Value in Logic\Mathematics

[doronshadmi]

Let us explore the traditional point of view about numbers (the values) and numerals (their representations).

According to the traditional point of view, any given R member (some real-number) is a unique value along the real-line (and so is some complex number (C member) in the complex plane).

This unique value can be represented by a unique and single symbol (for example let us use "@" for the ratio 1/4), but it is not useful to give a unique symbol for each given number, so during the years we developed several methods that produce numerals (representations of values) by systematic methods (actually this is similar to the informal way, which uses a finite amount of symbols in order to represent words and sentences according to certain rules).

The most useful one is the place value method that systematically uses a finite amount of basic symbols (their quantity is changed by the base value, for example: base-two has two basic symbols "0","1". Base-three has three basic symbols "0","1","2". Base-n has n basic symbols, ... etc.)

It is well known that the number of symbols that represent some value (some R member, in this case) can be changed if we use different bases to represent this value, and it does not matter if this value is a fraction or a whole number.

For example: in order to represent number five in base ten we need a single symbol, which is "5", but in order to represent number five in base three we need at least three symbols "101".

So, according to the traditional point of view "five", "5" or "101" are no more than different representations of the same value (where the value is the number itself).

Furthermore, it does not matter if we need infinitely many symbols or finitely many symbols in order to represent some value (some number) for example:

0.7 = 0.10110011001100110011001100110011001100110011... [base 2]

1 = 0.111...[base 2] = 0.222...[base 3] = ... = 0.999...[base 10] = ...

This is the standard mathematical framework.

-----------------------------------------------------------------------


My mathematical framework is a complementation between VSL and ASL, where Mathematics of the past 2500 years is mostly based on ASL.

Here is a comparison between ASL and VSL, based on Dr. Linda Kreger Silverman's research (please look at the difference between what is called Visual Special Learning and Auditory Sequential Learning ( http://www.visualspatial.org/Articles/intro.pdf , http://www.visualspatial.org/Articles/idvsls.pdf ). ):

http://www.geocities.com/complementarytheory/VSL-ASL.jpg



Things are changed if Symmetry is used as the universal principle of logic.

Let a 2-valued framework be represented by A B.

A B relation is:

A B
A A
A B
B A
B B

These relations can be reduced (without a loss of generality) to
symmetric (AA or BB) \ asymmetric (AB or BA) relations, represented as:

AB
XX is AB symmetry --> A=B (AB is the same)
XY is AB asymmetry --> A≠B (AB is not the same)

A=B can be reduced (without a loss of generality) to a single value X.

A≠B cannot be reduced to a single value without a loss of detail X or Y.

Furthermore, in order to conclude that A≠B, they must share the same realm.

So 2-valued framework is at least X (symmetry or sameness) \ XY (asymmetry or difference) relation.

Let us use SA (Symmetry\Asymmetry relation) on 2-valued Logic:

T F NXOR
F F considered
F T not considered
T F not considered
T T considered

T F XOR
F F not considered
F T considered
T F considered
T T not considered

T F NXOR\XOR
F F considered
F T considered
T F considered
T T considered

T F generalization of NXOR\XOR
X X considered
X Y considered

Let us examine 3-valued logic:

http://www.geocities.com/complementarytheory/SymmLogic.jpg

Both cases are reduced to SA (Symmetry\Asymmetry relation) without a loss of generality:

A B C
X X X --> X (symmetry)
X X Y --> X Y
X Y Z --> X Y Z (asymmetry)

3-valued logic can be extended to any x-valued logic where x is any standard or non-standard value of [0,1]. By using Symmetry\Asymmetry relation, we define the universal principle of any given logical system, standard or non-standard.

By Symmetry, Symmetry is Asymmetry.

By Asymmetry, Asymmetry is_not Symmetry.

If there is no common basis, then anything is totally isolated, and nothing can be compared in order to define some difference. If there is only a common thing, then anything is totally connected, and nothing can be found beyond total unity. In both cases we do not get the researchable. So, the researchable is at least a unified isolation. Let us represent this notion by using an ASL\VSL representation method.

Let "=" be is
Let "≠" be is_not
Let "S" be Symmetry
Let "A" be Asymmetry

S=A from S point of view.

A≠S from A point of view, but in order to compare and conclude that A≠S, there must be a common basis that enables the comparison. So, the researchable is at least a unified isolation, represented as:

http://www.geocities.com/complementarytheory/OP.jpg



http://www.geocities.com/complementarytheory/SA.jpg

A particular value is defined only by NXOR(unification)\XOR(isolation) relation.

Since any particular value is at least NXOR\XOR relation, then any number is a particular path along the symmetric ur-element real-line.

For example:

http://www.geocities.com/complementarytheory/base-frac.jpg

In this case 0.01[base 2] is a particular path and 0.25[base 2] is another particular path.

By the traditional point of view a particular value (a number) is only the particular case of zenith-path along the symmetric ur-element real-line.

Because of this arbitrary limitation the non-zenith path 0.111...[base 2] is equal to the non-zenith path
0.222...[base 3] and both of them are defined as some representations of the zenith-path 1.000...

But when path is a [b]general concept, then 0.111...[base 2] < 0.222...[base 3] < 1.000... as can be clearly seen in:

http://www.geocities.com/complementarytheory/base2_3.jpg

[Gate2501]

Get it published and reviewed by the mathematical community, stop arguing about it here.

I see you get owned over and over again in these threads, and you just can't seem to grasp that you are working with made up concepts and changing the definitions of standard terminology.

Get it published and prove everyone wrong, or put a lid on it.

Seriously.

[Alkatran]

My mathematical framework is a complementation between VSL and ASL, where Mathematics of the past 2500 years is mostly based on ASL.

Here is a compression between ASL and VSL, based on Dr. Linda Kreger Silverman's research (please look at the difference between what is called Visual Special Learning and Auditory Sequential Learning ( http://www.visualspatial.org/Articles/intro.pdf , http://www.visualspatial.org/Articles/idvsls.pdf ). ):

This is where your post starts to stray. You go from talking about representations of numbers and jump to methods of learning, without any lead-up or explanation on how these two things are related.


Things are changed if Symmetry is used as the universal principle of logic.

Let a 2-valued framework be represented by A B.

A B relation is:

A B
A A
A B
B A
B B

I'm not sure what you're saying here. You listed all the permutations of {A, B}, but you didn't actually provide a relation ( http://en.wikipedia.org/wiki/Relation_%28mathematics%29 ).

I have no idea what you're saying after this point. You need to seriously clear up your writing or everyone is going to ignore it as gibberish word salad (which it currently IS).

[Third Eye Open]

For example: in order to represent number five in base ten we need a single symbol, which is "5", but in order to represent number five in base three we need at least three symbols "101".

why not just '11'? as in 1, 2, 3, 10, 11

[doronshadmi]

This is where your post starts to stray. You go from talking about representations of numbers and jump to methods of learning, without any lead-up or explanation on how these two things are related.

The frist part is the standard ASL point of view of Value.

Thr second part is the VSL\ASL point of view of Value.



I'm not sure what you're saying here. You listed all the permutations of {A, B}, but you didn't actually provide a relation ( http://en.wikipedia.org/wiki/Relation_%28mathematics%29 ).

I have no idea what you're saying after this point. You need to seriously clear up your writing or everyone is going to ignore it as gibberish word salad (which it currently IS).
I am talking about the foundations of Logic itsef, which is based on Symmetry\Asymmetry complementation.

Please read http://www.geocities.com/complementarytheory/NXOR-XOR.pdf for more details.

[doronshadmi]

Get it published and reviewed by the mathematical community, stop arguing about it here.

I see you get owned over and over again in these threads, and you just can't seem to grasp that you are working with made up concepts and changing the definitions of standard terminology.

Get it published and prove everyone wrong, or put a lid on it.

Seriously.

The mathematical community is made of ASL-only persons. I can't air my view there.

[GreedyAlgorithm]

Things are changed if Symmetry is used as the universal principle of logic.

Let a 2-valued framework be represented by A B.

A B relation is:

A B
A A
A B
B A
B B
I still maintain that the first step is making your material understandable. Not understandable to you, understandable to us. So let's see what I can see. I'll tell you my thoughts as I read through it, and stop once (if) I have too many questions.

I'm not sure what you mean by a 2-valued framework. I'll assume for now you mean a set of two symbols with which you're going to do [something]. Now we're going to say without loss of generality that the symbols are "A" and "B".

"A B relation is:" does not tell me much. I know in standard set theory a relation R between two sets S and T is a set of ordered pairs where in each pair the first element comes from S and the second from T. The subsequent table appears to have all possible pairs (a,b) where a \in {A,B} and b \in {A,B}. This is one (set theory) relation from {A,B} to {A,B}, in fact the largest. But I'm guessing you mean something different because the table's heading,
A B
does not make much sense in this context. If I'm interpreting you right it should instead be
{A,B} {A,B}
Or possibly you're using relation here to mean only (set theory) relations from a set to itself. Unclear.

These relations can be reduced (without a loss of generality) to
symmetric (AA or BB) \ asymmetric (AB or BA) relations, represented as:

AB
XX is AB symmetry --> A=B (AB is the same)
XY is AB asymmetry --> A≠B (AB is not the same)
Hm. Previously we had one relation, I thought, given in the table. Now you refer to it (them?) as "relations", plural. Not sure what's going on here. Moving on, we have two new terms, "symmetric" and "asymmetric", also undefined. And I haven't figured out how to define them yet, mostly due to not knowing what you mean by "relation" and "relations". Let's start there, shall we?

[PixyMisa]

The mathematical community is made of ASL-only persons. I can't air my view there.
Convenient that you always have that excuse, isn't it?

[PixyMisa]

why not just '11'? as in 1, 2, 3, 10, 11
Typical ASList attack!

P.S. I think you mean 12. 0, 1, 2, 10, 11, 12.

[sol invictus]

For example: in order to represent number five in base ten we need a single symbol, which is "5", but in order to represent number five in base three we need at least three symbols "101".

You expect anyone to pay attention to you when you make incredible basic mistakes like that?

[Third Eye Open]

Typical ASList attack!

P.S. I think you mean 12. 0, 1, 2, 10, 11, 12.

arg, yes that is what I meant. Except I would get to it like this 1, 2, 3, 11, 12. Am I correct is assuming that zero would be counted as a digit in the count that you used above? wouldn't that be a base 4? If you use zero in a base 3 system i would think that it would go like this 0, 1, 2, 10, 11, 11 being five.

I guess I could go back and edit my post then claim that it's what I said in the first place.....

[Apathia]

Wait! Don't forget these telling threads:

http://forums.randi.org/showthread.php?t=108957

http://forums.randi.org/showthread.php?t=111891

[Third Eye Open]

oh jeez, i'm retarded. my example of 0, 1, 2, 10, 11, is of course wrong. What i was getting at is that in a base three i think you can only have 3 different symbols, is this correct?

ETA: You did only use 3 symbols! Hooray! I just explained away my own confusion!

[krelnik]

base-two has two basic symbols "0","1". Base-three has three basic symbols "0","1","2". Base-n has n basic symbols, ... etc.)



For example: in order to represent number five in base ten we need a single symbol, which is "5", but in order to represent number five in base three we need at least three symbols "101".


WRONG.

The number 5, in base 3 notation, is 12.

The 101 base 3 is actually 10 base 10.

I stopped reading your message at that point, because it is clear you don't even understand the basic concepts you are building on.

[GreedyAlgorithm]

People! Geez, come on! If doronshadmi is wrong, fine, but not liking him is no call to take a simple mistake of thinking "base two" and writing "base three" and turning it into "oh you must have absolutely no idea what you're talking about". What, does Third Eye Open have no idea what he's talking about either because he mistyped?

[LostAngeles]

The mathematical community is made of ASL-only persons. I can't air my view there.

I'm in the mathematical community and not only am I more heavily on the VSL side, but considering how many proofs I do that rely on mathematical reasoning and how little computation I have to do, I'd bet the entire damn department at UCLA is more VSL than ASL.

You know what does my computation most of the time? MAPLE. But then cryptography asks me to demonstrate my understanding of the methods by applying them.

Through Maple. I'm not taking 100 digit numbers to 100 digit powers mod another 100 digit number by hand.

I am proving certain propositions on exams and homeworks, however, and that requires mathematical reasoning.

All mathematicians do this training and the professionals spend their life doing mostly mathematical reasoning on theorems, propositions, and algorithms.

So...

Oh yes, just like BAGO, you have no idea what you're talking about.

[doronshadmi]

WRONG.

The number 5, in base 3 notation, is 12.

The 101 base 3 is actually 10 base 10.

I stopped reading your message at that point, because it is clear you don't even understand the basic concepts you are building on.
Please hold your horses, it is just a typo mistake "101" is five in octal representation of base two.

People! Geez, come on! If doronshadmi is wrong, fine, but not liking him is no call to take a simple mistake of thinking "base two" and writing "base three" and turning it into "oh you must have absolutely no idea what you're talking about". What, does Third Eye Open have no idea what he's talking about either because he mistyped?

I suggest you to listen to GreedyAlgorithm. We are here in order to re-examine fundamental mathematical ideas and I expect from anyone how enables to do it, to distinguish between typos and the very essence of this kind of dialog.

I do not expect that my point of view will be fully understandable by people that are trained by the traditional point of view of these fundamental concepts, but I will and do my best in order to air my non-traditional point of view of these subjects.

I think that a real dialog can enrich each real participator of it, and I hope that this time the moderator will not move this thread to the Philosophy\Religious forum just because a non-orthodoxy point of view is expressed here.

[shadron]

The mathematical community is made of ASL-only persons. I can't air my view there.

Doronshadmi, that is unfair to the math community. After all, geometry (even multi-dimensional geometry is within their scope, and I don't notice that it is slighted. Calculus relies on visual models as a teaching tool, even if not needed in rigorous expansion. If there is any community which should be able to analyze a visual abstract approach I would assume it would be math. An unconventional approach which enlightens would be certainly considered there. The key is having the work be impeccable, and yet having a new, refreshing way to do the computations and proofs.

Contact someone in your local community who is a math teacher and simultaneously tutors the GT individuals, and get him to vet your work. He should be able to get you a fair hearing, and will be invaluable in your development. I happen to know Dr. Silverman and her work, she might be a resource for you as well if you don't already know her. She is (or was, at least), affiliated with the University of Denver, and likely knows math people who have the orientation you seek.

Lastly, take seriously the words of the people who have criticized you here. Some of them are excellent people, and are at least partially a cross-section of the kind you will meet in academia as you advance your work.

Good luck.

[GreedyAlgorithm]

We are here in order to re-examine fundamental mathematical ideas
...
I do not expect that my point of view will be fully understandable by people that are trained by the traditional point of view of these fundamental concepts, but I will and do my best in order to air my non-traditional point of view of these subjects.

I am here because your writing is (to me) quite obviously not communicative, but also quite obviously based on ideas you have that are far more coherent than what is underneath the typical "no one understands my math" posts. I'd like to see if I can get past the communication issue to understand your ideas.

If indeed they are as I suspect at least somewhat coherent then I do expect that your point of view will be fully understandable by people that are trained in the traditional point of view. And if I can break that initial communication barrier I claim I can do a much better job communicating your ideas than you can, doronshadmi.

Either that or I will end up concluding that a) there is no coherent or nearly-coherent underlying idea, or b) you will not be able to communicate it to anyone.

[ddt]

doronshadmi, I've been following a couple of the threads you started and I too must say that I'm at a loss what you want to tell here.

You start with a basic exposé about representations of numbers, then you have an interlude about ASL vs. VSL, and then you write something about logic: first some basic truth tables, and then you mention 3-valued logic. That doesn't seem to mean in your world what's commonly meant with a 3-valued logic (having a third value with the intuitive notion of "maybe", or of "don't know"). You're also fond of the word "symmetry", without saying what you mean with that. You end your OP with some graphs which don't make sense tot me either.

On the whole, I don't see what the various parts of the post have to do with each other. Down to the sentence level, I see a lot of sentences with English words, with English grammar, but which are gibberish to me.

If you have to really say something interesting, you're doing so very very poorly. Take the advice of the various people who've tried to say that to you, or you'll simply remain the ridicule of the other posters.

[nathan]

O.M.G. I'm glad I wasn't drinking my coffee when I found this.

Doron, if the math community is so stuck on ASL, why are we all using visual symbols and not auditory ones? Why do we have these concepts of number line and complex plane? If it was auditory, wouldn't we have pitch and phase?

Anyway, you had a nice discussion about the distinction between representation and value, but I fail to see the relevance of that to the later pieces of the OP.

[doronshadmi]

Before we continue the dialog, let us try to define some common basis:

My framework first of all distinguishes between the researchable and the non-researchable.

Since this distinguishesability is fundamental to my framework, let us not talk about anything else before we have an agreement of it.

The idea is this:

I have found that the non-researchable is not examined, before we deduce some context dependent researchable mathematical\logical framework.

I think that by ignoring the non-researchable, we actually do not have a common basis for the mathematical science, and as a result we get context dependent frameworks that are disconnected from each other.

One may say that this is exactly the flexibility and diversity of an interesting mathematical science, that enables independent branches to be developed independently of each other, where each branch is an interesting mathematical\logical universe of its own (a context dependent one).

For example, words like "line" or "point" have different formal meanings in different contexts, and this flexibility is achieved exactly because "line" or "point" are undefined, unless they are addressed (defined) by the axioms of some context dependent framework.

Question: Can we keep this flexibility and also provide a common basis to the mathematical science?

If it can be done, then each independent branch can be used aloso as a fertilizer of any other branch, and as a result we are increasing our abilities to understand some formal framework from many other points of view that may enrich our abilities to develop each branch in many new unexpected rigorous ways.

This is fundamental for any Evolutionary non-trivial framework.

I have found that any non-researchable thing must be Total or Complete, for example:

An atom is a total thing because it is the basis of anything else and nothing is its basis.

There are at least two atomic states that are not based on each other (they are atomic):

A. Total symmetry:

At total symmetry we have sameness and nothing accept sameness can be found. This state is not researchable because a researchable thing is at least a connection between two things. Total symmetry is too strong for being researchable.

B. Total asymmetry:

At total asymmetry we have isolation and nothing accept isolation can be found. This state is not researchable because a researchable thing is at least a connection between two things. Total asymmetry is too weak for being researchable.


The elementary two things are the strongest (total symmetry) and the weakest (total asymmetry).

If associated with each other, we get a researchable framework, which is weaker than the strongest (the total and non-researchable connection) and stronger then the weakest (the total and non-researchable isolation).

In other words, no matter if ASL or VSL or both of them are used, the researchable cannot be total (complete).

In that case cardinality, for example, must be incomplete in order to be researchable.

In general, the term "for all …" and the researchable is a contradiction.

If this fundamental contradiction is understood, we can continue our dialog.

[nathan]

I have found that the non-researchable is not examined, before we deduce some context dependent researchable mathematical\logical framework.

Please define what you mean by non-researchable. I would have thought that BY DEFINITION it is not possible to examine the non-researchable.

An atom is a total thing because it is the basis of anything else and nothing is its basis.

Do you mean 'atom' in the original greek sense of 'fundamental building block'?

At total symmetry we have sameness and nothing accept sameness can be found. This state is not researchable because a researchable thing is at least a connection between two things. Total symmetry is too strong for being researchable.

B. Total asymmetry:

At total asymmetry we have isolation and nothing accept isolation can be found. This state is not researchable because a researchable thing is at least a connection between two things. Total asymmetry is too weak for being researchable.

Please give an actual concrete example of this.

[Apathia]

In that case cardinality, for example, must be incomplete in order to be researchable.

Ah, herein is the toll that must be paid by Mathematics for it to enter your new paradigm. This is your procrustean way of eliminating the paradoxes of the infinte. And what you must take to the axe includes summation to limits and convergence at infinity.
It's a heavy toll and a heavy axe, as far as mathematicians are concerned.
You might want to investigate how mathematics and the Philosophy of Mathematics address the paradoxes of the infinte and arrive at the synthesis that is mordern mathematics.

[doronshadmi]

Ah, herein is the toll that must be paid by Mathematics for it to enter your new paradigm. This is your procrustean way of eliminating the paradoxes of the infinte. And what you must take to the axe includes summation to limits and convergence at infinity.
It's a heavy toll and a heavy axe, as far as mathematicians are concerned.
You might want to investigate how mathematics and the Philosophy of Mathematics address the paradoxes of the infinte and arrive at the synthesis that is mordern mathematics.
Modern Mathematics ignores the non-researchable (but uses it as its hidden assumption, because the non-researchable is the basis of the researchable but not vice versa). As a result there are paradoxes that are naturally and simply solved at the moment that the non-researchable is not a hidden-assumption anymore.

Please this time try to understand my post by ask some detailed questions.

Thank you.

[sol invictus]

I am here because your writing is (to me) quite obviously not communicative, but also quite obviously based on ideas you have that are far more coherent than what is underneath the typical "no one understands my math" posts. I'd like to see if I can get past the communication issue to understand your ideas.

You're serious, aren't you?

Wow.

I suppose most people have not had the experience I have had with physics crackpots. There is a syndrome common enough to be classified as a (minor, mostly harmless) mental illness, in which someone is convinced they understand some deep fact about the universe. They are certain they are correct and that everyone else is wrong, and they believe the establishment is suppressing their ideas (either because it is afraid of them, or refuses to pay attention, or for some darker reason).

This crops up in varying degrees across a whole spectrum of people, from formerly good physicists gone a little nutty to taxi drivers to wealthy businesspeople to homeless guys on the street. I would say roughly once a week I get such an email from someone - over the years I've gotten maybe a hundred such emails, letters, self-published books, etc., and seen many more on the internet. After a while I started to appreciate them for their comedic value, but I also started to recognize the common factors they all share.

doronshadmi's posts are not fully typical of this pattern, but they have many of the common red flags. S/he is working in isolation, believes eveyone in the mainstream is wrong, believes s/he has discovered something new and fundamental, believes hir ideas are being suppressed and/or willfully ignored, displays a near total ignorance of the basics of the subject s/he's attacking (read the other threads), changes hir position often without acknowledging it when confronted with contradictions, etc.

So be very careful before you assign any weight to this - s/he is probably a slightly confused person with a knack for mystic writing.

[doronshadmi]

Please define what you mean by non-researchable. I would have thought that BY DEFINITION it is not possible to examine the non-researchable.
All we can say that an atom is not researchable at its self state, but anything that it is a result of associations between atoms, is researchable.

Do you mean 'atom' in the original Greek sense of 'fundamental building block'?
Atom is "that has no parts".

That has not parts is non-researchable at its self state.

Please give an actual concrete example of this.
Anything without you is not an actual concrete of an atom, because you are
using your thoughts, which are not atoms, in order to understand an atom.

The only way to get the atomic state is to be aware of the source of your thoughts, which is itself not a thought.

Any attempt to get the atomic state as a researchable thing does not hold, because any researchable thing is a non-atomic state but the result of interaction between atomic states.

So Nathan, you have no choice but to be aware of the atomic basis of your own mind in order to get a concrete example of the atomic state.

There is no Mysticism (mysticism is some opinion of feeling about the atomic state and formal system is some rigorous expression of thoughts, but any thought is machanically more complex than the atomic state, no matter what meaning it has) here, but a simple and direct way to get a concrete example of the atomic state.

[doronshadmi]

You're serious, aren't you?

Wow.

I suppose most people have not had the experience I have had with physics crackpots. There is a syndrome common enough to be classified as a (minor, mostly harmless) mental illness, in which someone is convinced they understand some deep fact about the universe. They are certain they are correct and that everyone else is wrong, and they believe the establishment is suppressing their ideas (either because it is afraid of them, or refuses to pay attention, or for some darker reason).

This crops up in varying degrees across a whole spectrum of people, from formerly good physicists gone a little nutty to taxi drivers to wealthy businesspeople to homeless guys on the street. I would say roughly once a week I get such an email from someone - over the years I've gotten maybe a hundred such emails, letters, self-published books, etc., and seen many more on the internet. After a while I started to appreciate them for their comedic value, but I also started to recognize the common factors they all share.

doronshadmi's posts are not fully typical of this pattern, but they have many of the common red flags. S/he is working in isolation, believes eveyone in the mainstream is wrong, believes s/he has discovered something new and fundamental, believes hir ideas are being suppressed and/or willfully ignored, displays a near total ignorance of the basics of the subject s/he's attacking (read the other threads), changes hir position often without acknowledging it when confronted with contradictions, etc.

So be very careful before you assign any weight to this - s/he is probably a slightly confused person with a knack for mystic writing.
Good work sol invictus. You did everything accepct one little (and non-importent) thing.

You did not reply to the content of this thread.

[Apathia]

Sorry Doron. I should let this thread take its natural course.

[Alkatran]

Please define what you mean when you say "researchable" or "not researchable". What does it mean for some thing 'A' to be not researchable?

[PixyMisa]

All we can say that an atom is not researchable at its self state, but anything that it is a result of associations between atoms, is researchable.

Atom is "that has no parts".

That has not parts is non-researchable at its self state.
Wrong-o. A thing that is not subdivisible must still have properties. Those properties are researchable, or the term has no meaning.

Anything without you is not an actual concrete of an atom, because you are using your thoughts, which are not atoms, in order to understand an atom.Drivel.

The only way to get the atomic state is to be aware of the source of your thoughts, which is itself not a thought.
The source of my thoughts is my brain, which is not a thought. You said something true... Albeit pointless.

Any attempt to get the atomic state as a researchable thing does not hold, because any researchable thing is a non-atomic state but the result of interaction between atomic states.Drivel.

So Nathan, you have no choice but to be aware of the atomic basis of your own mind in order to get a concrete example of the atomic state.Mystical drivel.

There is no Mysticism (mysticism is some opinion of feeling about the atomic state and formal system is some rigorous expression of thoughts, but any thought is machanically more complex than the atomic state, no matter what meaning it has) here, but a simple and direct way to get a concrete example of the atomic state.Drivel with whipped cream and a cherry on top.

[ddt]

Good work sol invictus. You did everything accepct one little (and non-importent) thing.

You did not reply to the content of this thread.

What content? With your follow-up posts, you seem to have gone off the deep end.

[nathan]

All we can say that an atom is not researchable at its self state, but anything that it is a result of associations between atoms, is researchable.

Atom is "that has no parts".

ok, that meaning of atom.

That has not parts is non-researchable at its self state.

Anything without you is not an actual concrete of an atom, because you are
using your thoughts, which are not atoms, in order to understand an atom.

Name a specific thing that is an atom in your thesis.

Name a specific thing that is total symmetry in your thesis

Name a specific thing that is total asymmetry in your thesis.

[LostAngeles]

Good work sol invictus. You did everything accepct one little (and non-importent) thing.

You did not reply to the content of this thread.

And yet I'm ignored again.

[Molinaro]

Atom is "that has no parts".

That has not parts is non-researchable at its self state.


Bolding mine.
What does "at its self state" mean? And please define it with examples!

I realy don't see any kind of definition of researchable or non-researchable. You seem to be going in circles and/or offering up definitions that include other non-defined phrases.

[jsfisher]

Please hold your horses, it is just a typo mistake "101" is five in octal representation of base two.


You aren't being completely honest, here, doron.

It may have been a typographic error when you first posted the same nonsense in another forum. Your error was pointed out then. But you aren't about correcting things, are you? You just press on, copying and pasting the same thing to every new place you stumble across, with prior errors still intact.

What's the point, doron, if you can't learn from your own mistakes? It must be difficult being stuck in kindergarten like that.

[doronshadmi]

The source of my thoughts is my brain, which is not a thought.

By my framework a thought is some expressed level of the association between non-locality and many local states, which one of its results is your personal brain. So your personal brain and your personal thought are based ob the same principle which is Non-local\Local Association.


Wrong-o. A thing that is not subdivisible must still have properties. Those properties are researchable, or the term has no meaning.

Wrong wrong-o.

Meaning is the result of a particular point of view of something.

An atom at its self state cannot have properties because any property is the result of an association between atoms.

When observed from the researchable point of view, two kinds of atoms are defined which are:

a. The non-local atom (which is non-researchable at its self state).

b. The local atom (which is non-researchable at its self state).


The non-local atom is at least _________

The local atom is at least .

. and ____ are not defined by each other but when associated we get a researchable framework where ____ is the connector of any researchable thing and . is the connected of any researchable thing.

We call ___ a line and . a point and Hilbert made a fundamental mistake by define ___ in terms of .

This mistake also exists in the model called "the real-line" where ___ (the continuum) is defined in terms of . (the discrete).

This mistake can be defined in the membership concept where {__}__ is defined in terms of {.}

This mistake exists in the basis of Logic where Symmetry (NXOR) does not complement Asymmetry (XOR) as the universal principle of Logic.

Now let us see your VSL ability to get it, because no ASL string of symbols is needed here to immediately understand that ____ cannot be defined by any amount of . and vice versa.

If you claim that it must be addressed by ASL representation, then you actually say that your notions are limited to some particular representation, or in other words, your framework is closed under a particular representation, which is defiantly not the value itself, which is naturally independent of any particular representation.

Also be aware that ___ or . are not geometric elements here and they are used here as abstract values that are not defined by each other.

If you get that, then and only then we can continue this dialog.

[nathan]

The non-local atom is at least _________

The local atom is at least .

. and ____ are not defined by each other but when associated we get a researchable framework where ____ is the connector of any researchable thing and . is the connected of any researchable thing.

So, is there exactly one 'non-local atom' and exactly one 'local atom'? (you're using 'The {non-,}local atom')

Are points and line segments atoms?

What do you mean by 'at least'? What else are these atoms?

Please give explicit examples of these things, be they oranges, rocks, the number 3, the glyph 3, mathemetical constructs, thoughts about ice cream, whatever.

[Gagglegnash]

Hi

Where I'm from, "octal," means base 8, and is often used as a shorthand for 16-bit machines (like the PDP series of DEC machines) because you get 5 octal digits, each digit representing 3 binary digits, (octal 5 = binary 101), and then the "sign," bit on the left, so:
octal 077777 = decimal 32767
octal 177777 = decimal -1 (two's compliment) or -32767 (one's compliment)

So, I think that 101 as octal representation would be 65, right?

[sol invictus]

It may have been a typographic error when you first posted the same nonsense in another forum.

Wow. (http://www.google.com/search?q=doronshadmi)

[doronshadmi]

Hi

Where I'm from, "octal," means base 8, and is often used as a shorthand for 16-bit machines (like the PDP series of DEC machines) because you get 5 octal digits, each digit representing 3 binary digits, (octal 5 = binary 101), and then the "sign," bit on the left, so:
octal 077777 = decimal 32767
octal 177777 = decimal -1 (two's compliment) or -32767 (one's compliment)

So, I think that 101 as octal representation would be 65, right?

Octal by base 2:

000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7

[doronshadmi]

So, is there exactly one 'non-local atom' and exactly one 'local atom'?

The non-researchable point of view:

From the non-researchable point of view there is one and only one atom, for example (be aware that any example is not the thing itself but some model of it):

The one atom is like a line that has no beginning and no end, where along this line there can be folds that are inseparable of the line, where each fold has its own unique (and limited) existence along the naturally undivided atom.

The researchable point of view:

From the researchable point of view the non-researchable appears as two kinds of atoms, as explained in post http://forums.randi.org/showpost.php?p=3669463&postcount=37.

The organic framework is non-researchable\researchable complementation, that from one hand it has a non-researchable atomic foundation, and from the other hand it has a researchable space based on non-locality\locality complementation (where non-locality and locality are two extreme aspects of a one and only one atom).

Furthermore, each extreme aspect of the non-researchable atom is itself non-researchable unless it is associated with the other extreme state of the non-researchable atom. This association is possible because the two extreme states are actually based on the same thing, which is the non-researchable atom.

Only the association is researchable, but then no result of this association is complete as the non-researchable (and complete) one and only one atom.

Some examples of this association that were given:

http://forums.randi.org/showpost.php?p=3561016&postcount=173

http://forums.randi.org/showpost.php?p=3566487&postcount=191

http://forums.randi.org/showpost.php?p=3567213&postcount=193

http://forums.randi.org/showpost.php?p=3568369&postcount=194

[drkitten]

Octal by base 2:

000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7

Repeating a mistake is different than correcting it, doron.

[ddt]

Where I'm from, "octal," means base 8, and is often used as a shorthand for 16-bit machines (like the PDP series of DEC machines) because you get 5 octal digits, each digit representing 3 binary digits
Wow, the memories of the PDP-11.

The big advantage of using octal over hexadecimal with the PDP-11 was that it had 8 registers and 8 addressing modes. The machine instructions were also thus laid out that when you wrote a machine instruction in octal, the 3 bits used for a register were neatly captured by one octal digit, the same for the 3 bits used for the addressing mode.

[nathan]

The non-researchable point of view:
<snipped>

You did not give explicit examples there, you attempted to define classes of things, AFAICT.

Why are you so studiously avoiding citing some explicit examples of things that have the properties you want to talk about? Are there no examples?

IS A POINT AN ATOM?

IS A LINE SEGMENT AN ATOM?

[Don At Work]

This is perhaps the most appropriate use of an icon ever. Please take note and feel free to use this as a shining example of correct usage.


:bunpan

[Apathia]

You did not give explicit examples there, you attempted to define classes of things, AFAICT.

Why are you so studiously avoiding citing some explicit examples of things that have the properties you want to talk about? Are there no examples?

IS A POINT AN ATOM?

IS A LINE SEGMENT AN ATOM?

Doron gets esoteric, but his paradigm busting point of view is really as simple and visual as he says.

A point is just a point.
A line is just a line.

They are not defined by anything but themselves.
They are not composed of anything less than themselves.
A line is not a collection of points.
A point is not the intersection of two lines.
Each is a fundamental item.
Doron goes on to build a logic based on their relationships.

His approach has some very far reaching results and implications.
Some quite disturbing to Mathematics since the days of Euclid.

It's bigger than a Maltese Falcon.

Play it again Doron. I want to see and understand what you can actually make of your "Monadic Mathematics." Can it make up for the losses it entails?

[nathan]

A point is just a point.
A line is just a line.

So are they atoms or not?

[Gagglegnash]

Hi

Octal by base 2:

000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7


Ummm... no... that's just plain old binary.

Three digit Binary:
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7

Octal:
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
10 8
11 9
12 10

Just using three binary digits doesn't make it octal.

[doronshadmi]

Ummm... no... that's just plain old binary.

Yes, and we need 3 symbols in order to represent five in base 2, where 3 symbols covering 8 (octal) different states from 000 to 111.

If you are talking about base 8, then we are talking about different things.

[drkitten]

Yes, and we need 3 symbols in order to represent five in base 2, where 3 symbols covering 8 (octal) different states from 000 to 111.

More words you don't understand. In this case, "octal."

[doronshadmi]

Doron gets esoteric, but his paradigm busting point of view is really as simple and visual as he says.

A point is just a point.
A line is just a line.

They are not defined by anything but themselves.
They are not composed of anything less than themselves.
A line is not a collection of points.
A point is not the intersection of two lines.
Each is a fundamental item.
Doron goes on to build a logic based on their relationships.

His approach has some very far reaching results and implications.
Some quite disturbing to Mathematics since the days of Euclid.

It's bigger than a Maltese Falcon.

Play it again Doron. I want to see and understand what you can actually make of your "Monadic Mathematics." Can it make up for the losses it entails?
No Apathia. My reasoning is a much better tool to define the Logic and the Number system of Quantum Mechanic, which is the most powerful physical theory ever, because redundancy and uncertainty are its first-order properties, exactly as they are first-order properties of my Number system.

Furthermore, the observer is a significant factor of the researched system without violating the Copernican principle ( http://en.wikipedia.org/wiki/Copernican_principle ) because it is not understood in terms of his subjective point of view, but in terms of Symmetry\Asymmetry complementation.

In other words, my suggested framework is the next step of Modern Mathematics, where the current paradigm that ignores the observer and forces completeness on a researched system is the obsolete and esoteric one.

[ddt]

Play it again Doron. I want to see and understand what you can actually make of your "Monadic Mathematics." Can it make up for the losses it entails?

What do you mean with "Monadic Mathematics"? Has it to do with Leibniz' monads, or with the monads from Category Theory?

[nathan]

the Number system of Quantum Mechanic

Tell us more about this number system of quantum mechanic. How does it differ from regular non-quantum mechanic number systems?

[Gagglegnash]

Hi

Yes, and we need 3 symbols in order to represent five in base 2, where 3 symbols covering 8 (octal) different states from 000 to 111.

If you are talking about base 8, then we are talking about different things.


Ok - I admire you for trying to start a new kind of mathematics, but if you want to explain it to people, you have to use the language used to explain the mathematics correctly.

oc·tal (http://dictionary.reference.com/browse/octal) /ˈɒktl/ Pronunciation[ok-tl]
–adjective
1. Also, octonary. of or pertaining to the number system with base 8, employing the numerals 0 through 7.
2. relating to or encoded in an octal system, especially for use by a digital computer.
3. (of an electronic device) having eight pins in its base for electrical connections.
–noun
4. octonary (def. 6).
[Origin: 1935–40; oct- + -al1]


oc·tal (ŏk'təl)
adj. Of, relating to, or based on the number eight: an octal number system.


octal
adjective
of or pertaining to a number system having 8 as its base; "an octal digit"


octal (ŏk'təl)
Relating to a number system having a base of 8. Each place in an octal number represents a power of 8. Octal notation has often been used in computer programming because three-digit binary numbers are readily converted into one-digit octal numbers from 0 to 7.


Modern Language Association (MLA):
octal. (n.d.). "The American Heritage® Science Dictionary". Retrieved May 02, 2008, from Dictionary.com website:
http://dictionary.reference.com/browse/octal

Three binary digits is just binary.

[doronshadmi]

Hi




Ok - I admire you for trying to start a new kind of mathematics, but if you want to explain it to people, you have to use the language used to explain the mathematics correctly.




Modern Language Association (MLA):
octal. (n.d.). "The American Heritage® Science Dictionary". Retrieved May 02, 2008, from Dictionary.com website:
http://dictionary.reference.com/browse/octal

Three binary digits is just binary.

Ok, thank you for your correction.

I mean 0 to 7 in base 2, you mean 0 to 7 in base 8.

End of story.

[doronshadmi]

Tell us more about this number system of quantum mechanic. How does it differ from regular non-quantum mechanic number systems?
The regular number system is not based on Symmetry\Asymmetry complementation. As a result there is no superposition of identities, but each number is distinct.

By my number system, we can research the vogue and the distinct as some particular aspects of a one comprehensive framework.

[doronshadmi]

What do you mean with "Monadic Mathematics"? Has it to do with Leibniz' monads, or with the monads from Category Theory?
The current name is Organic Mathematics.

[Molinaro]

I suppose most people have not had the experience I have had with physics crackpots. There is a syndrome common enough to be classified as a (minor, mostly harmless) mental illness, in which someone is convinced they understand some deep fact about the universe. They are certain they are correct and that everyone else is wrong, and they believe the establishment is suppressing their ideas (either because it is afraid of them, or refuses to pay attention, or for some darker reason).

This crops up in varying degrees across a whole spectrum of people, from formerly good physicists gone a little nutty to taxi drivers to wealthy businesspeople to homeless guys on the street. I would say roughly once a week I get such an email from someone - over the years I've gotten maybe a hundred such emails, letters, self-published books, etc., and seen many more on the internet. After a while I started to appreciate them for their comedic value, but I also started to recognize the common factors they all share.

doronshadmi's posts are not fully typical of this pattern, but they have many of the common red flags. S/he is working in isolation, believes eveyone in the mainstream is wrong, believes s/he has discovered something new and fundamental, believes hir ideas are being suppressed and/or willfully ignored, displays a near total ignorance of the basics of the subject s/he's attacking (read the other threads), changes hir position often without acknowledging it when confronted with contradictions, etc.

So be very careful before you assign any weight to this - s/he is probably a slightly confused person with a knack for mystic writing.



No Apathia. My reasoning is a much better tool to define the Logic and the Number system of Quantum Mechanic, which is the most powerful physical theory ever, because redundancy and uncertainty are its first-order properties, exactly as they are first-order properties of my Number system.

Furthermore, the observer is a significant factor of the researched system without violating the Copernican principle ( http://en.wikipedia.org/wiki/Copernican_principle ) because it is not understood in terms of his subjective point of view, but in terms of Symmetry\Asymmetry complementation.

In other words, my suggested framework is the next step of Modern Mathematics, where the current paradigm that ignores the observer and forces completeness on a researched system is the obsolete and esoteric one.

And there we have it. Nice call Sol.

Not only does Doronshadmi plan to redefine math, they plan/need to redefine most every word/phrase used along the way!

[ddt]

No Apathia. My reasoning is a much better tool to define the Logic and the Number system of Quantum Mechanic, which is the most powerful physical theory ever, because redundancy and uncertainty are its first-order properties, exactly as they are first-order properties of my Number system.
The main uncertainty I see in this thread is which well-understood mathematical term you're next to abuse.

Furthermore, the observer is a significant factor of the researched system without violating the Copernican principle ( http://en.wikipedia.org/wiki/Copernican_principle ) because it is not understood in terms of his subjective point of view, but in terms of Symmetry\Asymmetry complementation.

In other words, my suggested framework is the next step of Modern Mathematics, where the current paradigm that ignores the observer and forces completeness on a researched system is the obsolete and esoteric one.
Observer? In Mathematics?

Mathematics is a mind game - say, like draughts - with axioms as a beginning position and (classical) logic as the rules of movement, to arrive at theorems: the other positions you can arrive at. You can start with another set of axioms (another branch of mathematics) - that's like devising the game of checkers. When you're an intuitionist, you reject one of the rules ("tertium non datur") - that's like playing draughts without flying kings.

There's no observer in there; it's objective whether a theorem is true or not. Russel and Whitehead laid that out one century ago, and modern-day theorem provers do so. I admit, it's no fun playing mathematics purely as a manipulation of symbols. It wouldn't be very well directed either. Much of mathematics and the direction of research is inspired by modeling real-life problems. I doubt that, when purely using Euclid's axioms without the intuition of "points" and "lines", one would have come up with Feuerbach's nine-point circle. But ultimately, every mathematician can, when reading a paper, envisage the corresponding strings of symbols as in the Principia; and sometimes, they do when feeding it to a theorem prover.

[nathan]

The regular number system is not based on Symmetry\Asymmetry complementation. As a result there is no superposition of identities, but each number is distinct.

By my number system, we can research the vogue and the distinct as some particular aspects of a one comprehensive framework.

I asked about the quantum mechanic number system. Are you avoiding answering that question too?

[Molinaro]

The regular number system is not based on Symmetry\Asymmetry complementation. As a result there is no superposition of identities, but each number is distinct.

By my number system, we can research the vogue and the distinct as some particular aspects of a one comprehensive framework.

Bolding mine. Do you mean the Madonna song/dance?

Sorry I have to call word salad.

[nathan]

Doron, why are you avoiding giving any concrete example at all of anything you claim?

[ddt]

The current name is Organic Mathematics.

The best I could find about "Organic Mathematics" is this (http://www.cecm.sfu.ca/organics/announcement/):
The Organic Mathematics Project (OMP) is directed towards the exploration of the emerging network and information technologies within the context of mathematics. Numerous groups around the world are engaged in enhancing the specific aspects of the information highway and its associated processes for transporting data. However relatively few are actively integrating and adapting the raw technological building blocks to suit particular fields of endeavour. In our case, we are interested in incorporating several different mechanisms into a single coherent environment which will support the contributions and interaction between mathematics researchers in the field of experimental mathematics.

Nothing to do with a new approach to mathematics, but everything with better dissemination of information and global cooperation.

You should contact them; getting them to disseminate accurate information and concepts about mathematics would be a litmus test for success of the project.

[Apathia]

No Apathia. ....

OK, I'm out of here. There's simply no common ground of communication that could give an ordinary individual a point of entry to understanding your system. I have no idea now what your basic deffinitions, axioms, and even your point of view is.

[Apathia]

So are they atoms or not?

From reading Doron's material, I was under the impression that by "atom" he meant they were fundamental constituants without parts or a substructure of their own; like the original Greek meaning of atom.

However, I have no idea what his verbage means now. It seems that no one is able to get a hold on how he is using any of these words.

So, as I replied to him, I'm leaving this discussion. I cannot speak his language. And it doesn't seem he can speak ours.

[doronshadmi]

Mathematics is a mind game
Yes.

Without an observer's mind. Very interesting reasoning.

Any formal method is nothing but some observer's agent.

[doronshadmi]

The best I could find about "Organic Mathematics" is this (http://www.cecm.sfu.ca/organics/announcement/):


Nothing to do with a new approach to mathematics, but everything with better dissemination of information and global cooperation.

You should contact them; getting them to disseminate accurate information and concepts about mathematics would be a litmus test for success of the project.

http://www.geocities.com/complementarytheory/TOUM.pdf

[doronshadmi]

Doron, why are you avoiding giving any concrete example at all of anything you claim?

http://forums.randi.org/showpost.php?p=3669816&postcount=42

[ddt]

http://www.geocities.com/complementarytheory/TOUM.pdf

That paper contains the same gibberish you're spouting here.

[Molinaro]

http://www.geocities.com/complementarytheory/TOUM.pdf


Figure 5 ilustrates a proof that the number 0.111... is not a representation of the number 1 in base 2, but the non-local number 0.111...<1. Are there any numbers between 0.111... and 1? Yes, for any given base n>2, the non-local number 0.kkk... where k=n-1.

Are you kidding me? Is this what triggered all this from you? You saw a thread on the internet about 0.999... = 1 and you refuse to accept it and invented this word salad to try and refute it?

Well let's see what I get from that statement of your's for n = 2.

0.kkk... where k = n - 1 ; n = 2 gives

0.kkk... where k = 2 - 1 = 1

so,

0.111... oh and it's a non-local number

Let's compare that to:

0.111... a non-local number.

Hmmm.. having trouble seeing the < relationship here! They look very = to me. So how is 0.111... between 0.111... and 1 in your mind?

[ddt]

Are you kidding me? Is this what triggered all this from you? You saw a thread on the internet about 0.999... = 1 and you refuse to accept it and invented this word salad to try and refute it?
You actually got to page 9? Wow, kudos for your tenacity. I had to recover the file from the Trash can to see this quote.

[Molinaro]

Well I'll admit, much of the early pages can be described as accurate. Although, without meaning. Relationships and terms are defined and thankfully no conclusions are drawn :) So I can't realy complain too much about that.

But then, the diagrams come in.. ugh. Can't realy complain about those either because nothing is being said.

But finaly, figure 5 is an attempt to say something and it fails badly.

[ddt]

Well I'll admit, much of the early pages can be described as accurate. Although, without meaning. Relationships and terms are defined and thankfully no conclusions are drawn :) So I can't realy complain too much about that.
I got ticked off right at the start with the idiocy of the XOR and NXOR connectives. Apart from such lexical idiocies of using a backslash where a slash is normally used in English, or the interchanging use of "0" and "1" and "T" in the truth table on top of page 2, the idea that logic is "based on a connective" is ludicrous. Logic is based on the idea that "True" and "False" are different values. What happens when you mess with that is illustrated by that truth table on top of page 2:

0 0 → T (NXOR)
0 1 → T (XOR)
1 0 → T (XOR)
1 1 → T (NXOR)

You see? Everything is true! Yeah, every theorem is true. You can, right now, hear Gödel spinning in his grave.

And yes, I'm open to the idea of using other logics than classical logic - like intuitionistic logic.

[Apathia]

You see? Everything is true! Yeah, every theorem is true. You can, right now, hear Gödel spinning in his grave.

I said I was done with this thread, but the corollary is
http://www.albinoblacksheep.com/flash/wrong :D

[doronshadmi]

Are you kidding me? Is this what triggered all this from you? You saw a thread on the internet about 0.999... = 1 and you refuse to accept it and invented this word salad to try and refute it?

Well let's see what I get from that statement of your's for n = 2.

0.kkk... where k = n - 1 ; n = 2 gives

0.kkk... where k = 2 - 1 = 1

so,

0.111... oh and it's a non-local number

Let's compare that to:

0.111... a non-local number.

Hmmm.. having trouble seeing the < relationship here! They look very = to me. So how is 0.111... between 0.111... and 1 in your mind?

You are right, let us fix it.

First, n>1 and not n>2 (as you wrongly quoted).

Now let us fix it:

Figure 5 illustrates a proof that 0.111… is not a representation of the number 1 in base 2, but the non-local number 0.111… < 1. Are there any numbers between 0.111… and 1? Yes, for any given base n>1 and any 0.kkk…[base n] (where k=n-1) there is 0.nnn…[base n+1] such that:

0.kkk…[base n] < 0.nnn…[base n+1] < 1

If you find more mistakes in my paper, then please tell me.

Thank you.

[doronshadmi]

Logic is based on the idea that "True" and "False" are different values.

No. Logic is based on the ability of at least two opposites to be associated with each other without immediately eliminating each other during association.

This can be achieved only by the universal principle of Symmetry\Asymmetry complementation as shown in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .

[doronshadmi]

I said I was done with this thread, but the corollary is
http://www.albinoblacksheep.com/flash/wrong :D
Worng.

Not everything you know is wrong.

[Molinaro]

You are right, let us fix it.

First n>1 and not n>2 (as you wrongly quoted).

Now let us fix it:

For any 0.kkk…[base n] there is 0.nnn…[base n+1] such that:

0.kkk…[base n] < 0.nnn…[base n+1] < 1.

Yes I did typo the quote. And it's obviously a typo since what followed by me was based on the original text and not my typo.

So, you are saying:

0.111... [base 2] < 0.222... [base 3] < 0.333... [base 4] < 0.kkk... [base k+1] < 1

And that's just flat out wrong. They are all exactly equal to each other and they are all exactly equal to 1.

They all define the exact same cleave of the real line at exactly the same point, hence they are exactly the same value.


edit to add:

You are failing to consider infinitely many digits of k. That's your problem. When you write 0.111... that ellispsis means 1 and only 1 thing: that infinitely many 1s are being considered. You cannot write that down and then turn around and do anything less than consider infinitely many digits after the decimal point. The fact that infinitely many cannot be written down or held in your hand or any other meta-physical problem you have with infinity is totaly irrelevant.

[nathan]

It seems Doron is unable or unwilling to:
* give any example of any of this stuff (other than incomprehensible complicated diagrams)
* answer questions about whether something's an atom or not (other than incomprehensible responses)
* provide any definitions of terms that are not mutually dependent

Instead of providing such examples, answers or definitions, Doron persists in saying the response has already been given and one should reread some past post until one 'gets' it.

Doron, what is your purpose in posting here? Clearly it is not to propagate your theory.

[doronshadmi]

You see? Everything is true! Yeah, every theorem is true. You can, right now, hear Gödel spinning in his grave.
Every NXOR\XOR complementation is true because it is incomplete.

And yes, I'm open to the idea of using other logics than classical logic - like intuitionistic logic.
Are you open to the idea that any researchable thing must be incomplete (non-total) in order to be researchable ?

[ddt]

Not everything you know is wrong.
Considering your truth table on page 2, everything is True. Which makes your "logic" meaningless.

[jsfisher]

Every NXOR\XOR complementation is true because it is incomplete.

Are you open to the idea that any researchable thing must be incomplete (non-total) in order to be researchable ?


Doron, are you ever going to focus on some sort of mathy stuff, or will you persist with this philosophic gibberish? By the way, you could possibly reduce the level of gibberish if you actually explained what you meant by these terms you insist on abusing.

[ddt]

No. Logic is based on the ability of at least two opposites to be associated with each other without immediately eliminating each other during association.
Association? Like, logical values having sex with each other?

Eliminating each other? Give me a break.

Do you have any grasp of classical logic? Tell me, how does modus ponens look like in sequent calculus?

This can be achieved only by the universal principle of Symmetry\Asymmetry complementation as shown in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .

You don't expect me to download another load of bollocks, are you? You didn't refer to it in the previous paper, so that should be self-explanatory.

[doronshadmi]

Considering your truth table on page 2, everything is True. Which makes your "logic" meaningless.
It is true because it is incomplete.

Please do not force completeness on any researchable framework, because it cannot be both researchable AND complete.

This is exactly the paradigm-shift that no one of you can grasp (yet).

[ddt]

Every NXOR\XOR complementation is true because it is incomplete.
Your explanations of it surely are.

Are you open to the idea that any researchable thing must be incomplete (non-total) in order to be researchable ?
No. Evidence to the contrary: propositional logic is complete.

PS. Do you prefer to be mocked or to be verbally abused? There's certainly a masochistic streak in you that you keep posting.

[doronshadmi]

Association? Like, logical values having sex with each other?

Eliminating each other? Give me a break.

Do you have any grasp of classical logic? Tell me, how does modus ponens look like in sequent calculus?



You don't expect me to download another load of bollocks, are you? You didn't refer to it in the previous paper, so that should be self-explanatory.

ddt please see http://forums.randi.org/showpost.php?p=3672614&postcount=76 .

[Molinaro]

Doron, are you ever going to focus on some sort of mathy stuff, or will you persist with this philosophic gibberish? By the way, you could possibly reduce the level of gibberish if you actually explained what you meant by these terms you insist on abusing.

His pdf actualy does a clear job of defining the terms used. Let's see if I can list all the needed definitions (I make no claim of them having any kind of usefullness or consistency):

Are you open to the idea that any researchable thing must be incomplete (non-total) in order to be researchable ?

From that, the following definitions would be needed:

1) researchable
2) thing
Let a thing be nothing or something.
3) incomplete
4) non-total

Hmmm only 1 out of 4. Hey Doronshadmi, care to define these other terms?


And I want to comment on figure 6, as it pertains to my earlier post with the edited in comment. Your diagram shows you drawing a conclusion about the relative position of the values 0.111... base 2 and 0.222... base 3 on the number line, after some EQUAL AND FINITE NUMBER OF DIGITS n. For example, for n=5 you are comparing 0.11111 base 2 with 0.22222 base 3.

Why on earth would you expect the relationship between those values and the completely diferent values 0.111... and 0.222... to be the same?

[doronshadmi]

No. Evidence to the contrary: propositional logic is complete.
Only an atom (that has to parts) is complete.

propositional logic is not and atom, so it is incomplete.

[Molinaro]

Only an atom (that has to parts) is complete.

propositional logic is not and atom, so it is incomplete.


Did I bold a typo there? Did you mean to type no?

[ddt]

Only an atom (that has to parts) is complete.

propositional logic is not and atom, so it is incomplete.
You didn't define what you mean by complete; in your PDF, it doesn't appear before page 10. We're discussing here pages 1-2.

You didn't answer my question on the modus ponens. You didn't recognize in my remark "propositional logic is complete" that completeness has a valid usage in logic: meaning that every true proposition (true according to truth tables) is provable.

How can you propose a paradigm shift when you don't know jack about the old paradigm?

Your paper is incomplete, that's for sure.

[nathan]

Only an atom (that has to parts) is complete.

propositional logic is not and atom, so it is incomplete.

You're very good at saying what is not an atom. Care to name something that is an atom?

[jsfisher]

His pdf actualy does a clear job of defining the terms used. Let's see if I can list all the needed definitions (I make no claim of them having any kind of usefullness or consistency):


Oh, dear, you are being far too generous. You need to include:

Symmetry
Asymmetry
Complementation
point
line
ur-element real-line
related
local
non-local
complete

...and that's just off the top of my head. :)

Doesn't matter, though. The basis of all this cranky math is doron's inability to comprehend infinity. She's in denial over that, it creates a blind spot in her reasoning, and the rest follows.

[doronshadmi]

You are failing to consider infinitely many digits of k. That's your problem.
You are failing to consider infinitely many digits as an incomplete mathematical object that its exact place along the non-local ur-element real-line cannot be determined.

Time after time you and the rest of the participators here are forcing completeness on something that is not an atom, but it is the result of non-local atom (represented as ___)\ local atoms (represented as . , where each one of them it totally isolated without ___ ) complementation, that is not total and therefore researchable.

As long as you don't get ____(non-locality)\ .(locality) complementation result, you have no way to understand the suggested framework.

Be aware that you cannot use the standard point of view, that forces completeness of this complementation.

[Molinaro]

You are failing to consider infinitely many digits as an incomplete mathematical object that its exact place along the non-local ur-element real-line cannot be determined.

Time after time you and the rest of the participators here are forcing completeness on something that is not an atom, but it is the result of non-local atom (represented as ___)\ local atoms (represented as . , where each one of them it totally isolated without ___ ) complementation, that is not total and therefore researchable.

As long as you don't get ____(non-locality)\ .(locality) complementation result, you have no way to understand the suggested framework.

Be aware that you cannot use the standard point of view, that forces completeness of this complementation.

I understand it just fine thanks. I understand it so well that I see exactly why you are wrong in what you just said. You simply don't want to accept that 0.111... after considering infinitely many 1s is an exactly specified point on the real line. Your refusing to accept that fact, along with your inventions to classify all such points as something different, do not negate your error.

[nathan]

You are failing to consider infinitely many digits as an incomplete mathematical object that its exact place along the non-local ur-element real-line cannot be determined.

It would help if you defined what you meant by 'incomplete mathematical object' and 'non-local ur-element real-line'. Is the latter just a weird way of refering to the number line, or is it something else?

[nathan]

Time after time you and the rest of the participators here are forcing completeness on something that is not an atom, but it is the result of non-local atom (represented as ___)\ local atoms (represented as . , where each one of them it totally isolated without ___ ) complementation, that is not total and therefore researchable.

time after time you refuse to give non-mutually dependent definitions of your times.

Time after time you refuse to provide concrete examples of the things you wish to talk about.

To give meaning to the above sentence of yours, you need to define:

* atom
* completeness
* non-local atom
* local atoms
* totally isolated
* complementation
* total
* researchable

and by define I mean 'define in a non-mutually dependent fashion'. Giving examples of each of these things would help immensly. Why are you avoiding doing that?

So far I think all that's been established is that you do not believe non-terminating floating point numbers to exist (from your assertion about .1...[2] < .2...[3] etc). Is that correct?

[ddt]

It would help if you defined what you meant by 'incomplete mathematical object' and 'non-local ur-element real-line'. Is the latter just a weird way of refering to the number line, or is it something else?
The German sounding/looking word "ur-element" (but it's actually not German; in German, it has no hyphen and it has an uppercase U) is meant to evoke in the reader associations with revered German mathematicians who helped lay the foundations of mathematics, such as Dedekind, Cantor, Frege, Gentzen and Gödel.

But, of course, it's absolute gibberish. Doron can't even reproduce Cantor's diagonal argument faithfully, as shown in an earlier thread.

[nathan]

The German sounding/looking word.

ITYM 'German sounding\looking complementation' :)

[doronshadmi]

So far I think all that's been established is that you do not believe non-terminating floating point numbers to exist (from your assertion about .1...[2] < .2...[3] etc). Is that correct?
No.

The non-terminating floating point numbers are exactly non-local numbers.

These non-local numbers do not exist by any framework which claims that, for example, 0.999...[base 10] is not a number but it is some representation ( out of many representations) of number 1.

[doronshadmi]

The German sounding/looking word "ur-element" (but it's actually not German; in German, it has no hyphen and it has an uppercase U) is meant to evoke in the reader associations with revered German mathematicians who helped lay the foundations of mathematics, such as Dedekind, Cantor, Frege, Gentzen and Gödel.

But, of course, it's absolute gibberish. Doron can't even reproduce Cantor's diagonal argument faithfully, as shown in an earlier thread.
No.

By my framework Cantor's diagonal argument clearly shows that a non-finite collection of distinct objects, cannot be complete, as shown in http://www.geocities.com/complementarytheory/TOUM.pdf page 10.

You cannot understand it unless you get:

http://forums.randi.org/showpost.php?p=3664848&postcount=1

http://forums.randi.org/showpost.php?p=3666527&postcount=22

http://forums.randi.org/showpost.php?p=3669463&postcount=37

http://forums.randi.org/showpost.php?p=3669816&postcount=42

You cannot get it without fully understand ___\. complementation, which is researchable and incomplete (not total).

If you are going to force once again the traditional point of view on my framework, then you are going to waste your time.

[Gate2501]

No.

for example, 0.999...[base 10] is not a number but it is some representation ( out of many representations) of number 1.

I am no mathematician, but I think that .999~ is in fact a number.

It denotes the real number 1.

It seems to me that even though it does not visibly look like the number 1. .999~ is still for all intents and purposes, the real number 1.

[doronshadmi]

I understand it just fine thanks. I understand it so well that I see exactly why you are wrong in what you just said. You simply don't want to accept that 0.111... after considering infinitely many 1s is an exactly specified point on the real line. Your refusing to accept that fact, along with your inventions to classify all such points as something different, do not negate your error.
No dear Molinaro,

Your refusing to accept the fact that ___ is Logically not a collection of any amount (finite or not) of . , prevents from you to understand my framework.

If you really wish to get it, then this time real very carefully http://forums.randi.org/showpost.php?p=3673115&postcount=101 without forcing the standard point of view.

[nathan]

The non-terminating floating point numbers are exactly non-local numbers.
ok. Are these things identical? I.e. are all non-local numbers non-terminating floating point numbers? Are all non-terminating floating point numbers non-local numbers?

Please clarify how the base one is using to represent these numbers is determined. For instance one tenth is a terminating sequence in base 10, but a non-terminating sequence in base 2 or 3. Does this mean it's a local base-10 number but a non-local base-2 number?

These non-local numbers do not exist by any framework which claims that, for example, 0.999...[base 10] is not a number but it is some representation ( out of many representations) of number 1.

0.9..[10] is a perfectly good number representation. It just happens to have the same value as 1. What other representations are there for that value? You claim there are many.

Are you counting representations in other bases in this? Virtually all real numbers have different representations in different bases. The only real numbers which don't are:
* zero
* one
* Integers < either base
* negations of the above non-zero numbers using regular sign-magnitude representation

It's possible I've missed some, but given that all non-integral real numbers must have base-specific representations, and there are more reals than integers (Hi Cantor!), there must be a minority of values that have base-independent representations.

I'm confused about what you're claiming for non-local numbers. Do they exist or not exist? Please clarify.

[doronshadmi]

I am no mathematician, but I think that .999~ is in fact a number.

It denotes the real number 1.

It seems to me that even though it does not visibly look like the number 1. .999~ is still for all intents and purposes, the real number 1.
Only if you force completeness on the naturally incomplete, but then you make an arbitrary jump from the non-local number 0.999...[base 10] to the local number 1.

[Gate2501]

Only if you force completeness on the naturally incomplete, but then you make an arbitrary jump from the non-local nimber 0.999...[base 10] to the local number 1.

Dude...

I don't think that you are "completing" the infinite series of 9's when you come to the conclusion that 0.999~=1.

Even I understand this and I am just a high school grad.

[nathan]

Your refusing to accept the fact that ___ is Logically not a collection of any amount (finite or not) of .

I don't think any one is claiming that a line segment is a collection of points. Isn't it generally considered that one can fit an infinite number of points on a line segment though? (Aleph1 if one accepts the continuum hypothesis, IIRC). That doesn't make a line a collection of points though.

[nathan]

Only if you force completeness on the naturally incomplete, but then you make an arbitrary jump from the non-local number 0.999...[base 10] to the local number 1.
Um, not an arbitrary jump.

0.9..[10] is a representation of the value:
(N^k-1)/N^k

where
N=10 (the number base)
and
k -> infinity

Now, if I remembered more maths than I do, I'm sure I could show that that equaled 1 in the limit of k->infinity (aleph 0, to be precise).

[ddt]

By my framework Cantor's diagonal argument clearly shows that a non-finite collection of distinct objects, cannot be complete, as shown in http://www.geocities.com/complementarytheory/TOUM.pdf page 10.
And pigs can fly.


You cannot understand it unless you get:

Of course, you have said it all before. Just more word salad.


You cannot get it without fully understand ___\. complementation, which is researchable and incomplete (not total).
Morse code?


If you are going to force once again the traditional point of view on my framework, then you are going to waste your time.
Engaging your warped ideas ia waste of time anyway. Parrots are known to have a better grasp of math.

[doronshadmi]

Morse code?
http://www.geocities.com/complementarytheory/NXOR-XOR.pdf

[doronshadmi]

I don't think any one is claiming that a line segment is a collection of points. Isn't it generally considered that one can fit an infinite number of points on a line segment though? (Aleph1 if one accepts the continuum hypothesis, IIRC). That doesn't make a line a collection of points though.

___ is not a geometric object and also . in not a geometric object in my framework.

____ is a non-local atom (the basis of Not XOR connective).

. is a local atom (the basis of XOR connective).

___ is not researchable at its self state.

. is not researchable at its self state.


The researchable is ___ as a connector between infinitely many . connected objects, and no infinitely . objects (local atoms) can be ___ (a non-local atom).

As a result any collection of . objects (which is weaker than ____ and stronger than .) is incomplete if compared to ___ (the non-local atom).

As long as you don't get this simple and beautiful fact, you are unable to say any meaningful thing about my framework.

[ddt]

. is not researchable at its self state.


Why don't you call it "eigen state"? Sounds more posh. Gibberish it remains.

:boxedin:

[nathan]

___ is not a geometric object and also . in not a geometric object in my framework.

are ___ and . your glyphs for line segment and point respectively? Or are they something else?

____ is a non-local atom (the basis of Not XOR connective).

. is a local atom (the basis of XOR connective).

___ is not researchable at its self state.

. is not researchable at its self state.
Please define:
* non-local atom
* local atom
* researchable
* self state
* connective

using non-mutual definitions.

The researchable is ___ as a connector between infinitely many . connected objects, and no infinitely . objects (local atoms) can be ___ (a non-local atom).

As a result any collection of . objects (which is weaker than ____ and stronger than .) is incomplete if compared to ___ (the non-local atom).

As long as you don't get this simple and beautiful fact, you are unable to say any meaningful thing about my framework.
Until you actually provide definitions of your framework that are intelligible, the only meaningful thing anyone can say about it is that at best it is indistinguishable from gibberish.

How about getting back to the non-terminating floating point numbers? We seemed to be getting somewhere with them. Why are you not progressing that line of conversation?

[nathan]

____ is a non-local atom (the basis of Not XOR connective).

___ is not researchable at its self state.

Oh, are these two different series of _ characters the same symbol or different symbols?

[nathan]

are ___ and . your glyphs for line segment and point respectively? Or are they something else?
Oh, hang on, you've said they are not geometric objects. So they must be something else. Shall we call them Alpha and Beta? Do they have any properties beyond non-local/local atomicity? Do they have any properties that allow us to map them onto previously known objects -- like thoughts about ice cream, numbers or triskadecaphobia?

[ddt]

Are you counting representations in other bases in this? Virtually all real numbers have different representations in different bases. The only real numbers which don't are:
* zero
* one
* Integers < either base
* negations of the above non-zero numbers using regular sign-magnitude representation

To nitpick: not even those, if you count unary notation :). Then zero is just an empty string :).

[nathan]

To nitpick: not even those, if you count unary notation :). Then zero is just an empty string :).

Aren't Doron's claims restricted to integral bases >= two?

Poor unary, always forget about that. At least the Romans had the sense to compress it! Hey, I'm happy I didn't miss any values :)

ETA: <derail>Can unary represent fractional values?

[ddt]

Aren't Doron's claims restricted to integral bases >= two?
Yes indeed. I hadn't bothered to look.

Poor unary, always forget about that. At least the Romans had the sense to compress it!
:D :D :D

ETA: <derail>Can unary represent fractional values?
Why not? A fraction is just a number n/m, I don't see why you couldn't extend unary notation to fractional value by just writing n and m in unary too.

But there's not much use in it, is it? I know only of two places where unary is useful:

In a discussion on Turing machines, specifically their equivalence to recursive functions;
In a Perl-script to determine whether a number is prime.

[jsfisher]

For those of you who did not follow some of doronshadmi's other threads, I'll try to summarize a few of the conclusions from them:

doronshadmi is convinced kindergarten children are the key to understanding advanced concepts in Mathematics. The fact five year olds haven't yet developed the cognitive abilities needed to understand the abstract is not actually a limitation, but a tremendous advantage they have. Their lack of an ability to comprehend something fits perfectly with doronshadmi's outlook.

doronshadmi is fluent in gibberish. She sometimes uses standard terminology in her own non-standard way (asymmetry, for example) and other times makes up new terms (complementation). In either case, she seldom explains what her terms mean, and when she does, it is usually with more confounding gibberish. Mostly, doronshadmi just refers you to some prior post or one of her bizarre PDF files.

Absurd things Doronshadmi believes:


A set is equal to the union of its members.

2 is not part of { 2,3,4 } much like a severed finger is not part of your body.

2 may not be a member of { 2 }.

A if B, A only if B, and A if and only if B are all equivalent constructs.

Geometry is a very weak branch of Mathematics.

There is no such thing as a number in standard Mathematics.


By the way, doronshadmi's "mathematical framework" unifies Mathematics with morality.

[nathan]

Why not? A fraction is just a number n/m, I don't see why you couldn't extend unary notation to fractional value by just writing n and m in unary too.
ok then, irrational numbers?

[jsfisher]

ok then, irrational numbers?

You can't represent irrational numbers in any positional system with integer base.

(By the way, I assume by unary you mean tally marks. There is no "base-1" positional system.)

[ddt]

You can't represent irrational numbers in any positional system with integer base.
Come to think of it - you could of course represent a subset of irrational numbers with a finite representation: the algebraic numbers. Each algebraic number is a root of a polynomial with integer coefficients. So a representation consisting of the series of coefficients, together with the ordinal of the root, would constitute a finite representation. Say:

[1, -2 | 0 ] represents sqrt(2)
[1, -1, -1 | 1 ] represents the golden ratio

(By the way, I assume by unary you mean tally marks. There is no "base-1" positional system.)
Yes, that's what's normally meant with unary. Tally marks without each fifth being a diagonal stroke :). Costs a lot of room, but then, with Turing machines you have an endless tape anyhow :)

[ddt]

For those of you who did not follow some of doronshadmi's other threads, I'll try to summarize a few of the conclusions from them:
Great summary :D. I had lurked in some of the other threads, so I already knew what it was about.

I am tempted to follow the advice in your sig, but I'm hesitant as it only pertains to another poster, how bizarre her posts may be.

[doronshadmi]

For those of you who did not follow some of doronshadmi's other threads, I'll try to summarize a few of the conclusions from them:

doronshadmi is convinced kindergarten children are the key to understanding advanced concepts in Mathematics. The fact five year olds haven't yet developed the cognitive abilities needed to understand the abstract is not actually a limitation, but a tremendous advantage they have. Their lack of an ability to comprehend something fits perfectly with doronshadmi's outlook.
Five years old children has the natural ability to distinguish between the non-local and the local. The current community of adults (called mathematicians)using forced methods that are based on non-locality as their hidden assumption of their reasoning.


doronshadmi is fluent in gibberish. She sometimes uses standard terminology in her own non-standard way (asymmetry, for example) and other times makes up new terms (complementation). In either case, she seldom explains what her terms mean, and when she does, it is usually with more confounding gibberish. Mostly, doronshadmi just refers you to some prior post or one of her bizarre PDF files
Jsfisher is a good example of a scholar that cannot prodive an answer to this question:

How x and y, where x is not y, are examined in a one framework?


Absurd things Doronshadmi believes :


A set is equal to the union of its members.
Because a set is determined by its members (or their absence).



2 is not part of { 2,3,4 } much like a severed finger is not part of your body.
2 and {2} are not the same.



2 may not be a member of { 2 }.
Because 2 and {2} are not the same.



A if B, A only if B, and A if and only if B are all equivalent constructs.
At this part I used If not in its mathematical interpretation.



Geometry is a very weak branch of Mathematics.
If a line and a point are not defined as two different atoms.



There is no such thing as a number in standard Mathematics.
There is no general definition of Number, for example: There are Natural numbers, Rational numbers, Irrational number, Complex numbers etc. , but no one of them is a general definition of Number.





By the way, doronshadmi's "mathematical framework" unifies Mathematics with morality.
No it unifies Logic with ethic as two aspects of our consciousness, where our consciousness is examined as Symmetry\Asymmetry complementation.

[jsfisher]

No it unifies Logic with ethic as two aspects of our consciousness, where our consciousness is examined as Symmetry\Asymmetry complementation.

Ok, got it. Logic and ethics, not Mathematics and morality. By the way, thanks for confirming the rest of my post; I'd hate to have people think I just made all that stuff up.

[Molinaro]

Jsfisher is a good example of a scholar that cannot prodive an answer to this question:

How x and y, where x is not y, are examined in a one framework?


Ya jfisher, how come you can't answer that question? :D:D:D

[Molinaro]

A set is equal to the union of its members.
Because a set is determined by its members (or their absence).

No, because 2 and {2} are not the same. { 2,3,4 } = {2}U{3}U{4} <> 2 U 3 U 4



2 is not part of { 2,3,4 } much like a severed finger is not part of your body.
2 and {2} are not the same.

True that 2 and {2} are not the same. However, an element of a set is a part of a set. 2 is an element of the set { 2,3,4 } hence 2 is a part of { 2,3,4 }



2 may not be a member of { 2 }.
Because 2 and {2} are not the same.

True that 2 and {2} are not the same. However, a member of a set is a particular value of an element of a set. 2 is an element of the set { 2,3,4 } hence 2 is a member of { 2,3,4 }




A if B, A only if B, and A if and only if B are all equivalent constructs.
At this part I used If not in its mathematical interpretation.

Was it you who gave Bill the 'is' defence idea?




Geometry is a very weak branch of Mathematics.
If a line and a point are not defined as two different atoms.

Link to someone defining a point and a line as the same atom please.




There is no such thing as a number in standard Mathematics.
There is no general definition of Number, for example: There are Natural numbers, Rational numbers, Irrational number, Complex numbers etc. , but no one of them is a general definition of Number.

Sure there is: A number is an abstract object, tokens of which are symbols used in counting and measuring.





Try again please.

[nathan]

You can't represent irrational numbers in any positional system with integer base.
... in a finite amount of space.

I guess I wasn't thinking clearly. Really there's no difference between using X/Y to represent a value and a finite fixed point representation 0.ABC...XYZ.

unary output is great for watching FORTH engines blow up:

2 1 BASE ! .

[ddt]

Ok, got it. Logic and ethics, not Mathematics and morality.
Isn't it totally obvious to you, then, that Logic and Ethics are closely intertwined?

Let's review the values in logic:

True - telling the truth is GOOD. False - telling lies is BAD.

And the connectives:

XOR: that one tells us that we should provide at least one lie, so it's VERY BAD.
OR: that one condones a lie, so it's BAD too, but not as bad as XOR.
Equivalence (<=>): tells us that we can turn two lies into the truth, so it's even WORSE than XOR.
Implication (=>): tells us that you can think up anything after lying, so it promotes lying even more than the other ones. This connective is PURE UNADULTERATED EVIL.
AND: at last, a GOOD connective: it says we can only get truth from truth.

Concluding, we should strive for an ethical logic, and therefore do away with all the BAD things in logic. We should restrict our logic only to True and AND.

[nathan]

... still waiting on clarification about the mapping between terminating/non-terminating fixed point representations of reals and local/non-local atoms ...

[ddt]

... in a finite amount of space.

I guess I wasn't thinking clearly. Really there's no difference between using X/Y to represent a value and a finite fixed point representation 0.ABC...XYZ.
The latter representation can only adequately denote - in a finite amount of space - rationals with a normalized denominator only containing prime factors that are present as factor in the chosen base. A computer FPU, e.g., cannot precisely store 1/5, as the FPU uses base 2.

.unary output is great for watching FORTH engines blow up:

2 1 BASE ! .
What's the ! for? I never did Forth, but I know it's a stack-based language. Pretty stupid, by the way, that the built-in BASE doesn't check the value of the base before going off in recursion.

I love this Perl snippet, where $n is a variable containing a number:

"1" x $n =~ /^(11+)\1+$/

which checks whether $n is a prime.

[nathan]

What's the ! for? I never did Forth, but I know it's a stack-based language.
BASE is a variable, it causes the address of the storage to be pushed. The ! does the store (use TOS as the address and NOS as the value). To query a variable you'd use 'BASE ?' ? replaces TOS with the value at that location. FORTH did very little error checking :)

That's enough derailing, stop it now, or we'll be moved to computers etc.

[nathan]

I love this Perl snippet, where $n is a variable containing a number:

"1" x $n =~ /^(11+)\1+$/

which checks whether $n is a prime.

Hmm, doesn't look like it'll work for 3
* (11+) matches 2 or more 1's
* \1+ matches 1 or more copies of the first string

It looks like it'll match numbers that are the product of 2 integers. I suspect you may mean !~ not =~

gee, I didn't think I had much perl-fu :duel

[ddt]

That's enough derailing, stop it now, or we'll be moved to computers etc.
OK, I'll stick to math in this thread, but given the OP I'm quite at a loss what's on-topic and what's off-topic :D


It looks like it'll match numbers that are the product of 2 integers. I suspect you may mean !~ not =~

gee, I didn't think I had much perl-fu :duel
Indeed, right correction! and absolutely spot-on explanation. Regular expressions rule! Well, what counts as RE's - but that's really not regular, not even context-free in formal language theory, when you use things like backreferences. (for the moderators: formal language theory is applied mathematics)

[jsfisher]

It looks like it'll match numbers that are the product of 2 integers. I suspect you may mean !~ not =~

After the "does not match" cor