Deeper than primes

[jsfisher]

Please show the symmetry in definition #4:

Definition 4: If object x = or ≠ (where ≠ is < or >) w.r.t object y, then object x is called Local.

In your .PDF you explicitly define your notation thus: "= relation is equal to...≠ relation is not equal to..." In this very thread you restricted "equal" to just logical identity and cited a wikipedia article.

With or without that added qualifier, your use of = and ≠ are of symmetric relations.

...and that "w.r.t." doesn't mean what you think it means in that definition. It still makes it into gibberish.

[ddt]

Definition 4: If object x = or ≠ (where ≠ is < or >) w.r.t object y, then object x is called Local.
A definition that doesn't make sense - apart from the superfluous word "object" and the idiotic juggling with relation symbols, so let's first simplify that part:
If x = y, then x is called local.
What does this mean? Does it (a) mean:
If there is an y such that x = y, then x is called local.
which would be nonsense, as trivially, substituting x for y makes that every x is called local.

Or does it (b) mean:
If for all y, x = y holds, then x is called local.
which would be nonsense too as there surely will be at least one y for which x =y does not hold.

Or does it (c) mean:
If x = y, then x is called local to y
an addition that does make sense, but which you've emphatically denied previously.

In terms of logic propositions: you have an unbound variable in your definition.

You made a definition with a hole you can drive a truck through. Anyone with half a brain can spot that.


Definition 5: If object x = and ≠ (where ≠ is < or >) or < and > w.r.t object y, then object x is called Non-Local.
Ditto.

[The Man]

Please show the symmetry in definition #4:

Definition 4: If object x = or ≠ (where ≠ is < or >) w.r.t object y, then object x is called Local.

Also please show the symmetry in definition #5:

Definition 5: If object x = and ≠ (where ≠ is < or >) or < and > w.r.t object y, then object x is called Non-Local.

Hint: Do not force Y=X = X=Y on them.

Uhm you do remember this post don’t you

I have to add that I use "=" as self identity ( http://en.wikipedia.org/wiki/Identity_(philosophy) )


That is what self identity means (from your link).



Logic of identity
In logic, the identity relation is normally defined as the relation that holds only between a thing and itself. That is, identity is the two-place predicate, "=", such that for all x and y, "x = y" is true iff x is the same thing as y. Identity is transitive, symmetric, and reflexive. It is an axiom of most normal modal logics that for all x, if x = x then necessarily x = x. (These definitions are of course inapplicable in some areas of quantified logic, such as fuzzy logic and fuzzy set theory, and with respect to vague objects.)


Self identity or sameness infers Y = X (or Y same as X) is the same as X = Y (or X same as Y). No one is forcing “Y=X = X=Y” you have simply volunteered that association since you claim to “use "=" as self identity”. So your “x = or…” use in definition 4 confers the symmetry of self identity.


As for symbols, their meaning can be changed by using non-exclusive observations.


So, since you are using exclusive observations (claiming X w.r.t. Y is different or exclusive of Y w.r.t. X) indicates that you are not changing the meaning of ‘"=" as self identity’, when considering Y = X and thus X w.r.t. Y is the same as Y w.r.t. X in that consideration. Either you have abandoned that notion of Y w.r.t. X being different from X w.r.t. Y (when considering X = Y) or you do not “use "=" as self identity”, make up your mind then get back to us.

[doronshadmi]

In your .PDF you explicitly define your notation thus: "= relation is equal to...≠ relation is not equal to..." In this very thread you restricted "equal" to just logical identity and cited a wikipedia article.

With or without that added qualifier, your use of = and ≠ are of symmetric relations.

...and that "w.r.t." doesn't mean what you think it means in that definition. It still makes it into gibberish.



The asymmetry is that X is compared to Y but Y is not compared to X.

This is the meaning of y is obsereved through x, but not vice versa.

By using this asymmetry a non-local object is distingushed from a local object.

In the case of = or ≠ , both are non-local, because any relation cannot be but non-local.

You mix between relations and objects, which is gibberish from my point of view.

EDIT:

Again:

x = .

y= ___

x = y from x point of view (for example: .__ , _._ , __. )

But y < and = x from y point of view (for example: __. )

or

y < and > x from y point of view (for example: _._ )

or

y > = and x from y point of view (for example: .__ )


So where is your x=y = y=x symmetry?

[jsfisher]

The asymmetry is that X is compared to Y but Y is not compared to X.

That's not what you wrote, and that's not what "compare" means.

[The Man]

The asymmetry is that X is compared to Y but Y is not compared to X.

This is the meaning of y is obsereved through x, but not vice versa.

By using this asymmetry a non-local object is distingushed from a local object.

In the case of = or ≠ , both are non-local, because any relation cannot be but non-local.

You mix between relations and objects, which is gibberish from my point of view.

While you just make things up then apply them inconsistently (or asymmetrically as you now seem to prefer to call it) even by your own professed definitions, which results in gibberish, from anyone’s point of view.

[doronshadmi]

That's not what you wrote, and that's not what "compare" means.

You are right, your "compare" is symmetric, my "compare is not.

And no point of view is exclusive.

[doronshadmi]

While you just make things up then apply them inconsistently (or asymmetrically as you now seem to prefer to call it) even by your own professed definitions, which results in gibberish, from anyone’s point of view.

Magority does not meas exclusive.

Please read the EDIT: (<--- I have learned something from you) in http://forums.randi.org/showpost.php?p=4221692&postcount=754 .


EDIT: Any mathematical subject can be changed by using non-exclusive observations.

[doronshadmi]

Why? If considering a circle taken from some X Y origin and defined by X2 + Y2 = R2. Any Radius RXn,Yn that is not equal to RX1,Y1 would be defined as all radii both greater to and less then RX1,Y1 or RXn,Yn ≠RX1,Y1 is the same as RXn,Yn < and > RX1,Y1.

So you used the asymmetric case of:

x = _____

y = __

x < and > w.r.t y (for example: ______)

I wish to see you doing it when:

x = .

y = ___

[jsfisher]

You are right, your "compare" is symmetric, my "compare is not.

And no point of view is exclusive.


First, the word being used is "equal to", not "compare". You even provided a reference for your usage, and the reference is clear. "Equal to" is a symmetric relation.

Second, if you goal is to be obtuse and confuse the discussion, you are doing an excellent job. Continue to abuse common usage and hide behind secret meanings. Well done!

I was looking for communication. My bad.

[The Man]

I have no idea what Magority means, if you mean ‘Majority’ then I have no idea why you would associate that in the first place only to then try to dissociate it from exclusive.

Thanks anyway for giving me credit and I do appreciate the indications of edits and will naturally read and comment on them. Unfortunately the contents of that edit were effectively covered by my previous post.

http://forums.randi.org/showthread.php?postid=4221544#post4221544

You require the symmetry by claiming that you “use "=" as self identity”. Have you decided which you want to give up your claim of asymmetry or your claim that you “use "=" as self identity”?

[jsfisher]

Magority does not meas exclusive.

Please read the EDIT: (<--- I have learned something from you) in http://forums.randi.org/showpost.php?p=4221692&postcount=754 .


EDIT: Any mathematical subject can be changed by using non-exclusive observations.


Another word that doesn't mean what you think it means.

[doronshadmi]

First, the word being used is "equal to", not "compare". You even provided a reference for your usage, and the reference is clear. "Equal to" is a symmetric relation.

Second, if you goal is to obtuse and confuse the discussion, you are doing an excellent job. Continue to abuse common usage and hide behind secret meanings. Well done!

I was looking for communication. My bad.

Again

x = .

y = ___

x = y only from x point of view (for example: .__ , _._ , __. )

y >and= or <and> or <and= x olny from y point of view (for example: .__ , _._ , __. )

So as you see, the same interactions are understood differently from different points of view.

[doronshadmi]

Another word that doesn't mean what you think it means.

Non-exclusive is exactly what it is: there can be more than a one viewpoint of the same mathematical subject.

[doronshadmi]

I have no idea what Magority means, if you mean ‘Majority’ then I have no idea why you would associate that in the first place only to then try to dissociate it from exclusive.

Thanks anyway for giving me credit and I do appreciate the indications of edits and will naturally read and comment on them. Unfortunately the contents of that edit were effectively covered by my previous post.

http://forums.randi.org/showthread.php?postid=4221544#post4221544

You require the symmetry by claiming that you “use "=" as self identity”. Have you decided which you want to give up your claim of asymmetry or your claim that you “use "=" as self identity”?

x = .

y = ___

By self identity x = x , y = y , etc...

It does not mean that if x = y from x point of view (example: _.__) then y = x from y point of view (Y < and > x from y point of view).

x,y relations are non-commutative

[jsfisher]

Again...

Again, we were discussing your failed Definition #4 and the definitions that precede it.

According to your most recent version of Definition #4, everything is local.

If you are relying on some private meaning for the equal and not-equal relations, then please provide those meanings. Perhaps you can salvage Definition #4 yet.

[doronshadmi]

Again, we were discussing your failed Definition #4 and the definitions that precede it.

According to your most recent version of Definition #4, everything is local.

If you are relying on some private meaning for the equal and not-equal relations, then please provide those meanings. Perhaps you can salvage Definition #4 yet.

Definition 4: If object x = xor ≠ (where ≠ is < xor >) w.r.t object y, then object x is called Local.



Definition 5: If object x = and ≠ (where ≠ is < xor >) or < and > w.r.t object y, then object x is called Non-Local.

[jsfisher]

By self identity x = x , y = y , etc...

It does not mean that if x = y from x ... then y = x

Gee, according to the wikipedia link you yourself provided, that's exactly what it means.

x,y relations are non-commutative

Huh? x and y (as you used them) are objects, not relations.

[jsfisher]

Definition 4: If object x = xor ≠ (where ≠ is < xor >) w.r.t object y, then object x is called Local.

Ah! A brand new revision. I see you have reverted back to less than and greater than relations. You also are being a bit sloppy with your formula notation, so I need you to be a bit more precise:

You state "≠ is < xor >". So, in "A ≠ B" I can translate that to "A < xor > B", right? Well, "A < xor > B" is not a valid formula. Did you really mean that "A ≠ B is (A<B) xor (A>B)"?

May I similarly assume that your "= xor ≠" notation was meant as binary relation, call it %, such that A % B is equivalent to (A = B) xor (A ≠ B) ?

If not, what did you mean?

[doronshadmi]

Ah! A brand new revision. I see you have reverted back to less than and greater than relations. You also are being a bit sloppy with your formula notation, so I need you to be a bit more precise:

You state "≠ is < xor >". So, in "A ≠ B" I can translate that to "A < xor > B", right? Well, "A < xor > B" is not a valid formula. Did you really mean that "A ≠ B is (A<B) xor (A>B)"?

May I similarly assume that your "= xor ≠" notation was meant as binary relation, call it %, such that A % B is equivalent to (A = B) xor (A ≠ B) ?

If not, what did you mean?

I mean that x is considered as local wr.t y if for example:

x = .

y = ___

x = y (.__ , _._ , __.)

x ≠ y ( in this case x < y ( . __) or x > y( __ .))

EDIT:

In general:

If only a one relation between x and y satisfies the obseravtion of y through x , then x is local.

If only more than a one relation between x and y satisfies the obseravtion of y through x , then x is non-local.

[jsfisher]

I mean that x is considered as local wr.t y if:

x = .

y = ___

x = y (.__ , _._ , __.)

x ≠ y ( in this case x < y ( . __) or x > y( __ .))

You didn't understand my question, did you? So rather than explain your notation, even when I provided you the most likely interpretation, you dash off into your world of lines and dots.

Let's take this quoted post as your final word on local. According to you, for one thing to be local with respect to another thing, the first thing must be a dot and the other thing must be a line.

So, only the dot is local, and only with respect to a line.

Is that really what you wanted to say? How about answering my question about your notation, using words, without asides nor irrelevant symbols.


ETA: I see you've edited your original post. Doesn't matter. It still doesn't address the original question.

[The Man]

x = .

y = ___

By self identity x = x , y = y , etc...


It does not mean that if x = y from x point of view (example: _.__) then y = x from y point of view (Y < and > x from y point of view).

x,y relations are non-commutative

That is exactly what it means, that they are the same. If as you say "Y < and > x from y point of view" then Y ≠ X and X ≠ Y. Your problem seems to be you conflating a point within a line as being equal to or by some strange application in your thinking a “self identity” with that line from the perspective of the point. However that is easily dismissed as you assert that a line is not a collection of points, making your above augment irrelevant. If the line Y does not contain points, one of which being X, then X can never be part of Y. So what do you want to give up now your claim that a line is not a collection of points or your bizarre dot and dash diagrams intended to shown circumstances where point X is part of line Y?


ETA: Even if your were to concede that a line Y is a collection of points one of which being X that only means that Y contains X and not that X=Y from any point of view.

[doronshadmi]

ETA: I see you've edited your original post. Doesn't matter. It still doesn't address the original question.

Do you mean to this part?

In general:

If only a one relation between x and y satisfies the obseravtion of y through x , then x is local.

If only more than a one relation between x and y satisfies the obseravtion of y through x , then x is non-local.

If you get the idea, then please address it by your style.

[doronshadmi]

then X can never be part of Y

X = .

Y = ___


X is not a part of Y.
X = Y from the point of view of X (example: _._)

Y is not a part of X.
Y < and > X from the point of view of Y (example: _._)

Again, < and > is not ≠ (please see http://forums.randi.org/showpost.php?p=4221768&postcount=759 ).

[jsfisher]

Do you mean to this part?

No. That's not even a part of the post I was quoting.

Here's my question again:

You make use of what I'll call compound operators, like "< XOR >". I simply want to know what you explicitly mean by this. Since you tend to be inconsistent in your notation, and you conflate concepts, it is only reasonable I insist on a little precision, here.

If I use this compound operator with a pair of operands, A and B, I get:

A < xor > B

That is not a well-formed formula. It doesn't have meaning. However, the way I think you meant it, the way I'd interpret it coming from anyone with any sort of consistency in there notation would be:

(A < B) xor (A > B)

Is that what you would mean by it?

[doronshadmi]

No. That's not even a part of the post I was quoting.

It is, please look again at http://forums.randi.org/showpost.php?p=4221901&postcount=770 .

If you can adress it by your style, than for the first time we will have something in common.

[doronshadmi]

(A < B) xor (A > B)

Is that what you would mean by it?

Yes.

[jsfisher]

It is, please look again at http://forums.randi.org/showpost.php?p=4221901&postcount=770 .

If you can adress it by oyur style, than for the first time we will have something in common.

You need to address your notation issue, first.

[ddt]

No. That's not even a part of the post I was quoting.

Here's my question again:

You make use of what I'll call compound operators, like "< XOR >". I simply want to know what you explicitly mean by this. Since you tend to be inconsistent in your notation, and you conflate concepts, it is only reasonable I insist on a little precision, here.

If I use this compound operator with a pair of operands, A and B, I get:

A < xor > B

That is not a well-formed formula. It doesn't have meaning. However, the way I think you meant it, the way I'd interpret it coming from anyone with any sort of consistency in there notation would be:

(A < B) xor (A > B)

Is that what you would mean by it?
Of course, you're spot-on. And, as you undoubtedly realize, you'll never get a satisfactory answer from doron as his mathematical notation is consistently wrong out of deliberate ignorance (deliberate because he refuses to enroll in college courses) and his English his deliberately obtuse (deliberate because he's been called often enough on it).

The concept you describe is called lifting - at least, it was when I used to dabble in Squiggol. You lift a function/operator which operates on simple things to a higher-order function - one which operates on functions - which applies the original function to the results of the two function arguments. In a functional programming definition, lifting would be the function:
lift :: (c -> d -> e) -> (a -> b -> c) -> (a -> b -> d) -> (a -> b -> e)
lift f g h x y = f (g x y) (h x y)
Of course, in Squiggol we'd write lifting with some squiggly symbol over the operator being lifted. Doron, wallowing in his ignorance, probably doesn't even see the difference between the lifted and the not-lifted operator. Not that he'd understand my or your comments in the first place.

[jsfisher]

Yes.

Great! Progress. Here's Definition 4, revision 3 again:

Definition 4: If object x = xor ≠ (where ≠ is < xor >) w.r.t object y, then object x is called Local.

Let's parse the IF-part:

object x = xor ≠ w.r.t object y ==>
(object x = w.r.t. object y) xor (object x ≠ w.r.t object y)

The not-equal part has it's own set of questions. I'd rather not ask them now and create more distractions, so I'll focus on just the equal part.

(object x = w.r.t. object y) ==>
Object x is the same as with respect to object y.

Doron, do you see how your use of "w.r.t." makes nonsense out of that sentence? Either object x is the same as object y or it is not. So, now the next question that needs an answer: What do you actually mean by "object x = w.r.t. object y"?

[doronshadmi]

Great! Progress. Here's Definition 4, revision 3 again:

Definition 4: If object x = xor ≠ (where ≠ is < xor >) w.r.t object y, then object x is called Local.

Let's parse the IF-part:

object x = xor ≠ w.r.t object y ==>
(object x = w.r.t. object y) xor (object x ≠ w.r.t object y)

The not-equal part has it's own set of questions. I'd rather not ask them now and create more distractions, so I'll focus on just the equal part.

(object x = w.r.t. object y) ==>
Object x is the same as with respect to object y.

Doron, do you see how your use of "w.r.t." makes nonsense out of that sentence? Either object x is the same as object y or it is not. So, now the next question that needs an answer: What do you actually mean by "object x = w.r.t. object y"?

Let us do it in this way:

"satisfies the obseravtion of y through (or by) x" means that we can conclude something about x, which is based on how it is observing y.


Definition 4: If only a one relation between x and y satisfies the obseravtion of y through x , then x is local.

An example:

x = .

y= ___

We have state _._

In this case y is obsereved by x as:

x=y (we do not need more than a one relation) and by definiton 4 we can conclude that x is Local.



Definitionn 5: If only more than a one relation between x and y satisfies the obseravtion of y through x , then x is non-local.

An example:

x = ___

y= .

We have state _._

In this case y is obsereved by x as:

x < and > y (we need more than a one relation) and by definiton 5 we can conclude that x is Non-local.



Can you address 4 and 5 by using your style?

[jsfisher]

Definition 4: If only a one relation between x and y satisfies the obseravtion of y through x , then x is local.


Nope, no good on two counts.

#1: You need to be precise what you mean by "observation of y through x". Points and lines, for example, do not conventionally observe each other; inanimate objects generally aren't, well, animate.

#2: You are still going to end up with the same problem you had with your original definition. Nothing will be local.

[doronshadmi]

Nope, no good on two counts.

#1: You need to be precise what you mean by "observation of y through x". Points and lines, for example, do not conventionally observe each other; inanimate objects generally aren't, well, animate.

Again:

"satisfies the obseravtion of y through (or by) x" means that we can conclude something about x, which is based on how it is observing y (where we are x's point of view).

Please tell me what is not clear here?

This is the whole point of my work, to observe mathematical subjects from different points of view, where no point of view is exclusive.

Nothing is animated here because in any stage we are aware of us as the observers.


#2: You are still going to end up with the same problem you had with your original definition. Nothing will be local.

Definition 4: If only a one relation between x and y satisfies the obseravtion of y through x , then x is local.

Please tell me why do you think that x is non-local according to definition 4?

Please tell me what is not clear in the examples of definitions 4 and 5 in http://forums.randi.org/showpost.php?p=4222803&postcount=781 ?

Thanks

[jsfisher]

Again:

"satisfies the obseravtion of y through (or by) x" means that we can conclude something about x, which is based on how it is observing y (where we are x's point of view).

Please tell me what is not clear here?


I thought I did.

Take for example a point. It is simply a point. It doesn't have eyes or a sense of touch. It is just a point. So, your statement, "we can conclude something about x, which is based on how it is observing y", makes no sense.

Abstract objects don't observe other abstract objects.

[doronshadmi]

Abstract objects don't observe other abstract objects.

Do you aware of the fact that what you wrote in this quote is based on your observation (and so is "a point is simply a point")?

Again: Nothing is animated here because in any stage we are aware of us as the observers.


Anyway, here is another version of definitions 4 and 5:

x and y are objects.

Definition 4: If only a one relation is needed in order to define the relations from x to y, then x is local.

Definition 5: If more than a one relation is needed in order to define the relations from x to y, then x is non-local.

[jsfisher]

Do you aware of the fact that what you wrote in this quote is based on your observation (and so is "a point is simply a point")?

Are you aware the properties of a point are independent of my observation of them?

Be that as it may, my observation is irrelevant to your definition. You said, "something about x, which is based on how it is observing y". Clearly you have one inanimate object observing another.

Anyway, here is another version of definitions 4...:

Definition 4: If only a one relation is needed in order to define the relations of x to y, then x is local.

No good. Since multiple independent relations are always possible, you are back to nothing is local.

[doronshadmi]

Are you aware the properties of a point are independent of my observation of them?
Do you aware of the fact that what you wrote above depends on your observation?

Your observation is simply external to the obsereved object and it is not exclusive exactly as my internal observation through the object is not exclusive.

If you wish to be objective, you must not use any exclusive observation.

By not using exclusive observations, we may develop our understanding of the researched.


No good. Since multiple independent relations are always possible, you are back to nothing is local.

Yes good, because we don't care about the other possibilites if only a one relation is nedeed in order to define the relations from x to y.

[jsfisher]

Do you aware of the fact that what you wrote above depends on your observation?

Your observation is simply external to the obsereved object and it is not exclusive exactly as my internal observation through the object is not exclusive.

If you wish to be objective, you must not use any exclusive observation.

By not using exclusive observations, we may develop our understanding of the researched.

This is irrelevant to the point I raised.

Yes good, because we don't care about the other possibilites if only a one relation is nedeed in order to define the relations from x to y.

Do you know what "multiple independent relations" means? Your most recent version of Definition #4 allows nothing to be local.

[The Man]

<snip> An example:

x = .

y= ___

We have state _._

In this case y is obsereved by x as:

x=y (we do not need more than a one relation) and by definiton 4 we can conclude that x is Local. <snip>


But your one relation is not valid unless you are claiming..

. = ___



which would also mean

___ = .


If it takes more the one relation to relate Y to X then the same applies to the relationship of X to Y.

[Apathia]

This is the whole point of my work, to observe mathematical subjects from different points of view, where no point of view is exclusive.

There's a level at which I certainly aplaud your intent.
But your "mathematical" program to achieve this seems to me to leave quantity in a n indeterminate state. And you have never given clear answers and qualifications about this.

So I keep asking a stupid question in different ways.
Here it is again.
Applying your Organic Natural Number system to my bank account,
what is it that insures that everyone who keeps an account of my funds arrives at the same figure?
Or does ONN mean that the amount in my account is in a flux where different observers are summing it up to different amounts without adding or subtracing a single penny from the till?
Non-Locally I have billions in my account, don't I?
Why can't I claim them?

Indulge me please. Answer my stupid question.
What it amounts to is
Is number or quantity determinable? Can an amount be defined and even definitive till it changes?

Please do not smack me again with another link to a post or .pdf that doesn't answer my question.

[doronshadmi]

But your one relation is not valid unless you are claiming..

. = ___



which would also mean

___ = .


If it takes more the one relation to relate Y to X then the same applies to the relationship of X to Y.

There is state _._

From . point of view . = ___

From ___ point of view ___ < and > .

You simply used an external point of view of . and ___ relations.

I used an internal point of view of . and ___ relations.

No point of view is exclusive during research and this is the main idea of my work.

[doronshadmi]

There's a level at which I certainly aplaud your intent.
But your "mathematical" program to achieve this seems to me to leave quantity in a n indeterminate state. And you have never given clear answers and qualifications about this.

So I keep asking a stupid question in different ways.
Here it is again.
Applying your Organic Natural Number system to my bank account,
what is it that insures that everyone who keeps an account of my funds arrives at the same figure?
Or does ONN mean that the amount in my account is in a flux where different observers are summing it up to different amounts without adding or subtracing a single penny from the till?
Non-Locally I have billions in my account, don't I?
Why can't I claim them?

Indulge me please. Answer my stupid question.
What it amounts to is
Is number or quantity determinable? Can an amount be defined and even definitive till it changes?

Please do not smack me again with another link to a post or .pdf that doesn't answer my question.

The amount of your bank account depends on your knowledge about it, and your knowledge is changeable by observation.

If you observation is focused only on "how many"? you have to ask yourself "what observation gives this knowledge"?

I have found that this observation is not less than Relation\Element Interaction, where the relation in this case is + and the Element is some agreed unit measurement.

In this case, the order between the units is ignored and only the sum (the amount) is considered.

But this amount cannot be known unless REI is used.

I have found that Relation is always non-local where an Element can be local or non-local during REI.

[doronshadmi]

Do you know what "multiple independent relations" means? Your most recent version of Definition #4 allows nothing to be local.
"multiple independent relations" means that you have used + relation (which cannot be local) in order to conclude something about local elements.

In this case you have used the name "relation" in order to describe the observed elements.

For example:

* is an element (not the name "element")

__ is a relation (not the name "relation")



* name of a relation (where a name is an element w.r.t a relation)
|
* name of a relation (where a name is an element w.r.t a relation)
|
* name of a relation (where a name is an element w.r.t a relation)
|
* etc …

[Skeptic]

Stop the ******** with dots and lines and asterisks. Use normal notation that everyone understands.

But if he *does* do that, it will become obvious even to him that he has nothing of value to say about mathematics.

Essentially Doron's "contribution" to mathematics is (a) a new, cumbursome and unclear notation; and (b) the belief that since his notation makes even basic ideas impossible to understand, the new notation had unearthed some "deep problem" in mathematics which he alone can "solve".

[doronshadmi]

Quote:
Stop the ******** with dots and lines and asterisks. Use normal notation that everyone understands.

Since you are using only elements in "*******", each one of them is totally isolated, and we do not get a researchable framework.

The same holds for "__ __ __ __" because by using only relations, nothing is related and we do not get a researchable framework.

Some example:

2 34.675 pI 0 1 ... is ***** ...

/ + - ^ ... is __ __ __ __ ...

By this particular example, without REI there is no Arithmetic.


... which he alone can "solve".
Nobody can solve or "solve" things alone, because being alone is total isolation (a state of singularity) where nothing can be reseached.

Things are solved or "solved" by REI (Relation\Element Interaction).

[nathan]

Knowing doron's liking for venn diagrams, I think doron's trying to define:
doron_equal (a,b) := normal_equal (normal_intersection (a, b), a)

The intersection of a point and a line going through the point, is the point, so:
doron_equal (point, line-through-point) is true.

The intersection of a line and a point on the line, is not the line, so:
doron_equal (line, point-on-line) is false.

The intersection of a point and a line not though the point is neither the point nor the line, so:
doron_equal (line, point-off-line) is false
doron_equal (point, line-off-point) is false


Not really profound though, is it?

[doronshadmi]

Let us research _._ interaction

In this case . cannot be (in interaction) AND (not in interaction) with ___
but ___ can be (in interaction) AND (not in interaction) with .

If intersection is used, it can be understood only it terms of . (a point)

For example:

The intersection of a line and a point on the line, is not the line, so:
doron_equal (line, point-on-line) is false.

It is false because only a point of view through a point is considered.

So the term "interaction" (which enables to observe _._ from different points of view) has to be used for better conclusions.

[jsfisher]

"multiple independent relations" means that you have used + relation (which cannot be local) in order to conclude something about local elements.


Nope.

It refers to exactly what you don't want, but will always have, for any two objects. Your latest Definition #4 makes nothing local.

[doronshadmi]

Nope.

It refers to exactly what you don't want, but will always have, for any two objects. Your latest Definition #4 makes nothing local.

Yep.

It refers by relations, where any relation is non-local.

You simply uses relations between elements, where in your case the names of the elements are "relations" (as shown in http://forums.randi.org/showpost.php?p=4225191&postcount=793 ).

You have to define your building blocks before you use them; otherwise they are used as hidden assumptions, which have an influence on the conclusions.

x and y are objects.

Definition 4: If only a one relation is needed in order to define the relations from x to y, then x is local.

An example:

x = .

y= ___

We have state _._


x=y (we do not need more than a one relation in order to define the relations from x to y) and by definiton 4 we can conclude that x is Local.


Definition 5: If more than a one relation is needed in order to define the relations from x to y, then x is non-local.

An example:

x = ___

y= .

We have state _._


x < and > y (we need more than a one relation in order to define the relations from x to y) and by definiton 5 we can conclude that x is Non-local.

x≠y (we do not need more than a one relation in order to define the relations from x to y) and by definition 4 we can conclude that x is Local (by using ≠ we do not use the simultaneity of more than a one relation (like < and >, = and < , > and = , etc ...))

[nathan]

Let us research _._ interaction

In this case . cannot be (in interaction) AND (not in interaction) with ___
but ___ can be (in interaction) AND (not in interaction) with .

If intersection is used, it can be understood only it terms of . (a point)

For example:


It is false because only a point of view through a point is considered.

So the term "interaction" (which enables to observe _._ from different points of view) has to be used for better conclusions.

I suspected I was merely data mining random noise. Your response to my prediction suggests I was right about that.

[doronshadmi]

I suspected I was merely data mining random noise. Your response to my prediction suggests I was right about that.
Prediction is not an issue here (at this stage).

[Apathia]

The amount of your bank account depends on your knowledge about it, and your knowledge is changeable by observation.

If you observation is focused only on "how many"? you have to ask yourself "what observation gives this knowledge"?

I have found that this observation is not less than Relation\Element Interaction, where the relation in this case is + and the Element is some agreed unit measurement.

In this case, the order between the units is ignored and only the sum (the amount) is considered.

But this amount cannot be known unless REI is used.

I have found that Relation is always non-local where an Element can be local or non-local during REI.

I had a professor back in the seventies who was highly innefective because he was incapable of answering student questions. When a question was asked of him, he'd either answer with something irrelevant to the question or repeat word for word what he'd said before. This was very aggravating.

I'm never able to get an answer from you that is spot on, except perhaps for "no." But then I don't know where I have strayed because the fog has not cleared.

But I suppose the following is as close as it is going to get.
In this case, the order between the units is ignored and only the sum (the amount) is considered.

By conventional arithmetic my bank accounbt is saved from chaos. That there is an established method that yields an agreed amount to all accontants.
By these conventions, I can't go withdraw billions that aren't there, because I say that no quantity in a set is complete and definite.

Accounting counts only what you call the "serial" aspect of number. Contextual to that usage you can talk "complete" and "definite."

Of course that doesn't mean the amount is fixed. Change happens.
Empericist that I am, I agree that the bottom line is observation.

I've said before that you have a differerent concept of what is number.
You've denied that. But when it comes to what you call your "parallel" aspects of Organic Natural Numbers, you really do. It's not the way most people think of number. Most don't get to the concept of number till things are counted.

I have so many questions like:
When and why is a number reckoned but not counted?
Is any number always "metaphysically" present so that it is the virtual amount or a virtual member of any set?

But it seems I should ask Professor Holbrook these questions.

[jsfisher]

Yep.

It refers by relations, where any relation is non-local.

How very odd that you are telling me what I meant by my words. No, that isn't what I meant by "multiple independent relations", nor is it what could be deduced from any conventional reading of the phrase.

However, it is obvious, now, that your attempt to define local and non-local is circular since your definition for local and non-local depends on the meaning of relation which in turn depends on the meaning of non-local. Your definition for local is vacuous and circular. Neither attribute is good alone; you have them both.

You are not making things any better.

[doronshadmi]

However, it is obvious, now, that your attempt to define local and non-local is circular since your definition for local and non-local depends on the meaning of relation which in turn depends on the meaning of non-local.

Please read definitions 4 and 5 more carefully. They are about locality or non-locality of objects and not of relations.

The non-locality of relations is obvious (please see page 3 in http://www.geocities.com/complementarytheory/UR.pdf ).

1) Any relation is non-local.

2) An object called Point cannot be but local.

3) An object called Line segment can be non-local.

(2) and (3) are determined by the number of relations that are needed in order to define the relation from object x to object y.

Nothing is circular here because I do not use Relation's inherent non-locality, but I use the number of the relations that are needed.

Furthermore, in an expression like "< AND >" , "<" and ">" are objects if observed from "AND" relation.

[doronshadmi]

I had a professor back in the seventies who was highly innefective because he was incapable of answering student questions. When a question was asked of him, he'd either answer with something irrelevant to the question or repeat word for word what he'd said before. This was very aggravating.

I'm never able to get an answer from you that is spot on, except perhaps for "no." But then I don't know where I have strayed because the fog has not cleared.

But I suppose the following is as close as it is going to get.


By conventional arithmetic my bank accounbt is saved from chaos. That there is an established method that yields an agreed amount to all accontants.
By these conventions, I can't go withdraw billions that aren't there, because I say that no quantity in a set is complete and definite.

Accounting counts only what you call the "serial" aspect of number. Contextual to that usage you can talk "complete" and "definite."

Of course that doesn't mean the amount is fixed. Change happens.
Empericist that I am, I agree that the bottom line is observation.

I've said before that you have a differerent concept of what is number.
You've denied that. But when it comes to what you call your "parallel" aspects of Organic Natural Numbers, you really do. It's not the way most people think of number. Most don't get to the concept of number till things are counted.

I have so many questions like:
When and why is a number reckoned but not counted?
Is any number always "metaphysically" present so that it is the virtual amount or a virtual member of any set?

But it seems I should ask Professor Holbrook these questions.

In pure mathematics there is no process (time is not involved) here but immediate knowledge of the account value, which is based on the relations between elements, where the elements are agreed units.

So, serial or parallel observations have no influence on the number of the agreed units.

Serial and parallel observations have an influence about the knowladge of the exact location of each local object that can be found in your account.

In both cases REI is needed where Relation is naturally non-local and Element is Local or Non-local according to the observation.

[nathan]

Prediction is not an issue here (at this stage).

ha ha! That you cannot tell that I was talking about predicting behaviour and not maths speaks volumes.

It was my (internalized) prediction, it was fulfilled. I conclude you are indistinguishable from a random noise generator.

[nathan]

In pure mathematics there is no process (time is not involved) here but immediate knowledge of the account value, which is based on the relations between elements, where the elements are agreed units.

So, serial or parallel observations have no influence on the number of the agreed units.

Serial and parallel observations have an influence about the knowladge of the exact location of each local object that can be found in your account.

In both cases REI is needed where Relation is naturally non-local and Element is Local or Non-local according to the observation.

ha ha! good one. If time is not involved, then there's no distinguishing serial and parallel observations. You're a hoot!

[nathan]

1) Any relation is non-local.

2) An object called Point cannot be but local.

3) An object called Line segment can be non-local.



Calling a tail a leg does not make it a leg.

[Apathia]

In pure mathematics there is no process (time is not involved) here but immediate knowledge of the account value, which is based on the relations between elements, where the elements are agreed units.

So, serial or parallel observations have no influence on the number of the agreed units.

Serial and parallel observations have an influence about the knowladge of the exact location of each local object that can be found in your account.

In both cases REI is needed where Relation is naturally non-local and Element is Local or Non-local according to the observation.

Yup. I should have asked Professor Hollbrook.

I'll take it that my account is not in Non-Local flux, though you never really have assured me that it isn't.
Also, then, I have no idea what your ONNs are, since now quantity and number have nothing to do with "Serial" and "Parallel" Complementation.

Again, as the pathetic Mad Gardener, I thought I saw something I could make sense of in your ONNs, but what I really saw was an aurora on a stick.

I really should put all this on ignore and get on with my life.

[doronshadmi]

One claims that internal observation from x to y is subjective and does not provide the correct knowledge about x or y.

In that case let us use an external (objective) observation of x and y.

x = point

y = line

z = plane

w = volume

If x is observed through w w.r.t z, then x cannot be but on z XOR not on z.

By observation w x is local w.r.t z.

If y is observed through w w.r.t z, then y can be on z AND not on z.

By observation w y can be non-local w.r.t z.

[nathan]

One claims that internal observation from x to y is subjective and does not provide the correct knowledge about x or y.

In that case let us use an external (objective) observation of x and y.

x = point

y = line

z = plane

w = volume

If x is observed through w w.r.t z, then x cannot be but on z XOR not on z.

By observation w x is local w.r.t z.

If y is observed through w w.r.t z, then y can be on z AND not on z.

By observation w y can be non-local w.r.t z.

hurrah! my intersection hypothesis still fits the data.

[doronshadmi]

hurrah! my intersection hypothesis still fits the data.

No it does not because by your hypothesis:


The intersection of a line and a point on the line, is not the line, so:
doron_equal (line, point-on-line) is false.

So (If y is observed through w w.r.t z, then y can be on z AND not on z) is false by your hypothesis.

y on z is (by your intersection hypothesis) is a point (x) on y.

By using observation w, y is non-local w.r.t x (or z) and it does not fit your intersection hypothesis.

[doronshadmi]

quantity and number have nothing to do with "Serial" and "Parallel" Complementation.
Exactly.

But they have a lot to do with local-objects distinction under a given cardinal (where cardinality is not the sum of the local objects but it is the number of the local objects that are involved in order to get the sum).


I have no idea what your ONNs are

ONNs are the result of Non-locality\locality complementation, where:

1) Relation is always non-local w.r.t to an object.

2) An object called Point is always local w.r.t an object.

3) An object called Line can be non-local w.r.t an object.

Without Relation\Element(=Object) Interaction, no sum or no cardinality can be found.

[nathan]

No it does not because by your hypothesis:



So (If y is observed through w w.r.t z, then y can be on z AND not on z) is false by your hypothesis.

y on z is (by your intersection hypothesis) is a point (x) on y.

By using observation w, y is non-local w.r.t x (or z) and it does not fit your intersection hypothesis.

excellent! you've returned to form and unable to follow a simple function definition.

[Apathia]

But they have a lot to do with local-objects distinction under a given cardinal (where cardinality is not the sum of the local objects but it is the number of the local objects that are involved in order to get the sum).

So, any set is incomplete, because at the moment of encounter you can choose to ignore certain elements that are in the set or reckon certain elements that aren't?

I ask how many oranges are in the bowl. I see three. But you say four, because you count one that happens to be on the table, or could be on the table, if we brought it in from the Kitchen.

The set containing the square root of 144:
I say its sole member is 12, and that as {12} it is complete and all that it is.
You say no, because there are always other numbers in the environment one could choose to include in that set.

If this is what you wish to assert ...

[doronshadmi]

excellent! you've returned to form ...
Yes,

I use forms like any formal system.

[doronshadmi]

I see three ...

You see tree becuse you have used your memory as a relation between objects.

Without it three does not exist.

[nathan]

Yes,

I use forms like any formal system.

yay! doron the cargo cultist. You don't accurately use the form and you're not a formal system.

[Apathia]

You see tree becuse you have used your memory as a relation between objects.

Without it three does not exist.

But maybe your memory is different. You see four.
Or you see that orange in the Kitchen in the bowl on the table in the dining room.
And the square root of 144 is 58463 to your memory.

So a set is is a pourous container that can contain any amount without any way of determining a definite quantity.

Its all a spaced out, washed out, weed way of speaking.

The funny thing is that I agree with you about the primacy of the empirical.
But what you are doing is washing out mathematical language so my three can be your four.
You chuck away conventional language which is able to speak of collections as complete in relation to the specific definition of their classes.

Having no conventions of definition, does not yield creativity, but worthless slush.

[The Man]

There is state _._

From . point of view . = ___

From ___ point of view ___ < and > .

You simply used an external point of view of . and ___ relations.

I used an internal point of view of . and ___ relations.

No point of view is exclusive during research and this is the main idea of my work.
You do understand that “exclusive” means excluding something? Your “external point of view” that you ascribe to me excludes your “internal point of view” that you ascribe to only to yourself; you are actually the one using “exclusive” points of view. None of which refutes the fact that you do not use “=” as self identity as you claimed to do, but in fact confirms that you do not. It also confirms that you consider (although will not admit) “___” to be a collection of “.” otherwise you would not have noted “From . point of view . = ___” and “From ___ point of view ___ < and > . “ as an “internal point of view” (claiming “.” is internal to “___”).

[The Man]

I have come to the conclusion that “the main idea of my work” as expressed by doron is simply his attempt to exploit his own misunderstanding of basic geometry and by specifically doing what he claims he does not do as well as not doing what he specifically claims he does do.

If we consider an (X, Y, Z) coordinate system from some origin and a line segment starting at coordinates (4, 3, 1) and ending at (4, 3, 10). When viewing this segment along the Z axis it has no apparent spatial extent or would appear as a point at (X, Y) coordinates (4, 3) which is why he equates the line to a point (as he puts it) WRT that point. Unfortunately a line is definitively not a point although it could appear as one from some “exclusive” point of view. In this case along the Z axis, which excludes the spatial extent of the line along that axis. So it would seem that doron’s “main idea of my work” is specifically exploiting such “exclusive” points of view while claiming “No point of view is exclusive during research and this is the main idea of my work” as well as his own misunderstanding of basic geometry whereby he makes assertions like a point equals some line with the line being greater then and less then that point which is not contained within that line. Much the same way he claims to use “=” as self identity yet demonstratively shows that he does not.

[doronshadmi]

But maybe your memory is different. You see four.

Memory (as I mean it) is simply a relation between objects.

Without it any object is isolated of any other object.

So cardinality (the number of objects) or a sum of isolated values cannot be found unless memory\object (or REI) are interact with each other.

[doronshadmi]

"Exclusive" means that no other points of view are considered, in order to understand a thing.

In both cases (

(the internal point of view of _._ case, where different conclusions are found if _._ is observed from ___ to . (___ < AND > .) or _._ is observed from . to ___ (. = ___))

OR

(the external point of view, where . and ___ are not observed w.r.t to each other, but a volume observation is used to observe . and __ w.r.t a plane)

) no observation or observation's conclusion is exclusive.

[doronshadmi]

I have come to the conclusion that “the main idea of my work” as expressed by doron is simply his attempt to exploit his own misunderstanding of basic geometry and by specifically doing what he claims he does not do as well as not doing what he specifically claims he does do.

If we consider an (X, Y, Z) coordinate system from some origin and a line segment starting at coordinates (4, 3, 1) and ending at (4, 3, 10). When viewing this segment along the Z axis it has no apparent spatial extent or would appear as a point at (X, Y) coordinates (4, 3) which is why he equates the line to a point (as he puts it) WRT that point. Unfortunately a line is definitively not a point although it could appear as one from some “exclusive” point of view. In this case along the Z axis, which excludes the spatial extent of the line along that axis. So it would seem that doron’s “main idea of my work” is specifically exploiting such “exclusive” points of view while claiming “No point of view is exclusive during research and this is the main idea of my work” as well as his own misunderstanding of basic geometry whereby he makes assertions like a point equals some line with the line being greater then and less then that point which is not contained within that line. Much the same way he claims to use “=” as self identity yet demonstratively shows that he does not.

which is why he equates the line to a point (as he puts it) WRT that point.

No, in _._ case no extra dimension like a plane or a volume are used, but only the subjective point of view of __ w.r.t . or the subjective point of view of . w.r.t ___

A subjective point of view means that only the self dimension of an object is used in order to observe a thing.

In this case it is obvious that _._ case cannot be observed but as . = ___ from . view point.

It is also obvious that _._ case can be observed as ___ < AND > . from ___ view point.


Your examples are based on a local point of view of the observed objects, which is used by you as an exclusive point of view, that prevents from you to get non-locality.

You still get a line as as something that is defined by sub-objects (like points, for example).

Furthermore, you get a volume as a collection of points where each point has an x,y,z location.

From this collection of local objects, you have no choice but to conclude anything and everything by using the exclusive point of view of locality.

Again, a line segment is not made by any sub-objects, and its non-composed property is exposed if :

. is observed through ___ (let us call it a subjective viewpoint of ___ from ___ to .)

OR

a volume observation is used to observe . and __ w.r.t a plane (let us call it an objective viewpoint of . and __)

There is another problem in your case, because a concept like "atom" is not understood by you as a non-composed thing.

By this problem alone, you are not able to get my work.

Again, the main idea of my work is to understand the researchable by not using exclusive observations.

[Apathia]

Memory (as I mean it) is simply a relation between objects.

Without it any object is isolated of any other object.

So cardinality (the number of objects) or a sum of isolated values cannot be found unless memory\object (or REI) are interact with each other.

http://h1.ripway.com/Apathia/40268~The-Persistence-of-Memory-c-1931-Posters.jpg
The Persistance of Memory
by Salvador Dali

[doronshadmi]

http://h1.ripway.com/Apathia/40268~The-Persistence-of-Memory-c-1931-Posters.jpg
The Persistance of Memory
by Salvador Dali
Which is both parallel and serial w.r.t to the observed objects (I like this picture, thank you).

In that case "the art of non-exclusive observation" has to be developed.

It is quite clear that the community of mathematicians of the past 3000 years do not use "the art of non-exclusive observation" because observation is not considered as a significant factor of any known mathematical activity (external observation is exclusive in this community because mathematicians are not trained by other observations, which are not external).

[doronshadmi]

I think that we can learn here something from what I call "the paradox of the anthropologist"

An anthropologist has to understand a thing from within (to use a subjective point of view) and from external point of view (to use an objective point of view of a thing).

In that case he must learn how to combine internal AND external observations, otherwise his knowledge about the researched thing may be trivial.

I do not think that what I call "the paradox of the anthropologist" is limited to any particular research, and in this case also mathematicians have to deal with this paradox in order to develop the mathematical science.

[The Man]

"Exclusive" means that no other points of view are considered, in order to understand a thing.

In both cases (

(the internal point of view of _._ case, where different conclusions are found if _._ is observed from ___ to . (___ < AND > .) or _._ is observed from . to ___ (. = ___))

OR

(the external point of view, where . and ___ are not observed w.r.t to each other, but a volume observation is used to observe . and __ w.r.t a plane)

) no observation or observation's conclusion is exclusive.


So now finding that you do use “excusive” points of view in this “main idea of my work” where you stated “No point of view is exclusive during research” you now change it to “no observation or observation's conclusion is exclusive”. An obvious and ineffective dodge since in both the example observations and conclusions you gave you indicate the dependent elements of each point of view that are exclusive from the other.

[The Man]

No, in _._ case no extra dimension like a plane or a volume are used, but only the subjective point of view of __ w.r.t . or the subjective point of view of . w.r.t ___


So you assert that you are excluding other or “extra dimension like a plane or a volume” in oder to cliam “No point of view is exclusive during research and this is the main idea of my work.”


A subjective point of view means that only the self dimension of an object is used in order to observe a thing.

In this case it is obvious that _._ case cannot be observed but as . = ___ from . view point.

It is also obvious that _._ case can be observed as ___ < AND > . from ___ view point.


“A subjective point of view means that only the self dimension of an object is used in order to observe a thing” again admitting you depend on points of view that are exclusive or exclude certain dimensions to fit your preferred assertion at that time. You do understand that the statements you made confirm my assertions in the post you quoted that your “as . = ___ from . view point.” is based on you excluding the “the self dimension” of the line and thus its spatial extent. When you respond to a post with “No” it is usually customary to assert how that post was inaccurate not, as you have done, clearly assert that the post was in fact accurate.



Your examples are based on a local point of view of the observed objects, which is used by you as an exclusive point of view, that prevents from you to get non-locality.

Technical they are your examples and your exclusive points of view (as you assert above) I was simply explaining them in terms of standard geometry.


You still get a line as as something that is defined by sub-objects (like points, for example).

Furthermore, you get a volume as a collection of points where each point has an x,y,z location.

From this collection of local objects, you have no choice but to conclude anything and everything by using the exclusive point of view of locality.


No, a volume could be considered a collection of lines, planes or even smaller volumes, you are the only one using exclusive points of view then claiming you do not while considering others to be limited to some exclusive view.


Again, a line segment is not made by any sub-objects, and its non-composed property is exposed if :

. is observed through ___ (let us call it a subjective viewpoint of ___ from ___ to .)


In the example I gave the line segment (4, 3, 1) to (4, 3, 10) is comprised of any number of smaller line segments or an infinite number of points. As an example it can be considered two line segments (4, 3, 1) to (4, 3, 5) and (4, 3 ,5) to (4, 3, 10). Elementary school children have no problem with these fundamental concepts that you seem to struggle with so (shall we say) ‘pointlessly’.


OR

a volume observation is used to observe . and __ w.r.t a plane (let us call it an objective viewpoint of . and __)


Again with your dependence on exclusive points of view.

There is another problem in your case, because a concept like "atom" is not understood by you as a non-composed thing.


Your primary problem remains that simply because you choose to call something an “atom” does not make it a “non-composed thing” or mean that one can not break it down into subunits.


By this problem alone, you are not able to get my work.


By this problem alone you continue to waste your time trying to exploit the exclusive points of view that you claim you do not use, the use of “=” as not a self identity which you profess to use it as and your fundamental misunderstanding of standard geometry that would be explained in any grade school course.


Again, the main idea of my work is to understand the researchable by not using exclusive observations.


Again you lie to yourself more effectively then you lie to others, this entire post of yours clearly demonstrates the dependence of your “main idea of my work” upon such exclusive points of view and observation.

[Apathia]

Doron,

I'm glad you liked the Dali.
Let's go for another surreal scene.


New Math

Teacher: "Rodney, what's the square root of 144000?"

Rodney: "1200"

Danica: Raises hand and shouts, "That's wrong! it's an irrational number. 379.473 roughly."

Teacher: "Danica, you're rude! Did you use a calculator? Calculators are not allowed in this class. And everybody listen up. Rodney's answer is perfectly acceptable, because in The New Organic Paradigm of Mathematics there are no exclusively correct answers."

Danica: "But excuse me, Mr. Kruft. When I put on my test paper that 1 followed by a decimal point and a non ending string of 9s equals 2, you marked it as wrong. How can it be wrong if there are no wrong answers?"

Teacher: "I said there were no exclusively correct answers. I didn't say there weren't any exclusively incorrect answers."

[doronshadmi]

So now finding that you do use “excusive” points of view in this “main idea of my work” where you stated “No point of view is exclusive during research” you now change it to “no observation or observation's conclusion is exclusive”. An obvious and ineffective dodge since in both the example observations and conclusions you gave you indicate the dependent elements of each point of view that are exclusive from the other.

In my opinion, a research must not be limited to any exclusive observation.

It means that you can use any single or combinations of observations, in order to get to different conclusions that are related to the same examined things.

[doronshadmi]

Technical they are your examples and your exclusive points of view (as you assert above) I was simply explaining them in terms of standard geometry.

By standard geometry a line segment is defined by at least a pair of points.

In that case a line segment depends on the existence of points, and not vice versa.

In other words, standard geometry uses locality as the exclusive building-block of Geometry.

By using this exclusive observation, you cannot get non-locality, and indeed you did not understand my post.


No, a volume could be considered a collection of lines, planes or even smaller volumes, you are the only one using exclusive points of view then claiming you do not while considering others to be limited to some exclusive view.

A volume, a plane or a line can non-local w.r.t to each other, whare a point cannot be but local w.r.t to any other dimension.

Since you get a volume, a plane of a line as things that are based on sub-things, you cannot get their non-local nature in addition to their local nature.

In other words, your obvervation is closed under a one and only one exclusive observation, which is locality.



In the example I gave the line segment (4, 3, 1) to (4, 3, 10) is comprised of any number of smaller line segments or an infinite number of points. As an example it can be considered two line segments (4, 3, 1) to (4, 3, 5) and (4, 3 ,5) to (4, 3, 10). Elementary school children have no problem with these fundamental concepts that you seem to struggle with so (shall we say) ‘pointlessly’.
Bravo !

And by define a line segment as collection of sub-elements, you are unable to get it as a non-local object. The reason: you are using again locality as exclusive observation.


Your primary problem remains that simply because you choose to call something an “atom” does not make it a “non-composed thing” or mean that one can not break it down into subunits.

The meaning of "atom" is exactly "non-composed" or "indivisible". Actually an atomic state is the opposite concept of anything that is based on sub-elements (and please do not give me the physical atomic state as an example, because the name "atom" was originally given to it because people thought that it is non-composed or indivisible).


By this problem alone you continue to waste your time trying to exploit the exclusive points of view that you claim you do not use, the use of “=” as not a self identity which you profess to use it as and your fundamental misunderstanding of standard geometry that would be explained in any grade school course.

By this problem alone you cannot see beyond the exclusive observation of locality that is learned as the one and only one point of view of the mathematical science (geometry or not) for the past 3000 years.

By learning non-locality in addition to non-locality, the exclusive local observation is going to lose its exclusivity.

Non-locality is a new thing and cannot be found (yet) in any already established school that teaches locality as the one and only one possible observation of Math.


Again you lie to yourself more effectively then you lie to others, this entire post of yours clearly demonstrates the dependence of your “main idea of my work” upon such exclusive points of view and observation.

By using the Cyclops' local-only observation you cannot even lie to yourself, because you are under the illusion of one and only one observation.

[jsfisher]

By standard geometry a line segment is defined by at least a pair of points.

Wrong. A line can be determined by two distinct points.

In that case a line segment depends on the existence of points, and not vice versa.

Wrong again.

In other words, standard geometry uses locality as the exclusive building-block of Geometry.

That's quite a leap. There is also the word, locality, in there for which you have no serviceable definition.

By using this exclusive observation, you cannot get non-locality, and indeed you did not understand my post.

Well, perhaps if you provided valid premises, reasonable definitions, and a correct logic, this might change.

[The Man]

In my opinion, a research must not be limited to any exclusive observation.

It means that you can use any single or combinations of observations, in order to get to different conclusions that are related to the same examined things.
Again you admit that your notions depend on “exclusive” observations and now relate that the “ different conclusions that are related to the same examined things.” you assert are simply dependent on your use of “any single or combinations of observations” and therefore not intrinsic characteristics of “the same examined things” but just consequences of “any single or combinations of observations” “that you can use”. Thank you for supporting my assertions with your opinion.

[The Man]

By standard geometry a line segment is defined by at least a pair of points.
In that case a line segment depends on the existence of points, and not vice versa.

Says whom? A Point is just a geometrical abstraction, physically the Planck distance would be the lower limit of any spatial considerations. If you are arguing against the geometrical abstraction of points then you should remind yourself that you utilize that abstraction as well.

In other words, standard geometry uses locality as the exclusive building-block of Geometry.

By using this exclusive observation, you cannot get non-locality, and indeed you did not understand my post.

This is your fundamental confusion with standard geometry; a line is the nonlocal expression of points, just as a plane is the nonlocal expression of lines and a volume the nonlocal expression of planes and a hyper volume the nonlocal expression of volumes…ECT. Even as I mentioned before since any line segment can be considered to be comprised of smaller line segments a line segment is also the nonlocal expression of those smaller line segments. The same can be said of planes, volumes, hyper volumes and other aspects of geometry save the point which has no extents. If you bother to study geometry you would know this but you simply choose to make unfounded and irrelevant assertion to help you rationalize the time you have spent thinking you have been developing something new when you have simply been wasting your time.

A volume, a plane or a line can non-local w.r.t to each other, whare a point cannot be but local w.r.t to any other dimension.

It all depends on how one is geometrically defining ‘local’ in that application, another result of your misunderstanding of ‘local’ when applying it to geometry.

Since you get a volume, a plane of a line as things that are based on sub-things, you cannot get their non-local nature in addition to their local nature.
In other words, your obvervation is closed under a one and only one exclusive observation, which is locality.
Bravo !

And by define a line segment as collection of sub-elements, you are unable to get it as a non-local object. The reason: you are using again locality as exclusive observation.


As usual for you, the facts are precisely the opposite of what you say. Because of those subcomponents any local expression, a given line segment plane or volume, can also be a nonlocal expression of some combination of line segments, planes of volumes. You are the only one on this thread who “cannot get” it and your “observation is closed under” your own need to think you have come up with something new.


The meaning of "atom" is exactly "non-composed" or "indivisible". Actually an atomic state is the opposite concept of anything that is based on sub-elements (and please do not give me the physical atomic state as an example, because the name "atom" was originally given to it because people thought that it is non-composed or indivisible).
What you mean much the same way that you now think line segments, planes and volumes are indivisible?
We have been over this before on another thread (do you need me to refer you to that post and the link you continue to ignore?). The term “Atom” can also refer to something in its simplest form. A single line segment is its simplest form, this does not mean that said segment cannot be divided into smaller segments. 2 is the simplest form of 1 + 1 but it can still be replace or has a self identity with 1 + 1 it is just that 1 + 1 is a more complex form of 2. Another point that was addressed in that other thread in term rewiring, which you continue to ignore yet claim to use “=” as self identity, the foundation of term rewriting. With your assertion of “=” as self identity and “. = ___” that means anywhere we find “.” In your assertions we can rewrite it as “___”.



By this problem alone you cannot see beyond the exclusive observation of locality that is learned as the one and only one point of view of the mathematical science (geometry or not) for the past 3000 years.

By your sad devotion to your misinterpretation of basic geometry you have convinced yourself that you have found something new in what has been there all the time if you just bothered to look at it.

By learning non-locality in addition to non-locality, the exclusive local observation is going to lose its exclusivity.

Ironic, since your own assertions are based solely on what “local observation” you choose to use at that given time as exemplified by “From . point of view . = ___” while “From ___ point of view ___ < and > .”. You will see this only when you finally allow your selective conclusions from your exclusive points of view not to exclude you from seeing that non-locality has been a fundamental part of geometry from its inception.



Non-locality is a new thing and cannot be found (yet) in any already established school that teaches locality as the one and only one possible observation of Math.

As I have shown above non-locality is very easy to find in standard geometry, you would have to go out of your way not to find it and in fact it is geometry that lets us define what we consider local or nonlocal in some given consideration, but the fact that you miss such a fundamental aspect of geometry is understandable, as you have gone so far out of your way to try and claim you have found something new.

By using the Cyclops' local-only observation you cannot even lie to yourself, because you are under the illusion of one and only one observation.

I have no desire to lie to myself; you are the only one on this thread who seems to find the ability to lie to yourself as an admirable trait. As far as illusions go, that anyone considers (other than yourself) there is “one and only one observation” is an illusion you have created yourself that you ascribe to others yet depend on so intently in your own assertions that “From . point of view . = ___” while “From ___ point of view ___ < and > .” extolling the differences “From . point of view” as “only one observation” and “From ___ point of view” as “only one observation” and exclusive for the other “.”. You remark in this post about your distain for breaking things down in to sub components and have remarked before about exclusive points of view yet your whole approach is based on breaking the “.” and “___” relation of your example down into two (“From . point of view” and “From ___ point of view”) mutually exclusive points of view or sub components. We still might not agree with what you say but your assertion might carry more veracity if it were not so abundantly apparent that even you do not agree with what you say.

[doronshadmi]

Again you admit that your notions depend on “exclusive” observations and now relate that the “ different conclusions that are related to the same examined things.” you assert are simply dependent on your use of “any single or combinations of observations” and therefore not intrinsic characteristics of “the same examined things” but just consequences of “any single or combinations of observations” “that you can use”. Thank you for supporting my assertions with your opinion.

No dear,

I do not support your Cyclops' local-only observation.

[doronshadmi]

a line is the nonlocal expression of points
No dear,

We do not need more than that in order to show that you do not understand non-locality.

The rest of your post is based on this misunderstanding.

[doronshadmi]

Well, perhaps if you provided valid premises, reasonable definitions, and a correct logic, this might change.

It is in http://www.geocities.com/complementarytheory/UR.pdf and I clearly show in pages 6-7 how step-by-step local-only serial learners like you cannot get non-locality.

[The Man]

No dear,

I do not support your Cyclops' local-only observation.


No dear,

We do not need more than that in order to show that you do not understand non-locality.

The rest of your post is based on this misunderstanding.

Oh dear, such informative and well supported rebuttals from doron, I might feel sullen and smited by them if I did not know it was just him calling me “dear” that makes me feel so soiled, I have to go shower now.

[doronshadmi]

Doron,

I'm glad you liked the Dali.
Let's go for another surreal scene.


New Math

Teacher: "Rodney, what's the square root of 144000?"

Rodney: "1200"

Danica: Raises hand and shouts, "That's wrong! it's an irrational number. 379.473 roughly."

Teacher: "Danica, you're rude! Did you use a calculator? Calculators are not allowed in this class. And everybody listen up. Rodney's answer is perfectly acceptable, because in The New Organic Paradigm of Mathematics there are no exclusively correct answers."

Danica: "But excuse me, Mr. Kruft. When I put on my test paper that 1 followed by a decimal point and a non ending string of 9s equals 2, you marked it as wrong. How can it be wrong if there are no wrong answers?"

Teacher: "I said there were no exclusively correct answers. I didn't say there weren't any exclusively incorrect answers."

Wrong example.

Please see again http://forums.randi.org/showpost.php?p=4228228&postcount=813.

ONNs have nothing to do with arbitrary results.

All they show is:

1) How cardinality or sum can befound, in the first place.

2) How order can be in superposition and not in a superposition.

[doronshadmi]

Oh dear, such informative and well supported rebuttals from doron,

Anyone how divides atoms cannot get non-locality.

[drkitten]

Anyone how divides atoms cannot get non-locality.

This is actually true, but not in the way you mean.

Since your notion of "non-locality" is total gibberish, it cannot be "gotten" by anyone at all, regardless of whether or not they divide atoms.

Even you don't "get non-locality," as is amply demonstrated by your complete inability to express what it is in a meaningful way.

[doronshadmi]

This is actually true, but not in the way you mean.

Since your notion of "non-locality" is total gibberish, it cannot be "gotten" by anyone at all, regardless of whether or not they divide atoms.

Even you don't "get non-locality," as is amply demonstrated by your complete inability to express what it is in a meaningful way.

Please read the updated version of http://www.geocities.com/complementarytheory/UR.pdf

[drkitten]

Please read the updated version of http://www.geocities.com/complementarytheory/UR.pdf

Read it. It's still meaningless gibberish, without reason or foundation.

It's not right. It's not even wrong. And there are no traces of mathematical reasoning in it whatsoever.

[jsfisher]

It is in http://www.geocities.com/complementarytheory/UR.pdf and I clearly show in pages 6-7 how step-by-step local-only serial learners like you cannot get non-locality.


No point reading all the way to page 6. Your definitions failed on page 2, remember?

By the way, please stop spamming this forum posting and re-posting and re-posting URL's to your website.

[Apathia]

Wrong example.

Please see again http://forums.randi.org/showpost.php?p=4228228&postcount=813.

ONNs have nothing to do with arbitrary results.

All they show is:

1) How cardinality or sum can befound, in the first place.

2) How order can be in superposition and not in a superposition.

Another non-answer.
You don't even address what I'm having difficulty with.

[doronshadmi]

Another non-answer.
You don't even address what I'm having difficulty with.
Yes I did.

You took ONNs as something that can give different results of sum or cardinality from different observations.

It is wrong, ONNs sum or cardinality are not changed under different observations.

Given identities, ONNs are the different ids that can simultaneously be found between (superpositions of ids of the observed objects) AND (distinct id of each observed object).

It can be done only by Non-locality\Locality Interaction, and ONNs are exactly the result of this interaction.

If you get Non-locality\Locality Interaction, only then you can get ONNs.

Also you ignored http://forums.randi.org/showpost.php?p=4230971&postcount=827 (which is not connected to ONNs cardinality or sum).

[doronshadmi]

No point reading all the way to page 6. Your definitions failed on page 2, remember?

Do you get http://forums.randi.org/showpost.php?p=4225755&postcount=804 ?

Also you ignored http://forums.randi.org/showpost.php?p=4230971&postcount=827 .

Without them you cannot get my work.

By the way, please stop spamming this forum posting and re-posting and re-posting URL's to your website.

It is not spamming because I change UR.pdf as a result of the dialog here (and in other places).

[doronshadmi]

Read it. It's still meaningless gibberish, without reason or foundation.

It's not right. It's not even wrong. And there are no traces of mathematical reasoning in it whatsoever.

You have missed http://forums.randi.org/showpost.php?p=4230971&postcount=827 .

Did you read the current UR.pdf?

[doronshadmi]

I am probably more visual spatial learner ( http://www.gifteddevelopment.com/Product_Marketing/UDB/udb.htm ) , which may be one of the reasons of the misunderstandings between us.

[nathan]

Did you read the current UR.pdf?

Did you indicate your edits?

[doronshadmi]

Did you indicate your edits?
The edits are not independent of the work, exactly as no branch is independent of its tree.

Please read all of UR.pdf and only then you can ask questions about its branches (details).

Serial step-by-step observation of my work will not give the right knowledge about its content exactly as serial step-by-step observation does not give the right knowledge about Tree(whole)\Branch(part) relations.

Only reduction by analysis is the right way not to understand my work, and until now only reduction by analysis (step-by-step serial reasoning) was used by anyone of the participators that replied to my posts in this forum.

So I have to ask my self "what is the reason that only a research style that is based only on step-by-step serial reasoning is used by the participators here"?

My answer is:

Each one of them is an editorial sequential learner that has no ability to get things beyond step-by-step serial reasoning.

[nathan]

The edits are not independent of the work, exactly as no brach is independent of its tree.

Please read all of UR.pdf and only then you can ask questions about its branches (details).

No, we're not going to play spot the difference. If you want to engage in a discussion here, you're going to have to discuss it here.

[Apathia]

Yes I did.

You took ONNs as something that can give different results of sum or cardinality from different observations.

It is wrong, ONNs sum or cardinality are not changed under different observations.

Given identities, ONNs are the different ids that can simultaneously be found between (superpositions of ids of the observed objects) AND (distinct id of each observed object).

It can be done only by Non-locality\Locality Interaction, and ONNs are exactly the result of this interaction.

If you get Non-locality\Locality Interaction, only then you can get ONNs.

Also you ignored http://forums.randi.org/showpost.php?p=4230971&postcount=827 (which is not connected to ONNs cardinality or sum).

Thanks for finaly being direct about that
I was confused by some of your previous responses that seemed to indicate that cardinality was relative.

Previously I thought I understood where you got your Organic Natural Neumber in Local/Non-Local Interaction but couldn't understand what seemed like an insistance that the quantities of sets are always incomplete because elements not counted should be reckoned.

Well, I own my confusion.

I guess now that when you insist a set isn't "complete" what you mean is that it's not the final statement, last word, or exclusive configuration. A new set based on different relations or rules can replace or include it.
This is a trivial observation. It's not even hidden. We convene new collections all the time, even in ordinary mathematics.
(Though conventional Mathematics does not tag non-local, not counted elements, as your ONNs seem to do.)
With your unique usage of the word, I was expecting something out of the ordinary.

Having owned my own confusion, I ask you to be aware that your unique way of using words quickly creates misunderstandings. And they're often the same ones over and over.
I'm still guessing here. Struggling to interpret. It's very likely that I have again misundersood you.
I hope not.

[doronshadmi]

I guess now that when you insist a set isn't "complete" what you mean is that it's not the final statement, last word, or exclusive configuration. A new set based on different relations or rules can replace or include it.

Not at all.

I am talking about totality (completeness) and non-totality (incompleteness).

At the moment that you understand that any cardinal is the result of at least non-locality\locality interaction, you immediately understand (without using any step-by-step serial observation) that only locality is complete and total isolation, where only-non-locality is complete and total connectivity.

At the moment that you get these complete and total opposite states you immediately understand that any result that is based on non-locality\locality interaction is stronger than total (complete) isolation and weaker than total (complete) connectivity.

If you cannot get immediately that non-locality\locality interaction cannot be total (because it is an intermediate result of opposite totalities' interaction), you cannot get it at all, and again, no step by step serial reasoning can help you here.

In other words, if you have no abilities of a visual spatial learner ( http://www.gifteddevelopment.com/Product_Marketing/UDB/udb.htm ) you have no chance to get my mathematical work, and it does not matter how many step-by-step serial efforts you are using in order to get it.

I hope that I am very clear to you now.

[Apathia]

I am Immediately lost in the fog.
I can see some buildings, vaguely.
I think I can see how this "Totality" and "Non-Totality" pertains to your views on the Infinite.
But I still don't get how this applies to the "completeness" of a set.

You're right. I'm probably never going to get this, if i don't get it already, because our mental hardware isn't running the same software.

[doronshadmi]

I am Immediately lost in the fog.
I can see some buildings, vaguely.
I think I can see how this "Totality" and "Non-Totality" pertains to your views on the Infinite.
But I still don't get how this applies to the "completeness" of a set.

You're right. I'm probably never going to get this, if i don't get it already, because our mental hardware isn't running the same software.
If you understand that any set cannot be defined unless it is a result of non-locality\locality interaction (where this interaction cannot be but an intermediate result of opposite totalities, called total-isolation and total-connectivity) then you can understand why any set is incomplete by definition.

[jsfisher]

Do you get http://forums.randi.org/showpost.php?p=4225755&postcount=804 ?

Also you ignored http://forums.randi.org/showpost.php?p=4230971&postcount=827 .

Without them you cannot get my work.

Neither prior post repairs your defective definitions. Depending on which version you are currently promoting, either everything is local or nothing is. You cannot define, characterize it, or even talk about it in coherent English, so please do not attempt to shift the blame for getting it.

[drkitten]

You have missed http://forums.randi.org/showpost.php?p=4230971&postcount=827 .

Did you read the current UR.pdf?

I did, immediately after you suggested it, and it was still gibberish. The problematic definitions (#4 and 5, IIRC) are still problematic to the point of nonsensical.

[drkitten]

I am probably more visual spatial learner ( http://www.gifteddevelopment.com/Product_Marketing/UDB/udb.htm ) , which may be one of the reasons of the misunderstandings between us.

No, I can assure you, that's not the issue. I'm a professional teacher, and I deal with visual-spacial learners all the time.

The reasons for the misunderstandings are that you are wrong, your writings are nonsensical, and you completely fail either to recognize or adjust for that.

[Apathia]

If you understand that any set cannot be defined unless it is a result of non-locality\locality interaction (where this interaction cannot be but an intermediate result of opposite totalities, called total-isolation and total-connectivity) then you can understand why any set is incomplete by definition.

Yes, Doron, "incomplete" in the sense, definition, and context in which you are using it above.

But you understand don't you that the word, "complete" is used in a conventional way in which a set is said to be complete.
The set of all natural numbers greater than 2 and less than 4, {3}, is complete containing all it's defintion requires.

Now if you wish to insist that there is no such sense a set is complete, you claim a confusing dogmatism.

What I wish of you is a clarity of definition and qualification that shows how a set in your terminology is incomplete, but to its purpose is complete.

Of course no set is in its content the Totality. But it may be total as per its defined and required content.

You do make that distinction in usage, don't you?

[doronshadmi]

Neither prior post repairs your defective definitions. Depending on which version you are currently promoting, either everything is local or nothing is. You cannot define, characterize it, or even talk about it in coherent English, so please do not attempt to shift the blame for getting it.
No jsfisher,

You clearly show that you do not get non-locality, and in this case you do not have any meaningful thing to say abuot it.

[doronshadmi]

Yes, Doron, "incomplete" in the sense, definition, and context in which you are using it above.

But you understand don't you that the word, "complete" is used in a conventional way in which a set is said to be complete.
The set of all natural numbers greater than 2 and less than 4, {3}, is complete containing all it's defintion requires.

Now if you wish to insist that there is no such sense a set is complete, you claim a confusing dogmatism.

What I wish of you is a clarity of definition and qualification that shows how a set in your terminology is incomplete, but to its purpose is complete.

Of course no set is in its content the Totality. But it may be total as per its defined and required content.

You do make that distinction in usage, don't you?

{3} is researchable exactly because it is a result that is stronger than total isolation and weaker than total connectivity.

Actually your ability to define the member of set {3} as the thing that is greater than 2 and smaller than 4, is exactly because 2 and 4 are also results that are stronger than total isolation and weaker than total connectivity.

At the moment that you are able to research, you are not dealing with the complete.

Maybe this analogy can help here:

Totally white is complete.

Totally black is complete.

But there is no such a thing like totally grey, because given any grey, there are more grays that are not that grey.

In we know it exactly because we understand that any given grey is the result of Black\White interaction, that cannot be complete (total) as Black or White are.

[doronshadmi]

I'm a professional teacher, and I deal with visual-spacial learners all the time.
Yes, you deal with them by translating their immediate understanding to the traditional step-by-step serial reasoning, which can be analyzed only by cutting the parts from the whole.

In other words, your professionalism as a step-by-step teacher is the best way to not get visual spatial learners in their terms (which is not a step-by-step learning, and therefore can get things that you as a step-by-step observer, can never get).


The reasons for the misunderstandings are that you are wrong, your writings are nonsensical ...
Is this "detailed" criticism is used by you on visual-spatial learners in your class, which get at conclusions that do not fit your step-by-step observation, as you do to me here in this forum?

[jsfisher]

No jsfisher,

You clearly show that you do not get non-locality, and in this case you have any meaningful thing to say abuot it.


Provide a reasonable definition for non-locality. Is that such an impossible task for you?

[doronshadmi]

Provide a reasonable definition for non-locality. Is that such an impossible task for you?
It is clearly reasonable.

In order to get it you have to open your second eye (and you can do it only by yourself).

Until this very moment you are using one and only one eye.

[jsfisher]

It is clearly reasonable.

In order to get it you have to open your second eye (and you can do it only by yourself).

Until this very moment you are using one and only one eye.


All your recent attempts at a definition for non-locality carry the defect that either everything is non-local or nothing is non-local. No binocular vision effect, including looking cross-eyed, can change that.

[doronshadmi]

All your recent attempts at a definition for non-locality carry the defect that either everything is non-local or nothing is non-local.

You do not know what non-locality is ( http://forums.randi.org/showpost.php?p=4233919&postcount=865 ) remember?

So how can you recognize this "defect"?

For you a line is determined by points, and in that case your recognition of a non-local object (which is, by the way, not a relation, but you do not know the difference) does not hold water ( as can be seen in http://forums.randi.org/showpost.php?p=4225755&postcount=804 ).

[Apathia]

{3} is researchable exactly because it is a result that is stronger than total isolation and weaker than total connectivity.

Actually your ability to define the member of set {3} as the thing that is greater than 2 and smaller than 4, is exactly because 2 and 4 are also results that are stronger than total isolation and weaker than total connectivity.

At the moment that you are able to research, you are not dealing with the complete.

Maybe this analogy can help here:

Totally white is complete.

Totally black is complete.

But there is no such a thing like totally grey, because given any grey, there are more grays that are not that grey.

In we know it exactly because we understand that any given grey is the result of Black\White interaction, that cannot be complete (total) as Black or White are.

This is pretty much what I thought I was understanding of you.
Now you are continuing to assert "Complete (total)" in the context of your Local/Non-Local Interaction.
Fine. It's just that slow people like me will tend to think you're wanting to include the number 59 in the set of all natural numbers between 2 and 4, just because it is out there in Non-Local Land.

But aside from that, let's look at your interesting analogy above.
Would you then characterize the numeral three as similar to "grey," not being a difinitive point-like value, but a smudge?
It would fit an earlier interpetation I had of your ONNs as involving not just a nomnitive sense but an adjectival one.

[doronshadmi]

It's just that slow people like me will tend to think you're wanting to include the number 59 in the set of all natural numbers between 2 and 4, just because it is out there in Non-Local Land.
Again, non-locality\locality interaction does not change the fact that 59 is not between 2 and 4.

But aside from that, let's look at your interesting analogy above.
Would you then characterize the numeral three as similar to "grey," not being a difinitive point-like value, but a smudge?
Number 3 is a local number, but any number (including non-local numbers like 0.999...[base 10]) is the result of non-locality\locality interaction.

It would fit an earlier interpetation I had of your ONNs as involving not just a nomnitive sense but an adjectival one.
I do not understand what do you mean by that.

[jsfisher]

You do not know what non-locality is ( http://forums.randi.org/showpost.php?p=4233919&postcount=865 ) remember?


All that has been established is that you don't know what non-locality is.

Prove me wrong. Provide a real definition for local and non-local.

[doronshadmi]

All that has been established is that you don't know what non-locality is.

Prove me wrong. Provide a real definition for local and non-local.
You are not wrong or right here, because you get exactly nothing about my theory.

You did your best in order to take http://www.geocities.com/complementarytheory/UR.pdf down.

You have failed.

You are unable to face it.

End of story ( http://forums.randi.org/showpost.php?p=4233224&postcount=852 ).

[Apathia]

Number 3 is a local number, but any number (including non-local numbers like 0.999...[base 10]) is the result of non-locality\locality interaction.

I do not understand what do you mean by that.

I suppose the integer 3 would be a definite point value. But it appears from your diagrams that what you call "non-local numbers" are "hazy" in value, so to speak.

Your ONNs based in Local/Non-Local Interaction, seem to me to involve an adjectival use of numbers. There are different kinds of 3. For example there is the 3_3, which is our ordinary serial 3. And there is the 2_3 of which only 2 of the 3 is serialized or counted, while 1 of the 3 reamains parallel and not included in the count.
(Yes I realize the circularity in what I just wrote.)

[jsfisher]

You are not wrong or right here, because you get exactly nothing about my theory.

You did your best in order to take http://www.geocities.com/complementarytheory/UR.pdf down.

You have failed.

You are unable to face it.

Huh? I have done nothing to take down your website or any document it contains. This claim of yours is bogus. Why are you lying?

End of story ( http://forums.randi.org/showpost.php?p=4233224&postcount=852 ).

That post has nothing to do with my issue.

All I have asked for is a simple definition of what you mean by local and by non-local. They are your terms; why cannot you define them?

[Skeptic]

Jfisher -- don't take it personally. Doron isn't lying--he really believes you did your best to take his site down.

To paranoids like Doron, every server hiccup or bad internet connection which made their mastepiece unavailable for five minutes is a plot by "enemies" to "silence" them. When the connection is restored, it means Doron had, once again, defeated the forces of evil out to get him.

They usually blame whomever it is that they're arguing with on the internet at the time for being behind the evil plot. That's why you were chosen.

[doronshadmi]

Jfisher -- don't take it personally. Doron isn't lying--he really believes you did your best to take his site down.

To paranoids like Doron, every server hiccup or bad internet connection which made their mastepiece unavailable for five minutes is a plot by "enemies" to "silence" them. When the connection is restored, it means Doron had, once again, defeated the forces of evil out to get him.

They usually blame whomever it is that they're arguing with on the internet at the time for being behind the evil plot. That's why you were chosen.

Skeptic,

Your understanding of "take it down" is trivial.

As an evolutionist I believe that any idea has to survive criticism before it can be accepted, and even if it is accepted it is still opened to criticism, and so are the fundamental accepted notions of the mathematical science.

My arguments were improved exactly because of jsfisher's criticism and I thank him for that, but at the moment that his criticism is under loop, it is not affective anymore.

Jsfisher's last posts are criticism under loop that do not follow anymore in details about my arguments. In that case I do not define his criticism as something that can be used in order to reexamine my arguments.

As for you skeptic,

You did not contribute any meaningful thing to this forum accept for chip , armature and shallow psychology.

[doronshadmi]

Huh? I have done nothing to take down your website or any document it contains. This claim of yours is bogus. Why are you lying?
Are you kidding?

Who is talking about any website?

I am talking about your current under-loop criticism about the content of UR.pdf.


That post has nothing to do with my issue.

It does not work that way.

You have to show in details exactly why http://forums.randi.org/showpost.php?p=4233224&postcount=852 has nothing to do with your issue.


All I have asked for is a simple definition of what you mean by local and by non-local. They are your terms; why cannot you define them?
The answer was fully given in UR.pdf.

http://forums.randi.org/showpost.php?p=4225755&postcount=804 clearly shows that you do not get it.

From this point you are under loop and your criticism has lost its effective influence on my work.

I am not going to continue the dialog with you on this subject unless you convince me that you are not under loop.

A good point to start with is to reply to anything that was written in http://forums.randi.org/showpost.php?p=4233961&postcount=868 (including its links) and not only to its first sentence (as you did in http://forums.randi.org/showpost.php?p=4234292&postcount=871 ).

EDIT:

Another suggestion:

Please provide your definitions for Non-locality and Locality.

[Skeptic]

Well, that's true, Doron -- they laughed at Galileo, they laughed at Einstein, and they laugh at you. The problem is, they also laughed at creationists, flat-earthers, free-energy cranks, and at Bozo the clown. Chances are about a million to one that you're one of the clowns, not one of the geniuses.

Skeptic,

Your understanding of "take it down" is trivial.

Ah yes, I keep forgetting you keep using words in ways nobody else does, and then pretend that somehow proves you to be superior because people can't undestand you. But, 99% --or, more accurately, 100%--of the time, the reason people cannot undestand you is not because you're smarter or more profound than them, but simply because your writing is unclear and uses words in ridiculous fashion. Just because you're incoherent doesn't mean you're more intelligent. If anything, the opposite is probably the case.

You have to show in details exactly why http://forums.randi.org/showpost.php...&postcount=852 has nothing to do with your issue.

He doesn't have to do a damn thing. YOU are suggesting the theory, YOU have to show why it's worth the paper it's printed on. Why do you think anybody has to jump through your hoops just so you'll deign to discuss what the heck it is your theory is talking about with them? If you don't want to discuss it, don't. It's not as if there's anything to it except for vague redefinitions of obvious concepts, which you think are incredibly important for some reason.

How much time did you spend on this nonsense? Months? Years? Decades? Whatever it is, cut your losses: any day less you spend on this nonsensical theory of yours is one day more you have to learn something worthwhile about mathematics. Given the level of mathematical knowledge you've shown so far in your posts, I would suggest, first, a few remedial courses in formal logic, since you obviously have no idea what it's all about.

[nathan]

I am probably more visual spatial learner ( http://www.gifteddevelopment.com/Product_Marketing/UDB/udb.htm ) , which may be one of the reasons of the misunderstandings between us.

huh? I thought everybody thought in images. I'm always visualizing and drawing diagrams of maths, code, data, whatever. Doesn't prevent me explaining stuff to people though.

[doronshadmi]

Well, that's true, Doron -- they laughed at Galileo, they laughed at Einstein, and they laugh at you. The problem is, they also laughed at creationists, flat-earthers, free-energy cranks, and at Bozo the clown. Chances are about a million to one that you're one of the clowns, not one of the geniuses.
Let us be more modest.

They laughed at the first man that suggested negative numbers.



Ah yes, I keep forgetting you keep using words in ways nobody else does, and then pretend that somehow proves you to be superior because people can't undestand you.
Not superior but different.

Is there a special reason why you try to address me by using words like "superior" (megalomaniac),"paranoid", or other symptoms of severe mental disorders?

Your dramatic criticism lead me to guess that this is the case of "ha'posell, be'moomo hoo posell".



But, 99% --or, more accurately, 100%--of the time, the reason people cannot undestand you is not because you're smarter or more profound than them, but simply because your writing is unclear and uses words in ridiculous fashion. Just because you're incoherent doesn't mean you're more intelligent. If anything, the opposite is probably the case
I interpret agreed notions by using non-standard observations of them.

In that case especially professional persons find that they cannot use the agreed body of knowledge in order to understand my non-standard interpretations of the already agreed concepts, methods, axioms, models, etc …


He doesn't have to do a damn thing. YOU are suggesting the theory, YOU have to show why it's worth the paper it's printed on.
I do not agree with you.

Both sides (if they wish to) have to do their best in order to understand each other.

It is not an easy task but there are no shortcuts here.


How much time did you spend on this nonsense?
Currently you are not in a position to say any meaningful thing about my work, unless you argue in details about its content.

[nathan]

It is not an easy task but there are no shortcuts here.

Perhaps you should pay attention to that thought of yours, and stop taking shortcuts.

[doronshadmi]

huh? I thought everybody thought in images. I'm always visualizing and drawing diagrams of maths, code, data, whatever. Doesn't prevent me explaining stuff to people though.
Good.

So please tell me what prevents from you to immediately understand the simple notion that an object like a line segment is not determined by points?

[doronshadmi]

Perhaps you should pay attention to that thought of yours, and stop taking shortcuts.
Please give an example of such a shortcut, taken from http://www.geocities.com/complementarytheory/UR.pdf .

[jsfisher]

So please tell me what prevents from you to immediately understand the simple notion that an object like a line segment is not determined by points?


You don't understand what the sentence, "Two distinct points determine a line", means, do you?

[doronshadmi]

You don't understand what the sentence, "Two distinct points determine a line", means, do you?

I understand and disagree with it becuse no finitely or infinitely many points (where each point is local by nature) can determine a line segment (which is non-local by nature).

The reason is clearly seen in http://www.geocities.com/complementarytheory/UR.pdf .

[Molinaro]

I understand and disagree with it becuse no finitely or infinitely many points (where each point is local by nature) can determine a line segment (which is non-local by nature).

The reason is clearly seen in http://www.geocities.com/complementarytheory/UR.pdf .

But you are not disagreeing with what you quoted. What you quoted means something else entirely and you are poving that you do not understand what it is saying.

You are so hell bent on making your point you don't even realize, or even care, that you talking about something different from what you quoted.

[jsfisher]

Please give an example of such a shortcut, taken from http://www.geocities.com/complementarytheory/UR.pdf .


Consider Definition #3:

Set A is called non-finite if the cardinal of proper subset B of A can be |B| <= |A|.

Probably not what you were expecting as a shortcut, but it represents a shortcut, nonetheless. Doron, you rush so quickly to throw out words, symbols, and pictures, you must not realize the result doesn't mean at all what your want it to mean.

By this definition, all non-empty sets are non-finite.

[doronshadmi]

But you are not disagreeing with what you quoted.

Please explain why my disagreement with line determination has nothing to do with UR.pdf content?

[doronshadmi]

Consider Definition #3:

Set A is called non-finite if the cardinal of proper subset B of A can be |B| <= |A|.

Probably not what you were expecting as a shortcut, but it represents a shortcut, nonetheless. Doron, you rush so quickly to throw out words, symbols, and pictures, you must not realize the result doesn't mean at all what your want it to mean.

By this definition, all non-empty sets are non-finite.

I agree with you. Thank you.


The idea is to say that, not like definition 2 (where the cardinal of proper subset B of A cannot be but |B| < |A|) in definition 3 the cardinal of proper subset B of A is at least |B| < or = |A|.

Let us fix it to:

Definition 3: Set A is called non-finite if the cardinal of proper subset B of A is at least |B| < or = |A|.

[jsfisher]

I agree with you. Thank you.


The idea is to say that, not like definition 2 (where the cardinal of proper subset B of A cannot be but |B| < |A|) in definition 3 the cardinal of proper subset B of A is at least |B| < or = |A|.

Let us fix it to:

Definition 3: Set A is called non-finite if the cardinal of proper subset B of A is at least |B| < or = |A|.


Are you alleging a difference between the relation, "<=", and your shorthand notation, "< or ="? I see no change in meaning in your proposed "fix". Nor do I have any idea what utility you believe the phrase "at least" added to the definition.

By the way, your Definition #2 is also faulty. Be that as it may, though, are you totally unaware that if you successfully define "Property X", it then is unnecessary to define "Property not-X" (aka "Property non-X")?

[nathan]

Please give an example of such a shortcut, taken from http://www.geocities.com/complementarytheory/UR.pdf .

One shortcut is your failing to define your terms, as jsfisher keeps pointing out.

[nathan]

Good.

So please tell me what prevents from you to immediately understand the simple notion that an object like a line segment is not determined by points?

Well done for changing the subject. Bravo for not addressing the issue.

[doronshadmi]

oppss...

[doronshadmi]

Are you alleging a difference between the relation, "<=", and your shorthand notation, "< or ="? I see no change in meaning in your proposed "fix". Nor do I have any idea what utility you believe the phrase "at least" added to the definition.

By the way, your Definition #2 is also faulty. Be that as it may, though, are you totally unaware that if you successfully define "Property X", it then is unnecessary to define "Property not-X" (aka "Property non-X")?

Definition 2: Set A is called finite if the cardinal of proper subset B of A cannot be but |B| < |A|.

Definition 2 says that A is finite if its proper subset cannot be but |B| < |A|

What is not clear here? I do not think that by definition 2 we can conclude that property not-X is non-finite.

Let us try this version of definition 3:

Definition 3: Set A is called non-finite if the cardinal of proper subset B of A can be (|B| < |A|) AND (|B| = |A|).

[jsfisher]

Definition 2: Set A is called finite if the cardinal of proper subset B of A
cannot be but |B| < |A|.

Definition 2 says that A is finite if its proper subset cannot be but |B| < |A|

What is not cleat here?

I didn't say it was uncleat unclear; I said it was faulty. You exclude at least one perfectly ordinary finite set.

Let us try this version of definition 3:

Definition 3: Set A is called non-finite if the cardinal of proper subset B of A can be (|B| < |A|) AND (|B| = |A|).

This is worse. Are we now to the point were you tell me it is all my fault for not understanding what you mean?

[doronshadmi]

I didn't say it was uncleat unclear; I said it was faulty. You exclude at least one perfectly ordinary finite set.



This is worse. Are we now to the point were you tell me it is all my fault for not understanding what you mean?

Forget about the definitions in their current states.

The idea is this:


If a proper subset B of set A cannot be but |B| < |A|, then A is a finite set.

Please write definition 2 in your style.


If a proper subset B of set A can be |B| = |A| in addition to |B| < |A|, then A is a non-finite set.

Please write definition 3 in your style.


If you think that only a one definition is needed in order to distinguish between finite and non-finite sets, then please write the definition.

Thank you.

[jsfisher]

Forget about the definitions in their current states.

The idea is this:


If a proper subset B of set A cannot be but |B| < |A|, then A is a finite set.

Please write definition 2 in your style.

"Cannot be but...." You really like that phrase, don't you? Have you ever considered expressing things in the positive rather than the negative?

That question is rhetorical, by the way. Please just consider it, but don't answer it. The real question is this:

Why are you bothering to define finite and infinite sets at all? Does it come up later in the paper?

[doronshadmi]

"Cannot be but...." You really like that phrase, don't you? Have you ever considered expressing things in the positive rather than the negative?
"Cannot be but ..." is an understatement of "must be ..." and I prefer to use understatements.

The real question is this:

Why are you bothering to define finite and infinite sets at all? Does it come up later in the paper?
It will be come later.

At this stage I wish to clearly distinguish between finite and non-finite sets.

Please answer to http://forums.randi.org/showpost.php?p=4236183&postcount=896 .

[Little 10 Toes]

Forget about the definitions in their current states.
The idea is this:
If a proper subset B of set A cannot be but |B| < |A|, then A is a finite set.

Please write definition 2 in your style.


If a proper subset B of set A can be |B| = |A| in addition to |B| < |A|, then A is a non-finite set.

Please write definition 3 in your style.


If you think that only a one definition is needed in order to distinguish between finite and non-finite sets, then please write the definition.

Thank you.

Without knowing what definition #1 is, I'll take a stab at definition #2.


I will be using the following definitions:

Cardinality: "In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {1, 2, 3} contains 3 elements, and therefore A has a cardinality of 3." Using the example set shown, I will use the notation |A| = 3 .
Subset: "In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide."
Infinite: something that has no end, something that cannot have a value attached to, unmeasurable/uncountable, theoretical, unquantifiable. Example, the smallest/largest number; in geometry, a line.
Finite: something that does have an end, can have a value attached to, measurable/countable, practical, quantifiable. Example: the number of coins in my pocket, the number of grains of sand on a beach; in geometry, a line segment.
(My rough framework of doronshamdi's "definition #2")

Let A be a set.
Set B is a subset of A.


If the cardinality of B is less than the cardinality of set A, then set A is a finite set.

OR


|B| < |A|, then A is finite set.
(/end #2)



But I can immediatly call BS on definition #2 using the following example:
Set X is the set of all positive whole even numbers.
Subset Y is the set of all positive whole even numbers divisible by five.
Using just a small sample of the members of X (2,4,6,8,10), you will see that Y will only have one member.
The definition of subset (see above) states that Y will be included in X.
In fact, even though |Y| < |X|, X is still infinite because I did not limit the members of X.
(My rough framework of doronshamdi's "definition #3")


Let A be a set.
Set B is a subset of A.


If the cardinality of subset B is equal to the cardinality of set A, then set A is a finite set.
If the cardinality of subset B is also less than the cardinality of set A, then set A is a finite set.

Combining the two statements you can get:


If the cardinality of subset B is less than and equal to the cardinality of set A, then set A is a infinite set.

OR


|B| =< |A|, then A is an infinite set.
(/end #3)

Again, I call BS. If |B| < |A|, (meeting both #2 and #3) how can it be both infinite and non-infinite? In addition, how can a value be equal and greater to another value at the same time?

And if you're "At this stage I wish to clearly distinguish between finite and non-finite sets", why don't you give us your definitions of finite and non-finite sets? If you want to use your Local/Non-local relations, make sure you define them first. You know, like people have been asking you to. I'll now go back to my seat in the peanut gallery viewing section of this train wreck.

[RandFan]

I'm going to advise people not to respond to this thread. doronshadmi has a history of being totally incomprehensible and his threads always go for dozens of pages without any progress being made.

Doron, you are misusing common terms.
http://en.wikipedia.org/wiki/Information_entropy
http://en.wikipedia.org/wiki/Multiset

I will not be replying to this thread any more.:rolleyes:

[doronshadmi]

Little 10 Toes,

If we observe a non-local element, its value can be in more than a one relation w.r.t another element.

But this is not the case here.

In this case I am trying to define the difference between finite and non-finite sets, where each member is local (can be distinguished from another member by using only one relation).

Let us use the notion of proper subset in order to distinguish between finite and non-finite sets as follows:

Definition 3: If A is a set and B is some arbitrary proper subset of A, then if |B| cannot be but |B| < |A|, then A is finite.

If we can use definition 3 in order to conclude that anything that does not satisfy it, must be a non-finite set, then definition 3 is enough to distinguish between finite and non-finite sets.

What do you think?

[doronshadmi]

:rolleyes:
Snapshots of some notions may prevent the possibility to realize that they are actually movies (where in this case, no observation is exclusive (where the non-exculsive observation is the result of element or observers' motions w.r.t each other)).

Let us look at:

I'm going to advise people not to respond to this thread. doronshadmi has a history of being totally incomprehensible and his threads always go for dozens of pages without any progress being made.

Doron, you are misusing common terms.
http://en.wikipedia.org/wiki/Information_entropy
http://en.wikipedia.org/wiki/Multiset

I will not be replying to this thread any more.
He clearly likes only notion's snapshots (called also common terms).

[doronshadmi]

If the cardinality of B is less than the cardinality of set A, then set A is a finite set.

This is not my definiton for at least two reasons:

1) Subset is not the same as proper subset.

2) You ignored the term "cannot be but |B| < |A|".

[The Man]

Anyone how divides atoms cannot get non-locality.

I was simply referring to the fact that the term “Atom” is not always used to describe something inadvisable. So let’s look at what you consider to be inadvisable and what you do with it.




And by define a line segment as collection of sub-elements, you are unable to get it as a non-local object. The reason: you are using again locality as exclusive observation.



So you clearly define a line segment as undividable or in your limited use of the term an “Atom”.

Yet you also define a line (or line segment) WRT a point as


There is state _._

From . point of view . = ___

From ___ point of view ___ < and > .


Would you look at that, you have divided “___” into two segments one “<” “.” and one “>” “.”. You are the one who asserts and requires the inadvisability of lines or line segments but then needs to divide them in order to assert the multiple relationships you require for your varying definition of non-locality. Of course since you need to divide what you consider to be indivisible (line or line segment) in order to get the multiple relationships that cause you to define the line or line segment as non-local, by your own assertions then you “cannot get non-locality” as it requires you to divide what you have asserted is inadvisable. To put it succinctly, by your own assertions, in order for you to get non-locality you have to not get non-locality, I must say that I am certainly not surprised.

Again some of us would still disagree with your assertions but no one is likely to agree with your assertions when you can not even clearly demonstrate that you agree with your own assertions. Your whole process appears simply to be you claiming one thing (you use “=” as self identity or a line segment can not be divided into smaller segments) then basing your subsequent assertions on exactly the opposite of what you have claimed. That is just you lying to yourself and trying to lie to us, which is nothing new

[doronshadmi]

Would you look at that, you have divided “___” into two segments one “<” “.” and one “>”

The man,

< and > is true only by simultaneity.

There is no part of ____ that is < than the point and another part of ____ that is > than the point simply because there are no parts in ____

In that case _____ is simultaneously and without any divisions or parts < and > the point.

AND truth table is:

0 0 ---> 0
0 1 ---> 0
1 0 ---> 0
1 1 ---> 1

1 1 ---> True only if there is a one simultaneity between 1,1 .

If _._ state is observed from ___ to . and ___ is an atom, then ___ is
(without any parts or divisions) < AND > .

As long as you don't get this simple beauty, you are unable to get non-locality.

I am certainly not surprised, because all along our dialog all you get is the parts.

[The Man]

The man,

< and > is true only by simultaneity.

There is no part of ____ that is < than the point and another part of ____ that is > than the point simply because there are no parts in ____

In that case _____ is simultaneously and without any divisions or parts < and > the point.

AND truth table is:

0 0 ---> 0
0 1 ---> 0
1 0 ---> 0
1 1 ---> 1

1 1 ---> True only if there is a one simultaneity between 1,1 .

If _._ state is observed from ___ to . and ___ is an atom, then ___ is
(without any parts or divisions) < AND > .

As long as you don't get this simple beauty, you are unable to get non-locality.

I am certainly not surprised, because all along our dialog all you get is the parts.

You are the one dividing it into parts, one < and one >, that those parts are as you put it “simultaneous” is irrelevant you have still distinguished one part “<” form another “>”. I am certainly not surprised that you would bring up simultaneity, the AND truth table while simply claiming “There is no part of ____ that is < than the point and another part of ____ that is > than the point simply because there are no parts in ____” thereby asserting the different parts that you ascribe as “<” and “>” as part of your claim that “there are no parts in ____”. Perhaps you are saying your assertion

There is state _._

From ___ point of view ___ < and > .



is wrong since you now claim…


There is no part of ____ that is < than the point and another part of ____ that is > than the point simply because there are no parts in ____.

So there are no parts to “___” even though you specifically distinguish between some thing (just not a “part”) that is “<” and some thing (just not a “part”) that is “>”. You can call them whatever you choose or not call them whatever you choose, but in the common parlance they are just parts of “___”.




As long as you don't get this simple beauty, you are unable to get non-locality. .

By your own assertion “you are unable to get non-locality”, which does not matter to you as you simply do not care what you assert.

[jsfisher]

It will be come later.

At this stage I wish to clearly distinguish between finite and non-finite sets.


For what purpose? Can you produce some sort of coherent outline for the finished document? Infinite sets is not a trivial concept, and how you intend to use the concept may simplify what constitutes an acceptable definition.

By the way, your use of cardinality in your definitions is problematic. Your use of the relations greater-than and less-than is problematic, too.

[RandFan]

{snip} I could be wrong but I don't see any progress in this thread. The thread is composed of two dozen pages. That would seem to me to be an accurate prediction. Please to correct any error. What progress has been made? Is anyone in agreement with your thesis?

[jsfisher]

I could be wrong but I don't see any progress in this thread. The thread is composed of two dozen pages. That would seem to me to be an accurate prediction. Please to correct any error. What progress has been made? Is anyone in agreement with your thesis?


Can the circumference be used to measure progress?

[The Man]

I could be wrong but I don't see any progress in this thread. The thread is composed of two dozen pages. That would seem to me to be an accurate prediction. Please to correct any error. What progress has been made? Is anyone in agreement with your thesis?



No one that I have read on this thread, so far, agrees with doron and that includes doron himself, since he asserts that he uses “=” as self identity but does not. Claims no point of view is “exclusive” while using “From . point of view . = ___” yet “From ___ point of view ___ < and > .” as points of view that exclude each other. Requires “There is no part of ____ that is < than the point and another part of ____ that is > than the point simply because there are no parts in ____” after asserting in one of his exclusive points of view that “From ___ point of view ___ < and > .” So clearly, RandFan, no one agrees with doron, not even doron.

[RandFan]

Can the circumference be used to measure progress?:D If one travels some distance but ends up at the beginning is that progress? I guess in some sense.

[RandFan]

I've got to be honest. I'm not sufficiently competent to directly refute the ideas. I hesitate to use thesis because I'm not even certain you've advanced such. But I have honestly looked at the OP and and from my limited capability I've got to agree with PixyMisa.

No.

Likely the best response so far.

To the rest I would just like to say, good luck, were all counting on you. ;)

[doronshadmi]

You are the one dividing it into parts,
The man,

It is beyond your absract ability.

Also you have missed http://forums.randi.org/showpost.php?p=4228045&postcount=810 .

EDIT: Again, anyone who gets atom as a composed thing does not get non-locality.



So there are no parts to “___” even though you specifically distinguish between some thing (just not a “part”) that is “<” and some thing (just not a “part”) that is “>”. You can call them whatever you choose or not call them whatever you choose, but in the common parlance they are just parts of “___”.

Look at this (AND connective):



= 0 0 --> F
_ = 0 1 --> F
_ = 1 0 --> F
__ = 1 1 --> T


Get it?

In the case of _._ interaction, ___ is a one and only one thing that is both < AND > w.r.t .

[jsfisher]

Again, anyone who gets atom as a composed thing does not enables to get non-locality.


That is not a very common way to arrange those words.

[The Man]

The man,

It is beyond your absract ability.

Also you have missed http://forums.randi.org/showpost.php?p=4228045&postcount=810 .

EDIT: Again, anyone who gets atom as a composed thing does not get non-locality.




Look at this (AND connective):

Just what is connected by that connective? can you say “parts”?




= 0 0 --> F
_ = 0 1 --> F
_ = 1 0 --> F
__ = 1 1 --> T


Get it?


So one part FALSE AND one part FALSE results in FALSE

One part FALSE AND one part TRUE also results in FALSE

One part TRUE AND one part FALSE likewise results in FALSE

One part TRUE AND one part TRUE results in TRUE

I got that a long time ago studying Boolean logic. When are you going to “Get it?”



In the case of _._ interaction, ___ is a one and only one thing that is both < AND > w.r.t .

Sure one thing where one part is “<” “.” is TRUE (in your notation “ _ = 0 1” ) and another part is “>” “.” is TURE (in your notation “_ = 1 0” only then is “< AND >” TRUE. However you assert.




There is no part of ____ that is < than the point and another part of ____ that is > than the point simply because there are no parts in ____


So by your own assertions “< AND > w.r.t .” results in “ = 0 0 --> F” since there are no true parts for the connective AND to, well, connect.

Even your stilted and obscure notion belies your assertions with one part “_ = 1 0” combining with another part “ _ = 0 1” for you to get “__ = 1 1 --> T”. Your attempts to obscure your subdivision into parts within the connective AND only resulted in you confirming that you do have parts requiring that connective AND. Even by any broad definition of “Atom” your inclusion of a logical convective in “< AND >” makes it a compound proposition and thus “___” “In the case of _._ interaction” “w.r.t .” is not an “Atom” unless you assert that “Atom” as you use it contains logical connectives which would make them “a composed thing” thus you do “get non-locality” by you own assertions. So is it an “Atom” with the compound proposition “< AND >” meaning you just don’t “get non-locality” by your own assertion? Or is that “__” is simply not an “Atom” and you just do not get the terms “Atom”, “no- locality”, “self identity” and “exclusive” just to name a few?

[doronshadmi]

QUOTE=The Man;4238806]So by your own assertions “< AND > w.r.t .” results in “ = 0 0 --> F” since there are no true parts for the connective AND to, well, connect.[/QUOTE]

No The Man,

I see that you do not get the full picture which is NXOR\XOR (it does not matter if it is false or true, but it does matter both states are actually the same (a non-local atom), or not):

Look at NXOR connective:


= 0 0 --> T
_ = 0 1 --> F
_ = 1 0 --> F
__ = 1 1 --> T


Now Look at XOR connective:


= 0 0 --> F
_ = 0 1 --> T
_ = 1 0 --> T
__ = 1 1 --> F


By reduction without loss of generality ( http://en.wikipedia.org/wiki/Without_loss_of_generality ) we do not care if we deal with 0,1 or T,F.

In that case all we care is if both states are actually the same (a one thing that cannot be divided by any pair (or more) of different states) or not (a thing that cannot be the same under different states)

Furthermore, < AND > in the case of _._ must not be observed by serial observation (along the line w.r.t the point) but by parallel observation w.r.t to the point.

Without the parallel observation, non-locality cannot be understood.


Get it?

Be aware that we are not talking here about non-locality in general, but about the case of a non-local object (a line segment, in this case).

Please this time read also http://forums.randi.org/showpost.php?p=4228045&postcount=810 in order to see another observation that leads us to conclude that a point cannot but a local object, where a line segment can be a non-local object.

[The Man]

No The Man,

I see that you do not get the full picture which is NXOR\XOR (it does not matter if it is false or true, but it does matter both states are actually the same (a non-local atom), or not):

Look at NXOR connective:


= 0 0 --> T
_ = 0 1 --> F
_ = 1 0 --> F
__ = 1 1 --> T


Now Look at XOR connective:


= 0 0 --> F
_ = 0 1 --> T
_ = 1 0 --> T
__ = 1 1 --> F


By reduction without loss of generality ( http://en.wikipedia.org/wiki/Without_loss_of_generality ) we do not care if we deal with 0,1 or T,F.

Well you’re the one who brought the truth table up even though you now claim not to care about it.


In that case all we care is if both states are actually the same (a one thing that cannot be divided by any pair (or more) of different states) or not (a thing that cannot be the same under different states)

Speak for yourself, but please try to be more coherent and less self contradictory when you do that.


Furthermore, < AND > in the case of _._ must not be observed by serial observation (along the line w.r.t the point) but by parallel observation w.r.t to the point.

Without the parallel observation, non-locality cannot be understood.

Oops, there’s that exclusive point of view again. So no point of view is exclusive except the “parallel observation” that you require excluding anything “observed by serial observation “. You just can’t help always contradicting yourself, can you?



Get it?

I got it a long time ago and have been saying it since the other thread your entire notion is simply based on just you contradicting yourself and you seem to enjoy it to boot.




Be aware that we are not talking here about non-locality in general, but about the case of a non-local object (a line segment, in this case).

Please this time read also http://forums.randi.org/showpost.php?p=4228045&postcount=810 in order to see another observation that leads us to conclude that a point cannot but a local object, where a line segment can be a non-local object.


Be aware that what I have been and continue to talk about is just you contradicting your self and making excuses. You claim to use “=” as self identity but do not. You claim no point of view is exclusive, yet regularly assert some exclusive point of view as the required missing element for someone to get your notions. You claim that a line or line segment can not be divided then you divide it while simply asserting that you do not care about that division. I’ve said it before and I’ll say it again you will most likely not get anyone to agree with your assertions until you can at least clearly demonstrate that you agree with your assertions.

[doronshadmi]

Well you’re the one who brought the truth table up even though you now claim not to care about it.
In other words you did not get the generalization.


Oops, there’s that exclusive point of view again.
The Man,

Non exclusive means that a conclusion about X is changed by different observations.

In this case, ___ cannot be seen by serial observation, and can be seen by parallel observation.

In other words, we are not limited only to one and only one observation (the serial observation in your case).

By your replies there are two options:

1) No observation.

2) Serial observation, which is used by you as the one and only one point of view of X.

By (2) you are the one who using here an exclusive point of view, because you have no other alternative.

[jsfisher]

Look at NXOR connective:


= 0 0 --> T
_ = 0 1 --> F
_ = 1 0 --> F
__ = 1 1 --> T


Did you mean for there to be an "NXOR between the two operands? Also, didn't you mean for the operands and the result to have a common domain, either all (0,1) or all (F,T)? E.g.,

0 nxor 0 --> 0
0 nxor 1 --> 1
1 nxor 0 --> 1
1 nxor 1 --> 0

And what pray tell do those two NXOR operands represent? Are you saying that " " is equal to 0 (or F) and "_" is equal to 1 (or T)?

...By reduction without loss of generality ( http://en.wikipedia.org/wiki/Without_loss_of_generality ) we do not care if we deal with 0,1 or T,F.

You still don't understand that term, do you?

[The Man]

In other words you did not get the generalization.


The Man,

Non exclusive means that a conclusion about X is changed by different observations. .

Exclusive means to exclude or not include so non exclusive means inclusive, since your observationally dependent conclusions are, well, observational dependent then they exclude those conclusions based on other observations or perspectives. If you want to assert observational dependent conclusions then just call them that, calling them “non exclusive” is inaccurate because by asserting the dependence of the conclusion on the observation you also assert it’s exclusion of some other conclusion that would have been drawn from some other observation.

Since you are now asserting observational (or perspective dependent) conclusions I guess you now agree with what I had always said on the other thread that your assertions and ascriptions (local and non-local) are just a matter of perspective.




In this case, ___ cannot be seen by serial observation, and can be seen by parallel observation.

In other words, we are not limited only to one and only one observation (the serial observation in your case). .

So you limit non-locality to one particular perspective that you call “parallel observation” to claim “we are not limited only to one and only one observation”. Even in just two sentences you can not agree with yourself.

Just what is it that you claim to be seeing in “parallel” for “__” it couldn’t be “.” could it? Since you claim that “__” is not comprised of “.”. However I am sure if you had written another sentence about “__” you would have contradicted yourself on that as well.



By your replies there are two options:

1) No observation.

2) Serial observation, which is used by you as the one and only one point of view of X.

By (2) you are the one who using here an exclusive point of view, because you have no other alternative.

The alternatives are yours, you are the one limiting attributes and conclusions (by your own assertion) to particular exclusive perspectives and continue to profess the requirement of one exclusive perspective that you call “parallel” to get non-locality.

[doronshadmi]

I guess you now agree with what I had always said on the other thread that your assertions and ascriptions (local and non-local) are just a matter of perspective.
In the case of an object like line, I agree with you.

The alternatives are yours,
Yes indeed. Because there are alternatives, where no alternative is exclusive.

But someone like you that have no alternatives, has no choice but to use the exclusive case of serial observation.

Exclusive means that no other observation is allowed except the exclusive one (which is your case is the serial-only case, that has no alternatives).

[doronshadmi]

0 nxor 0 --> 0
0 nxor 1 --> 1
1 nxor 0 --> 1
1 nxor 1 --> 0

This is not NXOR. This is XOR.


You still don't understand that term, do you?

You still do not understand the generalization, do you?

[The Man]

In the case of an object like line, I agree with you.

Ok, so how about considering the line as a whole or as a combination of sub elements as a matter of perspective as well?


Yes indeed. Because there are alternatives, no alternative is exclusive.

I think you still need a better understanding of the term “exclusive” all alternatives that are not inclusive are by default exclusive or exclude the other alternatives not selected or not included.


But someone like you that have no alternatives, has no choice but to use the exclusive case of serial observation.


Again you are the one claiming “no choice” and “no alternatives” because as you assert.


In this case, ___ cannot be seen by serial observation, and can be seen by parallel observation.



Exclusive means that no other observation is allowed except the exclusive one (which is your case is the serial-only case, that has no alternatives).

Well that is precisely what you have asserted above that no other observation of “___” “In this case” except your exclusive “parallel observation”. So I will ask again just what do you think you are observing exclusively in “parallel”?

[jsfisher]

This is not NXOR. This is XOR.

You are correct in this, of course. My mistake. Permit me to correct my typographic error and re-present my questions:

Did you mean for there to be an "NXOR between the two operands? Also, didn't you mean for the operands and the result to have a common domain, either all (0,1) or all (F,T)? E.g.,

0 nxor 0 --> 1
0 nxor 1 --> 0
1 nxor 0 --> 0
1 nxor 1 --> 1

And what pray tell do those two NXOR operands represent? Are you saying that " " is equal to 0 (or F) and "_" is equal to 1 (or T)?


I am particularly interested in that last pair of questions.

[Little 10 Toes]

I will answer your questions out of order:

This is not my definiton for at least two reasons:

1) Subset is not the same as proper subset.

2) You ignored the term "cannot be but |B| < |A|".

1)It's not my fault that you are not using non-standard terms. You have not defined "proper subset". I defined subset, and used it accordingly. Please give your definition of subset and proper subset. Please then explain the differences.

2) Yes I have. "Cannot be but" is the same as "then". Example: If you continue to use standard terms in non-standard ways, you cannot be but misunderstood by 99.9% of the posters. If you use too many words when few will do, you cannot but be looked upon as being unclear.


Definition 2: Set A is called finite if the cardinal of proper subset B of A cannot be but |B| < |A|.

Definition 2 says that A is finite if its proper subset cannot be but |B| < |A|

What is not clear here? I do not think that by definition 2 we can conclude that property not-X is non-finite. What do you mean by property? We are only talking about if a set is either finite or non-finite based only on cardinality, not "not-X". In your quoted messages contained in this post, your definitions of #2 and #3 only talk about finite and non-finite.


Let us try this version of definition 3:

Definition 3: Set A is called non-finite if the cardinal of proper subset B of A can be (|B| < |A|) AND (|B| = |A|).

Using an example, how can 3 be equal and less than 4? Cardinality does not care about the members of a set, it just cares about how many, and then we compare those two values, using def #3, to see if set A is non-finite.

Little 10 Toes,

If we observe a non-local element, its value can be in more than a one relation w.r.t another element.

But this is not the case here.Then why bring it up?


In this case I am trying to define the difference between finite and non-finite sets, where each member is local (can be distinguished from another member by using only one relation). You have not defined "local". Defs #2 and Def #3 are only talking about cardinality, sets, and subsets. They don't mention members at all. Why are you bringing up members when you only care about defining finite and non-finite sets? One of your posts mention that want to define sets, but do not mention members. In fact, you posted this before I posted my message, remember?


(quoted message that does not show when I quote this message)
"Cannot be but ..." is an understatement of "must be ..." and I prefer to use understatements.
(another quoted message that does not show when I quote this message)
It will be come later.

At this stage I wish to clearly distinguish between finite and non-finite sets.

Please answer to http://forums.randi.org/showpost.php?p=4236183&postcount=896 (http://forums.randi.org/showpost.php?p=4236183&postcount=896) .

Let's continue with the original post:



Let us use the notion of proper subset in order to distinguish between finite and non-finite sets as follows:

Definition 3: If A is a set and B is some arbitrary proper subset of A, then if |B| cannot be but |B| < |A|, then A is finite.

If we can use definition 3 in order to conclude that anything that does not satisfy it, must be a non-finite set, then definition 3 is enough to distinguish between finite and non-finite sets.

What do you think? Well, it woud be nice to use the notion, but since you have a history of springing new words, or using common words but with different standard definitions, I can't since you have not defined "proper subset". In addition, you did not dispute my example of set A being all positive whole even numbers, and set B being all positive whole even numbers evenly divisible by five. Most mathematicians would say both sets are infinite, but by using def #2, set A is finite.




I think you are overthinking things. Would you agree to the following definitions of the following terms:

CardinalityWP (http://en.wikipedia.org/wiki/Cardinality): "In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {1, 2, 3} contains 3 elements, and therefore A has a cardinality of 3." Using the example set shown, I will use the notation |A| = 3 .
SubsetWP (http://en.wikipedia.org/wiki/Subset): "In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide."
Infinite: something that has no end or begining; something that cannot have a value attached to; unmeasurable/uncountable; unquantifiable. Example, the smallest/largest number; in geometry, a line. Synonym: non-finite.
Finite: something that does have an end; can have a value attached to; measurable/countable; practical; quantifiable. Example: the number of coins in my pocket, the number of grains of sand on a beach; in geometry, a line segment
"Cannot be but": synonym of "then"
Do you agree to these definitions to the words?

If you only think about sets and subsets, and use "standard" mathematical "grammer", my definitions are the same as yours, just cleaner. Can you give me your definition of subset, proper subset, and the difference between the two without using examples until requested?

[doronshadmi]

So I will ask again just what do you think you are observing exclusively in “parallel”?
No.

I observe ___ from more than a one and only one point of view.

In the case of observation from x to y:

1) If x = . and y = ___ and the researched case is _._ , then x = y from x point of view.

2) If x = __ and y = . and the researched case is _._ , then x < AND > y from x point of view.

Conclusion (2) is impossible by your observation; because you have no alternatives at all (you are using serial observation as an exclusive point of view, and cannot get __ from other points of view).

Furthermore, you continue to ignore the external point of view of __ and . , so here it is:

One claims that internal observation from x to y is subjective and does not provide the correct knowledge about x or y.

In that case let us use an external (objective) observation of x and y.

x = point

y = line

z = plane

w = volume

If x is observed through w w.r.t z, then x cannot be but on z XOR not on z.

By observation w x is local w.r.t z.

If y is observed through w w.r.t z, then y can be on z AND not on z.

By observation w y can be non-local w.r.t z.

[The Man]

No.

I observe ___ from more than a one and only one point of view.

So what, so can anybody else, but certain points of view have certain advantages like viewing the line segment perpendicular to your line of sight thus maximizing its apparent extents. In fact your claim of...



In this case, ___ cannot be seen by serial observation, and can be seen by parallel observation.


is the result of “one and only one point of view” that you call “parallel observation”.

So once again your denial of your use and dependence on exclusive points of view is in direct conflict with, well, your use and dependence on exclusive points of view. The problem is not with using exclusive points of view, they help us isolate aspects. The problem is with you saying no point of view is exclusive then depending entirely upon specific exclusive points of view as you clearly assert.



Non exclusive means that a conclusion about X is changed by different observations.

Observationally dependent conclusions are only the result of exclusive points of view. If those points of view did not exclude all other conclusions then the conclusion would not be dependent on the differences in the observations. Ideally the conclusions should be the same from all perspectives or points of view (by compensating for perspective dependent factors).




In the case of observation from x to y:

1) If x = . and y = ___ and the researched case is _._ , then x = y from x point of view.

2) If x = __ and y = . and the researched case is _._ , then x < AND > y from x point of view.

Conclusion (2) is impossible by your observation; because you have no alternatives at all (you are using serial observation as an exclusive point of view, and cannot get __ from other points of view).

You continue to delude yourself by not only depending on "one and only one" exclusive "parallel" point of view but by considering others as limited by your fallacies.

In the X Y Z coordinate system example I gave before with a line segment from coordinates (4, 3, 1) to (4, 3, 10) and in relation to a point at (4, 3, 5) one half of that line segment would have Z axis values < 5 and the other half >5. In other words it could be said that the line segment is”< AND >” the point in the Z axis. See by considering a line or line segment as defined by points your “< AND >” perspective dependent conclusion is no longer exclusive to your “parallel observation”.





Furthermore, you continue to ignore the external point of view of __ and . , so here it is:

One claims that internal observation from x to y is subjective and does not provide the correct knowledge about x or y.

In that case let us use an external (objective) observation of x and y.

x = point

y = line

z = plane

w = volume

If x is observed through w w.r.t z, then x cannot be but on z XOR not on z.

By observation w x is local w.r.t z.

If y is observed through w w.r.t z, then y can be on z AND not on z.

By observation w y can be non-local w.r.t z.You still do not understand the generalization, do you?

So now you want to introduce more exclusive points of view “external” and “internal” along with your own exclusive (incoherent and contradictory) conclusion to your notions where “no point of view is exclusive”. You still do not understand that by asserting “One claims that internal observation from x to y is subjective and does not provide the correct knowledge about x or y.” and then going to what you call an “external (objective) observation” you are utilizing exclusive points of view and now definitively asserting that “one and only one point of view” what you referred to as “external (objective) observation” is correct or as you put it “provide the correct knowledge about x or y.” If you can not make your subsequent posts consistent with your previous post then at least make some effort to have the end of some given post be consistent with its beginning.

[doronshadmi]

(4, 3, 5) one half of that line segment would have Z axis values < 5 and the other half >5. In other words it could be said that the line segment is”< AND >” the point in the Z axis.

No.

There are no half things in "< AND >" because ____ is an atom.

Since _____ is determined by you by coordinates (and any given coordinate is local by nature) you force them on the non-composed state of ____ , which causes you to use concepts like half line segments.

In other words, you are closed under Locality, as an exclusive point of view, that has no alternatives.

The rest of your post is nothing but locality as an exclusive point of view.

Some examples of Non-locality:

If the domain is . , then ____ is < AND > than . (notated as _._)

If the domain is . , then ____ is in AND out of . (notated as _._)

If the domain is [ ] , then ____ is in AND out of [ ] (notated as [_]_)


By your local exclusive point of view (where concepts like "half" are used), you cannot define Non-locality.


Analytic approach cannot be but a step-by-step serial observation, and your perception is limited to this thinking style.


As a result you have no chance (even if your life will be depended on it) to get Non-locality.


So now you want to introduce more exclusive points of view “external” and “internal” along with your own exclusive (incoherent and contradictory) conclusion to your notions where “no point of view is exclusive”.

Different alternatives of X cannot be considered as exclusive.

Only a Cyclops' view (like your view) is exclusive, exactly because X is observed from one and only one point of view (there are no alternatives).

[ddt]

:D If one travels some distance but ends up at the beginning is that progress? I guess in some sense.

That wholly depends on whether there's a singularity in the part of the plane that is bounded by the (Jordan) curve you traveled :).

For the rest of the discussion: I see there's some kind of work division where everyone deconstructs one of doron's definitions. As I've not yet downloaded the UR.pdf document - which definition would you recommend me to take up?

[doronshadmi]

The Man,

Also you have missed the following:

_._ is not a combination of the two cases:

x = _

y = .

x < y (example: _ .)

or

x > y (example: . _)

More precisely:

((_ .) or (. _)) ≠ (_._) = (__ < and > . from __ to . observation)

where ((__ .) and (. __)) is impossible.

Furthermore:

x = _

y = .

x = and > y (example: ._)

or

x < and = y (example: _.)

More precisely:

((_.) or (._)) ≠ (_._) = (__ < and > . from __ to . observation)

where ((_.) and (._)) is impossible, because . cannot be both on (_.) and on (._)

In order to bat this impossibility let us use two line segments in different colors:

____

If . is on __ , than it is red

If . is on __ , than it is blue


It is quite trivial to understand that . cannot be red and blue

On the contrary, if ____ are in each other's domain, they can be both red AND blue (exactly as __ is in and out of . domain, but not vice versa)


By understanding Non-locality\Locality Interactions one concludes that Dedekind's cut of the rational numbers cannot satisfy the fact that given any R member on the real-line it cannot be considered as a limit for anything that is < or > than it.

[jsfisher]

** bump **

Did you mean for there to be an "NXOR between the two operands? Also, didn't you mean for the operands and the result to have a common domain, either all (0,1) or all (F,T)? E.g.,

0 nxor 0 --> 1
0 nxor 1 --> 0
1 nxor 0 --> 0
1 nxor 1 --> 1

And what pray tell do those two NXOR operands represent? Are you saying that " " is equal to 0 (or F) and "_" is equal to 1 (or T)?


I am particularly interested in that last pair of questions.

[Little 10 Toes]

Bump ditto (or is it ditto bump?)


I think you are overthinking things. Would you agree to the following definitions of the following terms:

CardinalityWP (http://en.wikipedia.org/wiki/Cardinality): "In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {1, 2, 3} contains 3 elements, and therefore A has a cardinality of 3." Using the example set shown, I will use the notation |A| = 3 .
SubsetWP (http://en.wikipedia.org/wiki/Subset): "In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. Notice that A and B may coincide."
Infinite: something that has no end or begining; something that cannot have a value attached to; unmeasurable/uncountable; unquantifiable. Example, the smallest/largest number; in geometry, a line. Synonym: non-finite.
Finite: something that does have an end; can have a value attached to; measurable/countable; practical; quantifiable. Example: the number of coins in my pocket, the number of grains of sand on a beach; in geometry, a line segment
"Cannot be but": synonym of "then"
Do you agree to these definitions to the words?

If you only think about sets and subsets, and use "standard" mathematical "grammer", my definitions are the same as yours, just cleaner. Can you give me your definition of subset, proper subset, and the difference between the two without using examples until requested?

[doronshadmi]

Did you mean for there to be an "NXOR between the two operands? Also, didn't you mean for the operands and the result to have a common domain, either all (0,1) or all (F,T)? E.g.,

0 nxor 0 --> 1
0 nxor 1 --> 0
1 nxor 0 --> 0
1 nxor 1 --> 1

And what pray tell do those two NXOR operands represent? Are you saying that " " is equal to 0 (or F) and "_" is equal to 1 (or T)?


I am particularly interested in that last pair of questions.

By using a parallel observation of:

00
01
10
11

we are interested about the internal structure of this expression as the result of an whole\parts interaction.

From this point of view two basis structures are associated with each other, which are:

Symmetry (represented by 00 or 11)

Asymmetry (represented by 01 or 10)

Given any domain, Symmetry is not limited by it, for example:

Domain = []

Element = ___

Symmetry = [_]_ (simultaneously in and out)


Given any domain, Asymmetry is limited by it.

Domain = []

Element = ___

Asymmetry = [ ___ ] , [ ] ___ (not simultaneously in and out)

[jsfisher]

By using a parallel observation of:....


...which doesn't address any of my questions in the slightest. Care to try again?

[doronshadmi]

...which doesn't address any of my questions in the slightest. Care to try again?

Only if serial observation is the one and omly one point of view of the researched subject.

Care to try to use also parallel observation?

[jsfisher]

Only if serial observation is the one and omly one point of view of the researched subject.

Care to try to use also parallel observation?


You were taking shortcuts (again) with your notation, so I asked about it. Rather than simply answering directly, you wander off to some place irrelevant to the question.

Care to try again, or are you too busy on this random walk of yours?

[doronshadmi]

Some claims that 2 is both a member of the set of prime numbers AND the set of even numbers.

In this case 2 is non-local because it simultaneously belongs to two different sets.

This claim is wrong because an element is non-local only if it is related to another element by more than a one relation.

In that case 2 cannot be both a member and not a member of any given set; therefore 2 is local.

Actually, the whole idea of classes is limited by locality, because each researched thing must fully belong to a given class, or partially belong to it by using fuzzy logic's membership that is based on 0 to 1 value, which is itself local like any R member.

Non-locality holds only if a given thing is both 100% member AND not a member of a given domain, and this property is a strong mathematical framework.

By using analytic (serial only) observation, one must conclude that 100% member AND not a member is a contradiction or a weak framework like Paraconsistent Logic.

Both cases cannot get non-locality.

[doronshadmi]

You were taking shortcuts (again) with your notation, so I asked about it. Rather than simply answering directly, you wander off to some place irrelevant to the question.

Care to try again, or are you too busy on this random walk of yours?

My answer is direct to anyone who enables to use not only serial observation.

The bridge to get Organic Mathematics is in front of your mind. Only you can help yourself to see it and open yourself to new fundamental mathematical understanding.

You may say that I blame you in my inability to define my framework, but I really cannot help you to see things from parallel observation, because any observation is based on a direct perception of the observer.

If you get it you immediately understand what non-locality is, if you do not get it after 5 month dialog, you cannot get it.

[jsfisher]

Some claims that 2 is both a member of the set of prime numbers AND the set of even numbers.

Well, since 2 is both prime and even, it would be unreasonable to expect otherwise. Two is also an integer, positive, a solution to x^2 - 4 = 0, and a bunch of other things, too. Care to guess what that implies in terms of set membership?

By the way, are you claiming 2 is not both even and prime?

In this case 2 is non-local because it simultaneously belongs to two different sets.

First, since set membership is not a temporal phenomenon, the adverb simultaneously as no meaning in your statement.

Second, nothing you have suggested for your definition of non-local supports your statement.

This claim is wrong because an element is non-local only if it is related to another element by more than a one relation.

...which everything is, so everything must be non-local.

In that case 2 cannot be both a member and not a member of any given set; therefore 2 is local.

Even if your premises weren't faulty, there is no logical connection from them to this conclusion.

[jsfisher]

If you get you immediately understand what non-locality is, if you do not get if after 5 month dialog, you cannot get it.


Right. The chief should always blame the customers for the poor quality of the soup.

[doronshadmi]

Well, since 2 is both prime and even, it would be unreasonable to expect otherwise. Two is also an integer, positive, a solution to x^2 - 4 = 0, and a bunch of other things, too. Care to guess what that implies in terms of set membership?
This is not relevant because I am talking about the non-locality or locality of element X w.r.t element Y.

By the way, are you claiming 2 is not both even and prime?
No, I claim that 2 is local because it cannot both a member AND not a member of a given set.

By the way, your reply is a good example of a person that is using a step-by-step observation in order to understand thing.

Your two questions above clearly show that you do not read the whole post in order to answer parts of it, but you reply to each paragraph separately before you understand its whole\parts relations.

I promise you that by this thinking style, you are not going to get my posts.



First, since set membership is not a temporal phenomenon, the adverb simultaneously as no meaning in your statement

There is nothing temporal here if you get things in parallel, and in this case, a non-local element is both a member AND not a member of a given set.

The problem is in the limited one-and-only-one-serial-observation of Set.

Second, nothing you have suggested for your definition of non-local supports your statement
Again, my definition is about the non-locality of an element w.r.t another element.

You refuse to get it, and force on me a general definition of non-locality, which is something that I did not do.


...which everything is, so everything must be non-local.
You have no idea of what is non-local element, or how a relation (which is not an element) is non-local by nature.

This ignorance prevents from you to say any meaningful thing about non-locality.



Even if your premises weren't faulty, there is no logical connection from them to this conclusion.

You cannot say that, because you did not provide any evidence that clearly shows that you understand the non-standard observation of these mathematical subjects.

[doronshadmi]

Right. The chief should always blame the customers for the poor quality of the soup.

If you get it you immediately understand what non-locality is, if you do not get it after 5 month dialog, you cannot get it.

[The Man]

No.

There are no half things in "< AND >" because ____ is an atom.

Says you, without any support for your assertions (as usual). In the X Y Z coordinate system example before the line segment from (4, 3, 1) to (4, 3, 10) is as much a line segment as those from (4, 3, 1) to (4, 3, 5) and from (4, 3, 5) to (4, 3, 10).




Since _____ is determined by you by coordinates (and any given coordinate is local by nature) you force them on the non-composed state of ____ , which causes you to use concepts like half line segments.

No just line segments, one could be half, 2/3 , five times or the same size of the other. You are the only one trying force a “state of ____ “ so you can claim that


In this case, ___ cannot be seen by serial observation, and can be seen by parallel observation.


Yet you have not said what it is that you think can only “be seen by parallel observation”. We know standard geometry defines and distinguishes between line segments using coordinates. How do you do that?




In other words, you are closed under Locality, as an exclusive point of view, that has no alternatives.

Yet as noted in the quote from you above you assert it is you who “has no alternatives” but “parallel observation” since “In this case, ___ cannot be seen by serial observation”. Your process remains the same you claim one thing, do the exact opposite then claim what you are doing as a limitation of others.



The rest of your post is nothing but locality as an exclusive point of view.

Some examples of Non-locality:

If the domain is . , then ____ is < AND > than . (notated as _._)

If the domain is . , then ____ is in AND out of . (notated as _._)

If the domain is [ ] , then ____ is in AND out of [ ] (notated as [_]_)


By your local exclusive point of view (where concepts like "half" are used), you cannot define Non-locality.

Actually the definition was yours (what little of it there was) I simply showed how that conclusion could be obtained, explainable and suported by standard geometry, something you claimed was entirely dependent on your “parallel observation”


Analytic approach cannot be but a step-by-step serial observation, and your perception is limited to this thinking style.

Yes we are all well aware of your preference in not using an “Analytic approach” in your “thinking style”. As a result you make ludicrous assertions like what follows


As a result you have no chance (even if your life will be depended on it) to get Non-locality.

I already shown you how coordinates define the line segment as well as permit your “Non-locality” defining conclusion of “< AND >”.



Different alternatives of X cannot be considered as exclusive.

So all “alternatives” are all inclusive or include all other “alternatives”? That would make them all the same. I order for an “alternative” to be different from another it must include something excluded by the other alternative and/or exclude something included by the other alternative.



Only a Cyclops' view (like your view) is exclusive, exactly because X is observed from one and only one point of view (there are no alternatives).

Anyone can observe X from any point of view in a coordinate system by changing the origin of the coordinates or the system of coordinates itself. The conclusions that are independent of the choice of origin or the choice of coordinate systems are considered to be the defining characteristics and are supportable by the coordinate system (or frame of reference) invariance of those conclusions. Any conclusions you derive for your non-analytical, no coordinate system of imaginary dogmatic edicts are equally pointless as they are supportable. Fortunately for you that is not an issue as it would require an “Analytic approach” to understand the need of a coordinate system just to define and distinguish any given point (“.”) or line segment (“__”).




The Man,

Also you have missed the following:

Nope.



_._ is not a combination of the two cases:

x = _

y = .

x < y (example: _ .)

or

x > y (example: . _)

More precisely:

((_ .) or (. _)) ≠ (_._) = (__ < and > . from __ to . observation)

where ((__ .) and (. __)) is impossible.[\quote]

Based on your above assertions ((_ .) AND (. _)) does “= (__ < and > . from __ to . observation)”. Once again you start with a claim “is not a combination of the two cases” then use the alternative of cases “or” as opposed to combining “AND” the cases as you originally claimed as well as your conclusion requires. Finally you assert “where ((__ .) and (. __)) is impossible” while asserting ((__ .) and (. __)) in your symbolic notations.



[QUOTE=doronshadmi;4250243]
Furthermore:

x = _

y = .

x = and > y (example: ._)

or

x < and = y (example: _.)

More precisely:

((_.) or (._)) ≠ (_._) = (__ < and > . from __ to . observation)

where ((_.) and (._)) is impossible, because . cannot be both on (_.) and on (._)

In order to bat this impossibility let us use two line segments in different colors:

____

If . is on __ , than it is red

If . is on __ , than it is blue


It is quite trivial to understand that . cannot be red and blue

On the contrary, if ____ are in each other's domain, they can be both red AND blue (exactly as __ is in and out of . domain, but not vice versa)


By understanding Non-locality\Locality Interactions one concludes that Dedekind's cut of the rational numbers cannot satisfy the fact that given any R member on the real-line it cannot be considered as a limit for anything that is < or > than it.

You still continue to delude yourself, this was already described before and again above in the X Y Z coordinate system example where the line segment from (4, 3, 1) to (4, 3, 10) is as much a line segment as those from (4, 3, 1) to (4, 3, 5) and from (4, 3, 5) to (4, 3, 10). The point (4, 3, 5) is included within both the line segment (4, 3, 1) to (4, 3, 5) and from (4, 3, 5) to (4, 3, 10) as well as one from (4, 3, 2) to (4, 3, 8) or (4, 3, 3) to (4, 3, 15) and an infinite number of other line segments that could contain point (4, 3, 5). Coordinates describe the relationship between a point and a line segment “More precisely” then any of your non-analytical, imaginary and ‘pointless’ conclusions or dogmatic edicts. Those coordinates clearly demonstrate and define that a line segment (“__”) has a “domain”, like from (4, 3, 2) to (4, 3, 8) which includes an infinite number of points while a point (“.”) has a domain like (4, 3, 2) which only includes itself, yet can be included within an infinite number of line segments. As usual your assertion “exactly as __ is in and out of . domain, but not vice versa” is completely backasswards.

[jsfisher]

This is not relevant because I am talking about the non-locality or locality of element X w.r.t element Y.

Then why did you raise the topic in the first place?

No, I claim that 2 is local because it cannot both a member AND not a member of a given set.

Then why did you raise the topic of two different sets?

If even you cannot follow your own posts, why do you expect us to?

[jsfisher]

If you get it you immediately understand what non-locality is, if you do not get it after 5 month dialog, you cannot get it.


If you cannot define any of your concepts after 5 months of failure, you cannot explain them.

[doronshadmi]

Anyone can observe X from any point of view in a coordinate system by changing the origin of the coordinates or the system of coordinates itself.

The Man,

A point of view is not a point of some coordinate system.

A point of view is the perception's ability.

The rest of your post is based on this misunderstanding.

[doronshadmi]

Then why did you raise the topic in the first place?



Then why did you raise the topic of two different sets?

If even you cannot follow your own posts, why do you expect us to?

Because non-locality is understood by you as something that can be defined as:

The same result from different observations.

But I am talking about different observations that change the result of the same observed element.

From one observation the same element is local, and form another observation the same element is non-local.

This exactly the property of a line segment, which it is not a property of a point (a point is not changed under different observations).

[jsfisher]

Because non-locality is understood by you as something that can be defined as:

The same result from different observations.

Please don't speak for me. I am perfectly capable of speaking for myself.

But I am talking about different observations that change the result of the same observed element.

From one observation the same element is local, and form another observation the same element is non-local.

You are talking about Mathematics as if it were a sequence of science experiments. It isn't. It has rules, and those rules do not allow the alternate views you so ignorantly claim.

As you have been told so very many times, Mathematics is very adaptable, but if you want something shaped differently than what's found in the existing branches, you need to define your own branch of Mathematics. Simply taking an existing branch that you don't really understand in the first place, then declaring some parts wrong by fiat, is an exercise in insanity, not intellectual brilliance.

And before you go about inventing a new branch, you really need a better understanding of what is there already. After all, you are the one who impressed us with your mastery of logic by stating that the construct A if B, the construct A only if B, and the construct A if and only if B are all equivalent.

You have impressed us all with your insistence that a set is equal to the union of its members and that 2 may or may not be a member of the set, {2}. And we are well aware the you stated emphatically believe here is no such thing as a number in standard Mathematics.

You should actually learn a subject before you become critical of it.

[The Man]

The Man,

A point of view is not a point of some coordinate system.



As usual the misunderstanding is entirely yours “A point of view” can be specifically the view from some “point of some coordinate system” hence the word “point” being the defining factor. Just as a “A point of view” can be the expression of an opinion or a particular “point” in a subject of discussion, like the point I just made in my previous sentence or the point I made before about your observationally dependent non-local definition of “< AND >” not being “exclusive” to your “parallel observation” as you claim. It could even be the perspective from which a narrative is related like “Doron only perceives things from his singular point of view and therefore claims that anyone who disagrees with him does so because they are limiting themselves to only one point of view which he selects then ascribes to them”. Those are three standard points of view on “A point of view”, which you can find well supported by encyclopedias and reference materials should you care to get their point of view. Now lets see what is your perspective on “A point of view”.


A point of view is the perception's ability.


This is just you being silly again and combining “perception”, “ability” and “point of view” into some amorphic construct that you think constitutes a sentence. “The perception’s ability” to do what, perceive? That would make it both silly and redundant but if that is how you what to describe your point of view, silly and redundant would barley scratch the surface.


The rest of your post is based on this misunderstanding.

All of your posts and your notions in general are based on this and similar misunderstanding by you as well as your selective and exclusive “point of view” (however you choose to describe it).

[doronshadmi]

As usual the misunderstanding is entirely yours “A point of view” can be specifically the view from some “point of some coordinate system” hence the word “point” being the defining factor.

You are right.

This is exactly the reason why you do not get non-locality.

You are using serial\local-only perception as the one and only basis for any pre-condition, rule or conclusion, which naturally prevents any understanding of the non-local.

In other words, in your exclusive world of serial\local-only perception, a term like "can be ..." (as used in the quote above) cannot be found, simply because there are no alternatives in your universe.

[doronshadmi]

You are talking about Mathematics as if it were a sequence of science experiments. It isn't. It has rules, and those rules do not allow the alternate views you so ignorantly claim.
No, I am talking about perception as an inseparable factor the mathematical research (pure or applied, it does not matter).

By using non-exclusive perceptions of the mathematical subjects, one misses the ability to understand the researched mathematical universe from different and non-exclusive observations.

What you call common rules is nothing but the serial observation of the mathematical universe, where any premise rule or result is limited to serial observation, which is without a doubt an exclusive observation of this science for the past 2500 years.

The rest of your post is based on this artificial, arbitrary and limited observation of serial-only thinking style, which actually shapes the entire mathematical universe by a particular perception, used as the basic agreement between the community of mathematicians around the world.

I disagree with this agreement, and do my best in order to prevent any excusive perception at the basis of the mathematical science.

[doronshadmi]

jsfisher and the man,

I wonder why you do not reply in details to http://forums.randi.org/showpost.php?p=4230971&postcount=827 ?

[doronshadmi]

Typo corrections of the two first sentences of #951 ( http://forums.randi.org/showpost.php?p=4253652&postcount=951 ):

No, I am talking about perception as an inseparable factor of the mathematical research (pure or applied, it does not matter).

By using an exclusive perception of the mathematical subjects, one misses the ability to understand the researched mathematical universe from different and non-exclusive observations.

[jsfisher]

jsfisher and the man,

I wonder why you do not reply in details to http://forums.randi.org/showpost.php?p=4230971&postcount=827 ?



It did not present anything paradoxical.
It did not invoke a question.
It did support any point you are trying to make.
It had no apparent relevance to the discussion.

[The Man]

You are right.

This is exactly the reason why you do not get non-locality.

You are using serial\local-only perception as the one and only basis for any pre-condition, rule or conclusion, which naturally prevents any understanding of the non-local..

By your own definition of “non-local” as



Definition 5: If object x = and ≠ (where ≠ is < xor >) or < and > w.r.t object y, then object x is called Non-Local.

I have already demonstrated how a coordinate system can be used to obtain and support your “< and >” conclusion that you claim defines “Non-Local” and also claim is restricted to only one perception you claim as “parallel observation”. So not only is your defining conclusion of “Non-local” obtainable by a coordinate system or standard geometry, you are the only one trying to limit your defining conclusion to only one perspective, your own.




In other words, in your exclusive world of serial\local-only perception, a term like "can be ..." (as used in the quote above) cannot be found, simply because there are no alternatives in your universe.

Now you're just being silly again, by saying you cannot find something that you assert I used in what you quoted from me after you claimed “You are right” in my assertion that the misunderstanding is entirely yours.

As you have asserted.



Analytic approach cannot be but a step-by-step serial observation, and your perception is limited to this thinking style.



Your non-analytical approach has simply constricted you to such ridiculous and self contradictory statements that require you to remain in denial about what those statements assert.

[jsfisher]

No, I am talking about perception as an inseparable factor the mathematical research (pure or applied, it does not matter).

Which is your invention as an excuse for not knowing very much in the way of Mathematics.

By using non-exclusive perceptions of the mathematical subjects, one misses the ability to understand the researched mathematical universe from different and non-exclusive observations.

Timothy Leary might agree with you, but no sane mathematician would. Mathematics is not studied by observation. Moreover, you do not observe things differently -- you just flatly misunderstand them, then make stuff up to fill the voids.

You have demonstrated you inability to comprehend a simple syllogism, yet you believe your logic impeccable.

You have maintained repeatedly that a set is equal to the union of its members. That is blatantly, absolutely, irrefutably as bogus a claim as can be made, yet you cling to it like religious dogma.

Why is that?

[The Man]

jsfisher and the man,

I wonder why you do not reply in details to http://forums.randi.org/showpost.php?p=4230971&postcount=827 ?



It did not present anything paradoxical.
It did not invoke a question.
It did support any point you are trying to make.
It had no apparently relevance to the discussion.



I have to agree with jsfisher on that one.

However if you insist on an “analytical approach” or remarks (as you do not seem capable or willing to do that yourself), I would have to point out that an internal perspective is just as subjective as an external perspective. It is just that one perspective is subject to being, well, internal and the other to being external. An objective perspective only arises by being unbiased or considering attributes independent of the observer. This of course is in direct conflict with your entirely observer and perspective dependent conclusion process. So the “paradox” like the “misunderstanding” is again entirely yours.

[doronshadmi]

I have already demonstrated how a coordinate system can be used to obtain and support your “< and >”

No, you did not because for you ___ is made of sub-elements.

The rest of your post is based on this premise.

[doronshadmi]

An objective perspective only arises by being unbiased or considering attributes independent of the observer.
.

Yeh,

Like you, using coordinates as a point of view to determine a line segment, isn't it?

[doronshadmi]

It did not present anything paradoxical.
It did not invoke a question.
It did support any point you are trying to make.
It had no apparent relevance to the discussion.


5. You did not show that you understand the basic notions of this thread; therefore you cannot say any meaningful thing about it.

I did my best in order to communicate with you, you did not do anything to communicate with me, because you cannot get things beyond the analytic serial\local-only observation.

As I said, you are nothing but a community of people that are using an exclusive observation of the researched things.

By using this excusive observation a line segment is determined by sub-elements, and you are totally blind to any other alternative.

Furthermore this exclusive blindness is used by the members of your community to determine what Mathematics is or what Mathematics is not.

[jsfisher]

No, you did not because for you ___ is made of sub-elements.

Assuming by your symbolic gibberish you meant 'line segment', no. A line segment is not made of sub-elements. These are not construction projects where someone assembles these things from other, more basic components.

A line segment is a line segment. It does contain a variety of other elements, points and other line segments, but it is not made from them.

[The Man]

No, you did not because for you ___ is made of sub-elements.

The rest of your post is based on this premise.

Ah, your typical observer and perspective based conclusion. The inclusion of a logical connective such as “AND” creates a compound proposition or a proposition comprised of other propositions or “sub-elements”. If you do not what “sub-elements” in your defining conclusion of “Non-local” then do not require them in that conclusion yourself.

[The Man]

Yeh,

Like you, using coordinates as a point of view to determine a line segment, isn't it?

As I said one can choose whatever origin or coordinate system one whishes, being objective the line segment is independent of that selection.

You have as yet to assert how you distinguish between any pair of given points or any pair of given line segments without using some coordinate system. Coordinate systems are not “a point of view” but how one defines any given point of view and ensures that conclusions are not dependent only on that point of view. Of course this is of no concern to you as you are only interested in conclusions from your own exclusive point of view while ascribing some singular and opposing point of view to others.

[ddt]

Though it probably will lead nowhere, I have some questions about your UR "paper" too. Let's start with the begin of page 2. First of all, I note that the content of page 2 is radically different of nature than the content of page 1, so you really should have made this a new section or subsection.

A set (usually notated by "{" and "}") is a collection of distinct elements, where their order has no significance.
Example: {a,b,c}={b,a,c} , {a,a,b}={a,b}={b,a}, etc...
What use is it to (try to) define what a set is? Probably, the reader has a much better command of what a set is in mathematics than you have yourself, considering the many misconceptions you've shown here.

= relation is equal to ...
≠ relation is not equal to ...
< relation is smaller than ...
> relation is greater than ...
Again, what use is it to belabor the obvious? Unless you mean something entirely different with these relations than usual - in which case, you should have rigorously defined them in the first place.

Object=Member=Element
Why use three different words for the same concept? The only reason I can think of is in order to confound issues on purpose. Is that your aim?

| is a 1-1 mapping between objects.
What use is this? You only use it in informal diagrams. It is by no means an official notation. Moreover, it is wrong. A 1-1 mapping is a mapping between sets. You use the | in diagrams to show which elements are mapped to which by a particular mapping and as part of that mapping. In the case of the example below Definition 2, this mapping isn't even a 1-1 mapping.

REI is Relation\Element Interaction.
Nobody heard of this before. You don't define what it means.

w.r.t is "with respect to ..."
Everyone in your readership knows this. Everyone in your readership has a fine command of English - at least much better than yours, as you're showing with every posting here.

Cardinal (notated by "|" and "|") is the number of the members of a set.
Apart from the very clumsy description of the notation - why again belabor the obvious? Anyone with some mathematical education knows what cardinality is.

Definition 1: B is a proper subset of A if any object of B is an object of A, but there is an object of A that is not an object of B
Again, people with some mathematical education know what a (proper) subset is. And why do you use the word "object" instead of element, which is the usual definition?

[doronshadmi]

A line segment is a line segment. It does contain a variety of other elements, points and other line segments, but it is not made from them.

Great,

In this case, given any domain [], ___ is in AND out of it [_]_(in addition of in [ ___ ] OR out [ ] ___ of it.

Now do it by using a point.

A is A is not enough, in order to get these notions.

[jsfisher]

5. You did not show that you understand the basic notions of this thread; therefore you cannot say any meaningful thing about it.

This is a lie. I and others have have shown far more insight into what you have been saying in this thread than you, yourself, have. You put forth poorly conceived notions as absolute truths only to have them revealed to be contradictory nonsense or trivia buried in gibberish that they actually are.

And since you are incapable of framing a logical argument, your ultimate response is that everyone else is at fault for not understanding your brilliance.

Truth is your ideas are transparent.

I did my best in order to communicate with you, you did not do anything to communicate with me, because you cannot get things beyond the analytic serial\local-only observation.

The second part is a repeat of the lie, and if that was your best attempt at communication, how embarrassing for you.

As I said, you are nothing but a community of people that are using an exclusive observation of the researched things.

By using this excusive observation a line segment is determined by sub-elements, and you are totally blind to any other alternative.

Furthermore this exclusive blindness is used by the members of your community to determine what Mathematics is or what Mathematics is not.

As The Man has pointed out to you, you are very exclusive about your observations being the only correct ones. Too bad your "exclusive observations" require some much of Mathematics be contradicted. That pesky set-membership concept being a good example.

Here. Let's try some of these again:


Is 2 a member of the set {2} ?
Is a set equal to the union of its members?
Are 1/4 and 0.25 different numbers?
Are sets, maps, and functions all the same thing?
Is Geometry a very weak branch of Mathematics?
Is the construct A if B equivalent to A only if B?
Is there no such thing as a number in standard Mathematics?

[doronshadmi]

Coordinate systems are not “a point of view” but how one defines any given point of view and ensures that conclusions are not dependent only on that point of view.
You did not demonstrate such a thing.

On the contrary, by your point of view a line is determined by points.

In order to demonstrate such a thing you have to show how a line segment has properties that a point does not have.

Only by doing that, a line segment is independent of a point.

This independency can be understood only by observation.

In that case any observation must not be exclusive, otherwise the objects and their relations are understood only by this exclusive point of view.

You are definitely a community of people that their agreed body of knowledge is based on exclusive point of view of the researched objects.

I simply expose this exclusive agreement, whether you like it or not.

[doronshadmi]

This is a lie. I and others have have shown far more insight into what you have been saying in this thread than you, yourself, have. You put forth poorly conceived notions as absolute truths only to have them revealed to be contradictory nonsense or trivia buried in gibberish that they actually are.

And since you are incapable of framing a logical argument, your ultimate response is that everyone else is at fault for not understanding your brilliance.

Truth is your ideas are transparent.



The second part is a repeat of the lie, and if that was your best attempt at communication, how embarrassing for you.



As The Man has pointed out to you, you are very exclusive about your observations being the only correct ones. Too bad your "exclusive observations" require some much of Mathematics be contradicted. That pesky set-membership concept being a good example.

Here. Let's try some of these again:


Is 2 a member of the set {2} ?
Is a set equal to the union of its members?
Are 1/4 and 0.25 different numbers?
Are sets, maps, and functions all the same thing?
Is Geometry a very weak branch of Mathematics?
Is the construct A if B equivalent to A only if B?
Is there no such thing as a number in standard Mathematics?


Your exclusive observation of anything gives you the illusion that your agreement anything about 1 to 7 has one and only one interpretation.

[jsfisher]

In this case, given any domain [], ___ is in AND out of it [_]_(in addition of in [ ___ ] OR out [ ] ___ of it.


You are using meanings of 'in' and 'out' private to you. In any sort of conventional usage of these words, your statement is patently false. You also have jumped away from your failed attempts to define locality and non-locality. Is that because you cannot focus on one thing for very long, or is this digression somehow going to unify everything?

Either way, you'd need to define your two relations (in and out) and what it means to say a line segment is in or out of a domain. History says you won't be able to do this. Prove history wrong.

[The Man]

You did not demonstrate such a thing.

On the contrary, by your point of view a line is determined by points.

Actually a line segment is defined by points, I am still waiting for your explanation of how you would define and distinguish between line segments.



In order to demonstrate such a thing you have to show how a line segment has properties that a point does not have.

Only by doing that, a line segment is independent of a point.

No problem, it is a fundamental aspect of basic geometry that most people comprehend in the first minute or two. A point has no theoretical extents in any dimension while a line has theoretical extents in just one dimension. Consider it demonstrated and thus your ‘point’ conceded (while you will undoubtedly remain conceited).




This independency can be understood only by observation.

Technically that “independency” is determined by definition although it can be apparent by observation. You keep trying to limit things to just your biased “observational” perspective.



In that case any observation must not be exclusive, otherwise the objects and their relations are understood only by this exclusive point of view.

You mean as opposed to you what do by claiming your “< AND >” conclusion can only be understood by your “parallel observation”, or as you just asserted “This independency can be understood only by observation”, how contradictory of you.


You are definitely a community of people that their agreed body of knowledge is based on exclusive point of view of the researched objects.

While you are just a single persons who can not even agree with himself about his “exclusive point of view of the researched objects”


I simply expose this exclusive agreement, whether you like it or not.

Yet you continue to resist exposing yourself to your own exclusive disagreement, simply because you do not like it.

[Little 10 Toes]

Avoidance of posts defining words that you use uniquely noted. Since you won't answer questions, I feel that you are a fanatic of your own ideas and aren't open to using common terms. How can you share your "ideas" without a common language?

Your shalmerflik is so getuy of werlug, I'm klutairq that you can yiwl without hiltnerbrafing all over your reezlents!! You tell me what I said and I'll tell you if you're right.

[nathan]

Your exclusive observation of anything gives you the illusion that your agreement anything about 1 to 7 has one and only one interpretation.

You are still evading those questions.

[calebprime]

Your shalmerflik is so getuy of werlug, I'm klutairq that you can yiwl without hiltnerbrafing all over your reezlents!! You tell me what I said and I'll tell you if you're right.


Your [shawl] is so [full] of [weevils], I'm [wagering] that you can (not) [balance on a barrel floating in water] without [barfing] all over your [relatives*].


* here scholars are divided. Some think the word means weasels, others contend it might mean cheese doodles.

[doronshadmi]

The objectivity of mathematical objects is discovered by non-exclusive observations.

It means that different conclusions of the same object are discovered by different observations.

As a result our body of knowledge is sufficient enough in order to understand the interaction between different results, which are based on different observations of the same objects.

For example: a point properties or a line properties are discovered by different observations.

Then we are able to define more interesting relations between these objects, which enrich our body of knowledge about them.

By observing a point we define that a one relation with another object is enough in order to define the interaction with the other object.

This is not the case about a line segment because by using different observation we define that there are cases where a one relation with another object is not enough in order to define the interaction with the other object.

By using these results a point, a line and their possible interactions are not entirely determined by any particular observation of them.

The organic natural numbers are exactly the result of interactions that are based on different observations of objects like a point or a line segment.

Please pay attention that the concept of relation itself is inherently non-local and does not depend on observations.

This is not the case about objects. Their properties are discovered by observations.


A point has no theoretical extents in any dimension while a line has theoretical extents in just one dimension.

Great,

As a result any object that has "theoretical extents" w.r.t to other objects, can be non-local w.r.t to these objects.

A line segment is the simplest case of such an object.

This is not the case with any object that has no "theoretical extents" w.r.t to other objects.

A point is the simplest case of such an object.

The interaction between these simplest cases is one of the ways to get the organic natural numbers.


EDIT:


Technically that “independency” is determined by definition although it can be apparent by observation. You keep trying to limit things to just your biased “observational” perspective.
No, our undertanding can be based on direct immediate and parallel observation of the researched object, a step-by-step observation of it or any possible interaction of Parallel\Serial observations.

A definition (as currently understood) is nothing but the result of a serial step-by-step observation.

The current community of mathematicians is nothing but a group of people which are skilful to get things only if they are defined by a serial step-by-step observation.

Furthermore, over the past 2500 years the mathematical science itself was recognized by this particular observation.

The aim of my work is to show that the mathematical science is not the result of any particular observation.


Actually a line segment is defined by points, I am still waiting for your explanation of how you would define and distinguish between line segments.
No,

If a line segment is defined by a serial observation, then it is determined and distinguished by points.

This is not the case if a line segment is defined by parallel observation.

In that case objects like points or coordinates are not used in order to distinguish between different line segments and the non-local property of a line segment is considered in order to distinguish between line-segments, for example:

x = ____

y = ____


x < and = y (example: _____)

or

y > and = x (example: _____)

[doronshadmi]

Anoter example of distinction between line-segments, without using points (a point is 0 = . and it is a local atom):

1 = ______

2 = ____________

3 = ___________________

.5 = ___

pi = _____________________

Each line segment in this example is a non-local atom.

The name of each non-local atom is determined by its proportion to some arbitrary line-segment, called 1, which is used as the common unit measurement.

[jsfisher]

The objectivity of mathematical objects is discovered by non-exclusive observations.

It means that different conclusions of the same object are discovered by different observations.


Wrong.

...<stuff founded on false premise>...

[doronshadmi]

Wrong.

Right,

but not by the current paradigm that is based on a one and only one
observation's type (the serial step-by-step observation).

[jsfisher]

Right,

but not by the current paradigm that is based on a one and only one
observation's type (the serial step-by-step observation).


No, still wrong. Mathematics is not observation-based. It is defined by rules, definitions, and axioms. Nothing is left to viewpoint, observation, or (in your case) gross misunderstanding.

Despite your protestations, a point in Euclidean geometry, for example, has a set of properties determined by Euclidean geometry and not by your unique powers of observation.

If you'd like points with different properties, you'll need a different branch of Mathematics. You don't get to redefine Euclid.

[doronshadmi]

No, still wrong. Mathematics is not observation-based. It is defined by rules, definitions, and axioms.
These rules, definitions and axioms depends on observations and I am not talking about sensual observations of physical stuff but about the fundamental ability get a knowledge whether it is abstract or not.

Your community is ignorant about it because it is limited to one and only one observation type (the serial step-by-step one, which is also called analytic) and as a result any rule, definition or axiom is nothing but the outcome of this particular observation.

This thread is a very good example of my arguments about the community of mathematicians that shaped the mathematical science by a single observation's type.

[ddt]

Though it probably will lead nowhere, I have some questions about your UR "paper" too. Let's start with the begin of page 2. First of all, I note that the content of page 2 is radically different of nature than the content of page 1, so you really should have made this a new section or subsection.

A set (usually notated by "{" and "}") is a collection of distinct elements, where their order has no significance.
Example: {a,b,c}={b,a,c} , {a,a,b}={a,b}={b,a}, etc...
What use is it to (try to) define what a set is? Probably, the reader has a much better command of what a set is in mathematics than you have yourself, considering the many misconceptions you've shown here.

= relation is equal to ...
≠ relation is not equal to ...
< relation is smaller than ...
> relation is greater than ...
Again, what use is it to belabor the obvious? Unless you mean something entirely different with these relations than usual - in which case, you should have rigorously defined them in the first place.

Object=Member=Element
Why use three different words for the same concept? The only reason I can think of is in order to confound issues on purpose. Is that your aim?

| is a 1-1 mapping between objects.
What use is this? You only use it in informal diagrams. It is by no means an official notation. Moreover, it is wrong. A 1-1 mapping is a mapping between sets. You use the | in diagrams to show which elements are mapped to which by a particular mapping and as part of that mapping. In the case of the example below Definition 2, this mapping isn't even a 1-1 mapping.

REI is Relation\Element Interaction.
Nobody heard of this before. You don't define what it means.

w.r.t is "with respect to ..."
Everyone in your readership knows this. Everyone in your readership has a fine command of English - at least much better than yours, as you're showing with every posting here.

Cardinal (notated by "|" and "|") is the number of the members of a set.
Apart from the very clumsy description of the notation - why again belabor the obvious? Anyone with some mathematical education knows what cardinality is.

Definition 1: B is a proper subset of A if any object of B is an object of A, but there is an object of A that is not an object of B
Again, people with some mathematical education know what a (proper) subset is. And why do you use the word "object" instead of element, which is the usual definition?

Bump.

[ddt]

These rules, definitions and axioms depends on observations and I am not talking about sensual observations of physical stuff but about the fundamental ability get a knowledge whether it is abstract or not.

Your community is ignorant about it because it is limited to one and only one observation type (the serial step-by-step one, which is also called analytic) and as a result any rule, definition or axiom is nothing but the outcome of this particular observation.

This thread is a very good example of my arguments about the community of mathematicians that shaped the mathematical science by a single observation's type.

I'm wavering between the characterizations "word salad" and "bollocks"... Whatever way, you did your best again to show profound ignorance about mathematics. Great job!

[The Man]

The objectivity of mathematical objects is discovered by non-exclusive observations.

It means that different conclusions of the same object are discovered by different observations.

As a result our body of knowledge is sufficient enough in order to understand the interaction between different results, which are based on different observations of the same objects.

For example: a point properties or a line properties are discovered by different observations. .

No they were not “discovered” no one dug up a “point” or accidentally mixed some things together and suddenly created a “line”. They were simply defined as theoretical abstractions. Once defined however their usefulness was readily “discovered” and continues today.



Then we are able to define more interesting relations between these objects, which enrich our body of knowledge about them.

By observing a point we define that a one relation with another object is enough in order to define the interaction with the other object.

This is not the case about a line segment because by using different observation we define that there are cases where a one relation with another object is not enough in order to define the interaction with the other object.

By using these results a point, a line and their possible interactions are not entirely determined by any particular observation of them.

The organic natural numbers are exactly the result of interactions that are based on different observations of objects like a point or a line segment.

Please pay attention that the concept of relation itself is inherently non-local and does not depend on observations.

This is not the case about objects. Their properties are discovered by observations.

Again observational dependent conclusions are, well dependent on the observer or the observation. Objective conclusions are not dependent on the observer. You are simply arguing for subjective conclusions so that those “objects” can be subjected to whatever conclusions you choose to think they should be subjected to.





Great,

As a result any object that has "theoretical extents" w.r.t to other objects, can be non-local w.r.t to these objects.

A line segment is the simplest case of such an object.

This is not the case with any object that has no "theoretical extents" w.r.t to other objects.

A point is the simplest case of such an object.
Theoretical extents are not “w.r.t.” anything; you continue to insist upon subjecting everything to your exclusive and observationally dependent non-analytical process.

So you have refined your definition of non-local to include anything with theoretical extents?




The interaction between these simplest cases is one of the ways to get the organic natural numbers.


EDIT:


No, our undertanding can be based on direct immediate and parallel observation of the researched object, a step-by-step observation of it or any possible interaction of Parallel\Serial observations.

So now what you refer to as “a step-by-step observation” or an “analytical approach” is just as valid as your preferred and previously exclusively correct “parallel observation”?



A definition (as currently understood) is nothing but the result of a serial step-by-step observation.


To paraphrase you with the correct usage of some of words you use most but understand the least ‘A definition is noting without an analytical approach’.




The current community of mathematicians is nothing but a group of people which are skilful to get things only if they are defined by a serial step-by-step observation.

Furthermore, over the past 2500 years the mathematical science itself was recognized by this particular observation.

Well a least you got the part about them being skilful correct, but that particular skill seems to have eluded you or more likely you just fail to observe it.


The aim of my work is to show that the mathematical science is not the result of any particular observation.

Then why do you continually try to force things to your one particular point of view and remain in denial that other points of view (like coordinate systems) can obtain the same conclusions you use as your defining aspects. In fact above you have now associated your non-local definition to having theoretical extents. If current math and geometry can do things better then your own work so much so that you are now modifying your own work to emulate current math and geometry, why would anyone need your work?

Again it is only you that claims conclusions must be “the result of any particular observation”, specifically your own.



No,

If a line segment is defined by a serial observation, then it is determined and distinguished by points.

Horse hockey, I made no observations, serial or otherwise in the line segment examples I gave before. I simply defined a line segment by giving two points in a coordinate system.




This is not the case if a line segment is defined by parallel observation.

In that case objects like points or coordinates are not used in order to distinguish between different line segments and the non-local property of a line segment is considered in order to distinguish between line-segments, for example:

x = ____

y = ____


x < and = y (example: _____)

or

y > and = x (example: _____)

So from some point to some other point you have a line segment configured to be COLOR=”RED” then from some point to some other point you have a line segment configured to be COLOR=”BLUE” and claim this is a demonstration of you defining and distinguishing line segments without using points. You have absolutely no idea how “skillful” that “community of mathematicians” were so many thousands of years ago to develop a geometric system that even you use today (perhaps without realizing it) in your effort to assert that you do not use it.

[doronshadmi]

Theoretical extents are not “w.r.t.” anything;

Please demonstrate how extension is considered by ignoring anything but the extended thing.

I really wish to see such a trick.


They were simply defined as theoretical abstractions. Once defined however their usefulness was readily “discovered” and continues today.
These theoretical abstractions are based only on serial step-by-step thinking style.

The outcomes that are based on this thinking style are indeed very useful but they are not the one and only one thinking style that can be used in order to develop the mathematical science.

You are talking about past, present and future achievements that are based on a particular thinking style, the serial step-by-step analytic one.

I claim that by using more than a one thinking style, already known knowledge can fundamentally be changed in addition to a new knowledge, which is added to the considered body of knowledge.

In this case the considered is the body of knowledge of the mathematical science, which is not saved from fundamental changes of already agreed things, especially if these things are the outcome of a one and only one thinking style.

Then why do you continually try to force things to your one particular point of view and remain in denial that other points of view (like coordinate systems) can obtain the same conclusions you use as your defining aspects.
You did not show that using coordinates can obtain the same conclusions that I get about line segments.

Also please answer to http://forums.randi.org/showpost.php?p=4256330&postcount=975.


... even you use today (perhaps without realizing it) in your effort to assert that you do not use it.
You are right, but there is a very important difference between you and me.

You are using one and only one thinking style, where I do not.

This is the reason why you cannot get my work.

[jsfisher]

The outcomes that are based on this thinking style are indeed very useful but they are not the one and only one thinking style that can be used in order to develop the mathematical science.


As has been pointed out to you so many times before, if you'd like to develop something new in Mathematics, have at it. Nobody here objects to you coming up with a new branch. However, you don't get to redefine the existing branches on personal fiat.

[nathan]

You are using one and only one thinking style, where I do not.

That's trivially true, because you do not think.

[doronshadmi]

As has been pointed out to you so many times before, if you'd like to develop something new in Mathematics, have at it. Nobody here objects to you coming up with a new branch. However, you don't get to redefine the existing branches on personal fiat.
In order to talk about branches, you have to understand the tree.

Since you are ignorent of the trunk, you cannot talk about branches.

And yes, an existing branch can fundamentally be changed by a new understanding of it.

[drkitten]

In order to talk about branches, you have to understand the tree.

We've been telling you that for some time now.

We've even been trying to teach you the fundamentals.

A pity that you're so willfully ignorant that you don't even understand the basics of the fields you're botching.

[doronshadmi]

We've even been trying to teach you the fundamentals.
You can't because you are using only a one thinking style, which is nothing but a particular case of many other thinking styles that you don't use.

[drkitten]

You can't because you are using only a one thinking style

Well, I'm glad that at least you admit you're unteachable, even if you get the reason wrong.

[doronshadmi]

Well, I'm glad that at least you admit you're unteachable, even if you get the reason wrong.

Do you really think that there is a border between being a teacher and being a student?

I don't think so, each one of us is both a student and a teacher in the same time.

[drkitten]

Do you really think that there is a border between being a teacher and being a student?

Of course not.

Which explains why you can't explain your "ideas." You can't teach, either.



I don't think so, each one of us is both a student and a teacher in the same time.

Wrong. You're neither a teacher nor a student.

[Little 10 Toes]

In order to talk about branches, you have to understand the tree.

Since you are ignorent of the trunk, you cannot talk about branches.

And yes, an existing branch can fundamentally be changed by a new understanding of it.

But you won't acknowledge what terms and definitions we use about the trunk, so how can we use the same terms about the branch?

I think your tree is full of nuts. :D

Do you really think that there is a border between being a teacher and being a student?

I don't think so, each one of us is both a student and a teacher in the same time. Yes there is a border. A teacher has more experience in a selected field and is willing to pass on that knowledge to someone who wishes to understand further in that field. Stephen Hawking is someone who teaches the mysteries of the universe while a kid could teach him about Pokemon video games. If Steve doesn't want to learn, Steve is not a student. If the kid can't explain about Pokemon video games, then the kid is not a teacher.

You, however, do not fall in either one of those groups. You would be the law student that would not answer questions involving a police investigation because you believe you have the right to remain silent. (You do not have the right to remain silent because that applies to you when you are under arrest.)

So when are you going to start talking about your tree trunk? And avoidance of previously mentioned word definitions still noted.

[The Man]

Please demonstrate how extension is considered by ignoring anything but the extended thing.

I really wish to see such a trick.

Again it is called a coordinate system, which is not a ‘thing’ but an abstract concept. Do you have some difficulty distinguishing between the two? The key point is, much as you try to profess, the concept of coordinate systems gives us the ability to “perceive” things from multiple perceptivities, just what you claim to do but can not demonstrate. The consideration of coordinate systems is demonstrated by most of the technology you use and even your futile attempts to demonstrate that you do not use coordinate systems.


These theoretical abstractions are based only on serial step-by-step thinking style.

The outcomes that are based on this thinking style are indeed very useful but they are not the one and only one thinking style that can be used in order to develop the mathematical science.

No one but you is claiming that there is one and only one way to examine things, all we do claim is that such examination must produce some improvement. How one gauges improvement then becomes the question, you can just accept something offered as an improvement, or you can analyze what is presented to determine if there is some actual improvement. In the former everything is acceptable, or without examination everything one claims improves, does so, so everything improves. In the latter the only things that improve are those that have demonstrably improving attributes that one can demonstrate by analyzing those attributes.



You are talking about past, present and future achievements that are based on a particular thinking style, the serial step-by-step analytic one.

Nope, as I have always said it is you confined to one “thinking style” which simply seems to be you disagreeing with yourself. Nothing new in the past, present, or future, when you actually what to expand your perspectives you might actually learn what has been done in the past, is being done in the present and might be done in the future.



I claim that by using more than a one thinking style, already known knowledge can fundamentally be changed in addition to a new knowledge, which is added to the considered body of knowledge.

In this case the considered is the body of knowledge of the mathematical science, which is not saved from fundamental changes of already agreed things, especially if these things are the outcome of a one and only one thinking style.

Oh, except from your exclusive non-thinking style?



You did not show that using coordinates can obtain the same conclusions that I get about line segments.

Except for the fact that some given line segment can have coordinate positions greater then and less then some given point and that you have to think about it.


Also please answer to http://forums.randi.org/showpost.php?p=4256330&postcount=975.

No time now but I will give you the analytical approach you request later.



You are right, but there is a very important difference between you and me.

No doubt.


You are using one and only one thinking style, where I do not.

This is where you are worng, you have speficialy stated and contunue to assert the correctness of your “one and only one thinking style” of “parllel obsevation”.


This is the reason why you cannot get my work.

You do not get your work because you find analyzing your work as a determent, why should you expect anyone else to find it of any consequence if you are not willing yourself to take your work seriously.

[The Man]

Doron, for someone proclaiming the significance of alternate points of view you seem to take a singular approach. Coordinate systems enable us to take multiple approaches. For example, within certain coordinate systems line segments are straight in others they are curved. In such systems a line segment, still defined by two points, can also be referred to as a cord. In polar coordinates we can define such a cord as (in a radius angle notation) from 5 units at 90 degrees to 5 units at 180 degrees. I am curious to see if your work has addressed such alternative perspectives that are currently available within standard geometry.

[doronshadmi]

Again it is called a coordinate system
If a line segment is determined by points, its non-locality cannot be researched.

In other words, the rest of your post is limited to local observation.

A thing is used here for any abstract or non-abstract researchable.

[zooterkin]

The patience of some posters here never ceases to amaze me. Bravo!

For example, within certain coordinate systems line segments are straight in others they are curved. In such systems a line segment, still defined by two points, can also be referred to as a cord.

Just in case doronshadmi should choose to follow up on this, the spelling is 'chord'.

[doronshadmi]

Doron, for someone proclaiming the significance of alternate points of view you seem to take a singular approach. Coordinate systems enable us to take multiple approaches. For example, within certain coordinate systems line segments are straight in others they are curved. In such systems a line segment, still defined by two points, can also be referred to as a cord. In polar coordinates we can define such a cord as (in a radius angle notation) from 5 units at 90 degrees to 5 units at 180 degrees. I am curious to see if your work has addressed such alternative perspectives that are currently available within standard geometry.

If a line segment is an atom, then it is measured by relations between atoms.

For example: 1(= ____) – 0.5(= __) = 0.5(=__)

EDIT:

By understanding a line segment as an atom, the real-line is a 1D overlap of infinitely many different non-local atoms, ordered according to a local atom, for example:


0 = . (local atom)

1 = ____ (non-local atom)

.5 = __ (non-local atom)

Pi = ______________ (non-local atom)

Real-line example: ______________.______________

[nathan]

If a line segment is an atom, then it is measured by relations between atoms.

For example: 1(= ____) – 0.5(= __) = 0.5(=__)

Hurrah! Atoms that can be divided.

[nathan]

If a line segment is determined by points, its non-locality cannot be researched.

In other words, the rest of your post is limited to local observation.

A thing is used here for any abstract or non-abstract researchable.

Could you please highlight exactly where you used 'thing' in the two sentances prior to you claiming you used 'thing' in some way?

[nathan]

Just in case doronshadmi should choose to follow up on this, the spelling is 'chord'.

hehe, way to go picking on that misspelling :) Haven't you noticed Doron's misspellings are so complete they often hit a completely different word!