

Complexity
20th April 2010, 07:28 PM
I was wondering if "In the beginning was the word" might have anything to do with formal grammars? Or cognitive grammars? Or, even better, cognitive formal grammars? Does anyone here know much about any of that stuff? Especially the cognitive formal grammar one which would seem to me to have combination formation/transformation rules.


It has absolutely nothing to do with grammars, formal grammars, cognitive grammars, etc.

Don't give this another thought.

eijah
20th April 2010, 07:48 PM
Do you know a lot about formal and cognitive grammars? And cognitive formal grammars? Or are you just giving me a knee-jerk answer based on some things you know nothing about? Note: I am not saying you do not have the best of intentions!!! But I am looking for facts, not just sincere opinions.

Iconoclast08
20th April 2010, 07:55 PM
Why not divert these sorts of questions toward Hitchhiker's Guide to the Galaxy? The author of that one was drunk, too.

Robin
20th April 2010, 08:05 PM
Looking up cognitive grammars I find the idea was developed from 1982.

I believe St John might have been written a little earlier than that.

Robin
20th April 2010, 08:08 PM
And off the top of my head I would say that the prologue to St John is a borrowing of the Hindu Trinity.

eijah
20th April 2010, 08:12 PM
Finally, a reasonable well-thought out response!!! Yet I would prefer an answer from some expert in formal and cognitive -- and perhaps even formal cognitive grammars. Because my question is based less on history than on the nature of language and the logic of cognition.
But thanks for your response!

Brainache
20th April 2010, 08:21 PM
..."In the beginning was the word"...

I suppose it is possible to see the passage as a recognition that religions became possible only after humans had developed a language complex enough to transmit abstract ideas like God. Without the means to describe the numinous, the concept of religion could not spread.

Whether that means formal or cognitive grammar, I have no idea.

Complexity
20th April 2010, 08:50 PM
Do you know a lot about formal and cognitive grammars? And cognitive formal grammars? Or are you just giving me a knee-jerk answer based on some things you know nothing about? Note: I am not saying you do not have the best of intentions!!! But I am looking for facts, not just sincere opinions.


Actually, I do know a lot about formal grammars, etc.

I have a Ph.D. in computer science from Northwestern. I studied logic, automated reasoning and other aspects of AI (including natural language processing, two-level grammars, etc.). The three qualifying exams that I took and passed were in formal theory, programming languages and compiler theory, and artificial intelligence. Formal theory and compiler theory, in particular, get deeply into formal language theory and formal grammars.

I took several linguistics courses as an undergrad in the 70s, including a course on Chomsky's theory of linguistics that involved transformational grammars. In graduate school, I took two more linguistics courses, one on Chomsky's subsequent theory of linuistics (government/binding theory) and a cool linguistics/psychology seminar on cognitive models of linguistic performance.

I have continued to read in favorite aspects of linguistics, cognitive science, and computer science since getting my doctorate.

Nearly all of my research after graduate school has been on developing algorithms for some classic challenging problems - little to do with linguistics and formal language theory, but very cool nonetheless.

That said, one doesn't need these kinds of interests, education, or study to respond intelligently to your OP.

I do not think that any part of the bible is anything more than a myth.

I do not think that "In the beginning was the word..." has any truth, signficance, or importance.

I did appreciate your effort to tie it to formal grammars, etc., but I'm afraid that I regard that effort as misguided. The study of formal grammars is much more interesting to me than any religious studies.

I don't know what you mean about 'facts' in this context: "In the beginning was the word..." was written by a person who knew nothing about formal grammars. I think you are hoping that the study of formal grammars, etc. will illuminate the 'Word of God', but it can not, since there is no 'god' and no logos.

Sorry, but that's my two cents.

ddt
20th April 2010, 08:50 PM
I was wondering if "In the beginning was the word" might have anything to do with formal grammars? Or cognitive grammars? Or, even better, cognitive formal grammars? Does anyone here know much about any of that stuff? Especially the cognitive formal grammar one which would seem to me to have combination formation/transformation rules.

What would be the connection? The "in the beginning" is just the begin of a story, that of Jesus. Grammars is a tool to analyze natural or formal languages, or to define them. The two are entirely different concepts.

Iconoclast08
21st April 2010, 03:35 AM
Finally, a reasonable well-thought out response!!! Yet I would prefer an answer from some expert in formal and cognitive -- and perhaps even formal cognitive grammars. Because my question is based less on history than on the nature of language and the logic of cognition.
But thanks for your response!

What Complexity said.

While I think that you are a well-intentioned person, I do not think that the question you posed is of the caliber that warrants such a sophisticated and well-thought-out response drawing from the complexities of language and cognition. To me, it's the same as saying that you need a strong background in zoology to fully grasp what is meant in Eastman's Go, Dog. Go!

It just seems like a waste of time and effort. Why not apply this expertise to meaningful questions as opposed to limbic, iron-age musings?

HansMustermann
21st April 2010, 03:40 AM
The Greek idea of Logos was a lot more than "word" or "speech", though. While originally it did mean "word", but also "reason", starting from the 6'th century BC it became a far more profound philosophical concept. It was supposed to be an underlying principle of knowledge and order of the whole universe. It was the very principle that holds the universe together and working, basically.

In a way, when we study dark energy at one end, and quantum mechanics at the other, we are studying that very Logos of Heraclitus and later of the Stoics.

And yes, not all made it divine. A lot of stoics identified it with a reason and animating principle of nature, rather than of a god. In essence, when we study the big bang, we're looking at what the seminal logos that created the universe might have been or done.

In fact, by AD times, they never used "logos" to mean "word" any more. When they wanted to say literally "word", they said "lexis" instead.

For others, logos was any manifestation of divinity, including the universe itself. Any way divinity "speaks" to you, or reveals itself, was logos.

John was likely one step further, and was taking his ideas from Philo. Philo was bridging the gap in Platonism between the imperfect material world and the perfect divine spirit world, with the logos. Logos was not just a principle any more. (Although it still was principle too, and it was what held the world together in his view.) Logos was a living God, a demiurge, "the first-born of God", or the "angel of God", who acted basically as an intermediary between the two realms.

You can probably see by now how John starts basically with Philo's ideas from the first verses... and promptly makes a hash of them.

It's also likely that John didn't literally mean that the Logos as a whole became Jesus, or at least didn't think it through. A world which is no longer permeated and animated by the omnipresent Logos -- because now the Logos as a whole is concentrated in just one special human -- would have died and come apart.

Robin
21st April 2010, 04:20 AM
My earlier reference to the Hindu Trinity was from the Brihad-Aranyaka Upanishad:

This universe is a trinity and this is made of name, form and action. The source of all names is the word for it is by the word tha all names are spoken. The word is behind all names even as Brahman is behind the word.

I think this might have been the source of the Greek idea of Logos.

Compare with John:
In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning.
Through him all things were made; without him nothing was made that has been made
And this passage is, I believe, the source of the Christian Trinity. Although I could be wrong about that.

Dancing David
21st April 2010, 05:13 AM
Finally, a reasonable well-thought out response!!! Yet I would prefer an answer from some expert in formal and cognitive -- and perhaps even formal cognitive grammars. Because my question is based less on history than on the nature of language and the logic of cognition.
But thanks for your response!

Well, I take exception with your logic of cognition, what is that supposed to mean?

I can suppose, but i will wait for your response. My take will be that it is associative and not formal in the sense of Boolean logic.

HansMustermann
21st April 2010, 05:57 AM
In a way, "logic" is just about right. Logos is the root word for logic, which meant the way to reason right, rather than the way to speak right or use the right words. (The latter would be the domain of the lexikon, from lexis.) It's also the root for dialogue, via the Socratic Dialogue genre, also sometimes called the Socratic Logos, but which originally didn't just mean some people talking (although the genre was structured like that) but some wise person dispensing wisdom.

Logos as a proper noun was in a sense basically the logic or sense (as in, "making sense") of the universe.

eijah
21st April 2010, 06:07 AM
Thanks for your learned response! And I can see and appreciate your earlier reaction. And no I AM NOT trying to prove the existence of God, just trying to see if there are any things hidden in the bible that may be of a logical and cognitive nature.

And thus onto and into my program. I think it is well appreciated that natural languages are too complex for a cognitive formal grammar. However there seems to me to be a logical possibility of there being a kind of cognitive formal grammar for formal languages -- or at least one (perhaps trivial, perhaps not) formal language. And I may have stumbled upon it like a blind man who trips over a pot of gold. Or maybe Fools' God.

More specially, please consider what follows per the very limited, but perhaps not completely trivial formal language I have formulated:

1) Start out with an ordered alphabet OX1y, and a formal grammar formation (rewriting) rule of...

OX1y -> OOXO1y1OX11y

Obviously, replacing two characters in a four character string with four characters "should" produce a ten character string. BUT that is not what the rule says! So is the rule meaningless or wrong in some other way or what?

I think that its legitimacy can be seen only if and when one takes a second look (a more thoughtful and mindful look) and re-cognizes that O and 1 are operating as (and thus in a way mean that they are) parenthetical modifiers. And if so, that glimmer of semantic light now shining on what is normally seen as syntax's always semantic darkness seems at least to me to be enough to observe something else in retrospect: I.e., my trivial ordered alphabet OX1y also seems to have some kind of originally unsuspected meaning. (Sorry if I am pushing the term "meaning' too far!)

A long time ago, life took my ego away, so I am fully resigned to being wrong. Yet it does much seem to me that when seen in that glimmer of semantic light, my OX1y ordered alphabet both figuratively contains the left-hand side of the formation/rewriting rule AND also seems to me to be literally revealing that rule. And if so, do we not then have some kind of cognitive formal grammar? Perhaps not the kind that is academically rigorous and complete wnough to satisfy a Ph.D. in linguistics , but one that at least does (with a sense of cognitive adventure) minimally meet both the definitions of formal grammar and cognitive grammar?

And if so, perhaps/maybe/possibly... there is some kind of logic, in re-cognizing that beginning with the right word (and an understanding of that right word in a cognitively informed formal way) leads to more right words. AS WELL AS the ability to parse out all of the wrong non-sense words that were added the centuries by well-meaning fools and not well-meaning knaves. Note: I said perhaps/maybe/possibly. Not surely, but I think it would be a very cool way to look at and contemplate the words and wording of all kinds of scriptures if I am on to something -- other than on something! :-)

Complexity
21st April 2010, 06:11 AM
My dismissal of logos was with regard to its use in the bible and how xians love to think about it.

The word, untainted by religion, is quite cool.

It isn't by accident that I love to study ancient Greek history. It is so lovely to read about a world that knew nothing of xians and knew or cared nothing about the OT.

eijah
21st April 2010, 07:15 AM
Indeed, VERY cool! And from what you said, I suppose what I I am trying to see if some kind of cognitive formal grammar might be able to be used to parse various statements in various scriptures to separate the wheat from the chaff so to speak. :-) And even if not likely, perhaps possible.

In any case, what do you make of my ordered alphabet and an associated production rule which produces 12 letters instead of 10? And my possibly misguided, perhaps not observation that it in retrospect seems to add a glimmer of implicit meaning to the explicit syntax?

Robin
21st April 2010, 07:41 AM
I don't think you are seeing the big picture.

A method of parsing scriptures is tinkertoys. You have got to think bigger. Here is the text in question again.

In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning.
Through him all things were made; without him nothing was made that has been made

That is clearly talking about much more than a method of parsing scripture. That is saying that through the Word all things were made.

We know that there are various conjectures going around about a very simple rule being able to explain all of physics. Feynman briefly suggested something like this. Also Wolfram and more recently the idea has been taken up more seriously.

A very simple rule - an automaton - is something like a formal grammar.

And also you will recall that God calls himself the alpha and the omega. An alphabet is also necessary for a formal grammar.

So here is the idea - there is a word - say YVH and a rule for manipulating this word (encoded somewhere in the Bible, possibly Leviticus or the Apocalypse) using a particular alphabet.

And this would - given a sufficiently large number of iterations - would end up describing all the known laws of physics and provide the basis for solving all the outstanding problems of physics.

Am I onto something here? Oh, excuse me there is someone at the door. What is an albino monk doing out this time of night...?

eijah
21st April 2010, 08:07 AM
Hi Robin.

Alas, I think very small. not very big. So what I am looking to know is whether or not my production rule that produces 12 character instead of 10 has a glimmer of semantics in its syntax? And what the logical and cognitive consequences might be?

OTOH, I cheerfully cheer you on in your investigation of the unlikely, but I suppose possible possibility that the Tetragrammaton is the key that unlocks the secrets of the bible. And perhaps adds insights about physics and I suppose also biology, economics, politics... if I am correctly following your (at least to me) somewhat questionable logic.

drkitten
21st April 2010, 08:14 AM
Do you know a lot about formal and cognitive grammars?

Yes, he does. And for that matter, yes, I do.

And cognitive formal grammars?

Yes, I do.

And Complexity is dead-on accurate.

drkitten
21st April 2010, 08:16 AM
Alas, I think very small. not very big. So what I am looking to know is whether or not my production rule that produces 12 character instead of 10 has a glimmer of semantics in its syntax?

No, it doesn't.


And what the logical and cognitive consequences might be?

None.

HansMustermann
21st April 2010, 08:17 AM
Just to hammer on that some more: while such a parsing method may or may not exist, the Logos is not it. Logos was basically mis-translated as "word" there. Well, ok, not as much "mis-translated" as simply no other languages than Greek had a single word for that concept. "Word" is a probably the closest English word you can get that is still one single word, and yet horribly wrong sematically.

What John was very likely saying, really has _nothing_ to do with words, speech, grammar, or method of parsing a text.

Basically if you must start your quest for a bible-code from somewhere, well, at least don't base it on a mis-translation ;)

drkitten
21st April 2010, 08:25 AM
More specially, please consider what follows per the very limited, but perhaps not completely trivial formal language I have formulated:

1) Start out with an ordered alphabet OX1y, and a formal grammar formation (rewriting) rule of...

OX1y -> OOXO1y1OX11y

Obviously, replacing two characters in a four character string with four characters "should" produce a ten character string.

You're not "replacing" two characters with four in any meaningful sense. You might think that you're replacing the X and 1 with something (and leaving the O and the y alone) :

O OXO1y 1OX11 y

But if you look at that "replacement" the replacement is actually 5 for 1, not 4 for 1.


BUT that is not what the rule says! So is the rule meaningless or wrong in some other way or what?

No, the statement that is wrong is the meta-statement that "replacing two characters in a four character string with four characters "should" produce a ten character string." That doesn't have any connection with the particular production rule you described above.


I think that its legitimacy can be seen only if and when one takes a second look (a more thoughtful and mindful look) and re-cognizes that O and 1 are operating as (and thus in a way mean that they are) parenthetical modifiers.

No. Semantic interpretation is independent of the syntax; while you can impose a form of semantics on it if you like, that's completely inside the privacy of your own mind.

That's pretty fundamental set theory, actually; to any satisfiable set of (formal) productions there are usually zillions of models that instantiate and satisfy them. There's no such thing as _the_ semantics of a given syntactic production.

And if so, do we not then have some kind of cognitive formal grammar?

No.


Perhaps not the kind that is academically rigorous and complete wnough to satisfy a Ph.D. in linguistics , but one that at least does (with a sense of cognitive adventure) minimally meet both the definitions of formal grammar and cognitive grammar?

No.


And if so, perhaps/maybe/possibly... there is some kind of logic, in re-cognizing that beginning with the right word (and an understanding of that right word in a cognitively informed formal way) leads to more right words. AS WELL AS the ability to parse out all of the wrong non-sense words that were added the centuries by well-meaning fools and not well-meaning knaves.

:notm

Robin
21st April 2010, 08:30 AM
Hi Robin.

Alas, I think very small. not very big. So what I am looking to know is whether or not my production rule that produces 12 character instead of 10 has a glimmer of semantics in its syntax? And what the logical and cognitive consequences might be?

OTOH, I cheerfully cheer you on in your investigation of the unlikely, but I suppose possible possibility that the Tetragrammaton is the key that unlocks the secrets of the bible. And perhaps adds insights about physics and I suppose also biology, economics, politics... if I am correctly following your (at least to me) somewhat questionable logic.
No, you don't understand. It doesn't unlock the secrets of the Bible. It only unlocks the secrets of the universe.

eijah
21st April 2010, 08:49 AM
No, it doesn't.



None.

You may well be right. But just saying it is not does not make it not right, unless you are God. Which I very much doubt is the case for a number of logical reasons, including the fact that it is unlikely that there is a God.

So getting beyond your God Role-playing, I cannot see how you can be correct about what you are insisting is true by fiat. Although I suppose you might be correct from using a logic argument.

In any case, once again, here is my problem...

If we see formal grammar as syntax only, and we begin with OX1y and we simultaneously replace X and y with OX1y, we get OOX1y1OX1y, yes?

But our production rule instead gives us OOXO1y1Ox11y. So what is this revealing? That is, how can this production rule be made sense of?
I am inclined to believe only be realizing that O and 1 are parenthetical operators. I.e., O means () and thus OX is equivalent to (X) and 1 stands for [1] and thus Oy is equivalent to [y]. And if so, then there is at least a glimmer of semantics in what we originally took as wholly being syntax.

You may heartily disagree, and maybe you really are correct. But if you actually do have anything useful to contribute to this thread, please stop playing God and instead start being serious if you have the right expertise, and a helpful way of applying it.

eijah
21st April 2010, 08:51 AM
Jeez, this is so confusing to me. I mean OOXO1y1OX11y :-(

PixyMisa
21st April 2010, 08:59 AM
But our production rule instead gives us OOXO1y1Ox11y. So what is this revealing?
Absolutely nothing.

Robin
21st April 2010, 09:01 AM
In any case, once again, here is my problem...

If we see formal grammar as syntax only, and we begin with OX1y and we simultaneously replace X and y with OX1y, we get OOX1y1OX1y, yes?

But our production rule instead gives us OOXO1y1Ox11y. So what is this revealing?
That different rules give different results?

PixyMisa
21st April 2010, 09:13 AM
Well, there's that. ;)

Philosaur
21st April 2010, 09:18 AM
You are switching production rules mid-argument, which is the source of your confusion.

Here's your original rule:

OX1y -> OOXO1y1OX11y


And here's where you specify your second (pair of) rules:

we begin with OX1y and we simultaneously replace X and y with OX1y, we get OOX1y1OX1y, yes?

Which, when written out as rules is:

1. X -> OX1y
2. Y -> OX1y

So it's no surprise that you get 12 characters by applying your original production rule, and only 10 characters when applying this new pair of rules.

What's the mystery again?

eijah
21st April 2010, 09:27 AM
I think you are correct, but with a twist.

What I mean is that the statement "replace the X and y in OX1y with OX1y" gives both a purely syntactical right-hand of the rule AND a right-hand alternative one introducing us to some glimmer of meaning. This might be like the way changing the parallel lines stuff in Euclid introduced us to non-Euclidean geometry. Or maybe not. In any case, I am neither a linguist nor a mathematician, just for better and worse an iconoclastic bull in a conventional wisdom china shop. With the possibility of my having stumbled upon a cognitive formal grammar.

Robin
21st April 2010, 09:31 AM
I think you are correct, but with a twist.

What I mean is that the statement "replace the X and y in OX1y with OX1y" gives both a purely syntactical right-hand of the rule AND a right-hand alternative one introducing us to some glimmer of meaning.
But how does it lead to the alternate one? It doesn't as far as I can see.

drkitten
21st April 2010, 09:32 AM
In any case, once again, here is my problem...

If we see formal grammar as syntax only, and we begin with OX1y and we simultaneously replace X and y with OX1y, we get OOX1y1OX1y, yes?

But our production rule instead gives us OOXO1y1Ox11y. So what is this revealing?

That your second production rule is a different production rule (than the first).

That is, how can this production rule be made sense of?

Nothing else need be "made sense of." Production rules are arbitrary transformations.

Philosaur
21st April 2010, 09:37 AM
A long time ago, life took my ego away, so I am fully resigned to being wrong.
I am neither a linguist nor a mathematician, just for better and worse an iconoclastic bull in a conventional wisdom china shop. With the possibility of my having stumbled upon a cognitive formal grammar.

Whew, that was a quick 180!

Well, you may have stumbled upon a cognitive formal grammar, but neither your logos argument nor your production rules will ever convince anyone who knows anything about formal or cognitive grammars.

Have fun being the lonely, misunderstood genius you've cast yourself to be!

eijah
21st April 2010, 09:38 AM
You are switching production rules mid-argument, which is the source of your confusion.

Here's your original rule:


And here's where you specify your second (pair of) rules:

Which, when written out as rules is:

1. X -> OX1y
2. Y -> OX1y

So it's no surprise that you get 12 characters by applying your original production rule, and only 10 characters when applying this new pair of rules.

What's the mystery again?

Much thanks, and right on when we have two rules. But I think that when there is only one rule, we ironically end up with both the semantic ambiguity found in pure syntax per the first (conventional) interpretation of the rule AND also an optional (non-conventional) glimmer of semantics per the alternative.

Philosaur
21st April 2010, 09:42 AM
Much thanks, and right on when we have two rules. But I think that when there is only one rule, we ironically end up with both the semantic ambiguity found in pure syntax per the first (conventional) interpretation of the rule AND also an optional (non-conventional) glimmer of semantics per the alternative.

You're just re-stating your conclusion. Where's the argument (that we haven't already dealt with) to back it up? Or are you just expressing an opinion?

drkitten
21st April 2010, 09:48 AM
But I think that when there is only one rule, we ironically end up with both the semantic ambiguity found in pure syntax per the first (conventional) interpretation of the rule AND also an optional (non-conventional) glimmer of semantics per the alternative.

No. There is no "semantic ambiguity found in pure syntax" because pure syntax by definition has no semantics.

That's actually one of the deeper results in the fundamentals of 20th century logic and mathematics, and it underlays many (most?) of the major results -- the independence of the continuum hypothesis, the Löwenheim–Skolem theorem, and of course the various Gödelian incompleteness results, Tarski's undecidability of truth, &c. Basically, syntax cannot fully express semantics; semantics can only be imposed upon a system by an observer -- and any reasonably complex system can always have multiple valid interpretations imposed upon it (if it can have any at all).

Philosaur
21st April 2010, 10:01 AM
Gavagai!

eijah
21st April 2010, 11:16 AM
You're just re-stating your conclusion. Where's the argument (that we haven't already dealt with) to back it up? Or are you just expressing an opinion?

Neither. Just the observation that simultaneous replacing X and y in OX1y with OXly either produces OOX1OyOOX11y or OOX1y1OX1y, depending on whether O and 1 are parenthetical modifier operators or are not.

And, of course, asking those on this thread, per the former, the logical reasons why or why not OX1y -> OOx1OyOOx11y is a production rule for some kind of, apparently previously not examined, possible cognitive formal grammar. Note: resorting to authority in this case has as much weight with me as relying on a Scholastic proof of God to explain why apples fall from the limbs of trees. We can see two different results when O and 1 do and do not mean operating as parenthetical modifiers. Bringing in Goedel, Tarski and Hutch and Santa Claus and St. Augustine... seem to me to add nothing to answering my question.

BTW, considering the emotionally changed nature of many of the reactions in this section, and totally apart from my original Logos context (which was only a means of fitting my cognitive formal grammar question into this P&R section), perhaps exploring my and other possible cognitive formal grammars is better accomplished in some other topic in this Forum! Any suggestions?

drkitten
21st April 2010, 11:43 AM
Neither. Just the observation that simultaneous replacing X and y in OX1y with OXly either produces OOX1OyOOX11y or OOX1y1OX1y, depending on whether O and 1 are parenthetical modifier operators or are not.

But this "observation" has already been shown false.



And, of course, asking those on this thread, per the former, the logical reasons why or why not OX1y -> OOx1OyOOx11y is a production rule for some kind of, apparently previously not examined, possible cognitive formal grammar.

Because there's nothing "cognitive" about an arbitrary rewrite rule.


Note: resorting to authority in this case has as much weight with me as relying on a Scholastic proof of God to explain why apples fall from the limbs of trees. We can see two different results when O and 1 do and do not mean operating as parenthetical modifiers. Bringing in Goedel, Tarski and Hutch and Santa Claus and St. Augustine... seem to me to add nothing to answering my question.

In other words, you ask a question to which you do not know enough to understand the answer.


BTW, considering the emotionally changed nature of many of the reactions in this section, and totally apart from my original Logos context (which was only a means of fitting my cognitive formal grammar question into this P&R section), perhaps exploring my and other possible cognitive formal grammars is better accomplished in some other topic in this Forum! Any suggestions?

Absolutely. Abandon All Hope.

Robin
21st April 2010, 11:44 AM
Neither. Just the observation that simultaneous replacing X and y in OX1y with OXly either produces OOX1OyOOX11y or OOX1y1OX1y, depending on whether O and 1 are parenthetical modifier operators or are not.
As everyone is saying - different rules produce different results.

Stipulating that 0 and 1 are treated differently for the purposes of substitution just makes it a different rule.
And, of course, asking those on this thread, per the former, the logical reasons why or why not OX1y -> OOx1OyOOx11y is a production rule for some kind of, apparently previously not examined, possible cognitive formal grammar.
We would first need to see the reasons that you think that it is a rule for a previously not examined cognitive formal grammar.

But you have provided no support for your claim so far. Perhaps, since you are asking others for logical arguments, you could set an example and present a formal logical argument for your conclusion.

Philosaur
21st April 2010, 11:45 AM
Neither. Just the observation that simultaneous replacing X and y in OX1y with OXly either produces OOX1OyOOX11y or OOX1y1OX1y, depending on whether O and 1 are parenthetical modifier operators or are not.

Look, production rules are meant to act like functions: for any given input, there will be one--and only one--output. You are free to specify production rules that give ambiguous output, but then you aren't dealing with formal systems anymore.

The whole problem here is your phrase "depending on whether O and 1 are parenthetical modifier operators or are not." This question must be decided in order to write your production rules. If they *do* perform some grammatical function, then you specify that in your rules. It's not a question of whether they "might".


We can see two different results when O and 1 do and do not mean operating as parenthetical modifiers.

And those two different results come about because you are using two different sets of production rules. Again, no mystery about it.


Bringing in Goedel, Tarski and Hutch and Santa Claus and St. Augustine... seem to me to add nothing to answering my question.

You aren't even really asking a question here, are you?


BTW, considering the emotionally changed nature of many of the reactions in this section, and totally apart from my original Logos context (which was only a means of fitting my cognitive formal grammar question into this P&R section), perhaps exploring my and other possible cognitive formal grammars is better accomplished in some other topic in this Forum! Any suggestions?
Yeah, formal grammars are just the sort of hot-button topic that gets people all hot and bothered. Kind of like how I can't talk to my family about the ontology of mathematical objects or Calabi-Yau spaces at Thanksgiving.

Nobody's getting emotionally charged. It's just frustrating talking to people who are already convinced they are correct, but insist that they are merely searching for truth. You'll get the same reaction in any topic on this forum.

cienaños
21st April 2010, 12:00 PM
*snippers*

Yeah, formal grammars are just the sort of hot-button topic that gets people all hot and bothered. Kind of like how I can't talk to my family about the ontology of mathematical objects or Calabi-Yau spaces at Thanksgiving.

Whoa. Super cool nerd alert. Way cool. :)

Nobody's getting emotionally charged. It's just frustrating talking to people who are already convinced they are correct, but insist that they are merely searching for truth. You'll get the same reaction in any topic on this forum.

Is it woo that I can see elijah taking the piss?

eijah
21st April 2010, 12:52 PM
No. There is no "semantic ambiguity found in pure syntax" because pure syntax by definition has no semantics.

That's actually one of the deeper results in the fundamentals of 20th century logic and mathematics, and it underlays many (most?) of the major results -- the independence of the continuum hypothesis, the Löwenheim–Skolem theorem, and of course the various Gödelian incompleteness results, Tarski's undecidability of truth, &c. Basically, syntax cannot fully express semantics; semantics can only be imposed upon a system by an observer -- and any reasonably complex system can always have multiple valid interpretations imposed upon it (if it can have any at all).

Thanks for your very helpful response!

In trying to, as carefully as I can, parse your post so as to do justice to your expertise and what you are telling me, do I see a small, but potentially very significant modification of your position here. More specifically...

"Basically, syntax cannot fully express semantics; semantics can only be imposed upon a system by an observer "

Seems to me, Dr. Kitten, that what you are saying above is that syntax can at times -- at least partially -- express semantics. If so, then what is so absolutely wrong with the possibility that my production rule string of 12 characters may have some sort of meaning, a glimmer of semantics resulting from its initially unsuspected, and apparently easily dismissed parenthetical modifier operators? And, furthermore, addressing the second part of your statement, while I have no reason to deny that semantics needs to be fully imposed by the observer (other than referring you and others here to the work of post-Chomsky linguists such as Langacker), how about a less than full degree or level of semantics not needing to be fully imposed by the observer?

Giggywig
21st April 2010, 01:02 PM
Stupid question. Starting with OX1y and the rules X->OX1y and y->OX1y how are you getting to OOX1OyOOX11y? Specifically, how are you getting the 'Oy'? In the original and in the two rules y is always preceded by 1.

eijah
21st April 2010, 01:33 PM
Stupid if there are two rules. Incomprehensible to you if there is one rule.

On the other hand, what is still incomprehensible to you even IF there is only ONE rule is comprehensible to me. You simply have not invested the tiny amount of time and effort required to figure out why replacing X and y in OX1y with Ox1y can be OOXO1y1OX11y? I may be right or I may be wrong about the possibility of having stumbled upon a kind of cognitive formal grammar. Either way, thanks everyone for a very enjoyable day here in Randiland.

Giggywig
21st April 2010, 02:32 PM
Stupid if there are two rules. Incomprehensible to you if there is one rule.

On the other hand, what is still incomprehensible to you even IF there is only ONE rule is comprehensible to me. You simply have not invested the tiny amount of time and effort required to figure out why replacing X and y in OX1y with Ox1y can be OOXO1y1OX11y? I may be right or I may be wrong about the possibility of having stumbled upon a kind of cognitive formal grammar. Either way, thanks everyone for a very enjoyable day here in Randiland.

Ok, I will invest the time.
Start: OX1y
Replace x with OX1y: OOX1y1y
Replace (original) y with OX1y: OOX1y1OX1y

Hmmm not working. To get the result you mention I would have to do:
Start: OX1y
Replace x with OXO1y: OOXO1y1y
Replace (original) y with OX11y: OOXO1y1OX11y

So uhm... those are two different rules. How are you getting your result?

cienaños
21st April 2010, 02:57 PM
Ok, I will invest the time.
Start: OX1y
Replace x with OX1y: OOX1y1y
Replace (original) y with OX1y: OOX1y1OX1y

Hmmm not working. To get the result you mention I would have to do:
Start: OX1y
Replace x with OXO1y: OOXO1y1y
Replace (original) y with OX11y: OOXO1y1OX11y

So uhm... those are two different rules. How are you getting your result?


Might I have the sword, my liege? So that I may wash it. I say, quite impressive what you did back there. Quite. Impressive. Yes.

ddt
21st April 2010, 04:21 PM
"Basically, syntax cannot fully express semantics; semantics can only be imposed upon a system by an observer "

Seems to me, Dr. Kitten, that what you are saying above is that syntax can at times -- at least partially -- express semantics.
In the context of formal languages, a formal two-level grammar can encode those parts that are conventionally called "static semantics" - notably the type of an expression. See, e.g., the ALGOL-68 report for an example. In the context of natural languages, this would be aspects like number and gender of a word. See, e.g., this affix grammar (http://www.agfl.cs.ru.nl/grammars/meko.gra) for English.


If so, then what is so absolutely wrong with the possibility that my production rule string of 12 characters may have some sort of meaning,
I'm utterly confused what is so special about your production rule. Did you spot it one day while walking in the forest? I think not, you constructed it yourself. So could you also tell us which of those symbols are terminals and which are non-terminals, to begin with?

eijah
21st April 2010, 04:35 PM
Ok, I will invest the time.
Start: OX1y
Replace x with OX1y: OOX1y1y
Replace (original) y with OX1y: OOX1y1OX1y

Hmmm not working. To get the result you mention I would have to do:
Start: OX1y
Replace x with OXO1y: OOXO1y1y
Replace (original) y with OX11y: OOXO1y1OX11y

So uhm... those are two different rules. How are you getting your result?

Thank you VERY much for at least trying!!!

This is how I get the result in question...

OX1y = (X)[y] = (x[y

I
V

OOXO1y1OX11y = ((X))([y])[(X)][[y]] = ((X([y[(X[[y


As I have said many times here, I stumbled upon this (BTW, via a reference to the Lindenmayer Grammar). I have no idea at all what my "grammar" is or if it really is anything special. However, it does seem to an amateur like me from reading definitions of a formal grammar and a cognitive grammar, that the above represent three versions of a singular production rule of some kind of cognitive formal grammar. Of course, maybe not. But perhaps interesting and of use in some way(s) some time and some where, even if not here and now.

Note: I particularly like the O and 1 form. Because O and 1 conjure up for me curiously informative mathematics-like and perhaps physical-like images. For example, imagine, at some varying rate of change, squeezing/flattening (X) out of existence while at the same time, but (perhaps at some other varying rate of change) elongating [y] until it ends up as a very tall and skinny Y. Only an analogy, I readily admit, but to me very easy to imagine. Even if not very academically sound.

PixyMisa
21st April 2010, 05:59 PM
You're doing it wrong.

eijah
21st April 2010, 07:06 PM
I know that I am doing it differently, but that does not necessarily mean that I am doing it wrong. I think that one of the consequences of what I am exploring is that different classes of parentheses can possibly have unsuspected properties. I am not saying that I am correct about this, but, e.g., while it is relatively easy to see how OX1y can map into OOXO1y1OX11y, and how (X[y can map into ((X([y[(X[[y, seeing how (X)[y] maps into ((X))([y])[(X)][[y]] takes a lot of cpu power and time. Likely very much not worth your time. Nor the time of most others here. But considering that OX1y = (X)[y] = (X[y, seeing how the mapping of (X)[y] is done might be a very interesting puzzle. Maybe not.

PixyMisa
21st April 2010, 07:12 PM
I know that I am doing it differently, but that does not necessarily mean that I am doing it wrong.
In this case, yes, it does. A transformation rule always produces the same output for any given input. If it doesn't, it's not a transformation rule, it's just nonsense.

eijah
21st April 2010, 07:32 PM
OX1y -> OOXO1y1OX11y and (X[y -> ((X([y[(X[[y and -> (X)[y] -> ((X))([y])[(X)][[y]].

All are equivalent descriptions of the same production rule.

As also is OX1y -> O (OX1y) 1 (OX1y) and thus also is OOXO1y 1OX11y.

So what about the above is specifically not producing the same output?

Complexity
21st April 2010, 08:19 PM
I'm going to write a few posts on different aspects of the issues raised in this thread.

eijah has written a few constructive pms. Perhaps this is why I'm being far nicer that usual. While I don't find any merit in his proposal and program, there may be something reachable there.

eijah - I haven't encountered the phrase 'cognitive formal grammar' before.

What do you mean by your use of the term 'cognitive' with regards to formal grammars?

drkitten and several other responders have been quite correct, yet you discount what they say by using terms such as 'God Role-playing'.

While you pay some of us compliments, referring to our expertise, you nearly immediately discount that expertise and suggest that it may not apply.

You seem to feel that your ideas aren't understood.

Several of these traits are characteristic of people that many of like to refer to as 'woo'. Your manner of writing and interaction, as well as your newness to the disciplines and confidence that something very important has been discovered, have raised several of these 'woo' red flags.

If you don't want to be taken for a woo, please take some time to read through this thread again with these remarks in mind and see if you could have written differently and more constructively.

Robin
21st April 2010, 08:38 PM
OX1y -> OOXO1y1OX11y and (X[y -> ((X([y[(X[[y and -> (X)[y] -> ((X))([y])[(X)][[y]].

All are equivalent descriptions of the same production rule.

As also is OX1y -> O (OX1y) 1 (OX1y) and thus also is OOXO1y 1OX11y.

So what about the above is specifically not producing the same output?
Let me remind you of what you are saying:
In any case, once again, here is my problem...

If we see formal grammar as syntax only, and we begin with OX1y and we simultaneously replace X and y with OX1y, we get OOX1y1OX1y, yes?

But our production rule instead gives us OOXO1y1Ox11y. So what is this revealing? That is, how can this production rule be made sense of?

So the tranformation I have highlighted as blue gives a different output to the transformation I have highlighted in green. That was your whole point.

But now you seem to be saying something else (again). Now it is not clear what you are claiming.

Which is why I suggested earlier that you try to sort out in your own mind what your claim is and then set it out in a clear logical fashion.

Complexity
21st April 2010, 08:39 PM
Formal language theory (of which formal grammars are an important aspect) has to do with sequences of symbols, determine which sequences are part of a language and which are not, and many issues such as syntax, complexity, parsing, etc.

The symbols in formal language theory have no meaning. The sequences of symbols in formal language theory have no meaning. Syntax and grammar in this context can be used without any regard for semantics (meaning).

One poster mentioned two-level grammars that may involve some aspect of semantics. Without criticizing his statement, I'm afraid that it muddies the water a bit. Formal language theory is meaning-free - semantics does not have a place in it.

One can always attempt to mix semantics in, but semantics are always an add-on and irrelevant to the underlying mathematical structures that are being studied by formal language theory.

Production rules such as the ones that interest you are rules that transform one sequence of symbols into another sequence of symbols. The transformation is entirely mechanical and without inherent meaning. Production rules in formal language theory have nothing to do with semantics or meaning.

So where does meaning come into this?

As drkitten said, meaning is an act of interpretation - a mapping of the formal into the world of meaning. An interpretation of a formal construct is valid if it is consistent; otherwise it is invalid and useless. Formal language theory has nothing to do with interpretation and meaning.

Why do people study and enrich formal language theory? It is cool, it is an interesting area of mathematics, there are some beautiful theorems and proofs, and it is very useful, especially since the rise of computers and the development of programming languages. Programs written in programming languages need to be 'parsed', a level of analysis that can be meaning-free, in order to be translated into machine code so that they can be executed. Some of the analysis involved in the translation involves meaning, but not that part involving formal language theory.

To recap, formal grammars, production rules, and other aspects of formal language theory do not need meaning, do not profit from any pasted-on meaning, and do not result in meaning if they are peered at with meaning in mind.

Complexity
21st April 2010, 08:54 PM
You have said that you are interested in whether "some kind of cognitive formal grammar might be able to be used to parse various statements in various
scriptures to separate the wheat from the chaff so to speak".

Syntactic techniques of formal language theory, such as the development and use of production rules to transform sequences of uninterpreted symbols, can not be used to extract meaning from those sequences of uninterpreted symbols.

Formal language theory has nothing to do with meaning, and its techniques can not be used to extract meaning from text. We add the meaning through interpretation.

You are hoping to use formal syntactic techniques that involve no meaning to extract meaning from text. This is not possible.

Sequences of symbols, including text, have meaning only because of how we choose to interpret them. An interpretation that is not consistent has no value; however, that doesn't mean that an apparently consistent interpretation has value.

A consistent interpretation isn't necessarily true or useful in any sense - it is merely consistent, not resulting in contradictions. That is a pretty low standard.

You want to extract meaning from religious texts. You are assuming that there is meaning in those religious texts. I think that they are only myths, and that those myths are of minor interest only to the extent that their meaning is close to the surface. I don't think there are interesting or useful codes or mysteries in any of these religious texts.

If you want to extract meaning from a text, you have to apply techniques that involve meaning to the text. Formal-language-related syntactic techniques to a text can not yield meaning - that is not what they are for, and there is no meaning in the sequence of uninterpreted symbols to be extracted.

Complexity
21st April 2010, 09:04 PM
I do not think that there is any value in the bible or in the study of the bible. Any meaning - secrets, codes, mysteries, or purported wisdom - that is there was placed there by commonplace, uninspired people, not by a non-existent deity.

A few parts are pretty in a well-written translation, but overall I'd be content to let the thing be forgotten. Far too much damage has been done in its name.

We live in a wonderful universe. Your curiousity is commendable, but you are wasting your time on this sort of inquiry.

Please consider learning a real discipline (e.g. any field of hard science) and use it to investigate reality.

This attempt to tease meaning out of a hack religious text is unworthy of a human life. You can do much better, you deserve much better, and talking with you would be vastly more rewarding.

Complexity
21st April 2010, 09:08 PM
eijah - I hope that you read through this thread a few times before replying.

Think about things.

Don't rush into a defense of and re-presentation of your production rule. We get it and don't find the value in it that you hope is there. It is a shrub that is keeping you from seeing the forest.

Please put your program aside and start afresh. Turn aside from easy and worthless religious mysteries and look instead at reality with an open mind.

Robin
21st April 2010, 09:42 PM
Scriptural language is often the type of language that does not carry meaning, but gives the impression of carrying meaning. This allows people to invest it with their own meaning, or simply to associate a set of emotions with it.

So we get things like "blessed are the peacemakers for they will be called the sons of God", and people talk about the profound wisdom of this and how it underlies everything in Western culture and how Jesus was a Great Teacher even if he was not the Son of God.

But what does it actually mean? Nothing, as far as I can see.

PixyMisa
22nd April 2010, 02:00 AM
OX1y -> OOXO1y1OX11y and (X[y -> ((X([y[(X[[y and -> (X)[y] -> ((X))([y])[(X)][[y]].

All are equivalent descriptions of the same production rule.
No.

So what about the above is specifically not producing the same output?
All of it.

The input is different, the rules are different, and the output is different.

drkitten
22nd April 2010, 04:34 AM
"Basically, syntax cannot fully express semantics; semantics can only be imposed upon a system by an observer "

Seems to me, Dr. Kitten, that what you are saying above is that syntax can at times -- at least partially -- express semantics.

I strongly suggest that you read what I write instead of trying to shoehorn your own error-ridden interpretation of it.

If so, then what is so absolutely wrong with the possibility that my production rule string of 12 characters may have some sort of meaning,

The fact that all production rules are by definition arbitrary and meaningless by themselves.


And, furthermore, addressing the second part of your statement, while I have no reason to deny that semantics needs to be fully imposed by the observer (other than referring you and others here to the work of post-Chomsky linguists such as Langacker), how about a less than full degree or level of semantics not needing to be fully imposed by the observer?

Nope. Arbitrary rules are still arbitrary.

drkitten
22nd April 2010, 04:36 AM
In the context of formal languages, a formal two-level grammar can encode those parts that are conventionally called "static semantics" - notably the type of an expression.

And the keyword "encode" is the important one there. Because even the static semantics are arbitrary and imposed by the reader.

Yes, we know that if x and y are both of type 'int', and we have a syntactic rule that dictates that sums are the type of their constituents, then we know (statically), that x+y is also of type 'int.'

The interpretation of 'int' as an integer is still an arbitrary rule of interpretation, not a syntactic aspect of the language.

eijah
22nd April 2010, 04:39 AM
First, I would like to very much thank everyone here for their responses, especially Complexity. And yes I will VERY carefully reread all of the responses on this thread. BTW, the last few from Complexity have been especially helpful, as has this one from PixyMisa.

Second, I think this latest one from PixyMisa is giving a woo-two like me a glimmer of understanding about what you all have been trying to point out to me. (Note that I am defining a woo-two as a second class of woo (woo-second class lol), one that can be redeemed because he or she is either mis-guided And/oR has yet to be able to articulate adequatley why he or she is right about whatever he or she sees. Some examples of woo-twos are George Simon Ohm, Ignatz Semmelwiess, Boltzmann. You all know the list far better than I do.) In any case, it is incumbent on woo-two's to communicate in a way that authority figures in an area of knowledge can understand and appreciate, else woo-two's are consigned to the woo heap. So a heap of thanks for hanging in there with me and allowing me to as gracefully as I can hang my self but not to the point of being considered an un redeemable woo-first class.

And now that I have thanked everyone, here is what I think is the basic problem I have been having with you and that you have been having with me...

When I recently asked something along the lines of whether it was clear that

OX1y -> OOXO1y1OX11y and (X[y -> ((X([y[(X[[y and -> (X)[y] -> ((X))([y])[(X)][[y]]

are all equivalent descriptions of the same production rule, PixyMisa said no. And when I asked what about the above is specifically not producing the same output? the answer was everything.

And those responses just blew me away, folks. So I am now rightly or wrongly think that MY problem has been not seeing things the way all of you do per the use of the words syntax and semantics. Here is what I mean...

To me

OX1y -> OOXO1y1OX11y and (X[y -> ((X([y[(X[[y and -> (X)[y] -> ((X))([y])[(X)][[y]]

are a) the use of three different notations (each having a particular syntax) to describe the same production rule. Each of these uses of similar-looking syntaxes is meant by me to mean the same thing: replace the X and y in the ordered alphabet OX1y with the ordered alphabet Ox1y. b) To all of you -- I think -- the above are three different syntaxes, each being used to describe a different production rule, by definition different because each syntax is different. Please, per my above a and b, yes, no? And why?

Giggywig
22nd April 2010, 05:18 AM
Ok so let's try this again. I'm using curly braces to show where I am substituting.
OX1y -> O{OX1y}1{OX1y} -> OOX1y1OX1y
(X[y -> ({(X[y}[{(X[y} -> ((X[y[(X[y
(X)[y] -> ({(X)[y]})[{(X)[y]}] -> ((X)[y])[(X)[y]]

I am still unable to get your results.

drkitten
22nd April 2010, 05:19 AM
To all of you -- I think -- the above are three different syntaxes, each being used to describe a different production rule, by definition different because each syntax is different.

Yup. That's because production rules are defined in terms of string replacement; if you use different notation or different replacement schemes, it's a different rule.

That's not normally a problem because you can have two different but equivalent production rule -- for example, people will talk about various "normal forms" --- but you need to define what you mean by "equivalent." If you don't define it, people will usually assume that an equivalent production is functionally equivalent. Given the same input string, an equivalent production will by definition produce an identical output string.

You don't have that here. Therefore, your productions are by definition different, and also by conventional definition not equivalent. So why should we be surprised or interested by your finding that different rules are different?

eijah
22nd April 2010, 06:22 AM
I'm going to write a few posts on different aspects of the issues raised in this thread.

eijah has written a few constructive pms. Perhaps this is why I'm being far nicer that usual. While I don't find any merit in his proposal and program, there may be something reachable there.

eijah - I haven't encountered the phrase 'cognitive formal grammar' before.

What do you mean by your use of the term 'cognitive' with regards to formal grammars?

drkitten and several other responders have been quite correct, yet you discount what they say by using terms such as 'God Role-playing'.

While you pay some of us compliments, referring to our expertise, you nearly immediately discount that expertise and suggest that it may not apply.

You seem to feel that your ideas aren't understood.

Several of these traits are characteristic of people that many of like to refer to as 'woo'. Your manner of writing and interaction, as well as your newness to the disciplines and confidence that something very important has been discovered, have raised several of these 'woo' red flags.

If you don't want to be taken for a woo, please take some time to read through this thread again with these remarks in mind and see if you could have written differently and more constructively.

Hi Complexity, one at a time...

"eijah has written a few constructive pms. Perhaps this is why I'm being far nicer that usual. While I don't find any merit in his proposal and program, there may be something reachable there."

Thanks for the kind words, and for being open to "may".

"eijah - I haven't encountered the phrase 'cognitive formal grammar' before."

I guess I made it up. Although I thought there was such a term. Thanks for informing me of its novelty.

"What do you mean by your use of the term 'cognitive' with regards to formal grammars?"

My understanding of the conventional wisdom is that formal grammars define what strings of characters from an alphabet are valid in a language. And that those strings from a formal grammar point of view are devoid of specific meanings/semantics. I use the term "cognitive" in the sense of its use in Langacker's use of the term cognitive in his and others' "cognitive grammars" which seek to add semantics to syntax. If people here dismiss my notion of a cognitive formal grammar because they cannot conceive of a grammar with both syntax and semantics, then I think, by definition, they cannot conceive of a cognitive grammar. If that is the case, there definitely is a barrier to many here understanding of my notion of a cognitive formal grammar. But those who have a problem with me are also likely also to have a problem with Langacker, et al., none of whom I would suspect would be considered woos. Or might, depending on one's view of woo-dom.

"drkitten and several other responders have been quite correct, yet you discount what they say by using terms such as 'God Role-playing'.

When I read DrKitten's responses, they often seem to me to be delivered from on high. Like Moses (if not God) deeming to point out the error of my and others' ways. Usually not pointing out them in any very specific ways, but rather just chastising an idiot and fool. And while I may be an idiot and a fool, DrKitten strikes me as being quite pompous. But I may have the good doctor wrong. She, he or it may be a very reasonable and even delightful person with those who pass beyond woo-dom to a more sympatico state of grace.

"While you pay some of us compliments, referring to our expertise, you nearly immediately discount that expertise and suggest that it may not apply."

Ir may well apply. And/or it may get in the way. From a cogsci/cogpsych point of view, I think it is fair to say that people, even PH.D.'s, see things through the lenses of our beliefs and our knowledge bases. If something is very different per one of our most basic beliefs, that something tends to be immediately dismissed, usually without a second thought. And possibly immediately labeled as woo. If it has at least some of the look and feel of acceptable knowledge, it may be passed along to one's cognitive processing unit for some further deliberation. All of that is context for this response of mine to your question: I am much inclined to think that expertise provides an often much needed context for evaluating content. But what happens when the content in question subsumes the expert's context? That is, when he or she is trying to understand the content in question within a context that does not contain a place for that contentious content?

The history of science and math show over and over again that due to the tension between complexity and simplicity, when a new larger context destined to ultimate be seen is conceived of, the tendency is for experts to dismiss it as woo, until sooner or later that new context is accepted, usually by those who are not the established experts, but rather a new breed. On the other hand, sometimes it is an established expert who puts the new larger context on the map. It would be great if you turn out to end up being mine!!! :-)

"You seem to feel that your ideas aren't understood."

I do feel that my ideas are not being understood here. If I felt otherwise I would be as crazy as some folks here think I am. However, I do not feel that I am being dismissed because of stupidity or ignorance, either mine or the others here. But rather due to different perspectives and uses of terminology -- and different contexts and sets of content. Complexity is what cognition is all about, and thus makes for such a great moniker for this Forum, yes! :-)
As a complementary seeker of wisdom and truth, I'm thinking of changing mine to Simplicity.

"Several of these traits are characteristic of people that many of like to refer to as 'woo'. Your manner of writing and interaction, as well as your newness to the disciplines and confidence that something very important has been discovered, have raised several of these 'woo' red flags. "

I know it. But it does seem to come with thinking-out-of-the-box territory. And it raises an interesting cognitive science/cognitive psychology question, at least to me: How does an expert determine what is woo and what is not, if the question in question is a conceptual one? The simple answer is that the question in question is evaluated based on what the expert believes to be true and not true, and what the expert knows to be true and not true. By the way, I am using the term "belief" in the sense of "axiom". So what happens when there is no way for the question in question to fit into the expert's knowledge base, or, even worse, is counter to one or more of the expert's most fundamental beliefs? Alas, Complexity, I think the difference between eternal woo-dom and new wis-dom is often far less a matter of who is dumb and who is clever, and more a matter of being able to think out of the box. However, as we all know, most people who do think too far out of the box ought to be locked up in one. So we find ourselves in a very cool and interesting place. Either to entertain new and strange and objectionable ideas without believing them (I think Aristotle said it first), or to let others do that kind of heavy lifting and perhaps unrewarding thinking for us. Skeptics of course tend to do the former because they have neither the time nor the inclination, plus they tend to be guided exclusively by their knowledge based and barred by their beliefs. Woos and those who are not woos both do the latter. And as I would rather be considered one of you than a woo, I (as best the discoverer/inventor of cognitive formal grammar can) will do my best to try to follow your advice below in the context of what is above!

"If you don't want to be taken for a woo, please take some time to read through this thread again with these remarks in mind and see if you could have written differently and more constructively.

eijah
22nd April 2010, 06:26 AM
Yup. That's because production rules are defined in terms of string replacement; if you use different notation or different replacement schemes, it's a different rule.

That's not normally a problem because you can have two different but equivalent production rule -- for example, people will talk about various "normal forms" --- but you need to define what you mean by "equivalent." If you don't define it, people will usually assume that an equivalent production is functionally equivalent. Given the same input string, an equivalent production will by definition produce an identical output string.

You don't have that here. Therefore, your productions are by definition different, and also by conventional definition not equivalent. So why should we be surprised or interested by your finding that different rules are different?

MUCH THANKS for the details and the clarity of your very helpful recent response!!!

eijah
22nd April 2010, 06:54 AM
MUCH THANKS for the details and the clarity of your very helpful recent response!!!

I GET IT!!!

More to follow. And again MUCH THANKS!!! You are VERY cool!

Philosaur
22nd April 2010, 07:00 AM
To me

OX1y -> OOXO1y1OX11y and (X[y -> ((X([y[(X[[y and -> (X)[y] -> ((X))([y])[(X)][[y]]

are a) the use of three different notations (each having a particular syntax) to describe the same production rule. Each of these uses of similar-looking syntaxes is meant by me to mean the same thing: replace the X and y in the ordered alphabet OX1y with the ordered alphabet Ox1y. b) To all of you -- I think -- the above are three different syntaxes, each being used to describe a different production rule, by definition different because each syntax is different. Please, per my above a and b, yes, no? And why?


a) You cannot have the same production rule described in three notations. You only have three production rules. A production rule is inextricably bound to its notation, because a production rule is a rule for manipulating the symbols within that notation. But you were not fully getting this, because you said "Each of these...is meant by me to mean the same thing." Right here you are explicitly *assigning* the meaning to the rules.

Now, don't misunderstand, you are free to assign meaning to rules and symbols--that's what humans do. But the moment you start assigning meaning, you stop doing formal grammar and you've moved on into something else entirely.


b) Exactly. Three syntaxes, three rules.

Incidentally, has anyone else heard of "cognitive linguistics" or Ronald Langacker? That's apparently the jumping off point for this thread. I would be curious to see if there's any relation with Fodor's Language of Thought.

eijah
22nd April 2010, 07:35 AM
a) You cannot have the same production rule described in three notations. You only have three production rules. A production rule is inextricably bound to its notation, because a production rule is a rule for manipulating the symbols within that notation. But you were not fully getting this, because you said "Each of these...is meant by me to mean the same thing." Right here you are explicitly *assigning* the meaning to the rules.

Now, don't misunderstand, you are free to assign meaning to rules and symbols--that's what humans do. But the moment you start assigning meaning, you stop doing formal grammar and you've moved on into something else entirely.


b) Exactly. Three syntaxes, three rules.

Incidentally, has anyone else heard of "cognitive linguistics" or Ronald Langacker? That's apparently the jumping off point for this thread. I would be curious to see if there's any relation with Fodor's Language of Thought.

Much thanks. And please note that Ronald Langacker established "cognitive grammar". Which, apparently, is about only natural languages, not formal ones.

Also... To the best of my knowledge, no linguists have as yet moved into "cognitive formal grammar" territory. Thus, leaving the field completely my domain. Which, folks, seems to make me (ala, a Seinfeld episode) the master of my cognitive domain! Mental masturbation made legit! Ya' can't make this stuff up. although of course, that is what I have been apparently doing until now.

But seriously, to now help me get away from being or or even acting woo, does anyone know how we can properly formulate a single formal grammar production/re-write rule, where we begin with an ordered alphabet OX1y and we iteratively keep replacing X and y in OX1y with OX1y, such that we first end up with OOXO1y1OX11y -- in the same way that using a Lindermayer grammar can start with an equilateral triangle and with each new iteration end up producing a Koch curve?

drkitten
22nd April 2010, 07:36 AM
My understanding of the conventional wisdom is that formal grammars define what strings of characters from an alphabet are valid in a language. And that those strings from a formal grammar point of view are devoid of specific meanings/semantics. I use the term "cognitive" in the sense of its use in Langacker's use of the term cognitive in his and others' "cognitive grammars" which seek to add semantics to syntax. If people here dismiss my notion of a cognitive formal grammar because they cannot conceive of a grammar with both syntax and semantics, then I think, by definition, they cannot conceive of a cognitive grammar.

This is one of the key marks of the woo. "If people claim that I am wrong, it's because they can't conceive what I'm dong."

You're misinterpreting Langacker's work. He's not creating a grammar with both syntax and semantics; he's merely pointing out that human grammars follow certain grammatical constraints that reflect semantic categorization -- in other words, there are lots of grammars that are mathematically valid but not cognitively plausible. And of course this in and of itself isn't surprising; X-bar theory also says that there are mathematically but not cognitively plausible grammars, as do the various typological constraints.

Heck, we've known that all human languages have nouns and verbs for centuries. This means that any grammar that doesn't include those particular syntactic category is cognitively invalid even if mathematically legitimate.

Langacker just ties some of the constraints to semantics in a way that X-bar theory doesn't (i.e. the properties of a particular concept will restrict its expression; if the concept is a 'thing,' it will be expressed as a phrase head and most likely as a noun; actions are also phrase heads but verbs, and properties are generally not clause heads like adjectives and adverbs.)



Ir may well apply. And/or it may get in the way.

Another mark of the woo. "The reason that experts disagree with me is because they're seeing things through the lenses of their prejudices." It's not possible that the experts disagree because you get the basic facts wrong?


I do feel that my ideas are not being understood here.

A third mark of the woo. Well, maybe just the first in a different phrasing....


I know it. But it does seem to come with thinking-out-of-the-box territory. And it raises an interesting cognitive science/cognitive psychology question, at least to me: How does an expert determine what is woo and what is not, if the question in question is a conceptual one?

Compatibility with existing terminology and basic data is a good start. If you're using concepts and terminology in a non-standard way, you need to be able to start by expressing yourself in standard terms and explaining in standard terms how your viewpoints and theories differ from the standard. In the case of the syntax/semantics split, the very definition of syntax is that it includes no semantics. Pure syntax overgenerates (there are syntactically valid but meaningless sentences), especially if you're using an extremely general framework like arbitrary production rules.

Indeed, that was one of Chomsky's early findings: the notion of restricted grammars such as context-free grammars or regular grammars, which are better descriptors and thus presumptively more cognitive.

drkitten
22nd April 2010, 07:42 AM
Incidentally, has anyone else heard of "cognitive linguistics" or Ronald Langacker?

Yes, and yes. "Cognitive linguistics" is a hugely influential subfield that basically rejects the competence/performance distinction postulated by Chomsky and tries to understand how the influences of the human cognitive system affect language as we see it.

Simple example -- why don't people produce infinitely-long sentences? There's nothing in the mathematics to prevent it. Is it a memory limitation? Is it a limitation of the speaker or the hearer, or both? How can we adjust the mathematical descriptions of language to reflect this apparent cognitive limitation?

PixyMisa
22nd April 2010, 08:05 AM
a) You cannot have the same production rule described in three notations. You only have three production rules. A production rule is inextricably bound to its notation, because a production rule is a rule for manipulating the symbols within that notation. But you were not fully getting this, because you said "Each of these...is meant by me to mean the same thing." Right here you are explicitly *assigning* the meaning to the rules.

Now, don't misunderstand, you are free to assign meaning to rules and symbols--that's what humans do. But the moment you start assigning meaning, you stop doing formal grammar and you've moved on into something else entirely.
Exactly. I was going to come back and say this more explicitly myself, but you've done it for me. :)

eijah, you seem to be arguing that these rules are semantically equivalent. That's fine, but it's also arbitrary. Syntactically they're clearly distinct.

drkitten
22nd April 2010, 08:14 AM
eijah, you seem to be arguing that these rules are semantically equivalent. That's fine, but it's also arbitrary. Syntactically they're clearly distinct.

Is he about to re-invent transformational grammar?

eijah
22nd April 2010, 08:19 AM
Again, You are being VERY helpful!!! Whenever I can see where I have been wrong about something, that is good!! So thanks for taking the time to help me see the error.



This is one of the key marks of the woo. "If people claim that I am wrong, it's because they can't conceive what I'm dong."

You're misinterpreting Langacker's work. He's not creating a grammar with both syntax and semantics; he's merely pointing out that human grammars follow certain grammatical constraints that reflect semantic categorization -- in other words, there are lots of grammars that are mathematically valid but not cognitively plausible. And of course this in and of itself isn't surprising; X-bar theory also says that there are mathematically but not cognitively plausible grammars, as do the various typological constraints.

Heck, we've known that all human languages have nouns and verbs for centuries. This means that any grammar that doesn't include those particular syntactic category is cognitively invalid even if mathematically legitimate.

Langacker just ties some of the constraints to semantics in a way that X-bar theory doesn't (i.e. the properties of a particular concept will restrict its expression; if the concept is a 'thing,' it will be expressed as a phrase head and most likely as a noun; actions are also phrase heads but verbs, and properties are generally not clause heads like adjectives and adverbs.)




Another mark of the woo. "The reason that experts disagree with me is because they're seeing things through the lenses of their prejudices." It's not possible that the experts disagree because you get the basic facts wrong?



A third mark of the woo. Well, maybe just the first in a different phrasing....



Compatibility with existing terminology and basic data is a good start. If you're using concepts and terminology in a non-standard way, you need to be able to start by expressing yourself in standard terms and explaining in standard terms how your viewpoints and theories differ from the standard. In the case of the syntax/semantics split, the very definition of syntax is that it includes no semantics. Pure syntax overgenerates (there are syntactically valid but meaningless sentences), especially if you're using an extremely general framework like arbitrary production rules.

Indeed, that was one of Chomsky's early findings: the notion of restricted grammars such as context-free grammars or regular grammars, which are better descriptors and thus presumptively more cognitive.

Philosaur
22nd April 2010, 08:24 AM
Simple example -- why don't people produce infinitely-long sentences? There's nothing in the mathematics to prevent it. Is it a memory limitation? Is it a limitation of the speaker or the hearer, or both? How can we adjust the mathematical descriptions of language to reflect this apparent cognitive limitation?

Well, a simple non-cognitive reason--people die. But I'm sure that's not what you meant.

I'm not sure I understand the question. It's hard to imagine the need to express an infinitely long proposition. Maybe one day someone might want to recite a list of positive integers?

In any case, why would we adjust the mathematical descriptions of language to account for contingent, practical limitations imposed by human biology?

drkitten
22nd April 2010, 08:37 AM
Well, a simple non-cognitive reason--people die. But I'm sure that's not what you meant.

I'm not sure I understand the question. It's hard to imagine the need to express an infinitely long proposition. Maybe one day someone might want to recite a list of positive integers?

But that's exactly the sort of thing "cognitive linguistics" studies.

You're right, of course, that no human can actually utter an "infinitely long" sentence. But humans don't even utter (or write) novel-length sentences. Or even sentences of twenty-five hundred words.

I suggested that this was a memory limitation. You suggested that this was a pragmatic limitation (there's nothing we need to say that takes 100,000 words as a single sentence.) One of us is probably wrong. :D

And that's where the research comes in.


In any case, why would we adjust the mathematical descriptions of language to account for contingent, practical limitations imposed by human biology?

Because language is a product of human biology; to understand language, we need to understand the influence of biology. (And to fully understand biology, we need to understand language.) To understand something, we usually need to describe it first....

Philosaur
22nd April 2010, 09:10 AM
But that's exactly the sort of thing "cognitive linguistics" studies.

You're right, of course, that no human can actually utter an "infinitely long" sentence. But humans don't even utter (or write) novel-length sentences. Or even sentences of twenty-five hundred words.

Someone did publish a (/n albeit incomprehensible) novel length sentence:

http://www.prleap.com/pr/121058/


I suggested that this was a memory limitation. You suggested that this was a pragmatic limitation (there's nothing we need to say that takes 100,000 words as a single sentence.) One of us is probably wrong. :D

And that's where the research comes in.

I wonder if it's strictly necessary to remember much of anything while speaking. I know several people who would be hard pressed to remember what they said at the beginning of a conversation--and yet the conversation serves the communicative purpose. So on the surface, the inability to remember the beginning of the sentence would not be a problem.

Now it could be that the inability to think through to the end of the sentence might seem to be the issue. But I'm sure most people don't pre-construct their sentences before saying them.

In any case, sorry for the derail--I do realize that's why people are doing the research. It's very interesting stuff.


Because language is a product of human biology; to understand language, we need to understand the influence of biology. (And to fully understand biology, we need to understand language.) To understand something, we usually need to describe it first....

I was confusing the mathematical descriptions of human language with the mathematical descriptions of languages as formal systems.

...Which brings up another point: why don't we create infinitely long statements in computer languages? I would submit it's because computer languages, like human languages, are operational--they both have a communicative or declarative goal in mind, and an infinitely long statement in a computer language could not be executed.

Anyway, this is all off-the-cuff thinking, so it may be way off base. Eijah, sorry for the derail.

eijah
22nd April 2010, 09:28 AM
Ok so let's try this again. I'm using curly braces to show where I am substituting.
OX1y -> O{OX1y}1{OX1y} -> OOX1y1OX1y
(X[y -> ({(X[y}[{(X[y} -> ((X[y[(X[y
(X)[y] -> ({(X)[y]})[{(X)[y]}] -> ((X)[y])[(X)[y]]

I am still unable to get your results.


Thanks, and here I think is the crux of the problem. And, hopefully, a solution. Or at least pointing you to a solution.

I do not think you can do it the way you are trying yo do it. But it might be used with an additional facote to consider. Note I do not know why you cannot do it that way. Just that from what you are trying to do, it does not work that way.

On the other hand, there does seem to be a way of getting the result, IF one takes "replacing both the X and y in OX1y with OX1y" to mean doing those replacements in the way that a Lindermayer fractal/grammar does all of its re-writes, changes, replacements... simultaneously).

By doing both of our substitutions at the same time, seems to me to acceptably produce O(OX1y)1(Ox1y) = OOXOO1y1OX11y.

I am guessing that there is a way of using the kind of method you are trying to use to get this result, but that it requires somehow adding in the requirement of simultaneous substitution, which does exist in Lindenmayer grammar. But perhaps not in the method you are using. Either way, I greatly look forward to seeing if adding the requirement of simultaneity works!!!

eijah
22nd April 2010, 09:36 AM
Greatly hope that simultaneously doing the replacing works out!!!

Robin
22nd April 2010, 10:02 AM
Greatly hope that simultaneously doing the replacing works out!!!
But you only have one rule.

Giggywig
22nd April 2010, 10:13 AM
By doing both of our substitutions at the same time, seems to me to acceptably produce O(OX1y)1(Ox1y) = OOXOO1y1OX11y.
I am going to assume that's a typo and you meant to write: O(OX1y)1(Ox1y) = OOXO1y1OX11y
Simultaneous or not, doesn't matter. How is that an equality? On the left side you have the correct substitution (with parenthesis) and on the right, where you should have only removed the parenthesis all of a sudden you have something else entirely. Split it in two parts:
1) O(OX1y) = OOXO1y - Where is the third 'O' coming from?
2) 1(Ox1y) = 1OX11y - Where is the third '1' coming from?

Philosaur
22nd April 2010, 10:29 AM
I am going to assume that's a typo and you meant to write: O(OX1y)1(Ox1y) = OOXO1y1OX11y
Simultaneous or not, doesn't matter. How is that an equality? On the left side you have the correct substitution (with parenthesis) and on the right, where you should have only removed the parenthesis all of a sudden you have something else entirely. Split it in two parts:
1) O(OX1y) = OOXO1y - Where is the third 'O' coming from?
2) 1(Ox1y) = 1OX11y - Where is the third '1' coming from?

I had the same question, but it's pretty clear he's not doing formal grammar stuff.

First, there's no way to specify two discrete replacements in one rule. You have two replacements (like X and y), you get two rules.

Second, if we perform the (two separate) replacements simultaneously (in the same iteration), we get:

0X1y -> 0{0X1y}1{0X1y} -> 00X1y10X1y

If we perform the replacements serially with the X first, we get:

1. 0X1y -> 0{0X1y}1y -> 00X1y1y

we pull the last term from above, and now replace the y...

2. 00X1y1y -> 00X1{0X1y}1{0X1y} -> 00X10X1y10X1y


If instead, we do the replacements with the y first, we get:

1. 0X1y -> 0X1{0X1y} -> 0X10X1y

then replace the X...

2. 0X10X1y -> 0{0X1y}10{0X1y}1y -> 00X1y100X1y1y

In both cases, we get 13-character strings different from the string you've got.

Giggywig
22nd April 2010, 10:34 AM
Oh yeah I understand, I was being charitable in doing the changes simultaneously, because even then I can't get his results.

Philosaur
22nd April 2010, 11:02 AM
Oh yeah I understand, I was being charitable in doing the changes simultaneously, because even then I can't get his results.

Yeah, sorry. I quoted you, then referred the text to him.

We can't reproduce his results because there are undefined operations taking place. When asked to elucidate, he just says something like "Well, it's evident. You just replace them, and it works!"

eijah
22nd April 2010, 01:18 PM
I had the same question, but it's pretty clear he's not doing formal grammar stuff.

First, there's no way to specify two discrete replacements in one rule. You have two replacements (like X and y), you get two rules.

Second, if we perform the (two separate) replacements simultaneously (in the same iteration), we get:

0X1y -> 0{0X1y}1{0X1y} -> 00X1y10X1y

If we perform the replacements serially with the X first, we get:

1. 0X1y -> 0{0X1y}1y -> 00X1y1y

we pull the last term from above, and now replace the y...

2. 00X1y1y -> 00X1{0X1y}1{0X1y} -> 00X10X1y10X1y


If instead, we do the replacements with the y first, we get:

1. 0X1y -> 0X1{0X1y} -> 0X10X1y

then replace the X...

2. 0X10X1y -> 0{0X1y}10{0X1y}1y -> 00X1y100X1y1y

In both cases, we get 13-character strings different from the string you've got.

Great!!! I actually came to the same conclusion that this is not about formal logic by rereading all of the entries of this thread. SO let's for now remove ourselves from formal logic in all its respects and instead solve this puzzle...

How do we begin with OX1y and by simultaneously replacing x and y in OX1y with OX1y end up with OOXO1y1OX11y instead of OOX1y1OX1y? Please note that the solution becomes clear just by noticing that the 12 character result looks like the result of this math transformation:
O(OX1y)1(OX1y) = OOXO1y1OX11y.

From the above mathematical analogy, I think it is logical to guess that the 12 character result can be produced from the replacings when O and 1 in the alphabet are used in and by the transformation rule as () & (). And perhaps as () & [] (if we wish to distinguish O from 1.)

If we are looking at all this outside the field of formal grammar, does this hopefully non-woo resolution of the 10 character vs. 12 character conflict make sense to anyone here besides me? By the way, an interesting aside, from Gk. parenthesis, lit. "a putting in beside."

aggle-rithm
22nd April 2010, 01:22 PM
It's also likely that John didn't literally mean that the Logos as a whole became Jesus, or at least didn't think it through. A world which is no longer permeated and animated by the omnipresent Logos -- because now the Logos as a whole is concentrated in just one special human -- would have died and come apart.

Kind of like the concept of the Borg Queen!

I'm still angry about that.

drkitten
22nd April 2010, 01:24 PM
How do we begin with OX1y and by simultaneously replacing x and y in OX1y with OX1y end up with OOXO1y1OX11y instead of OOX1y1OX1y?

We don't. More accurately, only by making an error.

There is literally no way to end up with "OOXO1y1OX11y" as you suggest; the highlighted bigram is [provably] impossible.

Similarly, the '11' bigram is impossible.

Giggywig
22nd April 2010, 01:33 PM
How do we begin with OX1y and by simultaneously replacing x and y in OX1y with OX1y end up with OOXO1y1OX11y instead of OOX1y1OX1y? Please note that the solution becomes clear just by noticing that the 12 character result looks like the result of this math transformation:
O(OX1y)1(OX1y) = OOXO1y1OX11y.

I don't see the point in what you are trying to do. Are you trying to lead people to some sort of insight you believe you discovered by making us jump through hoops? Why not just come out and put a detailed step by step process of how you reached your solution?

Anyways...

1) OX1y
2) Replacing X and y with (OX1y) -> O(OX1y)1(OX1y)
3) "Realizing" that parenthesis can be substituted with a 0 or a 1 depending on, apparently, whim -> OOXO1y1OX11y

And voila! Of course step 3 seems a bit ill defined.

Or put it another way:
Phase 1: Collect Underpants
Phase 2: ?
Phase 3: Profit

eijah
22nd April 2010, 01:44 PM
I don't see the point in what you are trying to do. Are you trying to lead people to some sort of insight you believe you discovered by making us jump through hoops? Why not just come out and put a detailed step by step process of how you reached your solution?

Anyways...

1) OX1y
2) Replacing X and y with (OX1y) -> O(OX1y)1(OX1y)
3) "Realizing" that parenthesis can be substituted with a 0 or a 1 depending on, apparently, whim -> OOXO1y1OX11y

And voila! Of course step 3 seems a bit ill defined.

Or put it another way:
Phase 1: Collect Underpants
Phase 2: ?
Phase 3: Profit

Let me see if I have this right. Are you saying that you see no value in OOXO1y1Ox11y resulting from replacing the X and y in OX1y with Ox1y, when O and 1 are parenthetical modifiers? OR are you saying that you can't see how the 12 character string results from the four character alphabet when using O and 1 as parenthetical modifiers in the replacements?

Philosaur
22nd April 2010, 01:45 PM
Great!!! I actually came to the same conclusion that this is not about formal logic by rereading all of the entries of this thread. SO let's for now remove ourselves from formal logic in all its respects and instead solve this puzzle...

How do we begin with OX1y and by simultaneously replacing x and y in OX1y with OX1y end up with OOXO1y1OX11y instead of OOX1y1OX1y? Please note that the solution becomes clear just by noticing that the 12 character result looks like the result of this math transformation:
O(OX1y)1(OX1y) = OOXO1y1OX11y.

From the above mathematical analogy, I think it is logical to guess that the 12 character result can be produced from the replacings when O and 1 in the alphabet are used in and by the transformation rule as () & (). And perhaps as () & [] (if we wish to distinguish O from 1.)

If we are looking at all this outside the field of formal grammar, does this hopefully non-woo resolution of the 10 character vs. 12 character conflict make sense to anyone here besides me? By the way, an interesting aside, from Gk. parenthesis, lit. "a putting in beside."

You seem not to understand that the very similarity that would ever let you talk about this in terms of math instead of formal logic is exactly the same thing that invalidates your claim in either system.

eijah
22nd April 2010, 02:15 PM
You seem not to understand that the very similarity that would ever let you talk about this in terms of math instead of formal logic is exactly the same thing that invalidates your claim in either system.

You are indeed correct. I do not understand. Are you telling me that there is no similar pattern between O(OX1y)1(OX1y) and OOXO1y1OX11y?

Or are you telling there is no value to seeing the pattern. Or what? I truly am trying to understand where I am off-base. In particular what you mean by "very similarity that would ever let you talk about this in terms of math instead of formal logic is exactly the same thing that invalidates your claim in either system."

Giggywig
22nd April 2010, 02:31 PM
Let me see if I have this right. Are you saying that you see no value in OOXO1y1Ox11y resulting from replacing the X and y in OX1y with Ox1y, when O and 1 are parenthetical modifiers?
Yes. To reach your result you have to make arbitrary manipulations that are in no way obvious or meaningful, even when you consider 0 and 1 as "parenthetical modifiers."
OR are you saying that you can't see how the 12 character string results from the four character alphabet when using O and 1 as parenthetical modifiers in the replacements?
This as well. Whatever you mean by "using O and 1 as parenthetical modifiers" is not being done consistently or meaningfully to reach your result. In addition, I see nothing meaningful or valuable in your result.

Philosaur
22nd April 2010, 02:43 PM
You are indeed correct. I do not understand. Are you telling me that there is no similar pattern between O(OX1y)1(OX1y) and OOXO1y1OX11y?
It's *extremely* difficult to identify a pattern given a single sample without any context. Whatever you are seeing, apparently no one else is seeing. It's not for lack of trying, but because you have a set of assumptions or rules or processes that you are not communicating to us (though you may be trying).


Or are you telling there is no value to seeing the pattern.

Can't see the value if we can't see the pattern.

Or what? I truly am trying to understand where I am off-base. In particular what you mean by "very similarity that would ever let you talk about this in terms of math instead of formal logic is exactly the same thing that invalidates your claim in either system."
Mathematics and formal logic share a very large amount of conceptual space. I don't know whether it's more accurate or precise to say that math is a branch of formal logic, or to say that formal logic is a branch of math, or that they simply overlap.

But the point is, the thing that lets you move from talking about formal systems or grammars to math is that in both you are manipulating symbols via production or translation rules.

Since the moves you are making to get from one string to another seems to involve some unexpressed rules (or simply invalid moves), then shifting from one discipline to another doesn't help you at all.

In short: show your work! You keep simply re-typing the 0X1y -> 0X11y0X...blah thing and insisting that there's a pattern. No one here can see this pattern, because you seem to be violating your own rules to get there.

Complexity
22nd April 2010, 03:28 PM
But that's exactly the sort of thing "cognitive linguistics" studies.

You're right, of course, that no human can actually utter an "infinitely long" sentence. But humans don't even utter (or write) novel-length sentences. Or even sentences of twenty-five hundred words.

I suggested that this was a memory limitation. You suggested that this was a pragmatic limitation (there's nothing we need to say that takes 100,000 words as a single sentence.) One of us is probably wrong. :D

And that's where the research comes in.


I mentioned that I took a graduate seminar at Northwestern (1989, I think) that was offered jointly by linguistics and psychology faculty. We studied cognitive constraints on linguistic performance - how aspects of the brain constrain how well we generate and understand natural languages.

An example: Many of our sentences contain coordination and references between words and clauses. The distance in the sentence between a reference and the phrase referenced, or between two things that are coordinated, may have a lot to do with how easily we can parse the sentence. We can sketch the structure of a sentence as a tree. The types of boundaries that you have to cross in a sentence tree to get from a reference to the phrase being referenced may also have great impact on how easily parsed the sentence is.

Structural oddness may make a sentence difficult to parse even though references and things referred are close in the sentence.

We studied several ingenious experiments that established some practical limits on the complexity of sentences that can easily be parsed and held in one's head for a time. These experiments probe aspects of the brain and how it processes language.

Our most enjoyable and final task was to design an experiment to probe the brain's language processing capability with regard to some aspect of complexity. (I did really well at this. :))

One aspect of the subject that I found especially interesting had to do with complexity constraints that appeared to be independent of the natural languages being studied. Very cool stuff.

eijah
22nd April 2010, 03:29 PM
It's *extremely* difficult to identify a pattern given a single sample without any context. Whatever you are seeing, apparently no one else is seeing. It's not for lack of trying, but because you have a set of assumptions or rules or processes that you are not communicating to us (though you may be trying).


Can't see the value if we can't see the pattern.

Mathematics and formal logic share a very large amount of conceptual space. I don't know whether it's more accurate or precise to say that math is a branch of formal logic, or to say that formal logic is a branch of math, or that they simply overlap.

But the point is, the thing that lets you move from talking about formal systems or grammars to math is that in both you are manipulating symbols via production or translation rules.

Since the moves you are making to get from one string to another seems to involve some unexpressed rules (or simply invalid moves), then shifting from one discipline to another doesn't help you at all.

In short: show your work! You keep simply re-typing the 0X1y -> 0X11y0X...blah thing and insisting that there's a pattern. No one here can see this pattern, because you seem to be violating your own rules to get there.

OK. I won't be back until I can show it in a way that is acceptable you and everyone else here.

Which may mean I will never be back. But in either case, much thanks to everyone here for trying to help me get from woo-dom to wis-dom!!!

Complexity
22nd April 2010, 03:33 PM
...Which brings up another point: why don't we create infinitely long statements in computer languages? I would submit it's because computer languages, like human languages, are operational--they both have a communicative or declarative goal in mind, and an infinitely long statement in a computer language could not be executed.


A computer could handle parsing and processing incredibly long statements in programming languages.

At this point, people are the ones who usually write programming code and who have to maintain it. It is really important to respect the limitations of fairly average human brains if one wishes to write coherent, comprehensible, and maintainable code.

Robin
22nd April 2010, 04:52 PM
SO let's for now remove ourselves from formal logic in all its respects and instead solve this puzzle...

How do we begin with OX1y and by simultaneously replacing x and y in OX1y with OX1y end up with OOXO1y1OX11y instead of OOX1y1OX1y?
But it is not a puzzle.

It is like saying how do you begin by replacing all the s's in Mississippi with x's and end up with Missouri instead of Mixxixxippi.

I am pretty sure I could invent an arbitrariy mathematical rule that would do the trick, but what is the point?

Similarly I am sure I could invent all sorts of arbitrary mathematical rules that would allow your transform to get the result you want but, again, what would be the point?

aggle-rithm
23rd April 2010, 07:01 AM
A computer could handle parsing and processing incredibly long statements in programming languages.

At this point, people are the ones who usually write programming code and who have to maintain it. It is really important to respect the limitations of fairly average human brains if one wishes to write coherent, comprehensible, and maintainable code.

I once came across an almost incomprehensible line of code accompanied by the comment, "Good luck figuring this out."

Very nice.

Philosaur
23rd April 2010, 07:24 AM
A computer could handle parsing and processing incredibly long statements in programming languages.

At this point, people are the ones who usually write programming code and who have to maintain it. It is really important to respect the limitations of fairly average human brains if one wishes to write coherent, comprehensible, and maintainable code.
I know this well--I make my living by programming. I was referring explicitly to *infinitely long* lines of code.

I appreciate the idea of cognitive constraints on language use. I wonder how much different languages test these constraints differently--or cause the speaker's mind (or brain?) to develop different capacities.

Complexity
23rd April 2010, 02:38 PM
I think it unlikely that eijah will be back (PM suggested that this is the case).

One of the things that I discussed in my response was that trying to escape from the difficulties that he was encountering by 'removing the problem from formal logic' would accomplish nothing. It seemed like he was trying to counteract our objections by removing the problem from the context that he though was leading to the objections.

I told him that the problem remains unchanged. All that has been accomplished is that he is denying himself one of his best tools (formal logic) of investigation.

I also urged him to give this up entirely, to read, to learn a good discipline (e.g. a hard science) and to spend his life engaging with reality.

aggle-rithm
23rd April 2010, 08:15 PM
This thread has been a nice break from the conspiracy theory forums.

Complexity
23rd April 2010, 08:33 PM
This thread has been a nice break from the conspiracy theory forums.


I haven't been brave/foolish enough to look at those since I returned to the forums. I have to exhaust this level of crazy before I advance to that one.

Almo
23rd April 2010, 08:41 PM
The Bible, in my opinion, is not very useful except in the study of the history of humanity. We made it, and that fact is interesting. It holds no significance beyond being a set of myths that contains a grain of wisdom here and there.

tsig
23rd April 2010, 09:43 PM
Absolutely nothing.

This is starting to remind me of the ETcorngods translations.:boxedin:

quixotecoyote
23rd April 2010, 09:50 PM
This is starting to remind me of the ETcorngods translations.:boxedin:

Damn you tsig! http://i49.photobucket.com/albums/f253/quixotecoyote/smilies/getyou.gif

I read the first page and had just jumped to the end to ask whether anyone had proven the corngods yet.

tsig
23rd April 2010, 09:59 PM
Damn you tsig! http://i49.photobucket.com/albums/f253/quixotecoyote/smilies/getyou.gif

I read the first page and had just jumped to the end to ask whether anyone had proven the corngods yet.



It's OK, have four corndogs and a coke.:D

Hokulele
24th April 2010, 12:41 AM
Maybe it isn't what the OP intended, but this thread is very cool and I learned a few things. Thanks to all the participants.

eijah
24th April 2010, 05:13 AM
I think it unlikely that eijah will be back (PM suggested that this is the case).

One of the things that I discussed in my response was that trying to escape from the difficulties that he was encountering by 'removing the problem from formal logic' would accomplish nothing. It seemed like he was trying to counteract our objections by removing the problem from the context that he though was leading to the objections.

I told him that the problem remains unchanged. All that has been accomplished is that he is denying himself one of his best tools (formal logic) of investigation.

I also urged him to give this up entirely, to read, to learn a good discipline (e.g. a hard science) and to spend his life engaging with reality.

Hi Complexity and everyone!!! Paradoxically or not, you are both wrong and right. I am back, but with an update that I am very much hoping you will see as an improvement...

Your insistence on mathematical rigor is extremely helpful to someone like me who thinks about all sorts of things, but is not inclined to be mathematically precise! I woke up this morning realizing that this problem might be a lot easier to grasp, wrestle with and prevail over, simply if if were presented in this less notationally dense, and, of course, less mathematically interesting way. But of course, maybe not. So what do you all think?

Replace both X and y in both OX and 1y with both OX and 1y,

which I still think results in OOX O1y 1OX 11y. Albeit, there are nulls which may have to be addressed. And, of course, you can all do that very well, while I can't at all.

Or perhaps there is some other English language replacement rule that does indeed result in

OOXO1y1OX11y beginning with OX1y.

Hope in one way or another this resolves our impasse. And please forgive me if I am still terribly off-base. Which I realize that I may very well be!!! If you continue to show me the errors of my ways, I still hope to escape woo-dom, though, of course, never attain your undeniable states of mathematical wis-dom and intellectual "grace".

Robin
24th April 2010, 05:41 AM
Or perhaps there is some other English language replacement rule that does indeed result in

OOXO1y1OX11y beginning with OX1y.
How about 'Replace OX1y with OOXO1y1OX11y'?

eijah
24th April 2010, 05:51 AM
How about 'Replace OX1y with OOXO1y1OX11y'?

Thanks, but I do not think so. I could be wrong, but I think the over-whelming census has been that that would be wrong. Which is why I am now proposing

Replace both X and y in both OX and 1y with both OX and 1y, which I think does result in OOX O1y 1OX 11y.

aggle-rithm
24th April 2010, 03:24 PM
Thanks, but I do not think so. I could be wrong, but I think the over-whelming census has been that that would be wrong. Which is why I am now proposing

Replace both X and y in both OX and 1y with both OX and 1y, which I think does result in OOX O1y 1OX 11y.

This is the equivalent of a cross join in database theory. It is the basis of the cube structure used in data mining. Every possible combination is stored so they can be scanned for statistical relationships.

Robin
24th April 2010, 04:46 PM
Thanks, but I do not think so. I could be wrong, but I think the over-whelming census has been that that would be wrong. Which is why I am now proposing

Replace both X and y in both OX and 1y with both OX and 1y, which I think does result in OOX O1y 1OX 11y.
There is nothing wrong about it, it is just as valid as any rule.

If your purpose is only to begin with "OX1y" and end with "OOXO1y1OX11y" and nothing else then a direct substitution acheives this purpose perfectly.

So your extra steps add nothing as far as I can see. You still just end up in the same place.

The problem is that you appear to have a secondary purpose, beyond just transforming the first string to the second.

Or else you seem to want to have a constraint on how you get from the first string to the second.

Perhaps if you could explicitly state these it would made things clearer.

Robin
24th April 2010, 05:01 PM
This is the equivalent of a cross join in database theory. It is the basis of the cube structure used in data mining. Every possible combination is stored so they can be scanned for statistical relationships.
A cross join in database theory is equivalent to a cross product in general maths.

But if you were inclined you could think up any number of procedures that would transform one string to the other.

But I can't think why any would be better than a direct substitution, if the purpose is only to transform one string to the other and nothing else.

eijah
24th April 2010, 05:13 PM
There is nothing wrong about it, it is just as valid as any rule.

If your purpose is only to begin with "OX1y" and end with "OOXO1y1OX11y" and nothing else then a direct substitution acheives this purpose perfectly.

So your extra steps add nothing as far as I can see. You still just end up in the same place.

The problem is that you appear to have a secondary purpose, beyond just transforming the first string to the second.

Or else you seem to want to have a constraint on how you get from the first string to the second.

Perhaps if you could explicitly state these it would made things clearer.

OK. And much thanks! And thanks to everyone for helping me to better formulate what I was trying formulate earlier, but in a terrible woo-like way.

Can anyone here rewrite my rule in a formal grammar, starting with OX and 1y? As my original rule Ox 1y -> OOX O1y 1OX 11y was nonsense because the formalism could not work out right, I am now rightly or wrongly assuming that my restatement "Replace both X and y in both OX and 1y with OX and 1y" can be written in a grammatically precise formalized way, yes?

Warmest regards!

Robin
24th April 2010, 05:24 PM
OK. And much thanks! And thanks to everyone for helping me to better formulate what I was trying formulate earlier, but in a terrible woo-like way.

Can anyone here rewrite my rule in a formal grammar, starting with OX and 1y? As my original rule Ox 1y -> OOX O1y 1OX 11y was nonsense because the formalism could not work out right, I am now rightly or wrongly assuming that my restatement "Replace both X and y in both OX and 1y with OX and 1y" can be written in a grammatically precise formalized way, yes?

Warmest regards!
Do you mean using the standard mathematical definition of formal grammar?

Or do you have a specific variant in mind? Or do you mean by inventing a variant of formal grammar for the purpose?

eijah
24th April 2010, 06:05 PM
Do you mean using the standard mathematical definition of formal grammar?

Or do you have a specific variant in mind? Or do you mean by inventing a variant of formal grammar for the purpose?

Great question!!!

Standard mathematical grammar! Hopefully being able to start with the alphabet OX1y. Maybe not.

In any case, earlier it was clearly and emphatically and I am now totally accepting that there cannot be a production rule OX1y -> OOXO1y1OX11y. But we have by now also determined there can a replacing of both X and y in both OX 1y with both OX and 1y. So I am assuming there is a way of using a standard mathematical grammar to describe that production rule.

eijah
24th April 2010, 08:16 PM
Great question!!!

Standard mathematical grammar! Hopefully being able to start with the alphabet OX1y. Maybe not.

In any case, earlier it was clearly and emphatically and I am now totally accepting that there cannot be a production rule OX1y -> OOXO1y1OX11y. But we have by now also determined there can a replacing of both X and y in both OX 1y with both OX and 1y. So I am assuming there is a way of using a standard mathematical grammar to describe that production rule.

Does anyone know what the above standard mathematical grammar looks like?

David Henson
24th April 2010, 08:21 PM
Does anyone know what the above standard mathematical grammar looks like?

Is Jesus God? (http://thedaystar.webs.com/revelation/isjesusgod.html)

PixyMisa
24th April 2010, 09:04 PM
In any case, earlier it was clearly and emphatically and I am now totally accepting that there cannot be a production rule OX1y -> OOXO1y1OX11y.
Sure there can.

The rule:

OX1y -> OOXO1y1OX11y

Works fine, as already pointed out.

But what's the point? What are you trying to achieve?

Complexity
25th April 2010, 12:14 AM
Is Jesus God? (http://thedaystar.webs.com/revelation/isjesusgod.html)


No. Don't be silly.

Jeebus isn't even jeebus.

Robin
25th April 2010, 03:28 AM
Great question!!!

Standard mathematical grammar!
Here is what is usually meant by a grammar in maths:

http://mathworld.wolfram.com/Grammar.html

Do you mean that?
Hopefully being able to start with the alphabet OX1y. Maybe not.
You can if you want.
In any case, earlier it was clearly and emphatically and I am now totally accepting that there cannot be a production rule OX1y -> OOXO1y1OX11y.
Of course there can.

Why do you keep insisting that there cannot?

As I said before, if all you want to do is to transform the string "OX1y" to "OOXO1y1OX11y" then just use the production rule above.

But as I said before and as PixaMisa has also said, you must state clearly what you are trying to achieve.

eijah
25th April 2010, 04:16 AM
Here is what is usually meant by a grammar in maths:

http://mathworld.wolfram.com/Grammar.html

Do you mean that?

You can if you want.

Of course there can.

Why do you keep insisting that there cannot?

As I said before, if all you want to do is to transform the string "OX1y" to "OOXO1y1OX11y" then just use the production rule above.

But as I said before and as PixaMisa has also said, you must state clearly what you are trying to achieve.

I am insisting nothing. I am now yielding to Dr Kitten and others here who have shown me the errors in my original way of thinking about this. Clearly, just doing the OX1y -> OOXO1y1OX11y replacement is not mathematically sound. Unless there is something wrong with what Dr. Kitten and others here have over and over again pointed out. But obviously, that is impossible. E.g.,...


Originally Posted by eijah View Post

How do we begin with OX1y and by simultaneously replacing x and y in OX1y with OX1y end up with OOXO1y1OX11y instead of OOX1y1OX1y?
We don't. More accurately, only by making an error.

Response from Dr. Kitten View Post

There is literally no way to end up with "OOXO1y1OX11y" as you suggest; the highlighted bigram is [provably] impossible.

Similarly, the '11' bigram is impossible.


So if there is no way to go from OX1y to OOXO11y1Ox11y than we have no recourse but to accept that. On the other hand, it seems now from some others here that we can, "Replace both X and y in OX1y with both OX and 1y." So I am guessing that there is a standard mathematical grammar way of doing that. So. step by step, what is that step by step formation?

Robin
25th April 2010, 05:24 AM
I am insisting nothing. I am now yielding to Dr Kitten and others here who have shown me the errors in my original way of thinking about this. Clearly, just doing the OX1y -> OOXO1y1OX11y replacement is not mathematically sound. Unless there is something wrong with what Dr. Kitten and others here have over and over again pointed out. But obviously, that is impossible. E.g.,...


Originally Posted by eijah View Post

How do we begin with OX1y and by simultaneously replacing x and y in OX1y with OX1y end up with OOXO1y1OX11y instead of OOX1y1OX1y?
We don't. More accurately, only by making an error.

Response from Dr. Kitten View Post

There is literally no way to end up with "OOXO1y1OX11y" as you suggest; the highlighted bigram is [provably] impossible.

Similarly, the '11' bigram is impossible.

drkitten is responding to a different question, see the part I highlighted in blue.

You can't do it with the method suggested.

But OX1y -> OOXO1y1OX11y is a perfectly valid production (depending of course on a fuller description of this grammar). And it is the natural choice if all you want to do is to go from "OX1y" to "OOXO1y1OX11y".

You might be able to do it in the way you suggest or in any number of different ways, but why would you want to add unnecessary complication?
On the other hand, it seems now from some others here that we can, "Replace both X and y in OX1y with both OX and 1y." So I am guessing that there is a standard mathematical grammar way of doing that. So. step by step, what is that step by step formation?
You did not answer my question. I cited from the Wolfram cite in my earlier post what is normally referred to as a grammar. Is that what you are referring to?

http://mathworld.wolfram.com/Grammar.html

But at a first glance the procedure you propose does not appear to result in the string you say it does.

eijah
25th April 2010, 05:46 AM
drkitten is responding to a different question, see the part I highlighted in blue.

You can't do it with the method suggested.

But OX1y -> OOXO1y1OX11y is a perfectly valid production (depending of course on a fuller description of this grammar). And it is the natural choice if all you want to do is to go from "OX1y" to "OOXO1y1OX11y".

Much thanks for this response of yours! If you can tell me what that fuller description is, I think I may be able to adequately answer your question. Or at least enable you to answer it for yourself.



You might be able to do it in the way you suggest or in any number of different ways, but why would you want to add unnecessary complication?


I would MUCH prefer no complications, as I believe you also.



You did not answer my question. I cited from the Wolfram cite in my earlier post what is normally referred to as a grammar. Is that what you are referring to?

Sorry. Perhaps yes, perhaps not. I am inclined to guess that I may be referring to Lindermayer grammar or a variation. http://en.wikipedia.org/wiki/L-system

http://mathworld.wolfram.com/Grammar.html

Robin
25th April 2010, 05:57 AM
Much thanks for this response of yours! If you can tell me what that fuller description is, I think I may be able to adequately answer your question.
That would, as I said, depend upon which specific variant you are referring to
Or at least enable you to answer it for yourself.
But nobody can do that unless we know what you are trying to achieve, as I said.
Sorry. Perhaps yes, perhaps not. I am inclined to guess that I may be referring to Lindermayer grammar or a variation. http://en.wikipedia.org/wiki/L-system
Not familiar with that one. Only an undergrad you see. Perhaps one of the post-grads could help.

Robin
25th April 2010, 06:28 AM
However I have just downloaded "The Algorithmic Beauty of Plants" so let me have a look.

Obviously we have to bend the rules a little to accommodate your suggested productions.

Robin
25th April 2010, 06:35 AM
At a first iteration you have suggested something like a context free L-System (V,ω,P) :

V=OX1y
ω=OX1y
P=(X->Ox)(X->1y)(y->OX)(y->1y)

I think. Which sort of bends the rules, as I said, however since you are after a new sort of grammar then I think we can allow it for the sake of argument.

eijah
25th April 2010, 07:32 AM
However I have just downloaded "The Algorithmic Beauty of Plants" so let me have a look.

Obviously we have to bend the rules a little to accommodate your suggested productions.

I think you are right, but I am not certain. All I know is that I was not trying to invent anything new.

In any case, from reading about Lindenmayer fractals and Lindenmayer grammars, I realized in a flash that replacing X and Y in OX1y with OX1y does not produce OOX 1Oy 1OX 11y UNLESS the rules are as you say "bent a little". And I soon also noticed that the only way it works is when there is SOME sort of parenthetical-like property associated with O and 1, a kind of ( and [ that enables the production rule to be an alternative to producing OOx1y and 1OX1y as a result of replacing both X and y in OX1y.

If I am wrong, I am wrong. No big deal. Just another woo woo-woo-ing

However, if in the unlikely event I am right, then you may have just found a thesis that might make your career -- or at least get you some well-earned attention from some part of the academic community. Perhaps, helping you get into an elite graduate program. If that happens, I will be very happy to have assisted you in a non-woo way. Of course, you will have to be infinitely rigorous or you -- like me, will be seen as a woo. I would not want that to happen to you. There are enough real woos here and elsewhere, no need to have a reasonable fellow like like you added to that list!

PixyMisa
25th April 2010, 08:55 AM
I think you are right, but I am not certain. All I know is that I was not trying to invent anything new.

In any case, from reading about Lindenmayer fractals and Lindenmayer grammars, I realized in a flash that replacing X and Y in OX1y with OX1y does not produce OOX 1Oy 1OX 11y UNLESS the rules are as you say "bent a little". And I soon also noticed that the only way it works is when there is SOME sort of parenthetical-like property associated with O and 1, a kind of ( and [ that enables the production rule to be an alternative to producing OOx1y and 1OX1y as a result of replacing both X and y in OX1y.
No. That just means you have different production rules.

If I am wrong, I am wrong. No big deal. Just another woo woo-woo-ing
You're wrong.

Complexity
25th April 2010, 09:09 AM
eijah - Please don't try to run before you can crawl.

There is no reason for you to struggle with anything other than standard production rules at this point. Learn them - master them.

As I've said, however, I really don't think there is anything to your project. I don't think there is anything of value to be extracted from the religious texts that interest you. I don't think that the methods you hope to develop can discover anything of value where none exists. Garbage in, garbage out.

You would do far better to find a real discipline that interests you and study it well.

eijah
25th April 2010, 10:15 AM
You are well-intentedly advising me to stop thinking about this. But you also have as your motto, "Thought is subversive and revolutionary, destructive and terrible; thought is merciless to privilege, established intuititions, and comfortable habit. Thought looks into the pit of hell and is not afraid. Thought is great and swift and free, the light of the world, and the chief glory of man." It is my motto as well. Curious how freely thinking about things from different perspectives can lead to different points of view, and as a result, impossibilities for you and possibilities for me, yes? :-)

eijah
25th April 2010, 10:23 AM
No. That just means you have different production rules.


You're wrong.

You highlight an interesting thought, though you may not want to think about it further: what is grammatically different using formal grammar between replacing X and y in OX1y with OX1y vs. replacing both X and y in OX1y with both OX and 1y? And how is that similar and different when instead using a Lindenmayer grammar?

Complexity
25th April 2010, 10:23 AM
You are well-intentedly advising me to stop thinking about this. But you also have as your motto, "Thought is subversive and revolutionary, destructive and terrible; thought is merciless to privilege, established intuititions, and comfortable habit. Thought looks into the pit of hell and is not afraid. Thought is great and swift and free, the light of the world, and the chief glory of man." It is my motto as well. Curious how freely thinking about things from different perspectives can lead to different points of view, and as a result, impossibilities for you and possibilities for me, yes? :-)


eijah - Please don't confuse the 'thought' that is in that quotation with what passes for thought for many people.

I've advised you to avoid a mess that is soaked in woo and superstition.

You've politely declined to be steered away.

At this point, I don't know what can be constructively done with your situation, so I'm going to let you be. I won't be enabling what I regard as wasteful delusion by helping you understand anything about production rules. It pains me to see techniques for which I have respect coopted by woo.

Perhaps you'll grow out of this stuff, but I have better things to do than watch and hope.

eijah
25th April 2010, 11:11 AM
eijah - Please don't confuse the 'thought' that is in that quotation with what passes for thought for many people.

I've advised you to avoid a mess that is soaked in woo and superstition.

You've politely declined to be steered away.

At this point, I don't know what can be constructively done with your situation, so I'm going to let you be. I won't be enabling what I regard as wasteful delusion by helping you understand anything about production rules. It pains me to see techniques for which I have respect coopted by woo.

Perhaps you'll grow out of this stuff, but I have better things to do than watch and hope.

Complexity, farewell. But for what it is worth, I find it very thought-provoking that I have not mentioned even the slightest bit about religion since I began this thread -- which if you look at the beginning of this thread did not even take a stance on religion! On the other hand, you frequently bring religion up in this thread as if I am the one who can't seem to let go of religion.

If you need to see me as a woo due to what I say and what I ask, and if you need to think me as enthralled by the God meme the way you seem to me to be enthralled by the No-God meme, so be it. Our beliefs may be closer than you think, but our ways of applying our beliefs are as different as night and day. Yet even they meet twice a day, both at sunrise and sunset. Which if one cares to think about it (as I do and I am guessing you likely don't) is a wonderful example of the question of the union of complementary opposites. For many centuries, such has been thought about by such luminaries of thought as Heraclitus, Leibniz, Bohr, and Whitehead... often wholly outside of the scope of religion. Might I suggest that instead of you advising me not to think about things that you know are wrong simply because you know you are right, you instead read up on the aforementioned as, for example, found in http://books.google.com/books?id=AF09AAAAIAAJ&pg=PA3&lpg=PA3&dq=%22the+union+of+complementary+opposites%22&source=bl&ots=FFyJnE7D8V&sig=8VxsBWJkxYbJtJIL8N-eEJMP_I8&hl=en&ei=soPUS5yUF8H68AaClbnIDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAYQ6AEwAA#v=onepage&q=%22the%20union%20of%20complementary%20opposites% 22&f=false . You might find it useful to accept and enjoy the limits of others, even those whom you consider woos, as a means of going beyond your own limits. If you have any.

PixyMisa
25th April 2010, 07:40 PM
You highlight an interesting thought, though you may not want to think about it further: what is grammatically different using formal grammar between replacing X and y in OX1y with OX1y vs. replacing both X and y in OX1y with both OX and 1y? And how is that similar and different when instead using a Lindenmayer grammar?
None of that is relevant.

In any formal grammar, a given production rule always produces the same output for a given input. The only way to get a different output for a given input is to use a different production rule.

If you expect to get different outputs for the same input and the same production rule, then you've misunderstood the entire concept of formal grammars.

eijah
26th April 2010, 05:06 AM
None of that is relevant.

In any formal grammar, a given production rule always produces the same output for a given input. The only way to get a different output for a given input is to use a different production rule.

If you expect to get different outputs for the same input and the same production rule, then you've misunderstood the entire concept of formal grammars.

Sorry that I have not be saying it clearly. But you are right and I do know that you are right.

Yes. We are talking about these two different productions rules:

Replace X and y in OX1y with OX and 1y

vs.

Replace X and y in OX1y with both Ox and 1y .

In the first case, the production rule is OX1y -> OOX1y1OX1y

In the latter case, a different production rule is OX1y -> OOXO1y1OX11y

So my question is this...

Now that we have (per the much appreciated earlier answers on this thread) the formal grammar steps that take us from OX1y to OOX1y1OX1y,

how do we now also get from OX1y to OOXO1y1OX11y, a different production rule, using steps of the formal grammar. Note that I am no longer suggesting simultaneous replacing, and that it may well be that the second set of steps can also be done with standard formal grammar. Although that kind of replacing is typically done using a Lindenmayer grammar.

Hope the above adequately clears up the confusing which I've been causing!!

Giggywig
26th April 2010, 05:24 AM
Replace X and y in OX1y with both Ox and 1y .

In the latter case, a different production rule is OX1y -> OOXO1y1OX11y

So my question is this...

How are you getting there? Again, I am unable to reach this result.

1) OX1y
2) "Replace X and y with both Ox and 1y" -> O(0x1y)1(0x1y)
3) Result -> O0x1y10x1y

Again, as drkitten had pointed out earlier, getting 'O1x' and '11y' is not possible given the rules you are providing.

How about this:
y -> 1y : OX1y -> 0X11y
and
x -> OXO1y1OX : 0X11y -> OOXO1y1OX11y

eijah
26th April 2010, 05:56 AM
So my question is this...

How are you getting there? Again, I am unable to reach this result.

1) OX1y
2) "Replace X and y with both Ox and 1y" -> O(0x1y)1(0x1y)
3) Result -> O0x1y10x1y

Again, as drkitten had pointed out earlier, getting 'O1x' and '11y' is not possible given the rules you are providing.

How about this:
y -> 1y : OX1y -> 0X11y
and
x -> OXO1y1OX : 0X11y -> OOXO1y1OX11y

You might be right, but I don't think so.

What I do think is that by adding the word "both" in Replace X and y in OX1y with both X and 1y, the new and different rule OX1y -> OOX1y1OX1y does work. And I am now not alone in that belief. E.g., in response 115 on this thread Aggle-rithm says...


Originally Posted by eijah View Post
Thanks, but I do not think so. I could be wrong, but I think the over-whelming census has been that that would be wrong. Which is why I am now proposing Replace both X and y in both OX and 1y with both OX and 1y, which I think does result in OOX O1y 1OX 11y.

Aggle-rithm. This is the equivalent of a cross join in database theory. It is the basis of the cube structure used in data mining. Every possible combination is stored so they can be scanned for statistical relationships.

So please consider the possibility that adding the word "both" where I use it in the new rule does change the first production rule from one that obviously works as you and Dr. Kitten and others here agree into a NEW and DIFFERENT production rule that also works, but only if and when you are following the second rule using an explicit "both" OX and 1y.

Thanks.

Giggywig
26th April 2010, 06:01 AM
Oh ok, I see what is meant by that. Ok, so what is the significance of OOXO1y1OX11y?

dafydd
26th April 2010, 06:30 AM
Why not divert these sorts of questions toward Hitchhiker's Guide to the Galaxy? The author of that one was drunk, too.

He was on acid when he first thought of it.It would be hard to divert questions to him,he's brown bread.

Robin
26th April 2010, 06:33 AM
You might be right, but I don't think so.

What I do think is that by adding the word "both" in Replace X and y in OX1y with both X and 1y, the new and different rule OX1y -> OOX1y1OX1y does work. And I am now not alone in that belief. E.g., in response 115 on this thread Aggle-rithm says...


Originally Posted by eijah View Post
Thanks, but I do not think so. I could be wrong, but I think the over-whelming census has been that that would be wrong. Which is why I am now proposing Replace both X and y in both OX and 1y with both OX and 1y, which I think does result in OOX O1y 1OX 11y.

Aggle-rithm. This is the equivalent of a cross join in database theory. It is the basis of the cube structure used in data mining. Every possible combination is stored so they can be scanned for statistical relationships.

So please consider the possibility that adding the word "both" where I use it in the new rule does change the first production rule from one that obviously works as you and Dr. Kitten and others here agree into a NEW and DIFFERENT production rule that also works, but only if and when you are following the second rule using an explicit "both" OX and 1y.

Thanks.
Actually you have two different versions here. The one you claim aggle-rithm agreed worked:

Replace both X and y in both OX and 1y with both OX and 1y

and the latest wording:

Replace X and y in OX1y with both X and 1y

Even if he had agreed that the first form worked (and it is not clear to me that he did) that does not lend support for your second wording.

Which version is it that you claim works?

eijah
26th April 2010, 06:47 AM
Oh ok, I see what is meant by that. Ok, so what is the significance of OOXO1y1OX11y?

Great question!

I THINK one thing that is significance is that we have no problem with knowing that in the phrase "Replace X and y", we are talking about both X and y -- but when we use the phrase "with OX and 1y", we needs be usually take it to not mean "both OX and 1y". And get OX1y -> OOX1y1OX1y. Yet we do finally realize that "OX and 1y" can also mean "both OX and 1y", the result of the replacing of X and y in OX1y with OX and 1y can be a second and different production rule OX1y -> OOXO1y1OX11y. Interestingly, with the second production rule making and using the explicit nature of parentheses in Replace (X and y) in OX1y with both OX (and 1y).

I know that I am not explaining all this very well and I am very sorry for that. And of course it has taken far too long for us to get here. But I do hope that you are now getting something of what I intuited when I first came across the Lindenmayer fractals and Lindermayer grammar not too long ago. And I am still also hoping that you and/or others here can give me a step by step formal grammar description of "Replacing (both) X and y in OX1y with (both) OX and 1y" moving us forward -- the way that all of you most generous and well-meaning formal grammar experts have earnestly been showing this old semi-woo since the beginning of this thread that OX1y -> OOX1y1OX1y.

eijah
26th April 2010, 06:50 AM
Actually you have two different versions here. The one you claim aggle-rithm agreed worked:

Replace both X and y in both OX and 1y with both OX and 1y

and the latest wording:

Replace X and y in OX1y with both X and 1y

Even if he had agreed that the first form worked (and it is not clear to me that he did) that does not lend support for your second wording.

Which version is it that you claim works?

I think both work. But I would prefer to work with the latter as it seems to me to be used like an alphabet. What do you think?

Robin
26th April 2010, 07:22 AM
I think both work. But I would prefer to work with the latter as it seems to me to be used like an alphabet. What do you think?
But it is not clear to me that they work in any case. Your rule does not stipulate repeating the character that precedes the replacement string.

So your rule (Replace both X and y in both OX and 1y with both OX and 1y) would result in:


OOX1y1OX1y

and not

OOXO1y1OX11y

Giggywig
26th April 2010, 07:53 AM
But it is not clear to me that they work in any case. Your rule does not stipulate repeating the character that precedes the replacement string.

So your rule (Replace both X and y in both OX and 1y with both OX and 1y) would result in:


OOX1y1OX1y

and not

OOXO1y1OX11y
The thing is that the rules are not replacement rules (at least not how I remember them from long time ago). What is being done to achieve the result is:
1) Replace x in 0X with 0X
2) Replace x in 0X with 1y
3) Concatenate the result
So you get: 00X01Y
Then you do the same with 1y, then concatenate again.
00X01Y10X11Y

eijah
26th April 2010, 08:11 AM
But it is not clear to me that they work in any case. Your rule does not stipulate repeating the character that precedes the replacement string.

So your rule (Replace both X and y in both OX and 1y with both OX and 1y) would result in:


OOX1y1OX1y

and not

OOXO1y1OX11y



Ok. Explain to me where I am going wrong...

Replace X in OX with both OX and 1y & Replace X in OX both with OX and 1y. Both -> OOX and O1y.

Replace y in 1y with both OX and 1y & Replace y in 1y both with OX and 1y. Both -> 1OX and O1y.

Adding the above together, we get below

Replace both X in OX and y in 1y in both OX and 1y with both (and both with) Ox and 1y. Both of which -> OOX O1y 1OX 11y.

While not presented in a rigorous mathematical way, do you see any inkling of how, by us using the word "both" in the phrases "both with OX and 1y" and "with both OX and 1y", we get some kinds of parenthetical results of perhaps not always trivial substitutions of both OX and 1y for both X and y in both 1X and Oy -- results which I am inclined to think has/have the look and feel of O(OX and 1y) and 1(OX and 1y)?

eijah
26th April 2010, 08:14 AM
The thing is that the rules are not replacement rules (at least not how I remember them from long time ago). What is being done to achieve the result is:
1) Replace x in 0X with 0X
2) Replace x in 0X with 1y
3) Concatenate the result
So you get: 00X01Y
Then you do the same with 1y, then concatenate again.
00X01Y10X11Y

Giggywig, you may be correct as well. But I think we can also be talking of replacement per my response to Robin.

Robin
26th April 2010, 08:34 AM
Giggywig, you may be correct as well. But I think we can also be talking of replacement per my response to Robin.
I think giggywig is describing exactly what you are doing in your response to me.

In any case it does not seem to have the effect of your original transform because you are starting with two strings, not one.

PixyMisa
26th April 2010, 08:50 AM
While not presented in a rigorous mathematical way, do you see any inkling of how, by us using the word "both" in the phrases "both with OX and 1y" and "with both OX and 1y", we get some kinds of parenthetical results of perhaps not always trivial substitutions of both OX and 1y for both X and y in both 1X and Oy -- results which I am inclined to think has/have the look and feel of O(OX and 1y) and 1(OX and 1y)?
No, sorry, this is nonsense.

A production rule always produces the same output for any given input. If it doesn't, you're doing it wrong.

That's all there is to it.

Perhaps if you'd tell us what the point of all this is supposed to be, we could help you better. Mind you, the original post made no sense either.

drkitten
26th April 2010, 09:40 AM
Great question!

I THINK one thing that is significance is that we have no problem with knowing that in the phrase "Replace X and y", we are talking about both X and y -- but when we use the phrase "with OX and 1y", we needs be usually take it to not mean "both OX and 1y". And get OX1y -> OOX1y1OX1y. Yet we do finally realize that "OX and 1y" can also mean "both OX and 1y", the result of the replacing of X and y in OX1y with OX and 1y can be a second and different production rule OX1y -> OOXO1y1OX11y.

No.

It cannot mean this, because there is literally nothing you can "replace" in the original string to insert the addition (highlighted) O and 1, respectively.

Interestingly, with the second production rule making and using the explicit nature of parentheses in Replace (X and y) in OX1y with both OX (and 1y).

No. Again, this is simply word salad. You have not defined what "the explicit nature of parenthesis" means, and, frankly, I don't think you actually have any idea what it means.


I know that I am not explaining all this very well and I am very sorry for that.

Have you considered the possibility that your bad explanations are caused by the fact that yo9u don't understand what the hell you're going on about?


And I am still also hoping that you and/or others here can give me a step by step formal grammar description of "Replacing (both) X and y in OX1y with (both) OX and 1y" moving us forward

We can. (Simply put a duplication transformation in there : w -> ww, and then apply the x and y transformations separate to each half of the duplicated string.) But there's still no point, because it's still just an arbitrary and rather silly grammatical transformation.

Why should we care? What does it indicate or illustrate?

eijah
26th April 2010, 10:14 AM
No, sorry, this is nonsense.

A production rule always produces the same output for any given input. If it doesn't, you're doing it wrong.

That's all there is to it.

Perhaps if you'd tell us what the point of all this is supposed to be, we could help you better. Mind you, the original post made no sense either.

Guys, unfortunately though I honestly do keep trying, I simple do not see the logical source(s) of your problem(s) with what I am -- now -- saying.

Please tell me what is logically wrong about our replacing both X and y in both OX and 1y, first with Ox and then with 1y -- and getting OOX and O1y and 1OX and 11y -- which to me seems to be much like the way in some math equation replacing the X in OX and the y in 1y in OX and 1y, first with OX and last with 1y, for example, O(Ox and 1y) and 1[OX and 1y], and as a result of those substitutions getting OOx and O1y and 1Ox and 11y. Is this math version correct? If so, why is my production rule incorrect, i.e, why does not replacing both X and y in OX and 1y with first OX and then 1y not also produce OOx 1Oy 1Ox 11y?

Philosaur
26th April 2010, 10:14 AM
This is partly meant in humor, and partly to express the frustration that I think lots of us are feeling. Eijah, hopefully you'll be a good sport and see this as gentle ribbing, and not cruelty...
-----------------------
Eijah: I've discovered a new way to produce gasoline!

Forumites: Really?

Eijah: Yeah: You take milk, and you add flour, eggs, and sugar, and mix them together in my special way and you get gasoline!

Forumites: It sounds like you'd get cake batter.

Eijah: No, really. Here's the milk, flour, eggs, and sugar. I mixed the ingredients together in this new way I discovered, and got this bowl of gasoline.

Forumites: We can see no way for this to work unless you show us exactly how you mixed them.

Eijah: Well, I put the milk and the flour and the eggs and sugar into a bowl. Then I used a whisk to blend the ingredients with this new method, and then it was gasoline.

Forumites: No, see, you're just repeating yourself without explaining *how* you mixed them. Saying you used a bowl and a whisk are steps in the right direction, but they don't explain this "new method" you've discovered.

Eijah: Oh, it involves chemistry.

Forumites: That's not helpful.

Eijah: Maybe it's a new kind of chemistry. Can anyone help me figure it out?

Forumites: We don't know what it is that needs to be figured out, because you won't explain how you combined milk, flur, eggs, and sugar, and got gasoline.

Eijah: Oh, I just mixed them using this new method.

Forumites: *What* new method?

Eijah: Well, you start with eggs, flour, milk, sugar, and vanilla--and by combining the ingredients--you get gasoline.

Forumites: Wait, where did the vanilla come from?

Eijah: Oh, it's part of the method. I thought I made that clear...

Forumites: No, you've just introduced a totally new part to this "method" without any explanation. Which is very confusing.

Eijah: Like I said, maybe it's a new kind of chemistry--maybe it involves hexane bonds. Are there any chemists here who can help me?

Forumites: We don't need to be chemists to see that you can't possibly get gasoline by mixing the ingredients you've specified.

Eijah: Well, the key to this new method lies in how I'm using the word "mix"...

Forumites: Yeah, we get that. *How* are you using the word "mix"?

Eijah: Well, it's like this: first I combine the milk and eggs. Then I combine the vanilla extract, sugar, and flour. Then I superheat the crude oil until the vapors condense...

Forumites: Wait! Where did you get crude oil?

Eijah: From a well.

Forumites: But if you already have crude oil, then it's no stretch to get gasoline. The eggs and sugar and flour and stuff has *nothing* to do with the gasoline.

Eijah: But it's all about how I "mix" the ingredients...

[ad infinitum...]

Giggywig
26th April 2010, 10:31 AM
Guys, unfortunately though I honestly do keep trying, I simple do not see the logical source(s) of your problem(s) with what I am -- now -- saying.

Please tell me what is logically wrong about our replacing both X and y in both OX and 1y, first with Ox and then with 1y -- and getting OOX and O1y and 1OX and 11y -- which to me seems to be much like the way in some math equation replacing the X in OX and the y in 1y in OX and 1y, first with OX and last with 1y, for example, O(Ox and 1y) and 1[OX and 1y], and as a result of those substitutions getting OOx and O1y and 1Ox and 11y. Is this math version correct? If so, why is my production rule incorrect, i.e, why does not replacing both X and y in OX and 1y with first OX and then 1y not also produce OOx 1Oy 1Ox 11y?
How about this: Let's grant, for arguments sake, that we have a valid way to get from 0x1y to OOx1Oy1Ox11y. What is the significance of it? As far as I can tell, it's an arbitrary string of numbers to which you are *some* significance that relates to parenthesis.

eijah
26th April 2010, 10:45 AM
No.

It cannot mean this, because there is literally nothing you can "replace" in the original string to insert the addition (highlighted) O and 1, respectively.



No. Again, this is simply word salad. You have not defined what "the explicit nature of parenthesis" means, and, frankly, I don't think you actually have any idea what it means.



Have you considered the possibility that your bad explanations are caused by the fact that yo9u don't understand what the hell you're going on about?




We can. (Simply put a duplication transformation in there : w -> ww, and then apply the x and y transformations separate to each half of the duplicated string.) But there's still no point, because it's still just an arbitrary and rather silly grammatical transformation.

Why should we care? What does it indicate or illustrate?

Sorry that I do not have your level of education nor your higher intellect. And thanks for trying to set a dullard like me straight. Dr. Kitten, for better or worse, obviously worse, I have been assuming that my replacement rule is along the lines of a simple-minded math analogy. More specifically...

if we have a mathematical term AX + By, and we replace both X and y in AX + By with both AX + By, the result produced is AAX +ABy + BAX + BBy. This l regret still. alas, seems to a woo like me to have the same look and feel as my original OX1y term and its replacing of both OX and 1y in OX1y with first OX and last with 1y and my woo result OOX O1X 1Oy 11y.

By the way, two questions. What is wrong with my math? And if my math to turn out to end up being correct, what is logically so without any redeeming qualities wrong with my replacement rule as it maps to the math above?

eijah
26th April 2010, 10:56 AM
This is partly meant in humor, and partly to express the frustration that I think lots of us are feeling. Eijah, hopefully you'll be a good sport and see this as gentle ribbing, and not cruelty...
-----------------------
Eijah: I've discovered a new way to produce gasoline!

Forumites: Really?

Eijah: Yeah: You take milk, and you add flour, eggs, and sugar, and mix them together in my special way and you get gasoline!

Forumites: It sounds like you'd get cake batter.

Eijah: No, really. Here's the milk, flour, eggs, and sugar. I mixed the ingredients together in this new way I discovered, and got this bowl of gasoline.

Forumites: We can see no way for this to work unless you show us exactly how you mixed them.

Eijah: Well, I put the milk and the flour and the eggs and sugar into a bowl. Then I used a whisk to blend the ingredients with this new method, and then it was gasoline.

Forumites: No, see, you're just repeating yourself without explaining *how* you mixed them. Saying you used a bowl and a whisk are steps in the right direction, but they don't explain this "new method" you've discovered.

Eijah: Oh, it involves chemistry.

Forumites: That's not helpful.

Eijah: Maybe it's a new kind of chemistry. Can anyone help me figure it out?

Forumites: We don't know what it is that needs to be figured out, because you won't explain how you combined milk, flur, eggs, and sugar, and got gasoline.

Eijah: Oh, I just mixed them using this new method.

Forumites: *What* new method?

Eijah: Well, you start with eggs, flour, milk, sugar, and vanilla--and by combining the ingredients--you get gasoline.

Forumites: Wait, where did the vanilla come from?

Eijah: Oh, it's part of the method. I thought I made that clear...

Forumites: No, you've just introduced a totally new part to this "method" without any explanation. Which is very confusing.

Eijah: Like I said, maybe it's a new kind of chemistry--maybe it involves hexane bonds. Are there any chemists here who can help me?

Forumites: We don't need to be chemists to see that you can't possibly get gasoline by mixing the ingredients you've specified.

Eijah: Well, the key to this new method lies in how I'm using the word "mix"...

Forumites: Yeah, we get that. *How* are you using the word "mix"?

Eijah: Well, it's like this: first I combine the milk and eggs. Then I combine the vanilla extract, sugar, and flour. Then I superheat the crude oil until the vapors condense...

Forumites: Wait! Where did you get crude oil?

Eijah: From a well.

Forumites: But if you already have crude oil, then it's no stretch to get gasoline. The eggs and sugar and flour and stuff has *nothing* to do with the gasoline.

Eijah: But it's all about how I "mix" the ingredients...

[ad infinitum...]

I take it well! :-)

Also: Please see my recent reply to Dr. Kitten. And please at the very least correct my math. I'll be back in a while. I have to go to the store for some maple syrup that has the look and feel of motor oil. It might take a while. Because every time I ask for it, all of the folks in the supermarkets keep laughing at me.

Philosaur
26th April 2010, 11:04 AM
if we have a mathematical term AX + By, and we replace both X and y in AX + By with both AX + By, the result produced is AAX +ABy + BAX + BBy. This l regret still. alas, seems to a woo like me to have the same look and feel as my original OX1y term and its replacing of both OX and 1y in OX1y with first OX and last with 1y and my woo result OOX O1X 1Oy 11y.

Now we see the problem. You're using the distributive property of multiplication to get the extra A and B.

So given these equations (well, a term and two equations):

1. AX + By
2. X = AX + By
3. y = AX + By

AX + By = A(AX + By) + B(AX + By) = AAX + ABy + BAX + BBy

But you must think of this distributive property as a production rule spelled out for math (and NOT spelled out in your set of production rules). You can't just assume rules exist because they look similar to those in other domains.

In any case, you haven't discovered semantic content hidden in syntax, you've just mistakenly applied a well-known property from the mathematical domain to a theorem-string in your own domain. Still no mystery.


By the way, two questions. What is wrong with my math? And if my math to turn out to end up being correct, what is logically so without any redeeming qualities wrong with my replacement rule as it maps to the math above?
You don't get to just assume all rules from any domain to use for a domain you are specifying--unless you specify this in advance.

ETA: the previous edit didn't add to the conversation...

eijah
26th April 2010, 11:44 AM
Now we see the problem. You're using the distributive property of multiplication to get the extra A and B.

So given these equations (well, a term and two equations):

1. AX + By
2. X = AX + By
3. y = AX + By

AX + By = A(AX + By) + B(AX + By) = AAX + ABy + BAX + BBy

But you must think of this distributive property as a production rule spelled out for math (and NOT spelled out in your set of production rules). You can't just assume rules exist because they look similar to those in other domains.

In any case, you haven't discovered semantic content hidden in syntax, you've just mistakenly applied a well-known property from the mathematical domain to a theorem-string in your own domain. Still no mystery.


You don't get to just assume all rules from any domain to use for a domain you are specifying--unless you specify this in advance.

ETA: In any event, the equations above aren't terribly interesting.

Given:

1. AX + BY
2. X = AX + BY
3. Y = AX + BY

We can--without trouble--make the first term into an equation by specifying that Z is simply the sum of AX + BY. I do this so you don't just think I'm tossing out your first term...

1. Z = AX + BY
2. X = AX + BY
3. Y = AX + BY

But now we get X = Y = Z. Which means we can replace X and Y with Z:

Z = AZ + BZ

And factoring out Z gives us

1 = A + B

An altogether uninteresting equation, given that there's no context.

Great! and MUCH thanks!!! Am I glad that we are now in a better place of understanding! Though "we" meaning much more you than me because I still need to study formal grammars as best as I can. However, I am old, and as you have seen, I am also dense. :-(

Indeed, we are talking about an equation which to you and most others here, maybe everyone but me, is both uninteresting AND trivial. But, for better or worse, it still holds a fascination to a woo like me.

In any case, now that you understand what I am saying, have you just given me a standard formal grammar way of step by step getting from OX1y to OOX1Oy1OX11y -- of course, factoring in whatever syntax is needed in that grammar to use the distribution property -- if there is such a distribution property available?

Or can you do that now. I see what you have done for the math equation, but it seems to me not the same as what has been done before (before the recognition of the distributive aspect.) And I would love to be able to now contrast what was shown to be correct when the distribution property was not being used vs. how the rule plays out step-by-step when the distribution is added.

drkitten
26th April 2010, 01:19 PM
Great! and MUCH thanks!!! Am I glad that we are now in a better place of understanding! Though "we" meaning much more you than me because I still need to study formal grammars as best as I can. However, I am old, and as you have seen, I am also dense. :-(

Indeed, we are talking about an equation which to you and most others here, maybe everyone but me, is both uninteresting AND trivial. But, for better or worse, it still holds a fascination to a woo like me.

[QUOTE]
In any case, now that you understand what I am saying, have you just given me a standard formal grammar way of step by step getting from OX1y to OOX1Oy1OX11y -- of course, factoring in whatever syntax is needed in that grammar to use the distribution property -- if there is such a distribution property available?

Sort of. Essentially, you are expanding your system by adding a new production rule, something roughly equivalent to

Oab -> OaOb

... reflecting distributing O(a and b) across to be Oa and Ob. [and similarly for 1ab -> 1a1b as well.]

The actual details could be hashed out if anyone were sufficiently interested.

But the first key question is "why should such a distribution property be available?"

It's not generally available "in the real world," for example. If I substitute Canadian bacon for ham in "ham and eggs," I get "Canadian bacon and eggs," not "Canadian bacon and Canadian eggs." Similarly, if I substitute French fries for hash browns in "hash browns and toast," I get
"French fries and toast," not "French fries and French toast." As your server can tell you, these are entirely different orders.... So there's no reason in general to assume that a distributional property applies -- and there's a well developed theory of algebra studying the properties of systems that do have a distributional property. (And formal grammars isn't usually one of those systems.)

But beyond that, there's still the second and even more key question : "So what?"

What's so fascinating about this particular string of letters and numbers?

eijah
26th April 2010, 02:11 PM
[QUOTE=eijah;5869522]Great! and MUCH thanks!!! Am I glad that we are now in a better place of understanding! Though "we" meaning much more you than me because I still need to study formal grammars as best as I can. However, I am old, and as you have seen, I am also dense. :-(

Indeed, we are talking about an equation which to you and most others here, maybe everyone but me, is both uninteresting AND trivial. But, for better or worse, it still holds a fascination to a woo like me.



Sort of. Essentially, you are expanding your system by adding a new production rule, something roughly equivalent to

Oab -> OaOb

... reflecting distributing O(a and b) across to be Oa and Ob. [and similarly for 1ab -> 1a1b as well.]



Yes, indeed! Great and much thanks!




The actual details could be hashed out if anyone were sufficiently interested.

But the first key question is "why should such a distribution property be available?"

It's not generally available "in the real world," for example. If I substitute Canadian bacon for ham in "ham and eggs," I get "Canadian bacon and eggs," not "Canadian bacon and Canadian eggs." Similarly, if I substitute French fries for hash browns in "hash browns and toast," I get
"French fries and toast," not "French fries and French toast." As your server can tell you, these are entirely different orders.... So there's no reason in general to assume that a distributional property applies -- and there's a well developed theory of algebra studying the properties of systems that do have a distributional property. (And formal grammars isn't usually one of those systems.)



And once again VERY helpful and Much thanks!




But beyond that, there's still the second and even more key question : "So what?"

What's so fascinating about this particular string of letters and numbers?

Well, I could say I have no idea. But that would be wrong. It is admittedly much more woo than that. And as such, VERY annoying to me, as well as to you and others here! But it is what it is! :-(

In any case, as I said earlier, it came to me one day not too long ago while musing about Lindermayer fractals and Lindenmayer grammar (the first I love reading about, but understand little about and the latter I have NO idea about, that replacing X and y in OX1y with OX1y result in both what you saw (OOX1y11OX1y) AND also could produce OOXO1y1Ox11y -- if there was some kind of parenthetical operation involved. That seemed to me to raise the possibility of some sort of semantics being in there some where, but apparently not. And then the thread got very contentious until with your very helpful prodding and that of others I realized that using mathematical terminology might get us past the impasse of my own making. At least it is a relief to know that by adding something that accommodates the distributive property inherent in my rule, things do work out as I have been saying as well as you have been saying. Hope that makes me less than a woo (except for how the idea came to me!)

Philosaur
26th April 2010, 02:48 PM
In any case, as I said earlier, it came to me one day not too long ago while musing about Lindermayer fractals and Lindenmayer grammar (the first I love reading about, but understand little about and the latter I have NO idea about,

L-systems are a strict subset of logical languages in which production rules are applied recursively and as nearly simultaneously as possible. *Please* for the love of anything you consider good, right, and just in the world--do NOT treat L-systems as some unexplored territory rife with mystical possibility. They are a useful tool in studying iterative processes--not a secret language of the universe.

http://en.wikipedia.org/wiki/L-system

that although replacing X and y in OX1y with OX1y result in both what you saw (OOX1y11OX1y) and also could produce OOXO1y1Ox11y -- if there was some kind of parenthetical operation involved. That seemed to me to raise the possibility of some sort of semantics being in there some where, but apparently not.

I know it's disappointing to realize that the discovery was based on a misunderstanding, but in the long run you are better off accepting it and moving on.

And then the thread got very contentious until with your very helpful prodding and that of others I realized that using mathematical terminology might get us past the impasse of my own making. At least it is a relief to know that by adding something that accommodates the distributive property inherent in my rule, things do work out as I have been saying as well as you have been saying. Hope that makes me less than a woo (except for how the idea came to me!)
I doubt anyone here would begrudge you for the way you get your ideas. Plenty of so-called geniuses get their inspiration from dreams, while listening to music, looking at art, meditating, or sitting on the toilet.

As long as you are able to hold the idea before you, examine it in relation to reality, and be willing to toss it if it doesn't measure up--that's the only thing that matters.

eijah
26th April 2010, 03:42 PM
L-systems are a strict subset of logical languages in which production rules are applied recursively and as nearly simultaneously as possible. *Please* for the love of anything you consider good, right, and just in the world--do NOT treat L-systems as some unexplored territory rife with mystical possibility. They are a useful tool in studying iterative processes--not a secret language of the universe.


I am not. Please point out to me where I may have unintentionally said otherwise.



http://en.wikipedia.org/wiki/L-system

I know it's disappointing to realize that the discovery was based on a misunderstanding, but in the long run you are better off accepting it and moving on.



What makes you think I am or would be disappointed? Where have I unintentionally given you that erroneous impression?



I doubt anyone here would begrudge you for the way you get your ideas. Plenty of so-called geniuses get their inspiration from dreams, while listening to music, looking at art, meditating, or sitting on the toilet.



Toilet not as often as when waking up in the morning. But much thanks for not seeing my occasional "Aha!'s" as necessarily woo.



As long as you are able to hold the idea before you, examine it in relation to reality, and be willing to toss it if it doesn't measure up--that's the only thing that matters.

That is what I have been willing to do here. I had no desire to let go of my alternate result because I was implictly using the distributive property to do the substitutions without understanding it had to be explicitly articulated to all of you. I suppose it is because at my age I have the luxury of intuitively approaching science and math questions now as if they are mysteries to be solved, ideally as a game based as much as possible purely on using as few facts as possible. NOT "mystery" in a woo-ly religious sense, but rather as in a Sherlock Holmes sense. Much like sin x being the rather simple-minded opposite side over the hypotenuse solution vs. the result of a Taylor series.

However, it is very interesting to me that no one here thought of adding the distributive property so that my rule could be accommodated. I think that folks here were and seemingly still are so intent on seeing me as a woo it that clouded their otherwise superb and much admired by me powers of scrutiny, analysis and creativity. Complexity's fixation about my never stated by me in any way supposed obsession with god and religion especially comes to mind. Good God! What a waste of time and silly and patronizing misguided "guidance"! I think if one is not careful, being a Woo Whisperer can end up being like when you have a hammer, seeing everything as a nail. Ironically, such a set in stone, snap judgment viewpoint seems to me to be too much like being a woo. The humor in that kind of folly and hubris would make the gods laugh -- if there were gods. And for all I know they are laughing, but God Willing not at me. :-)

drkitten
26th April 2010, 04:49 PM
However, it is very interesting to me that no one here thought of adding the distributive property so that my rule could be accommodated.

Er,.... actually, quite a number of people thought of that. Let me check --- yes, posts 24, 29, 31, and 34 all point out that your proposed finding is simply a consequence of using two different sets of production rules. And that's just on the first page....

Although no one explicitly mentioned "adding the distributive property," that's largely because no one could figure out what the hell you were talking about when you used phrases like "whether O and 1 are parenthetical modifier operators or not." (Philosaur was fairly explicit about this in post #43; you were directly asked to show your work in post #46.)

We all knew that you were using a set of unexpressed rules. The problem is that you wouldn't or couldn't even say what the rules you were using [i]were. And precisely because production rules are arbitrary (and arbitrarily powerful), there's literally an infinite number of things that we could guess you meant, but what's the point of that.

I think that folks here were and seemingly still are so intent on seeing me as a woo it that clouded their otherwise superb and much admired by me powers of scrutiny, analysis and creativity.

Or you were simply rattling off ill-defined gibberish.

We shouldn't need to be telepathic to understand what you meant to write. Words have meanings; once you admit that you're using non-standard meanings, it's up to you to define the meanings you're using.

eijah
26th April 2010, 05:05 PM
Er,.... actually, quite a number of people thought of that. Let me check --- yes, posts 24, 29, 31, and 34 all point out that your proposed finding is simply a consequence of using two different sets of production rules. And that's just on the first page....

Although no one explicitly mentioned "adding the distributive property," that's largely because no one could figure out what the hell you were talking about when you used phrases like "whether O and 1 are parenthetical modifier operators or not." (Philosaur was fairly explicit about this in post #43; you were directly asked to show your work in post #46.)

We all knew that you were using a set of unexpressed rules. The problem is that you wouldn't or couldn't even say what the rules you were using [i]were. And precisely because production rules are arbitrary (and arbitrarily powerful), there's literally an infinite number of things that we could guess you meant, but what's the point of that.



Or you were simply rattling off ill-defined gibberish.

We shouldn't need to be telepathic to understand what you meant to write. Words have meanings; once you admit that you're using non-standard meanings, it's up to you to define the meanings you're using.

Fair enough. Now how about all those push-backs and slurs about religious views I never stated?

Robin
26th April 2010, 05:08 PM
Fair enough. Now how about all those push-backs and slurs about religious views I never stated?
Can you give an example?

You did begin by linking the whole thing to religion yourself.

eijah
26th April 2010, 05:42 PM
Can you give an example?

You did begin by linking the whole thing to religion yourself.

True I did begin with The Logos as a kind of formal and/or cognitive grammar

and

I was wondering if "In the beginning was the word" might have anything to do with formal grammars? Or cognitive grammars? Or, even better, cognitive formal grammars? Does anyone here know much about any of that stuff? Especially the cognitive formal grammar one which would seem to me to have combination formation/transformation rules.

However, if you read the above VERY carefully and without making any snap judgments, you see that I in no way say anything about my beliefs and my disbeliefs. From the beginning and all the way through to the end, I give absolutely no mention about what I believe or not, other than the fact that like you folks I am not a religious woo. The fact that so many of you seem to have taken me for a religious woo is I believe a sad commentary on how easy it is even for atheists to be as irrational as the craziest religious fanatics. This Forum is filled with extremely intelligent and well-educated Skeptic sharks. And my original and only very neutral reference to the logos was so bloody fishy in your minds that it drove some of you wild treating my question with extreme disdain instead of quickly helping a kindred spirit out. You toyed with your image of woo, the way the Romans toyed with Christians in the Colosseum -- because it is good sport. But as I had as much fun as you without being either a religious woo or any other kind, so let's call the game on account of reign: what we both know reigns most high -- or at least should. Logic, aka, logos. :-)

Robin
26th April 2010, 06:04 PM
True I did begin with The Logos as a kind of formal and/or cognitive grammar

and

I was wondering if "In the beginning was the word" might have anything to do with formal grammars? Or cognitive grammars? Or, even better, cognitive formal grammars? Does anyone here know much about any of that stuff? Especially the cognitive formal grammar one which would seem to me to have combination formation/transformation rules.

However, if you read the above VERY carefully and without making any snap judgments, you see that I in no way say anything about my beliefs and my disbeliefs. From the beginning and all the way through to the end, I give absolutely no mention about what I believe or not, other than the fact that like you folks I am not a religious woo. The fact that so many of you seem to have taken me for a religious woo is I believe a sad commentary on how easy it is even for atheists to be as irrational as the craziest religious fanatics.
As I said before, can you give me an example of one of these comments?

Complexity
26th April 2010, 06:19 PM
And no I AM NOT trying to prove the existence of God, just trying to see if there are any things hidden in the bible that may be of a logical and cognitive nature...

And if so, perhaps/maybe/possibly... there is some kind of logic, in re-cognizing that beginning with the right word (and an understanding of that right word in a cognitively informed formal way) leads to more right words. AS WELL AS the ability to parse out all of the wrong non-sense words that were added the centuries by well-meaning fools and not well-meaning knaves. Note: I said perhaps/maybe/possibly. Not surely, but I think it would be a very cool way to look at and contemplate the words and wording of all kinds of scriptures if I am on to something -- other than on something! :-)


eijah - No one would invest their time and energy into such a project if they didn't believe that there are things of value hidden in the bible and other scriptures. Perhaps you are an atheist scholar who has a peculiar interest in the bible, thinks that people have hidden human thoughts in it, and think that those thoughts are worth retrieval. Perhaps, but I don't think so - I haven't met anyone other than True Believers who would do this.

Perhaps you are not a True Believer - perhaps you are this unexpected scholar. If so, I apologize for assuming the worst of you.

However, if you are honest with yourself and with us, I think you'll discover that you believe in supernatural origins of those things that you think are hidden in the bible and other scriptures. In this case, I regard your beliefs and, hence, you as woo.

As I said early on, I don't regard you as beyond all hope, though I've had recent concerns, but honesty, at least with yourself, is essential to making progress.

eijah
26th April 2010, 07:25 PM
eijah - No one would invest their time and energy into such a project if they didn't believe that there are things of value hidden in the bible and other scriptures. Perhaps you are an atheist scholar who has a peculiar interest in the bible, thinks that people have hidden human thoughts in it, and think that those thoughts are worth retrieval. Perhaps, but I don't think so - I haven't met anyone other than True Believers who would do this.

Perhaps you are not a True Believer - perhaps you are this unexpected scholar. If so, I apologize for assuming the worst of you.

However, if you are honest with yourself and with us, I think you'll discover that you believe in supernatural origins of those things that you think are hidden in the bible and other scriptures. In this case, I regard your beliefs and, hence, you as woo.

As I said early on, I don't regard you as beyond all hope, though I've had recent concerns, but honesty, at least with yourself, is essential to making progress.

I am inclined much towards etymology. And I think it can teach us a lot.

For example, "superstition" means "over standing" as much as it means "standing over". So let's say that there are six things needed to perform a successful task. Anyone who adds a seventh unnecessary thing to that task for good luck is being super-stitious. Yes? And whether or not he or she even believes in a deity. And to carry this to a silly extreme, one might even say that unnecessary steps in a mathematical proof can end up turning out to be super-stitious. By the way, my under-standing of math is that the more trivial the proof, the better. So perhaps there is some of value in at least some trivial equations. For example, if 1 = A + B is devoid of context, it IS its own context. Shades of Leibniz's Monads, and Hawking's Singularity, yes? :-)

One might even say that when an atheist even entertains the meme of God, having earlier blessedly escaped that aweful meme's power over him or her, the fear engendered by catching himself or herself playing with that devil of a God is also a kind of being super-stitious. Because does a real atheist need fear to stay on the logical straight and narrow? NO!

I am neither a true believer nor a false believer, in just about anything other than what I can occasionally see, smell, hear, taste, touch or surmise. With the possible exceptions of seeing magical tricks, hearing politicians, smelling a rat, tasting the good life, and being a soft touch. I would like to see myself as a free-thinker in the tradition of those not afraid of the meme called God -- nor afraid of playing with that meme in the cool way Aristotle talked about entertaining a notion without accepting it. And I do believe there are things in various scriptures having nothing to do with religion or God and everything to do with some of the most basic aspects of math and science and other disciplines. I just don't know what they are. Or if I am right to guess so. So I keep looking at things the way a scientist would if he were living in the days of Newton and Boyle and Dee and others who had not the advantages of modern science and math, and thus also not its baggage. Just in case, there is something to discover that no one thinks is there to be discovered. If that makes me a woo, boo-hoo! :-)

PixyMisa
27th April 2010, 12:43 AM
And I do believe there are things in various scriptures having nothing to do with religion or God and everything to do with some of the most basic aspects of math and science and other disciplines.
Why?

I just don't know what they are.
Then why do you believe they are there in the first place?

Or if I am right to guess so.
So again, why do you believe they are there in the first place?

So I keep looking at things the way a scientist would if he were living in the days of Newton and Boyle and Dee and others who had not the advantages of modern science and math, and thus also not its baggage.
No.

Just in case, there is something to discover that no one thinks is there to be discovered.
Suggestion: Discover something first, then believe in it. It will save you a lot of grief.

eijah
27th April 2010, 04:52 AM
Why?


Then why do you believe they are there in the first place?



Believing myself to have free will and also believing in axiomization (which of course is not simply a matter of free will), I chose to begin with that belief as an axiom, just to see what might possibly be viewable in terms of intellectual dis-covery. I chose that axiom on the assumption quite different (or maybe not completely different from an unorthodox interpretation of "The Assumption", time may tell, maybe not) that we do not see what we do not believe is possible to see. Seems to me to be especially true per seeing or re-seeing new or forgotten legitimate concepts. I.e., we all tend not to give passing inklings of something new and/or strange a second glance if we see them as anomalies or mistakes or horrifying to our beliefs. Said another way, I believe that we do not re-cognize something as possibly worth more scrutiny, analysis... if it assaults our bedrock beliefs and disbeliefs -- scientific as well as religious ones. You may think starting with such an axiom is folly. And that is your right, even though that does not make you right. I am guessing you will flush my axiom down your toilet because you need to be right. However disagreeing with me is counter-productive. Because starting with an axiom to see where it might take one is a bedrock too. Arguably, the bedrock of the best math and science as well as common sense. And the preferred method of those who get Nobel Prizes and Field ones, not just tenure, as it is the time and again proven bedrock for building logical edifices in science and mathematics and blessedly available to all believers and non-believers of everything, BUT only if and when they are not afraid of seeking and seeing what other truths may lie beyond what is already known to be true and what is already already known to be false.


So again, why do you believe they are there in the first place?



See again above answer.

You think me a fool. And I may well be. But maybe I am not the one being self-fooled. In any case, to me, "What if...?" is always a whole lot better than "It has to be." For I prefer to try to cognitively benefit from humility rather than suffer from hubris. But you are entitled to make your own Type One and Type Two errors your way. If you ever do make such errors.



No.


You say no, I say yes, you are damned, I am blessed. Sounds like a Beatles song. By the way, "damned" NOT in a religious sense, but rather damned in the sense of being doomed to not see what you insist upon not seeing -- which are things that are there but can be cognitively a-voided. And "blessed" NOT in a religious sense, but in a cognitive sense, where what might be seen is more likely to be seen.



Suggestion: Discover something first, then believe in it. It will save you a lot of grief.

Suggestion in return: As an experiment, try my axiom and see what happens? It's a bit like buying a new car and then beginning to notice how many others of them are on the road. You can always return to your old one. Can't hurt. And might help a lot. But only doable if your belief system is not set in stone.

aggle-rithm
27th April 2010, 05:29 AM
Believing myself to have free will and also believing in axiomization (which of course is not simply a matter of free will), I chose to begin with that belief as an axiom, just to see what might possibly be viewable in terms of intellectual dis-covery.

You could waste a lot of time taking that approach. Where would it end? You could choose to believe that there is special meaning in your Alpha Bits cereal. Or in the time intervals between light changes on one of the traffic lights on your way to work. Or in the arrangements of stars in the sky. Just to see what might possibly be viewable in terms of intellectual discovery.

I think it's better to have some sort of filter, and begin with things that are more likely to have meaning than randomly selected arrangements of words, lights, or stars.

eijah
27th April 2010, 05:59 AM
You could waste a lot of time taking that approach. Where would it end? You could choose to believe that there is special meaning in your Alpha Bits cereal. Or in the time intervals between light changes on one of the traffic lights on your way to work. Or in the arrangements of stars in the sky. Just to see what might possibly be viewable in terms of intellectual discovery.

I think it's better to have some sort of filter, and begin with things that are more likely to have meaning than randomly selected arrangements of words, lights, or stars.

Hi A-R. You are absolutely right. In EVERYTHING you are saying!!!!!!!!!!!!!!!!

Now let's see why you are right, and the consequences of you being right...

1) My approach CAN waste a lot of time. And it is possibly a non-teminating amount of time (limited by my lifetime) with NO assurance of ANY positive result.

So how is that any different from the nature of "pure exploration"? I do not see any difference, but I am open to your view of "pure exploration".

2) As for Alpha-Bits and time intervals of traffic light changes, I completely agree as well. Seeing meaning in any random occurrences is usually quite silly. On the other hand, seeing meaning in probability distributions of electrons in hydrogen atoms is kind of fundamental in QM. SO when does one ignore random occurrences and when does one pay close attention to them? And why not the first vs. why the latter? I am open to your views.

3) As for the need for a filter, Yes, yes, YES! And I think that your anser(s) to 2) will give us the filter(s), So please fire away. But please note that when ever we have a filter we are prone to make Type One and Type Two errors that may be different from those that emerge using a different filter. So perhaps to be using different filters at the same time in parallel is the best way to proceed, including seemingly silly filters as well as orthodox ones (orthodox, of course, in the scientific sense!)?

Complexity
27th April 2010, 06:19 AM
And to carry this to a silly extreme, one might even say that unnecessary steps in a mathematical proof can end up turning out to be super-stitious.

Nonsense. You are writing twaddle.

A mathematician places in a proof enough detail (steps) to convey the proof. Steps that should be obvious to his/her intended audience are usually sketched out or omitted. More detail may be added for clarity or to facilitate a reader's appreciation of the proof. This has nothing to do with superstition.

By the way, my under-standing of math is that the more trivial the proof, the better. So perhaps there is some of value in at least some trivial equations. For example, if 1 = A + B is devoid of context, it IS its own context. Shades of Leibniz's Monads, and Hawking's Singularity, yes? :-)


No. If you replace 'trivial' with 'simple' and you are less wrong.

Your second sentence is silliness based badly upon an error.

Your use of 'context' suggests 'meaning' - it is wrong in any case.

To your last sentence: No.

One might even say that when an atheist even entertains the meme of God, having earlier blessedly escaped that aweful meme's power over him or her, the fear engendered by catching himself or herself playing with that devil of a God is also a kind of being super-stitious. Because does a real atheist need fear to stay on the logical straight and narrow? NO!


More nonsense. This reminds me of the writings of several other woo that think of themselves as being 'beyond logic'.

And I do believe there are things in various scriptures having nothing to do with religion or God and everything to do with some of the most basic aspects of math and science and other disciplines. I just don't know what they are. Or if I am right to guess so. So I keep looking at things the way a scientist would if he were living in the days of Newton and Boyle and Dee and others who had not the advantages of modern science and math, and thus also not its baggage. Just in case, there is something to discover that no one thinks is there to be discovered. If that makes me a woo, boo-hoo! :-)


"Oh, to be back in those glorious days before math and science ruined everything!"

Nonsense. Search away for meaning in those crusty scriptures. You'll find nothing that people haven't put there. You'll find nothing of value.

If you want to learn about the most basic aspects of math and science, I suggest that you read some good books about math and science.

You see, that is where mathematicians and scientists have chosen to have their work appear, rather than encoding them in those steaming piles of woo called scripture.

There is nothing wrong and everything right with taking a fresh look at the world - that is certainly how I conduct my research. Doing so proudly from the standpoint of willfull ignorance is simply wrong.

Do as you wish. I'm disappointed in you.

Complexity
27th April 2010, 06:25 AM
Believing myself to have free will and also believing in axiomization (which of course is not simply a matter of free will), I chose to begin with that belief as an axiom, just to see what might possibly be viewable in terms of intellectual dis-covery. I chose that axiom on the assumption quite different (or maybe not completely different from an unorthodox interpretation of "The Assumption", time may tell, maybe not) that we do not see what we do not believe is possible to see. Seems to me to be especially true per seeing or re-seeing new or forgotten legitimate concepts. I.e., we all tend not to give passing inklings of something new and/or strange a second glance if we see them as anomalies or mistakes or horrifying to our beliefs. Said another way, I believe that we do not re-cognize something as possibly worth more scrutiny, analysis... if it assaults our bedrock beliefs and disbeliefs -- scientific as well as religious ones. You may think starting with such an axiom is folly. And that is your right, even though that does not make you right. I am guessing you will flush my axiom down your toilet because you need to be right. However disagreeing with me is counter-productive. Because starting with an axiom to see where it might take one is a bedrock too. Arguably, the bedrock of the best math and science as well as common sense. And the preferred method of those who get Nobel Prizes and Field ones, not just tenure, as it is the time and again proven bedrock for building logical edifices in science and mathematics and blessedly available to all believers and non-believers of everything, BUT only if and when they are not afraid of seeking and seeing what other truths may lie beyond what is already known to be true and what is already already known to be false.


Long and dense enough (as in no having white space) to qualify as a Wall of Woo.

As an experiment, try my axiom and see what happens?


State your 'axiom' clearly and concisely. No arguments, no elaboration. Use as few words as possible.

eijah
27th April 2010, 06:43 AM
"Oh, to be back in those glorious days before math and science ruined everything!"

Nonsense. Search away for meaning in those crusty scriptures. You'll find nothing that people haven't put there. You'll find nothing of value.


Where did I say that it was not people who put meaning there? You continue to see things in what I say that I did not say, and then base your conclusions on those errors of observation. A self-important, self-fulfilling prophecy worthy of the silliest woo.



If you want to learn about the most basic aspects of math and science, I suggest that you read some good books about math and science.

Complexity, I'll match what I have read against anything you have read. The lives of Newton and Boyle, the lives of Grassmann, Cantor, Boltzmann, Ohm, Cusa, Bruno... all of which indicate that not being limited to the prevailing views of one's time can lead to new knowledge, often at the risk of one's academic position, or even one's life. Not always, but sometimes. And when such intellectual adventure leads to successful new insights, it is both wonderful for those ready to move ahead, and terrible for those stuck in the past, even the past of science and math.

Of course, such lacks of limitations can lead to woo-dom. But isn't anyone who is afraid of occasionally exploring new possibilities using logic as a guard and guide also a kind of woo? Complexity, you do not disappoint me. I would expect nothing less from you. Your cup runneth under.

eijah
27th April 2010, 07:21 AM
[QUOTE=eijah;5869522]Great! and MUCH thanks!!! Am I glad that we are now in a better place of understanding! Though "we" meaning much more you than me because I still need to study formal grammars as best as I can. However, I am old, and as you have seen, I am also dense. :-(

Indeed, we are talking about an equation which to you and most others here, maybe everyone but me, is both uninteresting AND trivial. But, for better or worse, it still holds a fascination to a woo like me.



Sort of. Essentially, you are expanding your system by adding a new production rule, something roughly equivalent to

Oab -> OaOb

... reflecting distributing O(a and b) across to be Oa and Ob. [and similarly for 1ab -> 1a1b as well.]

The actual details could be hashed out if anyone were sufficiently interested.

But the first key question is "why should such a distribution property be available?"

It's not generally available "in the real world," for example. If I substitute Canadian bacon for ham in "ham and eggs," I get "Canadian bacon and eggs," not "Canadian bacon and Canadian eggs." Similarly, if I substitute French fries for hash browns in "hash browns and toast," I get
"French fries and toast," not "French fries and French toast." As your server can tell you, these are entirely different orders.... So there's no reason in general to assume that a distributional property applies -- and there's a well developed theory of algebra studying the properties of systems that do have a distributional property. (And formal grammars isn't usually one of those systems.)

But beyond that, there's still the second and even more key question : "So what?"

What's so fascinating about this particular string of letters and numbers?

Dr. Kitten, you may be the smartest non-woo on this thread, maybe on the whole Forum!!!

I have been wondering a lot about your "But beyond that, there's still the second and even more key question : "So what?" What's so fascinating about this particular string of letters and numbers?"

I do not know if this has actually any significance, but you tell me...

Start out with an O and a 1 and an X and a y in an ordered alphabet. And determine how many other permutions and combinations there are that seem meaningful, and such that the first letter is capitalized and the last letter is a small letter.

I think we get:

OX1y
1YOx
1XOy
OY1x
OXOy
OYOx
1X1y
1Y1x

Does that have any meaning to you? Any significance per your vast and more and more admired knowledge base? We may not agree on a lot, but we do agree on that!

Philosaur
27th April 2010, 07:21 AM
Where did I say that it was not people who put meaning there?

To be fair, I think you did mention during some post that you understood that the writers gave the Bible whatever meaning it has. But this only begs another question: why trust the stories of the Bible writers over the research of scientists? To do so is irrational. And willful irrationality overlaps woo-dom to a very large degree.

Complexity, I'll match what I have read against anything you have read. The lives of Newton and Boyle, the lives of Grassmann, Cantor, Boltzmann, Ohm, Cusa, Bruno... all of which indicate that not being limited to the prevailing views of one's time can lead to new knowledge, often at the risk of one's academic position, or even one's life.

And this EXACT sentiment is what fuels the fires of pseudo-scientifically-minded True Believers. What the Believers fail to realize is that Newton, Boyle, Einstein, and others were able to do the basic math and science that allowed them to see fruitful areas of study, and disregard others.

The great ones crawled before they walked, walked before they ran, and ran before they hurtled into the cosmos to find greatness.

You, on the other hand, are tripping around the back yard with toy rockets and a fish bowl on your head claiming you may have made the Next Great Discovery.

You talk about humility, yet in the same breath you compare yourself to the greatest scientists of all time.

We all tell you to learn the basics first, but you will probably rejoin with "But I don't want to be tainted by the narrow-minded conventional view".

So we come back to what I said before: have fun being the lonely, misunderstood genius you are painting yourself to be.
Not always, but sometimes. And when such intellectual adventure leads to successful new insights, it is both wonderful for those ready to move ahead, and terrible for those stuck in the past, even the past of science and math.

Of course, such lacks of limitations can lead to woo-dom. But isn't anyone who is afraid of occasionally exploring new possibilities using logic as a guard and guide also a kind of woo? Complexity, you do not disappoint me. I would expect nothing less from you. Your cup runneth under.[/QUOTE]

Giggywig
27th April 2010, 07:35 AM
I'm confused, what does ox1y have to do with the Bible or any other scripture? Or have we moved on from the transformations into... whatever it is that's being discussed now?

eijah
27th April 2010, 07:41 AM
To be fair, I think you did mention during some post that you understood that the writers gave the Bible whatever meaning it has. But this only begs another question: why trust the stories of the Bible writers over the research of scientists? To do so is irrational. And willful irrationality overlaps woo-dom to a very large degree.

And this EXACT sentiment is what fuels the fires of pseudo-scientifically-minded True Believers. What the Believers fail to realize is that Newton, Boyle, Einstein, and others were able to do the basic math and science that allowed them to see fruitful areas of study, and disregard others.

The great ones crawled before they walked, walked before they ran, and ran before they hurtled into the cosmos to find greatness.

You, on the other hand, are tripping around the back yard with toy rockets and a fish bowl on your head claiming you may have made the Next Great Discovery.

You talk about humility, yet in the same breath you compare yourself to the greatest scientists of all time.

We all tell you to learn the basics first, but you will probably rejoin with "But I don't want to be tainted by the narrow-minded conventional view".

So we come back to what I said before: have fun being the lonely, misunderstood genius you are painting yourself to be.
Not always, but sometimes. And when such intellectual adventure leads to successful new insights, it is both wonderful for those ready to move ahead, and terrible for those stuck in the past, even the past of science and math.


Please show me where I have said I have made any discovery, other than the apparently trivial one that under the right circumstances OX1y can -> OOXO1y1Ox11y ?

AND where I have put myself in the category of the great scientists and mathematicians of history, other than like them I also being willing to ask myself, "What if..." -- which admittedly is a child-like question and a woo-like one, HOWEVER, also one asked by the greats of math and science.

I think you continue to be unfair to me because you insist on seeing me as a woo, instead of as an asker of questions outside of your orthodox constraints, which seems to me to be no less cognitively limiting than orthodox religious constraints.

eijah
27th April 2010, 07:52 AM
I'm confused, what does ox1y have to do with the Bible or any other scripture? Or have we moved on from the transformations into... whatever it is that's being discussed now?

We are talking about the apparent folly of asking unorthodox "What if...?" questions? At least apparent to most people on this thread, aside from me.

I think it logical to believe that anything that specifically smacks of the bible or other scriptures per my responses on this thread is in the eye of the beholder or non-beholder who is reading my responses, and depends on his or her own beliefs and disbeliefs -- across the entire spectrum of all of his or her beliefs and disbeliefs.

Also please note that in my first string, I am talking about OX1y, NOT ox1y. I think that difference may be significant, and I have asked Dr. Kitten about that.

Giggywig
27th April 2010, 08:03 AM
Also please note that in my first string, I am talking about OX1y, NOT ox1y. I think that difference may be significant, and I have asked Dr. Kitten about that.
The difference is as significant as you want it to be. It's an arbitrary 4 character string, and the only meaning it has is what is assigned to it by somebody else. If under your rules 0x1y is different from oX1y or 0X1Y or Ox1Y or any other string that's fine, but that's only under your rules. Under different rules they can all be equivalent.

eijah
27th April 2010, 08:18 AM
The difference is as significant as you want it to be. It's an arbitrary 4 character string, and the only meaning it has is what is assigned to it by somebody else. If under your rules 0x1y is different from oX1y or 0X1Y or Ox1Y or any other string that's fine, but that's only under your rules. Under different rules they can all be equivalent.

Ok. I accept what you say.

And now having said that, a question: Is there ANY way that might be any cognitive implications of the properties and the order of different characters in an ordered alphabet having different properties? For example, -X+y vs. +Y-x vs. -Y+x?

drkitten
27th April 2010, 08:20 AM
Believing myself to have free will and also believing in axiomization

I'm not quite sure what you mean by this. "Believing in axiomization" is about as pointless as "believing in bishops moving diagonally" or "believing in 3 point field goals." Axiomization isn't an empirical fact about the world that can be true or false, it's simply one approach among many to the study of mathematics.

And it's also been used as an approach to the study of natural sciences -- but with much less success, precisely because science, unlike math, is bound by empirical evidence. Aristotle reasoned from first principles that an arrow shot from a bow moved in a straight line --- and of course got it wrong as anyone can confirm with a high speed camera today.


I chose to begin with that belief as an axiom, just to see what might possibly be viewable in terms of intellectual dis-covery.

Which belief?

I chose that axiom on the assumption quite different (or maybe not completely different from an unorthodox interpretation of "The Assumption", time may tell, maybe not) that we do not see what we do not believe is possible to see.

Well, starting out with an assumption that is known to be false is generally not a good way to do science. It works occasionally (relativity theory started from Einstein daydreaming about riding on a photon and realizing all the things wrong with that idea) but you have to be able to figure out what's wrong with your wrong assumption at the end....

1) My approach CAN waste a lot of time. And it is possibly a non-teminating amount of time (limited by my lifetime) with NO assurance of ANY positive result.

So how is that any different from the nature of "pure exploration"? I do not see any difference, but I am open to your view of "pure exploration".

As a card-carrying real scientist, one of the things that I need to do from time to time is review grant proposals and recommend which get funded. And this is indeed one of the key questions.

There are two aspects that need to be considered here. One is the likelihood of some sort of positive result originating from this approach. Basically, "what supporting evidence can you bring to bear before running your proposed study?" Based on everything else we know about related fields, is there anything at all to suggest that there's something in your proposal?

In this case, is there anything at all to suggest a connection between formal grammars, cognition, and the Book of John? I submit that the answer is "no." Complexity would presumably agree.

Basically, even when you explore, you usually have some idea of what you're exploring. You may not know what's on the other side of that mountain, or up that river, but you know at least that the mountain or river is there in the first place. Here you don't even seem to have a river in mind.



2) As for Alpha-Bits and time intervals of traffic light changes, I completely agree as well. Seeing meaning in any random occurrences is usually quite silly. On the other hand, seeing meaning in probability distributions of electrons in hydrogen atoms is kind of fundamental in QM. SO when does one ignore random occurrences and when does one pay close attention to them? And why not the first vs. why the latter? I am open to your views.

Again, this is the sort of thing I have to review on a regular basis; this is the second key question, which is basically -- "if your hypothesis were true, so what?" What is the likely impact of even a successful finding?

In the case of hydrogen electrons, learning about this tells us a hell of a lot about the fundamental nature of matter. Learning how hydrogen is put together tells us about helium, neon, silicon, sodium, and so forth. It tells us about how electricity works. It tells us about ways to make improved electrical devices such as the transistor or the laser. What does your proposed link between formal grammar and the book of John tell us about the book of Acts? What does it tell us about history? About psychology?

Hell, what does it tell us about the book of John?

If the answer is "nothing much," then there's no reason to pursue your line of thought.

drkitten
27th April 2010, 08:22 AM
Ok. I accept what you say.

And now having said that, a question: Is there ANY way that might be any cognitive implications of the properties and the order of different characters in an ordered alphabet having different properties? For example, -X+y vs. +Y-x vs. -Y+x?

Not that I can see. Not that anyone else participating in this thread can see. If you think that there is such a way, the burden is on you to articulate it in a clear and convincing manner. But given how entirely arbitrary the symbol set is in a typical formal grammar, I would be astonished to learn that there was a formal relationship between cognition and character sets.

Giggywig
27th April 2010, 08:25 AM
And now having said that, a question: Is there ANY way that might be any cognitive implications of the properties and the order of different characters in an ordered alphabet having different properties? For example, -X+y vs. +Y-x vs. -Y+x?
Could you rephrase that?

eijah
27th April 2010, 08:42 AM
Not that I can see. Not that anyone else participating in this thread can see. If you think that there is such a way, the burden is on you to articulate it in a clear and convincing manner. But given how entirely arbitrary the symbol set is in a typical formal grammar, I would be astonished to learn that there was a formal relationship between cognition and character sets.

Can you define for me in as much detail as you can what you mean by a formal relationship between cognition and character sets? Thanks!

drkitten
27th April 2010, 08:48 AM
I have been wondering a lot about your "But beyond that, there's still the second and even more key question : "So what?" What's so fascinating about this particular string of letters and numbers?"

I do not know if this has actually any significance, but you tell me...


Well,....


Start out with an O and a 1 and an X and a y in an ordered alphabet. And determine how many other permutions and combinations there are that seem meaningful, and such that the first letter is capitalized and the last letter is a small letter.

Four objects produce 4! (4x3x2x1) permutations, irrespective of object type. There are therefore 24 different arrangements. Combinatorics is well understood.

If you restrict yourself to only the arrangements that end in a letter, then there are twelve arrangements. If you allow the first letter to be either upper or lower case, then you're back to 24. (And so forth. As I said, this is all well-understood from a purely mathematical point of view; if there's a connection to the book of John, I'm not seeing it.)

Having said that, none of the 24 arrangements "seem meaningful" to me.



I think we get:

OX1y
1YOx
1XOy
OY1x
OXOy
OYOx
1X1y
1Y1x


You're missing O1Xy, 1OXy, O1Yx, 1OYx. You're also missing YO1x, XO1y, Y1Ox, and X1Oy. And some of the elements listed above violate your proposed rule, because they have two ones and no zeros or vice versa.

So again, you're not actually describing the rules you are following -- or following the rules you are describing.

But the elephant in the room remains:


Does that have any meaning to you?

None whatsoever.

eijah
27th April 2010, 08:50 AM
Not that I can see. Not that anyone else participating in this thread can see. If you think that there is such a way, the burden is on you to articulate it in a clear and convincing manner. But given how entirely arbitrary the symbol set is in a typical formal grammar, I would be astonished to learn that there was a formal relationship between cognition and character sets.

By the way, the glimmer of a possible idea is emerging in my poor excuse for a brain.

And it seems to map in very nicely to everything that you and others have been saying to me about the separation of semantics from syntax. I would be extremely happy if you are right, and I have been wrong in one or more assumptions I have been using which may have clouded other aspects of what I have been intuitively seeing, perhaps rightly, perhaps also wrongly!

drkitten
27th April 2010, 08:52 AM
Can you define for me in as much detail as you can what you mean by a formal relationship between cognition and character sets? Thanks!

We have lots of information about psycholinguistic relationships between signifiers and cognition that are based on the properties of the signified.

For example, we read words faster when they're the names of common objects than when they're the names of uncommon objects.

But that's not a relationship between the sign and the mind. That's a relationship between the mind and the real world that is carried across the (arbitrary) relationship between the sign and the real world.

eijah
27th April 2010, 09:05 AM
Well,....



Four objects produce 4! (4x3x2x1) permutations, irrespective of object type. There are therefore 24 different arrangements. Combinatorics is well understood.

If you restrict yourself to only the arrangements that end in a letter, then there are twelve arrangements. If you allow the first letter to be either upper or lower case, then you're back to 24. (And so forth. As I said, this is all well-understood from a purely mathematical point of view; if there's a connection to the book of John, I'm not seeing it.)

Having said that, none of the 24 arrangements "seem meaningful" to me.




You're missing O1Xy, 1OXy, O1Yx, 1OYx. You're also missing YO1x, XO1y, Y1Ox, and X1Oy. And some of the elements listed above violate your proposed rule, because they have two ones and no zeros or vice versa.

So again, you're not actually describing the rules you are following -- or following the rules you are describing.

But the elephant in the room remains:



None whatsoever.

I keep asking myself this question you asked me: Of what [possible] significance? The only thing that keeps popping into my poor excuse for a brain now is that the eight "alphabet" variations kind of map into the four corners of a Cartesian coordinate system.

Which probably is just a coincidence, but perhaps not. In any case, if you are saying that these eight sets of characters have no significance at all, I am by now more than willing to yield to you and my other betters on this thread. At least until something of real significance comes along which may or may not completely satisfy your and others' rigorous intellectual requirements.

Giggywig
27th April 2010, 09:10 AM
I keep asking myself this question you asked me: Of what [possible] significance? The only thing that keeps popping into my poor excuse for a brain now is that the eight "alphabet" variations kind of map into the four corners of a Cartesian coordinate system.
Let's see...
Start out with an O and a 1 and an X and a y in an ordered alphabet. And determine how many other permutions and combinations there are that seem meaningful, and such that the first letter is capitalized and the last letter is a small letter.
You arrived at those 8 by filtering out those that did not seem meaningful to you, and then you ask why the remaining ones appear meaningful? The answer is because you constructed them to appear meaningful to you.

tsig
27th April 2010, 09:55 AM
He was on acid when he first thought of it.It would be hard to divert questions to him,he's brown bread.

Believers talk to the dead all the time. "Jesus said" is one of their favorite phrases and they're not always talking about the bible when they say it.

tsig
27th April 2010, 09:57 AM
No, sorry, this is nonsense.

A production rule always produces the same output for any given input. If it doesn't, you're doing it wrong.

That's all there is to it.

Perhaps if you'd tell us what the point of all this is supposed to be, we could help you better. Mind you, the original post made no sense either.

I'm betting god.

eijah
27th April 2010, 10:30 AM
We have lots of information about psycholinguistic relationships between signifiers and cognition that are based on the properties of the signified.

For example, we read words faster when they're the names of common objects than when they're the names of uncommon objects.

But that's not a relationship between the sign and the mind. That's a relationship between the mind and the real world that is carried across the (arbitrary) relationship between the sign and the real world.

Ok. And thanks. But unless I have missed something here, I still do not see a formal definition of the relationship between cognition and character sets. And very sorry if you have given a precise and complete "formal" definition to me above and, as I often, I missed it. :-(

eijah
27th April 2010, 10:37 AM
I'm betting god.

How much are you REALLY willing to bet? Especially as (if you look VERY carefully as to what I have said and not said here, not what others have said here about what I have said and not said -- which by the way, all too often happens in religion and sometimes even in science), I can take this anywhere. And to win a lot of bucks, I will! :-)

eijah
27th April 2010, 10:42 AM
Believers talk to the dead all the time. "Jesus said" is one of their favorite phrases and they're not always talking about the bible when they say it.

Are you saying that any real Jesus currently worshiped by Christians (in order sorts of contradictory ways) ever existed?

Or that such a real Jesus is now dead?

Or is still alive in some way?

Or what?

You sound VERY woo to me.

PixyMisa
27th April 2010, 10:57 AM
Believing myself to have free will
Define free will.

and also believing in axiomization
What is that supposed to mean? As someone else pointed out, axiomization is just one approach in mathematics. You don't need to "believe in" it; it's a real and valid approach.

I chose to begin with that belief as an axiom
Then you're doing it wrong. Again.

What you do is you form a hypothesis. You don't believe it. You say, maybe this is true. If it is true, then this and this and this would necessarily follow. Let's see if those are true. Oh, they're not? Discard hypothesis and try again.

Belief is what you do after you have demonstrated that the hypothesis is actually likely to be correct.

just to see what might possibly be viewable in terms of intellectual dis-covery.
You're doing it wrong.

I chose that axiom on the assumption quite different (or maybe not completely different from an unorthodox interpretation of "The Assumption", time may tell, maybe not) that we do not see what we do not believe is possible to see.
This assumption is false. Common among purveyors of nonsense, and false.

Seems to me to be especially true per seeing or re-seeing new or forgotten legitimate concepts.
(a) No and (b) what forgotten legitimate concepts? Why do you believe there are any such forgotten legitimate concepts?

I.e., we all tend not to give passing inklings of something new and/or strange a second glance if we see them as anomalies or mistakes or horrifying to our beliefs.
Sorry, this is not true. Proof: All scientific progress ever.

Said another way, I believe that we do not re-cognize something as possibly worth more scrutiny, analysis... if it assaults our bedrock beliefs and disbeliefs -- scientific as well as religious ones.
You're wrong. Oh, this may apply to you, and to others who wallow in folly and superstition, but it sure as hell doesn't apply to the scientists and engineers and technicians who actually get things done. They get things done by dealing with the world as it is rather than dreaming about how things should be.

You may think starting with such an axiom is folly.
It is folly.

And that is your right, even though that does not make you right.
No, what makes me right is that your approach is based on falsehood and does not work.

I am guessing you will flush my axiom down your toilet because you need to be right.
No, I'll flush your so-called axiom down the toilet because it's based on falsehood.

However disagreeing with me is counter-productive.
That's the stupidest thing you've said so far.

Because starting with an axiom to see where it might take one is a bedrock too.
No.

Arguably, the bedrock of the best math and science as well as common sense. And the preferred method of those who get Nobel Prizes and Field ones, not just tenure, as it is the time and again proven bedrock for building logical edifices in science and mathematics and blessedly available to all believers and non-believers of everything, BUT only if and when they are not afraid of seeking and seeing what other truths may lie beyond what is already known to be true and what is already already known to be false.
No, wrong. The most important thing is that they are willing to discard their own ideas when the facts show them to be wrong.

You think me a fool.
Yeah, at this point, pretty much.

And I may well be.
Yes.

But maybe I am not the one being self-fooled.
Yes, you are.

In any case, to me, "What if...?" is always a whole lot better than "It has to be."
A strawman and a non-sequitur.

For I prefer to try to cognitively benefit from humility rather than suffer from hubris.
And an ad hominem.

By the way, "damned" NOT in a religious sense, but rather damned in the sense of being doomed to not see what you insist upon not seeing -- which are things that are there but can be cognitively a-voided.
I don't insist on not seeing anything; that's just an ad hominem attack you're presenting as an excuse for your own failure.

What I insist on is evidence.

Get the evidence, then believe in it.

In that order.

Always.

All else is folly.

And "blessed" NOT in a religious sense, but in a cognitive sense, where what might be seen is more likely to be seen.
No. This does not work.

Suggestion in return: As an experiment, try my axiom and see what happens?
What happens is that I promptly reject the axiom as contrary to all available evidence.

It's a bit like buying a new car and then beginning to notice how many others of them are on the road.
Except in this case, there is no car.

You can always return to your old one.
I have. Took less than three seconds.

Can't hurt. And might help a lot. But only doable if your belief system is not set in stone.
Again, this is an ad hominem attack used as an excuse for your own failure.

Evidence first, then belief.

So where is your evidence?

PixyMisa
27th April 2010, 11:00 AM
Are you saying that any real Jesus currently worshiped by Christians (in order sorts of contradictory ways) ever existed?

Or that such a real Jesus is now dead?

Or is still alive in some way?

Or what?
Since he didn't say any of those things, or imply any of those things, and since none of those things can reasonably be inferred from what he did say, I'd say, no.

You sound VERY woo to me.
Here's a mirror.

Philosaur
27th April 2010, 11:20 AM
Please show me where I have said I have made any discovery, other than the apparently trivial one that under the right circumstances OX1y can -> OOXO1y1Ox11y ?

How about here:

In any case, I am neither a linguist nor a mathematician, just for better and worse an iconoclastic bull in a conventional wisdom china shop. With the possibility of my having stumbled upon a cognitive formal grammar.

or here:

However, if in the unlikely event I am right, then you may have just found a thesis that might make your career -- or at least get you some well-earned attention from some part of the academic community. Perhaps, helping you get into an elite graduate program.

People who DO know the territory of formal grammars have repeatedly stated that you have made NO such discovery. And while you keep pleading your ignorance and maintaining the front of "but I'm only an explorer...", you still will not let the issue die. Instead, you repeat your questions, you reiterate your production rule, and you reply with (honestly, ingratiating) politeness that you appreciate the help, but would still like us to just *consider* that you are on to something.

As others have said: this smacks of woo.


AND where I have put myself in the category of the great scientists and mathematicians of history, other than like them I also being willing to ask myself, "What if..." -- which admittedly is a child-like question and a woo-like one, HOWEVER, also one asked by the greats of math and science.

The claim that you are only asking "what if" like other great scientists is just wrong. Great scientists may ask "what if", but they almost always only do it from within their field of expertise. And where they do ask it of other fields, they are generally wise enough (Roger Penrose notwithstanding) to accept the input of experts in those other fields.

I think you continue to be unfair to me because you insist on seeing me as a woo, instead of as an asker of questions outside of your orthodox constraints, which seems to me to be no less cognitively limiting than orthodox religious constraints.
Our "orthodox constraints" are the constraints of logic and of time-tested axioms like "Inference is a valid form of argument", or "Extraordinary claims require extraordinary evidence". Think of these constraints as the basic necessities you'd need to survive in the wilderness of scientific exploration. Would you go into the jungle without your machete, boots, and canteen? I mean, you can if you want, but you probably won't get very far.

Or since you are so fond of the great scientists who came before: think of these constraints as the "shoulders of giants" that Newton spoke of.

drkitten
27th April 2010, 11:48 AM
I keep asking myself this question you asked me: Of what [possible] significance? The only thing that keeps popping into my poor excuse for a brain now is that the eight "alphabet" variations kind of map into the four corners of a Cartesian coordinate system.

So what?

First, of all, it's not clear to me that 8 "kind of maps" into 4. It either maps or it doesn't.

Second, it also maps -- and much more clearly -- into the number of legs of a spider, the number of planets in the solar system, the number of home games played by a professional NFL team during a season, the number of white pawns in a chess set, the number of sides of a stop sign, the number of notes in a Western musical scale, and the number of players on a baseball team who don't pitch.

None of which is particularly interesting, given the degree of arbitrariness involved. The Japanese play shogi (a variant of chess) with nine pawns, there were nine recognized planets until extremely recently, and the American League accepts a ninth position (the designated hitter). The Japanese use a triangle as a stop sign, and the Bahamas use a circle with an inscribed triangle. And I believe Indonesian music uses a pentatonic scale.

You've picked eight of the twelve/twenty-four/whatever possible patterns that seem interesting to you and find that there are also eight of them. If you decide later that only six of these eight were really interesting, will the fact that there are six sides in a cube and six legs on a butterfly suddenly become an "insight"?

Again, this is a classic mark of the woo.

eijah
27th April 2010, 01:32 PM
Define free will.


What is that supposed to mean? As someone else pointed out, axiomization is just one approach in mathematics. You don't need to "believe in" it; it's a real and valid approach.


Then you're doing it wrong. Again.



What I mean is that I believe in the prominence of axiomization as espoused by Gian-Carlo Rota in Indiscrete Thoughts. For more on him see http://www.springerlink.com/content/kn6n0p485rfp5uxv/

The reason that I say I believe in (rather than use) axiomization is that I am not capable of using it in the rigorous mathematical way(s) that some of you do, and I do not seek to give the false impression that I do. On the other hand, if OX -> were to be an axiom, i THINK that OOXO1y1OX11y may be a kind of axiomization result in a broader sense. Though I might be very wrong about this.



What you do is you form a hypothesis. You don't believe it. You say, maybe this is true. If it is true, then this and this and this would necessarily follow. Let's see if those are true. Oh, they're not? Discard hypothesis and try again.



If one takes a belief to be something that is considered self-evidently true, it has the look and feel of an axiom. Call that a starting point, hypothesis or place of initial understanding or what, be as picky as you would like, don't try to work with the way I say things. I could not care less.

I feed on your negativity as much as you gag on my views, which are often much re-informed and revised by even comments such as yours. You simply cannot comprehend that there are non-woos who do not have to be certain of everything all of time, and who, unlike woos, do as much as they can to not hold onto their tentative working assumptions beyond the time of their useful employment, and often useful even when they lead to dead ends.



Belief is what you do after you have demonstrated that the hypothesis is actually likely to be correct.



Yes. Typically. And very often very usefully. BUT it can also be a starting point. Cognitively speaking, you can cooly have a starting hypothesis, and/or you can also affectively have a beginning belief. The former is likely to be tepid and safe, the latter is more likely to feverish and bold. Both have their pros and cons. You only see the pros of the former and the cons of the latter. No problem to me or for me. I try to see the pros and cons of both.


You're doing it wrong.


Like Frank, I'm doing it my way. Different from yours? Yes. More prone to end up early on with possible errors? Yes!!! But not necessarily in the end wrong. And sometimes magnificently correct. See all manner of great discoveries from the history of science and math which were initially derided by the great scientists and mathematicians of the time that prove my point. For God's Sake (just a figurative phrase, guys :-), read about Mach hounding Boltzmann to his death. :-(


This assumption is false. Common among purveyors of nonsense, and false.



I am not surprised that you sincerely believe that it is easy for someone to see what he or she believes to their core is impossible to see. Yet, see Planck's statement about how QM will prevail over time as old-time physicists die out. Old authoritative stick-in-the-mud. head in the sands types. I am more and more inclined to think that either your knowledge of the actual history of math and science is abysmal. Or your understanding of that history is pathetic. Either way, not my problem.



(a) No and (b) what forgotten legitimate concepts? Why do you believe there are any such forgotten legitimate concepts?


You will have to buy my book to learn what they are. If I find out what they are and if write a book about that. A book that of course may never be written if I do not find any forgotten legitimate concepts. :-) But ya' never know until ya' try.


Sorry, this is not true. Proof: All scientific progress ever



If you are saying that all scientists immediately welcome with open arms every new discovery that turns out to end up greatly advancing science
(or at least is open to learning more at the beginning of an evolving new concept), once again you do not have sufficient knowledge and appreciation of the history of science. There are innumerable examples of what I am saying. V=IR, entropy, epigenetics...

In any case, thanks for your latest series of push-backs. And, sorry, I have no more time for your view of the nature of intellectual exploration. Be well!

eijah
27th April 2010, 01:57 PM
How about here:

or here:

People who DO know the territory of formal grammars have repeatedly stated that you have made NO such discovery. And while you keep pleading your ignorance and maintaining the front of "but I'm only an explorer...", you still will not let the issue die. Instead, you repeat your questions, you reiterate your production rule, and you reply with (honestly, ingratiating) politeness that you appreciate the help, but would still like us to just *consider* that you are on to something.

As others have said: this smacks of woo.



Maybe I did get this wrong. Maybe not. You tell me...

I initially said I had discovered OX1y -> OOXO1y1OX11y was a production rule. (By the way, I NEVER said I was the FIRST to discover it. Nor am I now offering it is important to anyone but me.)

Then we went through a number of pages of responses where everyone said that in no way could that be. Because OX1y could only be -> OOX1y1OX1y.

When eventually, after too long a time, I offered the mathematical analogy A(AX + By) + B(AX + By), I was informed by several of you that, yes, IF a production rule employing the distributive property were added, then we would have a legitimate OX1y -> OOXO1Oy1Oy11y.

Am I correct about this series of events? And the current legitimate status of OX1y -> OOXO1Oy1Oy11y -- as a different, but correct rule, when the distributive property is used? Or is OX1y -> OOXO1Oy1Oy11y still woo?

Giggywig
27th April 2010, 02:10 PM
Maybe I did get this wrong. Maybe not. You tell me...

I initially said I had discovered OX1y -> OOXO1y1OX11y was a production rule. (By the way, I NEVER said I was the FIRST to discover it. Nor am I now offering it is important to anyone but me.)

Then we went through a number of pages of responses where everyone said that in no way could that be. Because OX1y could only be -> OOX1y1OX1y.

When eventually, after too long a time, I offered the mathematical analogy A(AX + By) + B(AX + By), I was informed by several of you that, yes, IF a production rule employing the distributive property were added, then we would have a legitimate OX1y -> OOXO1Oy1Oy11y.

Am I correct about this series of events? And the current legitimate status of OX1y -> OOXO1Oy1Oy11y -- as a different, but correct rule, when the distributive property is used? Or is OX1y -> OOXO1Oy1Oy11y still woo?
You are incorrect. Nobody says that OX1y -> OOXO1Oy1Oy11y is not a legitimate production rule. In itself, that is a valid production rule. What you said was that given some production rules you could get to two different results with the same input. That part was wrong then and it's still wrong now. There are an infinite number of ways to get from OX1y to OOXO1Oy1Oy11y (the most trivial of which is using OX1y -> OOXO1Oy1Oy11y as a production rule), but your original production rules were not one of them. And you still have not said what is so meaningful about getting from OX1y to OOXO1Oy1Oy11y.

eijah
27th April 2010, 02:26 PM
You are incorrect. Nobody says that OX1y -> OOXO1Oy1Oy11y is not a legitimate production rule. In itself, that is a valid production rule. What you said was that given some production rules you could get to two different results with the same input. That part was wrong then and it's still wrong now. There are an infinite number of ways to get from OX1y to OOXO1Oy1Oy11y (the most trivial of which is using OX1y -> OOXO1Oy1Oy11y as a production rule), but your original production rules were not one of them. And you still have not said what is so meaningful about getting from OX1y to OOXO1Oy1Oy11y.


Pardon my continued denseness or bad memory, But as I remember, I was originally told that there was NO way of replacing X and Y in OX1y with OX1y and getting OOXO1X1Oy11y. However, after I offered the math analogy with its distributive property, I was told that there is a way to replace X and y in OX1y with OX1y. But I need to add a production rule that uses a distributive property. Yes? Or do I have this wrong as well as everything else?

Giggywig
27th April 2010, 02:31 PM
Pardon my continued denseness or bad memory, But as I remember, I was originally told that there was NO way of replacing X and Y in OX1y with OX1y and getting OOXO1X1Oy11y.
That is not what your previous post said. You said "...initially said I had discovered OX1y -> OOXO1y1OX11y was a production rule." These two statements are not the same.
However, after I offered the math analogy with its distributive property, I was told that there is a way to replace X and y in OX1y with OX1y. But I need to add a production rule that uses a distributive property. Yes? Or do I have this wrong as well as everything else?
You need to add more than a distributive property rule, you need to change the way production rules are used. You are in effect not using formal grammar, you are using arbitrary string manipulation.

eijah
27th April 2010, 02:38 PM
That is not what your previous post said. You said "...initially said I had discovered OX1y -> OOXO1y1OX11y was a production rule." These two statements are not the same.

You need to add more than a distributive property rule, you need to change the way production rules are used. You are in effect not using formal grammar, you are using arbitrary string manipulation.

Ok. Great. And much thanks!

Is there any place you can point me to so that I can at least somewhat understand what it takes to do that? I.e., what field of grammar are you talking about? Dr. Kitten pointed out that I was not in the area of formal grammar. So what I am I woefully more than woo-fully noodling in? Is it (perhaps some extention) of Lindermayer grammar http://en.wikipedia.org/wiki/L-system, or what?

Philosaur
27th April 2010, 02:39 PM
Maybe I did get this wrong. Maybe not. You tell me...

I initially said I had discovered OX1y -> OOXO1y1OX11y was a production rule. (By the way, I NEVER said I was the FIRST to discover it. Nor am I now offering it is important to anyone but me.)

One doesn't "discover" production rules. A production rule is a completely (not partially, not mostly, not just a little bit) arbitrary construction that has a string on one side, some variant of an arrow symbol in the middle, and another string on the other side.

Production rules do not exist out there, somewhere in the ether, waiting to be discovered. They are stipulated. No one *cares* whether you are the first to write down this production rule.

Here are sample production rules, and some comments about them:

a -> b
Allows you to replace "a" with "b". Simple.

cat -> dog
Allows you to replace "cat" with "dog". Does not imply that cats are better than dogs. Does not mean that cats can become dogs.

cat -> catcatcatcat
Does not imply that cats multiply.

1+1 -> 5
This is *not* a statement about mathematics. It is neither true nor false in the realm of mathematics, because the individual symbols in the alphabet have no *inherent* relationship to those in mathematics.

10010101001101101001 -> purple
Production rules can shorten a string, too.

e -> mc^2
This may *look* like a famous equation, but it's NOT. It's a rule stating that the string "e" can produce the string "mc^2". Nothing more. To impose the meaning behind in the equation of relativity is to make an unwarranted assumption.


Then we went through a number of pages of responses where everyone said that in no way could that be. Because OX1y could only be -> OOX1y1OX1y.

No. You misunderstood *everything* that everyone here said. If you stipulate that the production rule allows you to turn any given string into any other string, then the rule is--by definition (because it IS a sort of definition) correct!

What we said is that you cannot properly form a production rule with one string on the left side which produces two different strings on the right side. It is nonsensical.

[Please, no one muddy the water by bringing up stochastic grammars.]


When eventually, after too long a time, I offered the mathematical analogy A(AX + By) + B(AX + By), I was informed by several of you that, yes, IF a production rule employing the distributive property were added, then we would have a legitimate OX1y -> OOXO1Oy1Oy11y.

Which is an altogether unsurprising result. The fact that we went through so many pages simply illustrates your ignorance of formal grammars. Trust those of us who *do* know something about formal grammars when we say that you are barking up the wrong tree.

Learn the basics first. Then presume to think you are offering something novel and interesting to the field.

Am I correct about this series of events? And the current legitimate status of OX1y -> OOXO1Oy1Oy11y -- as a different, but correct rule, when the distributive property is used? Or is OX1y -> OOXO1Oy1Oy11y still woo?
First: no. You are not correct, as I've pointed out.

Second: Yes, this is a legitimate rule. But it's as arbitrary as any of the examples I've given above. And as interesting.

Third: It has nothing to do with the distributive property. That was offered up as a way of understanding your misguided talk about parentheses. It does not legitimize your claim that a single input can give two outputs.

Fourth: the rule is not woo. Your attitude--coupled with the fact that you are ignorant of formal grammars and yet insistent, in the face of constant, unanimous correction from people who do know more than you, is very woo.

Philosaur
27th April 2010, 02:45 PM
Ok. Great. And much thanks!

Is there any place you can point me to so that I can at least somewhat understand what it takes to do that? I.e., what field of grammar are you talking about? Dr. Kitten pointed out that I was not in the area of formal grammar. So what I am I woefully more than woo-fully noodling in? Is it (perhaps some extention) of Lindermayer grammar http://en.wikipedia.org/wiki/L-system, or what?

The simple fact is that nobody quite knows *what* you are doing. It's not formal grammars. It's not L-systems (which are a strict subset of formal grammars). It's not math. It's not theology. It's not cognitive grammars. I hope that helps to narrow down the field for you, because that's all anyone here can probably say.

Complexity
27th April 2010, 03:09 PM
Complexity, I'll match what I have read against anything you have read.


It would be somewhat interesting but meaningless to do so. You see, it isn't just a matter of how much you have read, but how well you have read, and how well prepared you were to read that material.

The lives of Newton and Boyle, the lives of Grassmann, Cantor, Boltzmann, Ohm, Cusa, Bruno... all of which indicate that not being limited to the prevailing views of one's time can lead to new knowledge, often at the risk of one's academic position, or even one's life. Not always, but sometimes. And when such intellectual adventure leads to successful new insights, it is both wonderful for those ready to move ahead, and terrible for those stuck in the past, even the past of science and math.

Of course, such lacks of limitations can lead to woo-dom. But isn't anyone who is afraid of occasionally exploring new possibilities using logic as a guard and guide also a kind of woo?


This is a theme that you and many others keep returning to.

Many wonderful things have been invented and discovered by people who are amateurs or professionals who disregard convention. All of these people, however, have studied their disciplines deeply, mastering the techniques and knowledge necessary to accomplish their goals.

I'm afraid that you are nothing like any of the people that you have mentioned. You are a dabbler, a poser, a wannabe. You want to take bows without having accomplished anything yet.

Perhaps you have some potential and enough drive to begin to achieve something, but you will accomplish meaningful things in life only by avoiding the short-cuts.

You utterly mangled your interpretation of the second quote in my signature. It is time for you to read the first quote.

Creative and meaningful research in mathematics and science is difficult and beyond the capabilities of most people. Years of preparation and careful thought are necessary just to get started. Persistence is essential.
This work is life consuming and well worth the investment.

Complexity, you do not disappoint me. I would expect nothing less from you. Your cup runneth under.


I wasn't seeking your disdain, but I can live with it.

Complexity
27th April 2010, 03:26 PM
State your 'axiom' clearly and concisely. No arguments, no elaboration. Use as few words as possible.


We are all still waiting for your response to my request, eijah.

I think that we deserve a prompt and succinct response.

eijah
27th April 2010, 03:43 PM
One doesn't "discover" production rules. A production rule is a completely (not partially, not mostly, not just a little bit) arbitrary construction that has a string on one side, some variant of an arrow symbol in the middle, and another string on the other side.

Production rules do not exist out there, somewhere in the ether, waiting to be discovered. They are stipulated. No one *cares* whether you are the first to write down this production rule.

Here are sample production rules, and some comments about them:

a -> b
Allows you to replace "a" with "b". Simple.

cat -> dog
Allows you to replace "cat" with "dog". Does not imply that cats are better than dogs. Does not mean that cats can become dogs.

cat -> catcatcatcat
Does not imply that cats multiply.

1+1 -> 5
This is *not* a statement about mathematics. It is neither true nor false in the realm of mathematics, because the individual symbols in the alphabet have no *inherent* relationship to those in mathematics.

10010101001101101001 -> purple
Production rules can shorten a string, too.

e -> mc^2
This may *look* like a famous equation, but it's NOT. It's a rule stating that the string "e" can produce the string "mc^2". Nothing more. To impose the meaning behind in the equation of relativity is to make an unwarranted assumption.


No. You misunderstood *everything* that everyone here said. If you stipulate that the production rule allows you to turn any given string into any other string, then the rule is--by definition (because it IS a sort of definition) correct!

What we said is that you cannot properly form a production rule with one string on the left side which produces two different strings on the right side. It is nonsensical.

[Please, no one muddy the water by bringing up stochastic grammars.]


Which is an altogether unsurprising result. The fact that we went through so many pages simply illustrates your ignorance of formal grammars. Trust those of us who *do* know something about formal grammars when we say that you are barking up the wrong tree.

Learn the basics first. Then presume to think you are offering something novel and interesting to the field.

First: no. You are not correct, as I've pointed out.

Second: Yes, this is a legitimate rule. But it's as arbitrary as any of the examples I've given above. And as interesting.

Third: It has nothing to do with the distributive property. That was offered up as a way of understanding your misguided talk about parentheses. It does not legitimize your claim that a single input can give two outputs.

Fourth: the rule is not woo. Your attitude--coupled with the fact that you are ignorant of formal grammars and yet insistent, in the face of constant, unanimous correction from people who do know more than you, is very woo.

This really is all very helpful. And I do very sincerely thank you. But there is something that I do have to stress once again, something woo-ish, but that does not necessarily make me a woo. At least I do not think so.

A few weeks ago, the concept of Lindermayer fractals unaccountably popped into my head one morning as I was waking up. (I had first come across them many yeara=s ago in the book Chaos and Fractals http://books.google.com/books?id=jVpS_u0Lg4gC&printsec=frontcover&dq=lindermayer+fractals+chaos&source=bl&ots=oLYawNHced&sig=v59Qt4rvZkgQIaeYXLTkP6Y7ncA&hl=en&ei=vmDXS-KkMMOB8gbp-9HJBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAkQ6AEwAA#v=onepage&q&f=false .

So I googled "Lindenmayer fractals" and came across the wikipedia entry describing them AND the LIndenmayer grammar rewriting system. Somewhat woo-ish, but not too much.

But then soon after that a re-writing example popped into my head, that of replacing of X and y in OX1y with OX1y -> OOXO1y1Oy11y (via the use of the distributive property), although as it has been made very apparent here that I know NOTHING about formal grammars, production rules...

So what's an old guy with time on his hands and this stuff on his mind to do? Of course learn as much as his feeble mind can about this stuff? And a friend suggested I turn to all of you. Little did I realize how exciting and interesting as well as educational my experiences would be. But that is just icing on the cake. I am still hoping to hear from someone here the details of "what is needed to add more than a distributive property rule, you need to change the way production rules are used. You are in effect not using formal grammar, you are using arbitrary string manipulation." But it has already been a great ride.

As I said before, I really am not a woo, but I so see where most of you would think so. I am also obviously not a great scientist, not a bad one, nor one at all. But like many of the great ones, I do tend to pursue the answers to questions that pop into my head more often and further than most people with and without advanced degrees. By the way, I do have an old one, much out of date.

And I have an inordinately great passion for the histories of both math and science. So I rejoice when I read about what Oresme knew well before Newton and Leibniz, just as I am curious about how Newtons' mucking around with theological and alchemical matters may have helped him developed his mathematical and physics of matter and light concepts? And that Leibniz was much enamored of the binary nature of the I Ching, being one of the first Europeans to encounter it. You all would of course see no possible connection as Keynes also did not per Newton's woo and non-woo interests, but the history of science and of math clearly show that what is obvious now may be wrong in years to come. We really never know anything for sure in science, do we? And sometimes even what mathematicians know for two thousand years turns out to be wrong.

In any case, hope this does a little level setting. Though probably not too much. But please know that my above woo-ish experiences are more of a shock to me than they are disturbingly woo-ish to you.

eijah
27th April 2010, 03:54 PM
We are all still waiting for your response to my request, eijah.

I think that we deserve a prompt and succinct response.

Fair enough. But a few questions before I can do that...

1st) Are replacement rules the same as production rules? And are re-writing rules the same as replacement rules?

tsig
27th April 2010, 04:29 PM
How much are you REALLY willing to bet? Especially as (if you look VERY carefully as to what I have said and not said here, not what others have said here about what I have said and not said -- which by the way, all too often happens in religion and sometimes even in science), I can take this anywhere. And to win a lot of bucks, I will! :-)

You will what?

tsig
27th April 2010, 04:31 PM
Are you saying that any real Jesus currently worshiped by Christians (in order sorts of contradictory ways) ever existed?

Or that such a real Jesus is now dead?

Or is still alive in some way?

Or what?

You sound VERY woo to me.

You sound completely unintelligible to me.

tsig
27th April 2010, 04:33 PM
Since he didn't say any of those things, or imply any of those things, and since none of those things can reasonably be inferred from what he did say, I'd say, no.


Here's a mirror.

I keep thinking he left and "L" out of his username.

Tnx

Complexity
27th April 2010, 06:33 PM
Fair enough. But a few questions before I can do that...

1st) Are replacement rules the same as production rules? And are re-writing rules the same as replacement rules?


No questions first.

You claim to have an axiom. Present it.

(I am not interacting with you to enable you to pursue this.)

eijah
27th April 2010, 08:10 PM
No questions first.

You claim to have an axiom. Present it.

(I am not interacting with you to enable you to pursue this.)

So be it. And to be consistent, in a like fashion I shall not explain my answer,

which is 1YOx.

But I will point to why...

Clearly the above is the "In the beginning"/initial state for all those who have eyes to see what is there to be seen. However, one has to be able to think out of the box to see why. On the other hand, there is no compelling reason on earth why fans of this Forum would ever want to do that. So let's call it a day and a night. And thank you very much, Complexity, for getting all of us to where it is simply obvious to me that this is the end of my part icipation in this thread.

Complexity
27th April 2010, 08:38 PM
So be it. And to be consistent, in a like fashion I shall not explain my answer,

which is 1YOx.

But I will point to why...

Clearly the above is the "In the beginning"/initial state for all those who have eyes to see what is there to be seen. However, one has to be able to think out of the box to see why. On the other hand, there is no compelling reason on earth why fans of this Forum would ever want to do that. So let's call it a day and a night. And thank you very much, Complexity, for getting all of us to where it is simply obvious to me that this is the end of my part icipation in this thread.


1YOx is not an axiom.

You persist in thinking that you are the only one who can think out of the box or find value in doing so.

What you have been doing is not thinking out of the box. You don't understand what the box is. You wouldn't recognize the box if you tripped over it. You don't have the capabilities required to think well about the problems that you have attempted to solve in conventional ways, let alone in unconventional ways.

You aren't ready to be a genius or to behave like one.

Thinking out of the box with regard to my research is something that I excel at. I had to spend decades of time learning, developing my techniques and knowledge, and thinking in order to become effective at doing research in my field, especially to become really creative in coming up with new approaches to classic problems.

It pisses me off that you waltz in here, without particular knowledge, skill, or insight, and ever-so-humbly proclaim your 'breakthrough'.

There is nothing to it. Drop it. It has no value.

Choose another hobby.

I've pursued this thread recently only so that we can document the endgame for posterity. I am under no illusion that you have learned anything from it.

PixyMisa
27th April 2010, 09:14 PM
What I mean is that I believe in the prominence of axiomization as espoused by Gian-Carlo Rota in Indiscrete Thoughts. For more on him see http://www.springerlink.com/content/kn6n0p485rfp5uxv/

The reason that I say I believe in (rather than use) axiomization is that I am not capable of using it in the rigorous mathematical way(s) that some of you do
Then you're doing it wrong, and anything you might think you come up with is meaningless.

and I do not seek to give the false impression that I do. On the other hand, if OX -> were to be an axiom, i THINK that OOXO1y1OX11y may be a kind of axiomization result in a broader sense. Though I might be very wrong about this.
You are.

If one takes a belief to be something that is considered self-evidently true, it has the look and feel of an axiom. Call that a starting point, hypothesis or place of initial understanding or what, be as picky as you would like, don't try to work with the way I say things. I could not care less.
You should, because axioms and hypotheses are not equivalent. What you need is a hypothesis. If you start with an axiom, you're doing it wrong - and you've already said that you're unable to maintain logical rigour anyway.

I feed on your negativity as much as you gag on my views, which are often much re-informed and revised by even comments such as yours.
No. It's the same nonsense that you started with. It hasn't changed at all.

You simply cannot comprehend that there are non-woos who do not have to be certain of everything all of time
WRONG.

We are not "certain of everything all of time". We know perfectly well that there is far more we do not know than we do know. We know that there are things that we think we know that may be wrong, and we know that we don't necessarily know which things these might be.

None of which is any excuse for you spouting nonsense. It's just an ad hominem attack, an excuse for your inability to construct any sort of coherent argument.

and who, unlike woos, do as much as they can to not hold onto their tentative working assumptions beyond the time of their useful employment, and often useful even when they lead to dead ends.
Wrong, wrong, wrong, wrong, wrong.

Yes. Typically. And very often very usefully. BUT it can also be a starting point.
Only if you're doing it wrong.

Like Frank, I'm doing it my way. Different from yours? Yes. More prone to end up early on with possible errors? Yes!!!
Yes. Our way works. Yours doesn't. Stop it.

But not necessarily in the end wrong.
No, it is possible that you might accidentally stumble upon the truth. It's possible you might accidentally stumble upon a winning lottery ticket just lying in the street.

But it's a safe bet that you will go your entire life without that ever happening.

And sometimes magnificently correct.
Name one instance. Just one.

See all manner of great discoveries from the history of science and math which were initially derided by the great scientists and mathematicians of the time that prove my point.
No.

For God's Sake (just a figurative phrase, guys :-), read about Mach hounding Boltzmann to his death. :-(
Didn't happen.

I am not surprised that you sincerely believe that it is easy for someone to see what he or she believes to their core is impossible to see.
Because we do it all the time.

Yet, see Planck's statement about how QM will prevail over time as old-time physicists die out.
Why? Historically, factually, it was untrue. We didn't have to wait for anyone to die, we went right ahead and established QM experimentally.

Old authoritative stick-in-the-mud. head in the sands types.
What of them? They're either right or wrong, and their authority is irrelevant in either case.

I am more and more inclined to think that either your knowledge of the actual history of math and science is abysmal. Or your understanding of that history is pathetic. Either way, not my problem.
You're the one inventing scientific history from whole cloth, so yes, it very much is your problem.

You will have to buy my book to learn what they are.
Yeah, right.

If I find out what they are and if write a book about that.
Again, you assert that these things exist before you have any evidence.

A book that of course may never be written if I do not find any forgotten legitimate concepts. :-) But ya' never know until ya' try.
But you can stop asserting as fact hypotheses for which you have no evidence at all.

If you are saying that all scientists immediately welcome with open arms every new discovery that turns out to end up greatly advancing science (or at least is open to learning more at the beginning of an evolving new concept), once again you do not have sufficient knowledge and appreciation of the history of science. There are innumerable examples of what I am saying. V=IR, entropy, epigenetics...
I'm saying that evidence steamrolls authoritative wrongness every time. Every time.

In any case, thanks for your latest series of push-backs. And, sorry, I have no more time for your view of the nature of intellectual exploration. Be well!
Door, ass, etc.

aggle-rithm
28th April 2010, 05:28 AM
And I have an inordinately great passion for the histories of both math and science. So I rejoice when I read about what Oresme knew well before Newton and Leibniz, just as I am curious about how Newtons' mucking around with theological and alchemical matters may have helped him developed his mathematical and physics of matter and light concepts? And that Leibniz was much enamored of the binary nature of the I Ching, being one of the first Europeans to encounter it.

Most of the great mathematicians and physicists have done all their useful work early in their careers, leaving the rest of their lives to goof around with whatever suits them.

Look at Stephen Hawking and his alien colonists.

drkitten
28th April 2010, 10:18 AM
So be it. And to be consistent, in a like fashion I shall not explain my answer,

which is 1YOx.

1YOx is not an axiom.

An axiom is a statement with propositional content that is assumed to be true.

1YOx has no propositional content, and therefore can neither be true nor false.

Of course, if you want to assign a (propositional) meaning to that particular string of characters, the meaning might be true or false --- and for purposes of discussion, we can certainly assume it to be true. But the meaning needs to be there -- and furthermore, it must be a well-defined meaning, and it must be propositional.

"frammis" cannot be an axiom because it has no conventional meaning.
"banana" cannot be an axiom, because, although it has a conventional meaning (imposed via the standard semantics of English words), it's not propositional."
"bananas are red" can be an axiom. Although it's false by convention, we can certainly assume it to be true and see what follows from it. (E.g. if bananas are red, then "no red things exist" is demonstrably false.)


Clearly the above is the "In the beginning"/initial state for all those who have eyes to see what is there to be seen.

There's nothing at all "clear" about that statement.

However, one has to be able to think out of the box to see why.

Not a problem. There are some professional-scale out-of-the-box thinkers on this board, including a number of researchers who earn their daily bread by thinking out-of-the-box. I believe Complexity is in fact one of them.


On the other hand, there is no compelling reason on earth why fans of this Forum would ever want to do that.

That's right. Because something else is needed beyond the mere capacity to think out-of-the-box to make sense of the ill-described and ill-informed musings you've been typing.

aggle-rithm
29th April 2010, 06:03 AM
1YOx is not an axiom.


Easily fixed.

"1YOx = gibberish"

eijah
29th April 2010, 07:16 AM
Easily fixed.

"1YOx = gibberish"


MUCH thanks! Actually very helpful to me. And reminds me of the poor taste joke. "I see!" said the blind man to the deaf man.

Holy guacamolie! What just popped into my head is a picture of a circle. And on it is a point that has both an arrow head and tail at the same point! Do you see what I am picturing? And sorry if it is woo.

In any case, it seems to me and (and, of course, I realize I am likely to be wrong), that this picture of a circle with an arrow head and tail on it -- is like a "syntax". And, by factoring in what everyone here has been trying to teach me, that my imagining the arrow head and tail moving around the circle, both away from its first point (the point of departure X), and at the same time, coming towards its last point (the point of arrival y), as it is both going through and coming through a cycle -- is like the "semantics" of the picture.

Sorry again if this all woo, but that is just the way this feeble mind of mine sees things.

All you guys and gals, please fire away at will!

drkitten
29th April 2010, 08:07 AM
Holy guacamolie! What just popped into my head is a picture of a circle. And on it is a point that has both an arrow head and tail at the same point! Do you see what I am picturing? And sorry if it is woo.

In any case, it seems to me and (and, of course, I realize I am likely to be wrong), that this picture of a circle with an arrow head and tail on it -- is like a "syntax". And, by factoring in what everyone here has been trying to teach me, that my imagining the arrow head and tail moving around the circle, both away from its first point (the point of departure X), and at the same time, coming towards its last point (the point of arrival y), as it is both going through and coming through a cycle -- is like the "semantics" of the picture.


Holy cow! What just popped into my head is a picture of a martini, with an olive. And it seems to be that the olive is like a "syntax" and the vodka is like a"semantics" with the vermouth as a "pragmatics" and the glass itself being a "phonotactics."

I.e. don't take argument by Amazingly Bad Analogy seriously.

Giggywig
29th April 2010, 08:53 AM
MUCH thanks! Actually very helpful to me.
I doubt it, unless all you wanted was attention.

And reminds me of the poor taste joke. "I see!" said the blind man to the deaf man.
Are you the blind, the deaf, neither or both?

Holy guacamolie! What just popped into my head is a picture of a circle. And on it is a point that has both an arrow head and tail at the same point! Do you see what I am picturing? And sorry if it is woo.
If I could see what you were picturing, that would be woo. It would imply some sort of telepathy. But as I have no idea what you mean, no, it's not woo.

In any case, it seems to me and (and, of course, I realize I am likely to be wrong), that this picture of a circle with an arrow head and tail on it -- is like a "syntax". And, by factoring in what everyone here has been trying to teach me, that my imagining the arrow head and tail moving around the circle, both away from its first point (the point of departure X), and at the same time, coming towards its last point (the point of arrival y), as it is both going through and coming through a cycle -- is like the "semantics" of the picture.
Could you please tell me what is your definition for "syntax" and "semantics?" Because this made no sense at all.

PixyMisa
29th April 2010, 09:38 AM
MUCH thanks! Actually very helpful to me. And reminds me of the poor taste joke. "I see!" said the blind man to the deaf man.

Holy guacamolie! What just popped into my head is a picture of a circle. And on it is a point that has both an arrow head and tail at the same point! Do you see what I am picturing? And sorry if it is woo.

In any case, it seems to me and (and, of course, I realize I am likely to be wrong), that this picture of a circle with an arrow head and tail on it -- is like a "syntax". And, by factoring in what everyone here has been trying to teach me, that my imagining the arrow head and tail moving around the circle, both away from its first point (the point of departure X), and at the same time, coming towards its last point (the point of arrival y), as it is both going through and coming through a cycle -- is like the "semantics" of the picture.

Sorry again if this all woo, but that is just the way this feeble mind of mine sees things.

All you guys and gals, please fire away at will!
If you could work in something about the Kennedy assassination or alien lizards I could nominate you for an award.

Philosaur
29th April 2010, 09:59 AM
MUCH thanks! Actually very helpful to me. And reminds me of the poor taste joke. "I see!" said the blind man to the deaf man.

No, apparently is was not very helpful to you. No, you apparently do not see.


Holy guacamolie! What just popped into my head is a picture of a circle. And on it is a point that has both an arrow head and tail at the same point! Do you see what I am picturing? And sorry if it is woo.

In any case, it seems to me and (and, of course, I realize I am likely to be wrong), that this picture of a circle with an arrow head and tail on it -- is like a "syntax". And, by factoring in what everyone here has been trying to teach me, that my imagining the arrow head and tail moving around the circle, both away from its first point (the point of departure X), and at the same time, coming towards its last point (the point of arrival y), as it is both going through and coming through a cycle -- is like the "semantics" of the picture.

Why (no really--why?) did it take all of that to describe a rotating circle?

It's clear you are trying to express the notion that "syntax leads to semantics which leads to syntax which leads to semantics...". Are you thinking that if we understand your circle, we'll agree with your proposition?


Sorry again if this all woo, but that is just the way this feeble mind of mine sees things.

All you guys and gals, please fire away at will!
Nope, not woo, just wrong. Woo would at least be more interesting.

Your idea was--and is--a non-starter.

aggle-rithm
29th April 2010, 10:29 AM
I.e. don't take argument by Amazingly Bad Analogy seriously.

Your words are like overripe cantaloupes. I shall cherish them until my wife forces me to throw them out.

drkitten
29th April 2010, 11:08 AM
It's clear you are trying to express the notion that "syntax leads to semantics which leads to syntax which leads to semantics...".

Is it?

That's not at all clear to me.

Actually, that particular sentence you just wrote is not bad as a description of language development in infants (except that semantics precedes syntax as the first step) and as a description of some of the processes in language evolution and change (such as grammaticalization).

But that particular sentence you just wrote also (as far as I can tell) has nothing to do with the book of John, with the string 1XOy, with the distributive property of algebraic fields, with axiomatic mathematics, or with anything that eijah has written in this thread.

drkitten
29th April 2010, 11:15 AM
If you could work in something about the Kennedy assassination

Well, that's at the center of the circle.

or alien lizards I could nominate you for an award.

I believe the alien lizards are the creatures that drew this image in eijah's head.

Presumably via the Orbital Mind Control Lasers.

.... which were placed there by the Rothschilds through their secret control of the CIA, under the code name of Project HARRP.

... which is deliberately named to be confused with project HAAARP, which is a secret Mossad plot, carried out by their agent Britney Spears (whose code name suggests the Spear of Longitude) to replace the fluorine in our water with matzo balls.

... which will only be prevented by project SHAARP, which is a counterplot by the Mafia to eliminate Britney's effectiveness as an agent by secretly sending doubles out through the streets of America to be photographed without underwear.

... none of which is to be confused with project HAARP, which is a research project funded by DARPA to study the ionosphere. And mostly harmless, unless you happen to have adenine somewhere in your DNA, in which case you will almost certainly die.

Philosaur
29th April 2010, 11:51 AM
Is it?

That's not at all clear to me.

I should have said "it's clear to me", though now I don't know why I'd want to give eijah the notion that anything he wrote was actually clear.

What I should perhaps have said is that it's clear to me that he is still trying to convince us that there is semantic content inherent in syntax.

My fault for not being clear in my interpretation. :P


Actually, that particular sentence you just wrote is not bad as a description of language development in infants (except that semantics precedes syntax as the first step) and as a description of some of the processes in language evolution and change (such as grammaticalization).

Yes, it does reflect how semantic content allows us to transmit the notion of syntax, which allows us to express more semantic content, which allows us to grasp more intricate syntax, and so on. But that's a very different notion from what eijah seems to be saying, which (as far as he's saying anything, I guess) is that an arbitrary syntax inherently implies semantic content--or that semantic content inherently implies a particular syntax.

Sure, I might be putting words into his mouth, but that's only a result of trying to be charitable in my interpretation of the ill-formed, vague metaphors and half-baked notions he's actually producing.



But that particular sentence you just wrote also (as far as I can tell) has nothing to do with the book of John, with the string 1XOy, with the distributive property of algebraic fields, with axiomatic mathematics, or with anything that eijah has written in this thread.

I think you are being a little bit uncharitable to me here.

As best as I can grasp, eijah has the idea that the logos, whatever it may have been, acted as a cosmic semantic-cum-syntactic seed. Because the logos-seed contains all the necessary machinery, materials, and instructions, it could do a little dance of sui generis and *poof* a world is born.

I was merely replying that this notion--while elegant--cannot be derived from anything he's posted here, much less the "arrow going in a circle" image.

eijah
29th April 2010, 12:04 PM
If you could work in something about the Kennedy assassination or alien lizards I could nominate you for an award.

The Kennedy assassination. $2,000 per day minimum. Eight hours per day. Plus expenses, of course. Five days a wk. No week-ends. Please leave word with my agent.

eijah
29th April 2010, 01:47 PM
I should have said "it's clear to me", though now I don't know why I'd want to give eijah the notion that anything he wrote was actually clear.


I don't either. But I am guessing a woo would say, God made you say it." :-)



What I should perhaps have said is that it's clear to me that he is still trying to convince us that there is semantic content inherent in syntax.

Please at least try to reflect on what I am now saying, instead of what you think I am saying, which is that I think my static circle and its non-moving arrow head and tail are syntax. Not semantics, not syntax with a little or lot of semantics. Just S-Y-N-T-A-X.

Plus, that my idea, notion, image of the arrow head moving around the circle is a meaning imposed by me and other viewers who can imagine the arrow both going around and coming around the circle as it initiates and completes different cycles . I.e., semantics. No syntax, just semantics.

If you need to interpret that I am at this stage of the thread I am still saying anything about semantic content inherent in syntax, please explain to me how you arrive at that contrary interpretation based on what I am now saying.


My fault for not being clear in my interpretation. :P


Your fault for misinterpreting what I said. But quite understandable. You are looking to see what you want to see, and you do.


Yes, it does reflect how semantic content allows us to transmit the notion of syntax, which allows us to express more semantic content, which allows us to grasp more intricate syntax, and so on. But that's a very different notion from what eijah seems to be saying, which (as far as he's saying anything, I guess) is that an arbitrary syntax inherently implies semantic content--or that semantic content inherently implies a particular syntax.

Bravo! I did not say that. But I do like what you said. Can I use it?



Sure, I might be putting words into his mouth, but that's only a result of trying to be charitable in my interpretation of the ill-formed, vague metaphors and half-baked notions he's actually producing.


Hopefully, by now three quarters baked! And in any case, one does not have to be a woo to be charitable. You are just a decent person who wants to help out someone in need. Thanks!




I think you are being a little bit uncharitable to me here.

As best as I can grasp, eijah has the idea that the logos, whatever it may have been, acted as a cosmic semantic-cum-syntactic seed. Because the logos-seed contains all the necessary machinery, materials, and instructions, it could do a little dance of sui generis and *poof* a world is born.



Here is what I currently think as a working hypothesis, based on all of your suggestions and well-formed and non-well-formed critiques... PLEASE pay close attention to what I am and am not saying. If you do the do's and don't do the don'ts, what I am actually saying and not saying may seem less woo to you...

I am currently inclined to hypothesize that the wording of "In the beginning God created the heavens and the earth," is pregnant with many possible interpretations, both religious ones and non-religious ones. And one or more of the non-religious ones might include factoring in the fact that a vertical "1" is a logical symbol for pointing up towards the heavens, whereas "O" is a logical symbol for the action of waving one's hand around in all horizontal directions to signify the earth. Of course they are also logical symbols for up/down, on/off... all of which for me highlights the fact that such opposites as heaven(s)/earth, up/down, yes/no, on/off, good/bad. right/wrong... can have orthogonal as well as polar relationships.

I am not saying here that 1YOx is the Tetragrammaton. I am inclined to think it is not. I am inclined to guess as just a possibility that it MIGHT have some significance, but I can not tell you what that significance might be.


I was merely replying that this notion--while elegant--cannot be derived from anything he's posted here, much less the "arrow going in a circle" image.

The ouroborus is a thousands of years old symbol, more recently found in alchemical texts such as those used by Newton. I submit to you that the circle with the arrow head and tail can not just be seen as signifying a cyclical change, it can also if one is open to looking at it poetically been seen as a mathematical version of the ouroborus. Does that mean that there is anything to alchemy. Newton thought so, Boyle thought so, Dee thought so. I am not saying so. But what I am saying is that when I now look at the ouroborus I think of lots of things, frequency distributions, integrating derivatives, undulating sine waves, caterpillars turning into butterflies... And I am disinclined to see that as woo-ish, even if you folks do.

drkitten
29th April 2010, 01:55 PM
Here is what I currently think as a working hypothesis, based on all of your suggestions and well-formed and non-well-formed critiques... PLEASE pay close attention to what I am and am not saying. If you do the do's and don't do the don'ts, what I am actually saying and not saying may seem less woo to you...

I have paid close attention. It is no less woo than it was in post #1, and barely better defined.


I am currently inclined to hypothesize that the wording of "In the beginning God created the heavens and the earth," is pregnant with many possible interpretations, both religious ones and non-religious ones.

Of course. Since anyone can interpret anything they like as anything at all, this is trivial. If you choose to interpret the Washington monument as a giant phallic symbol, or as a reference to ancient Egypt, or at a statement about the political power of marble quarries --- you have so chosen. Any of those "meanings" can be read into it. Or into the Golden Gate bridge, for that matter.

And one or more of the non-religious ones might include factoring in the fact that a vertical "1" is a logical symbol for pointing up towards the heavens, whereas "O" is a logical symbol for the action of waving one's hand around in all horizontal directions to signify the earth.

Or a phallus and vulva, respectively. Or a side and top view of a nickel.

You can use anything you like to symbolize anything you like, because you have complete freedom to choose any symbol set you like.

Of course they are also logical symbols for up/down, on/off...

bacon/eggs, offense/defense, Burns/Allen, Lennon/McCartney, ...

all of which for me highlights the fact that such opposites as heaven(s)/earth, up/down, yes/no, on/off, good/bad. right/wrong... can have orthogonal as well as polar relationships.

Note the emphasis. You can read whatever woo-ish drivel you like into whatever you like.

It's still woo, it's still drivel, and it's still a waste of your time and ours.

eijah
29th April 2010, 02:24 PM
I have paid close attention. It is no less woo than it was in post #1, and barely better defined.



Of course. Since anyone can interpret anything they like as anything at all, this is trivial. If you choose to interpret the Washington monument as a giant phallic symbol, or as a reference to ancient Egypt, or at a statement about the political power of marble quarries --- you have so chosen. Any of those "meanings" can be read into it. Or into the Golden Gate bridge, for that matter.



Or a phallus and vulva, respectively. Or a side and top view of a nickel.

You can use anything you like to symbolize anything you like, because you have complete freedom to choose any symbol set you like.



bacon/eggs, offense/defense, Burns/Allen, Lennon/McCartney, ...



Note the emphasis. You can read whatever woo-ish drivel you like into whatever you like.

It's still woo, it's still drivel, and it's still a waste of your time and ours.
I noticed that you did not address my request to show me where in my recent circle and arrow head & tail description I was still insisting on syntax and semantics, Not syntax first. Then semantics.

That aside, how is it that in a formal language, syntax comes first, and then semantics is added on, whereas infants begin with the semantics first? What is the reason for the difference?

Philosaur
29th April 2010, 02:29 PM
I noticed that you did not address my request to show me where in my recent circle and arrow head & tail description I was still insisting on syntax and semantics, Not syntax first. Then semantics.

That aside, how is it that in a formal language, syntax comes first, and then semantics is added on, whereas infants begin with the semantics first? What is the reason for the difference?

It happens for the same reason that 0 comes before 1 mathematically, but Biblically the heavens came before Earth. It's basically a chicken and egg problem. Yin and Yang.

eijah
29th April 2010, 03:44 PM
It happens for the same reason that 0 comes before 1 mathematically, but Biblically the heavens came before Earth. It's basically a chicken and egg problem. Yin and Yang.
I noticed you have not yet addressed your belief that I am still saying syntax and semantics, Not syntax first than semantics. In formal grammars.

Nor answering why semantics first, then syntax? In natural language.

drkitten
29th April 2010, 03:53 PM
That aside, how is it that in a formal language, syntax comes first, and then semantics is added on, whereas infants begin with the semantics first? What is the reason for the difference?

Because -- and feel free to read this slowly to make sure you understand --- infants are not formal languages.

Did you get that?

The theory of formal languages was invented more or less independently in the 1950s by John Backus and Noam Chomsky. In Chomsky's case, he was explicitly trying to develop a theory of adult linguistic competence and explicitly ignored both questions of cognitive performance and of the development of language in children;

"Linguistic theory is concerned primarily with an ideal speaker-listener, in a completely homogeneous speech community, who know its (the speech community's) language perfectly and is unaffected by such grammatically irrelevant conditions as memory limitations, distractions, shifts of attention and interest, and errors (random or characteristic) in applying his knowledge of this language in actual performance." (Chomsky, Aspects of the Theory of Syntax, p. 3)

In other words, not only are infants not formal languages, and not only do infants not speak formal languages, but, by design, adults don't speak formal languages either, since formal languages only model linguistic competence.

I've heard this book (where he first formalized the competence/performance distinction) described as "the biggest promissory note in the history of science" for this reason; he promised that he'd develop a theory that included cognitive aspects after he had completed his analysis of abstract language. Fifty years later, we're still waiting....

Backus, of course, was not interested in questions of infant development at all. He wanted to develop a language that could be efficiently converted (by computer) into machine-executable code (e.g., he wanted to develop a compiler). And computers don't learn programs; they simply load programs in which complex/complete knowledge is presented to them to be executed.

So if you're wondering why our mathematical models of language don't match infant development, it's because our mathematical models are not only not infants, but weren't even designed to model infant language. And they don't. Which is why cognitive scientists have been designing and using other models (e.g. artificial neural networks) which appear to match infant data more accurately.

eijah
29th April 2010, 05:28 PM
Because -- and feel free to read this slowly to make sure you understand --- infants are not formal languages.

Did you get that?

The theory of formal languages was invented more or less independently in the 1950s by John Backus and Noam Chomsky. In Chomsky's case, he was explicitly trying to develop a theory of adult linguistic competence and explicitly ignored both questions of cognitive performance and of the development of language in children;

"Linguistic theory is concerned primarily with an ideal speaker-listener, in a completely homogeneous speech community, who know its (the speech community's) language perfectly and is unaffected by such grammatically irrelevant conditions as memory limitations, distractions, shifts of attention and interest, and errors (random or characteristic) in applying his knowledge of this language in actual performance." (Chomsky, Aspects of the Theory of Syntax, p. 3)

In other words, not only are infants not formal languages, and not only do infants not speak formal languages, but, by design, adults don't speak formal languages either, since formal languages only model linguistic competence.

I've heard this book (where he first formalized the competence/performance distinction) described as "the biggest promissory note in the history of science" for this reason; he promised that he'd develop a theory that included cognitive aspects after he had completed his analysis of abstract language. Fifty years later, we're still waiting....

Backus, of course, was not interested in questions of infant development at all. He wanted to develop a language that could be efficiently converted (by computer) into machine-executable code (e.g., he wanted to develop a compiler). And computers don't learn programs; they simply load programs in which complex/complete knowledge is presented to them to be executed.

So if you're wondering why our mathematical models of language don't match infant development, it's because our mathematical models are not only not infants, but weren't even designed to model infant language. And they don't. Which is why cognitive scientists have been designing and using other models (e.g. artificial neural networks) which appear to match infant data more accurately.

As is very often the case, you are often exceedingly informative. And I am delighted this one of those times. Regards and be well.

Philosaur
30th April 2010, 08:06 AM
I noticed you have not yet addressed your belief that I am still saying syntax and semantics, Not syntax first than semantics. In formal grammars.

Nor answering why semantics first, then syntax? In natural language.

If you're now saying syntax first, then semantics--fine. If you're saying semantics first, then syntax--cool. My question is--do you really understand what you're saying when you say either of these things?

"Semantics first" only makes sense if you're talking about language acquisition or the development of language over human history. The simple answer is that before there was language of any kind, there existed things that could be referred to by language. The planet, the sky, water, animals, etc, all existed before language. So you first have potential semantic content.

The first proto-humans probably pointed at things. Now, you *might* make the argument that the pointing finger was the first signifier (i.e. the first element of syntax). But before the finger was the thing needing to be pointed at--the semantic content.

Same holds true for babies. There is stuff in the world before there are words for the stuff.

eijah
30th April 2010, 01:02 PM
If you're now saying syntax first, then semantics--fine. If you're saying semantics first, then syntax--cool. My question is--do you really understand what you're saying when you say either of these things?


I think I do as of now due to your efforts, Dr. Kitten's and others. Thanks!!!


"Semantics first" only makes sense if you're talking about language acquisition or the development of language over human history.

The simple answer is that before there was language of any kind, there existed things that could be referred to by language. The planet, the sky, water, animals, etc, all existed before language. So you first have potential semantic content.

The first proto-humans probably pointed at things. Now, you *might* make the argument that the pointing finger was the first signifier (i.e. the first element of syntax). But before the finger was the thing needing to be pointed at--the semantic content.

Same holds true for babies. There is stuff in the world before there are words for the stuff.

I think I understand this a lot better now. So I am glad we are beyond an impasse.

And now what I hope is a non-woo question, with a preface...

I was in an "Implementing Database Technology" class about forty years ago in the very early days of corporate databases, and DBMS's such as IMS, Total, IDMS, System 2000, and as I remember, Adabas.

And the students had everything from three months of COBOL to ten or more years of Assembler. I still remember the teacher at the start of the first session of the course drawing a Venn diagram. Each circle represented one of the five quite different DBMS's, overlapped on the others. He pointed to the area where they all overlapped and said, "Here is what makes each of these a DBMS." And then hw pointed to the outside parts of the different circles, and said, "This one is what makes IMS. the IMS DBMS, this is what makes IDMS, the IDMS DBMS," etc. And then he worked with us to come up with a generic definition of a DBMS. The rest of the term was learning about the similarities vs. differences of each. It gave everyone in the class both a generic view of DBMS's, plus specific understandings of the strengths and weakness of each relative to the others.

So following that model of trying to see how focusing on similarities, while for the moment disregarding differences, can be used to come up with a generic definition of a "grammar", surely there is such a generic definition of grammar? Yes? One that covers infant and adult natural grammar and formal grammar. Or is there?

Complexity
30th April 2010, 01:38 PM
I think I do as of now due to your efforts, Dr. Kitten's and others. Thanks!!!



I think I understand this a lot better now. So I am glad we are beyond an impasse.

And now what I hope is a non-woo question, with a preface...

I was in an "Implementing Database Technology" class about forty years ago in the very early days of corporate databases, and DBMS's such as IMS, Total, IDMS, System 2000, and as I remember, Adabas.

And the students had everything from three months of COBOL to ten or more years of Assembler. I still remember the teacher at the start of the first session of the course drawing a Venn diagram. Each circle represented one of the five quite different DBMS's, overlapped on the others. He pointed to the area where they all overlapped and said, "Here is what makes each of these a DBMS." And then hw pointed to the outside parts of the different circles, and said, "This one is what makes IMS. the IMS DBMS, this is what makes IDMS, the IDMS DBMS," etc. And then he worked with us to come up with a generic definition of a DBMS. The rest of the term was learning about the similarities vs. differences of each. It gave everyone in the class both a generic view of DBMS's, plus specific understandings of the strengths and weakness of each relative to the others.

So following that model of trying to see how focusing on similarities, while for the moment disregarding differences, can be used to come up with a generic definition of a "grammar", surely there is such a generic definition of grammar? Yes? One that covers infant and adult natural grammar and formal grammar. Or is there?


Since you haven't abandoned your program to tease meaning from 'scriptures' where there is none, and since what you are asking about is in furtherance of that ridiculous program, you are on your own.

Read a book. Read several.

Philosaur
30th April 2010, 02:25 PM
I think I do as of now due to your efforts, Dr. Kitten's and others. Thanks!!!

<snip>

So following that model of trying to see how focusing on similarities, while for the moment disregarding differences, can be used to come up with a generic definition of a "grammar", surely there is such a generic definition of grammar? Yes? One that covers infant and adult natural grammar and formal grammar. Or is there?

Well, within natural language (no need to separate infant and adult here), grammar is generally thought of as going in two directions: prescriptive and descriptive.

When linguists study a language, they try to discern the general patterns the speakers or writers follow in combining sounds, words, or phrases. The catalog of these patterns is called a grammar. This is a descriptive grammar, as it is meant to describe the patterns the linguists discover.

Prescriptive grammar is what kids learn in school. These are *generally* the same patterns that the linguists identify, but they are meant allow speakers to generate meaningful, unambiguous sentences.

Formal or mathematical grammars are (as far as I know) only prescriptive. There is no analog in mathematics to "descriptive grammars". No one (again--as far as I know) studies mathematicians in their natural environment in order to decipher the patterns used in their equations. Mathematicians have had to stipulate the patterns and practices of their notations, which are a type of production rules.

I don't have a great definition of grammar at the ready, so here's a quick attempt:

Grammar is the pattern or patterns into which information is encoded in order to facilitate communication, storage, or use of that information.

eijah
30th April 2010, 02:37 PM
Well, within natural language (no need to separate infant and adult here), grammar is generally thought of as going in two directions: prescriptive and descriptive.

When linguists study a language, they try to discern the general patterns the speakers or writers follow in combining sounds, words, or phrases. The catalog of these patterns is called a grammar. This is a descriptive grammar, as it is meant to describe the patterns the linguists discover.

Prescriptive grammar is what kids learn in school. These are *generally* the same patterns that the linguists identify, but they are meant allow speakers to generate meaningful, unambiguous sentences.

Formal or mathematical grammars are (as far as I know) only prescriptive. There is no analog in mathematics to "descriptive grammars". No one (again--as far as I know) studies mathematicians in their natural environment in order to decipher the patterns used in their equations. Mathematicians have had to stipulate the patterns and practices of their notations, which are a type of production rules.

I don't have a great definition of grammar at the ready, so here's a quick attempt:

Grammar is the pattern or patterns into which information is encoded in order to facilitate communication, storage, or use of that information.

Wow! That seems great to me! Simple, comprehensive and robust. I am very glad that you are here! Much thanks.

eijah
30th April 2010, 02:40 PM
Since you haven't abandoned your program to tease meaning from 'scriptures' where there is none, and since what you are asking about is in furtherance of that ridiculous program, you are on your own.

Read a book. Read several.

See Philosaur's response. I think everyone will agree that as of now, his is a lot better than yours. Care to try again?

aggle-rithm
30th April 2010, 03:01 PM
I don't have a great definition of grammar at the ready, so here's a quick attempt:

Grammar is the pattern or patterns into which information is encoded in order to facilitate communication, storage, or use of that information.

I heard that grammar is an invention of the aristocracy to make it easier to identify one of their own by speech patterns.