Deeper than primes

[doronshadmi]

Here there is total "Uncertainty," because none of the items have a known or definite identity.

Uncertainty is a superposition of ids, that prevents the strict id of a given element.

X
X
X
X
X, does not represent superposition of ids of a given element, unless X is used here as a placeholder.

X,X,X,X,X does not represent redundancy of ids, if it used as a placeholder.

and I have no idea what a parallel quantity is in contrast to a serial one,

Quantity does not have parallel or serial aspects.

Quantity is complete if it can be summarized (and it can be done only under finite quantity).

 

[jsfisher]

Use your poor imagination.

So, you have no idea why you used the word, and now you want me to explain it to you.

Meanwhile, you are using this aside in an attempt to evade another Doron blunder: It is meaningless to consider the boolean value of membership (or its negation) disassociated from its two operands just as it is idiotic to ask about the numeric value of the plus operator without naming its addends.

Care to correct your membership truth table, or are you unable to figure out how?

 

[Apathia]

Uncertainty is a superposition of ids, that prevents the strict id of a given element.

X
X
X
X
X, does not represent superposition of ids of a given element, unless X is used here as a placeholder.

X,X,X,X,X does not represent redundancy of ids, if it used as a placeholder.

So my "X" is not something with an unknown identity. It's anything. It has all identities.
Not that that's clearing things up for me, but it does sound a bit more sensible.

Quantity does not have parallel or serial aspects.

But number does??
And quantity is not a sum (or result of a mathematical calculation)?
(Again it seems you have something else in mind when you talk about "numbers.")

Quantity is complete if it can be summarized (and it can be done only under finite quantity).

Ah, now here's a possible distinction:
OM includes quantities that are incomplete or indefinite.
a "3" in OM may not be "3" as in serial numerality, but could be (In the uncertain sense above) any quantity untill it is quantified.

Is there a distinction between "serial" quanity and "non-local," "uncertain," "incomplete" quanity?

Above, you say no.

And you said to me,

I see that you are able to get the concept of Number only in terms of (A,B,C,D,E,F,...) asymmetric form.

So there must be a sense or aspect of "Number" in the "Symmetric" form.
Just what is that if it's not a matter of quantity which does not have a serial or parallel aspect?

These puzzle pieces are not from the same box.

 

[The Man]

After more than 250 pages, you still can't get that your definition of line by a collection of localities, is not my definition of a line as the non-local aspect of the atomic self-state.

After more than 250 pages, you still can't get that whatever you want to call it “the non-local aspect of the atomic self-state”, a “superposition” without superposition or a little pink unicorn, it simply does not matter what you call a line Doron that ascription is linear. That is what linear means Doron represented by a line or lines. Not to worry Doron, with your “superposition of ID’s” that you claim does not use superposition, your inference of your “definition” of a line that is not, well, linear is hardly a surprise.

What a poor reasoning you are using.

What a complete lack of reasoning you are using.

Wrong:

The truth table of XOR is: 0110
00 --> 0 (Non-locality)
01 --> 1 (Locality)
10 --> 1 (Locality)
11 --> 0 (Non-locality)

The truth table of NXOR is: 1001
00 --> 1 (Non-locality)
01 --> 0 (Locality)
10 --> 0 (Locality)
11 --> 1 (Non-locality)

If you try to get 1001 in terms of 0110 you get a contradiction, and this is exactly what you are doing all along this thread.

A XOR not_A is the logic of Locality.

A NXOR not_A is the logic of Non-locality, but since you are forcing XOR on NXOR you are missing it all along this thread.

Once again Doron the only “forcing” is entirely yours, again exemplified by the different outputs I gave before and you quoted.

“Ranges of values, variables and even degrees of error” are all the particular case of (A,B,C,...) form (where order can also be ignored in some of the cases).

You still do not get the notion of superposition of ids, which can be superposition of variables, constants, functions, any other thinkable things or any mixture of them.

In all these cases only the mount is clearly known if it is a finite superposition, and in the case of an infinite superposition also the amount is unknown.

That would be your “superposition of ids” where you claim you do not use superposition. So again, who cares? Why should anyone care when you obviously do not care what you are saying?

 

[The Man]

You better check Reply #10247 where you were found "wrong" pertaining to the above. He effectively flunked 1+1=2, right there. I knew it would happen one day.

Well, what can we expect with "superposition" without superposition and evidently a non-linear line.

 

[epix]

This is the whole idea, it is a novel notion. You will not find it in any "external" article, because traditional Math gets Non-locality in terns of a collection of localities.

Novel ideas based on arbitrary property assignments are really hard to teach. There is no problem to accept the novelty in the domain of religion, but in math, such an acceptance is impossible without examining the fundamental structure of the novel propositions, and I guess the task of proving the soundness of your new insight into the theory of information proves to be very difficult. I understand, coz I too ran into difficulties in assigning more logical opposite to the word NOPE that you've mentioned:

Old opposite: NOPE <=> YEP

New opposite, the intermediate version: NOPE <=> EPON

New opposite, the final version: NOPE <=> CLOSE

Under the first/last opposite, letter N becomes the last, thus transforming NOPE into OPEN and under the natural mutually exclusive opposite not OPEN = CLOSE

What can I tell ya? The close-minded orthodox racoons rejected the novel re-assignment. Yep, that's what happened.

 

[The Man]

...flunked 1+1=2 ??

What are you talking about?



The Man is focused only on the local aspect of NXOR connective (where the examined values are different, for example: A,not_A or 0,1 etc...) which is indeed always False, for example:

The truth table of NXOR is: 1001
00 --> 1 (Non-locality) (True)
01 --> 0 (Locality) (False)
10 --> 0 (Locality) (False)
11 --> 1 (Non-locality) (True)

Doron the only “focus” was to show you the different result XOR gives from what NXOR would give under the same input conditions, with one result being a contradiction and the other being a tautology. Evidently though you were too busy “forcing” things (particularly your own claims or “focus” onto others) that you obviously missed that particular “focus”

...
By doing that he misses the true value of Non-locality.

What you mean your “superposition” without superposition? Nope I didn’t miss that.

 

[Apathia]

Doron,

Here's another question in bold:

Just what do you mean by "Uncertainty" anyway?

Is it that individual elements have Ids of their own, but it's uncertain if those ids entail a "Redundancy" bridging into a collective?
Cucumber Ice-Cream for example. It has an identity, but is it a Baskin Bobbins or a Ben & Jerry flavor?

Or does "Uncertainty" mean that a given individual element has every identity there ever was or will be, till it gets narrowd down to one by a bridging collective id. (Redundancy? What does that mean, as well?
It's every flavor of ice-cream and a turkey sandwich till it gets a group lable slapped on it.

Is "Uncertainty" about amount or quantity?
In what way is it an uncertainty of quantity?
I'm having a lot of trouble fitting these diverse concepts into the simple does everything Local/Non-local Bridging diagram.

Or am I trying to pin down a word that is supposed to be a writhing, slippery eel?

 

[doronshadmi]

Doron the only “focus” was to show you the different result XOR gives from what NXOR would give under the same input conditions, with one result being a contradiction and the other being a tautology.

The same input conditions for both XOR and NXOR are 00,01,10,11 as follows:

The truth table of XOR is: 0110
00 --> 0 (Non-locality)
01 --> 1 (Locality)
10 --> 1 (Locality)
11 --> 0 (Non-locality)

The truth table of NXOR is: 1001
00 --> 1 (Non-locality)
01 --> 0 (Locality)
10 --> 0 (Locality)
11 --> 1 (Non-locality)

Contradiction is 0000 and Tautology is 1111.

Now please show us where exactly there is Contradiction or Tautology among 1001 or 0110?

 

[doronshadmi]

So, you have no idea why you used the word, and now you want me to explain it to you.

Again.

Use your poor imagination (Hint: the opposite of NOPE is YEP http://www.internationalskeptics.com/forums/showpost.php?p=6046213&postcount=10185).

 

[Apathia]

Doron,

You've stated that quantity does not have separate "parallel" and "serial" aspects.
Yet your're clear in your statements that "number" does.

Please help me to get the concept of number in its "Symmetric," "Element-only," "Uncertainty."

I keep hitting a disconnect here where the concepts of what number is supposed to be, apart from its traditional "serial" sense, don't fit together.

So what is number aside from quantity?

 

[The Man]

The same input conditions for both XOR and NXOR are 00,01,10,11 as follows:

The truth table of XOR is: 0110
00 --> 0 (Non-locality)
01 --> 1 (Locality)
10 --> 1 (Locality)
11 --> 0 (Non-locality)

The truth table of NXOR is: 1001
00 --> 1 (Non-locality)
01 --> 0 (Locality)
10 --> 0 (Locality)
11 --> 1 (Non-locality)

Contradiction is 0000 and Tautology is 1111.

Now please show us where exactly there is Contradiction or Tautology among 1001 or 0110?

Already done.

... again A XOR NOT A is always TRUE (a tautology) while A NXOR NOT A is always FALSE (a contradiction).

Similarly A XOR A is always FALSE (a contradiction) while A NXOR A is always TRUE (a tautology).

A contradiction or Tautology is not an aspect of some logical operator as you seem to assert with “Contradiction is 0000 and Tautology is 1111”, but an aspect of the entire logical statement (including the input propositions). An operator that always returns FALSE (as in your “Contradiction is 0000”) would indeed be a contradiction as one that always returns TRUE (as in your “Tautology is 1111”) would be a Tautology. However as mentioned before Tautologies and Contradictions are not limited to logical operators that only have one output and such operators are, by that very nature, without any practical use. The Contradictions and Tautologies I have show above and before do not depend on the logical value of proposition A (it can be TRUE or FALSE) they are simply a result of using the same proposition as both inputs of the operator or using that proposition with its negation as those inputs. The key asspect I think you’re missing is when the value of the input propositions are dependent upon each other, or just one is dependent upon the other, as can often be the case. Certainly the input values do not have to be dependent on each other, or just one is dependent upon the other, and A NXOR B would not always be TRUE (a tautology) or always be FALSE (a contradiction). However if B = NOT A then those inputs are dependent upon each other and A NXOR B is always FALSE (a contradiction).

If C is always TRUE when A = FALSE but can be TRUE or FALSE when A=TRUE then C is only partially dependent on the value of A (specifically when A is FALSE), but A is entirely independent of the value of C (the value of A does not depend upon the value of C and more specifically the value of C is independent of A when A is TRUE).

A= “It is raining”

B = “It is cooler than 70 degrees”

C= B OR NOT A

C is dependent on both A and B but neither A nor B depend on C. A and B are also mutually independent of each other, but are not mutually independent of C as C depends on both.

The whole concept of mutual dependence in contrast to dependence that is not mutual as well as mutual independence in contrast to independence that is not mutual (the same thing as dependence that is not mutual, one is dependent on the other but the other is independent of that one) seems to be one of your major stumbling blocks.

 

[doronshadmi]

Already done.



Similarly A XOR A is always FALSE (a contradiction) while A NXOR A is always TRUE (a tautology).

A contradiction or Tautology is not an aspect of some logical operator as you seem to assert with “Contradiction is 0000 and Tautology is 1111”, but an aspect of the entire logical statement (including the input propositions). An operator that always returns FALSE (as in your “Contradiction is 0000”) would indeed be a contradiction as one that always returns TRUE (as in your “Tautology is 1111”) would be a Tautology. However as mentioned before Tautologies and Contradictions are not limited to logical operators that only have one output and such operators are, by that very nature, without any practical use. The Contradictions and Tautologies I have show above and before do not depend on the logical value of proposition A (it can be TRUE or FALSE) they are simply a result of using the same proposition as both inputs of the operator or using that proposition with its negation as those inputs. The key asspect I think you’re missing is when the value of the input propositions are dependent upon each other, or just one is dependent upon the other, as can often be the case. Certainly the input values do not have to be dependent on each other, or just one is dependent upon the other, and A NXOR B would not always be TRUE (a tautology) or always be FALSE (a contradiction). However if B = NOT A then those inputs are dependent upon each other and A NXOR B is always FALSE (a contradiction).

If C is always TRUE when A = FALSE but can be TRUE or FALSE when A=TRUE then C is only partially dependent on the value of A (specifically when A is FALSE), but A is entirely independent of the value of C (the value of A does not depend upon the value of C and more specifically the value of C is independent of A when A is TRUE).

A= “It is raining”

B = “It is cooler than 70 degrees”

C= B OR NOT A

C is dependent on both A and B but neither A nor B depend on C. A and B are also mutually independent of each other, but are not mutually independent of C as C depends on both

Being independent means that there is no connectivity between A,B propositions (total isolation).

Being mutual means that A,B propositions can't be expressed (total connectivity).

These extremes are not C= B OR NOT A, or in other words, mutual-independency is fundamental for intermediate conditions, which actually enable to discus on something like "if C is always TRUE when A = FALSE but can be TRUE or FALSE when A=TRUE ...", in the first place.

… then C is only partially dependent on the value of A (specifically when A is FALSE)

You get dependency in terms of the possible logical results of the involved propositions (in this case you claim that C is partially dependent on A according to its strict/non-strict True or False values). By doing that you are missing mutual-independency as the fundamental condition that enables to discus on these subjects, in the first place.

In other words, you do not get what mutual-independency is.

Already done.

Wrong.

 

[doronshadmi]

So what is number aside from quantity?

OM's view of Number does not ignore Non-locality/Locality qualitative aspects of this concept, as the traditional view of this concept does.

As a result OM's view of Number is not closed only under the clear ids aspect ( (A,B,C,…) form or (A,A,A…) form ) of a given quantity.

 

[The Man]

Being independent means the there is no connection between A,B propositions (total isolation).

No it simply means not dependent.

http://dictionary.reference.com/browse/independent

in•de•pend•ent
   ˌɪn dɪˈpɛn dəntShow Spelled[in-di-pen-duh nt] Show IPA
–adjective
1.
not influenced or controlled by others in matters of opinion, conduct, etc.; thinking or acting for oneself: an independent thinker.
2.
not subject to another's authority or jurisdiction; autonomous; free: an independent businessman.
3.
not influenced by the thought or action of others: independent research.
4.
not dependent; not depending or contingent upon something else for existence, operation, etc.

….

13.
Mathematics . (of a quantity or function) not depending upon another for its value.


….

15.
Logic .
a.
(of a set of propositions) having no one proposition deducible from the others.
b.
(of a proposition) belonging to such a set.

Again A and B are mutually independent, and although C is dependent on both neither is dependent on C.

Please show from what referance source you obtained a definition of independent that requires “no connection between” and “(total isolation)”.

Being mutual means that A,B propositions can't be expressed (total connectivity).

No it simply means “Held in common; shared:”or “reciprocal:”


http://dictionary.reference.com/browse/mutual

mu•tu•al
   ˈmyu tʃu əlShow Spelled[myoo-choo-uh l] Show IPA
–adjective
1.
possessed, experienced, performed, etc., by each of two or more with respect to the other; reciprocal: to have mutual respect.
2.
having the same relation each toward the other: to be mutual enemies.
3.
of or pertaining to each of two or more; held in common; shared: mutual interests.
4.
having or pertaining to a form of corporate organization in which there are no stockholders, and profits, losses, expenses, etc., are shared by members in proportion to the business each transacts with the company: a mutual company.

In the case of mutual independence what is “Held in common; shared:”or “reciprocal:” is that independence from each other meaning the mutual lack of dependence upon each other. Just as in the case of mutual dependence what is “Held in common; shared:”or “reciprocal:” is that dependence upon each other.

Why this is such a difficult concept for you to understand or accept is only indicative of your apparent preference for self contradiction.

If it were ‘totally connective total isolation’ as you assert it would simply be self contradictory as well as generally contradictory. However the actual meaning as a ‘reciprocal lack of dependence’ it is entirely self consistent and generally consistent.

These extremes are not C= B OR NOT A,

Your “extremes are not” the meanings of the words you ascribe them to either. So again who cares what you claim they are not?

or in other words, mutual independency is fundamental for intermediate conditions,

That would be those other words “total connectivity” and “total isolation” that are not the same as mutual and independent. Your “other words” fail you just as your “direct perception” does. Not surprising as the only reason you seem to ascribe your own contradictory “extremes” to the words mutual and independent would undoubtedly be your flawed “direct perception”.

which actually enable to discus on something like "if C is always TRUE when A = FALSE but can be TRUE or FALSE when A=TRUE", in the first place.

Back to your old standard hiding position Doron, that your contradictory notions are the only reason that “enable to discus on something like” (insert argument Doron can not refute or apparently understand) “in the first place”.

In other words, you do not get what mutual-independency is.

As usual Doron and in the same words repeated throughout this thread you are just making up your own self contradictory meaning for mutually independent. So again who cares what you claim I or anyone does “not get” about your own personal self contradictory and generally contradictory language?

Wrong.

Indeed you demonstrably are.

 

[doronshadmi]

http://dictionary.reference.com/browse/independent

http://dictionary.reference.com/browse/mutual

You do not get that OM is a novel view of the discussed subjects, so using dictionary can't help here, because what you find in the dictionary is the local-only traditional view of the discussed subjects.

You are still closed under your dogmatic view of the discussed subjects.

... again A XOR NOT A is always TRUE (a tautology) while A NXOR NOT A is always FALSE (a contradiction).

A represents "member".

~A represents "not a member".

Non-locality as expressed by NXOR:

A NXOR ~A
------------
F       F --> T (Non-locality) (True)
F       T --> F (Locality) (False)
T       F --> F (Locality) (False)
T       T --> T (Non-locality) (True)

Locality as expressed by XOR:

A XOR ~A
------------
F      F --> F (Non-locality) (False)
F      T --> T (Locality) (True)
T      F --> T (Locality) (True)
T      T --> F (Non-locality) (False)

In other words, you are wrong exactly because you are using a local-only view of the discussed subject.

That would be those other words “total connectivity” and “total isolation” that are not the same as mutual and independent. Your “other words” fail you just as your “direct perception” does.

Another phrase that is derived form a local-only view of the discussed subject.

 

[The Man]

http://dictionary.reference.com/browse/independent

http://dictionary.reference.com/browse/mutual

You do not get that OM is a novel view of the discussed subjects,

No it isn’t Doron, people just making up their own meanings for words and concepts certainly is not “a novel view of the discussed subjects” on this forum.

so using dictionary can't help here,

Sure it can, you just have to find the right words to express what you mean instead of just trying to give your own meaning to other words. It may take a little more effort on your part, but it will facilitate communication.

because what you find in the dictionary is the local-only traditional view of the discussed subjects.

Doron the dictionary is not a “view of the discussed subjects” it is just the common usages of words and there are plenty of them to use. One expresses a view by putting the appropriate words together. If you are simply not interested in accurately expressing your “view of the discussed subjects” why should anyone care about your “view of the discussed subjects”. The indication is Doron that you are trying to use certain words (like cardinality and superposition) in order to associate your notions to established concepts in math and quantum mechanics. However in your usage you specifically assert that you do not use those same concepts, thus your use of those words is a lie, a sham an attempt to deceive on your part by using the same words without the same meaning. If you actually believed in your own notions they should stand on their own merits and you would not have to try to use the same words with different, often undefined and self-contradictory meanings. The fact that you continue to do this simply confirms that you are not as interested in accurately representing your notions as you are interested in just applying your own meaning to well established concepts by simply changing the meaning of the words so they no longer represent those established concepts (or anything self –consistent and generally consistent). Present your own notions with the proper words Doron (if you used the right words to begin with you wouldn’t be saying “in other words” so often) and stop trying to claim some kind of ownership to well established concepts by using words common to those established concepts without the meanings common to those concepts. It just shows how hollow, vapid and meaningless your use of language actually is.

A represents "member".

~A represents "not a member".

Non-locality as expressed by NXOR:

A NXOR ~A
------------
F       F --> T (Non-locality) (True)
F       T --> F (Locality) (False)
T       F --> F (Locality) (False)
T       T --> T (Non-locality) (True)

Locality as expressed by XOR:

A XOR ~A
------------
F      F --> F (Non-locality) (False)
F      T --> T (Locality) (True)
T      F --> T (Locality) (True)
T      T --> F (Non-locality) (False)

In other words, you are wrong exactly because you are using a local-only view of the discussed subject.

Doron again it does not matter what “A represents” A and “~A” are still mutually dependent.

... again A XOR NOT A is always TRUE (a tautology) while A NXOR NOT A is always FALSE (a contradiction).

Similarly A XOR A is always FALSE (a contradiction) while A NXOR A is always TRUE (a tautology).

Again you are wrong exactly because you are just making up nonsense about “the discussed subject”.

 

[Apathia]

OM's view of Number does not ignore Non-locality/Locality qualitative aspects of this concept, as the traditional view of this concept does.

As a result OM's view of Number is not closed only under the clear ids aspect ( (A,B,C,…) form or (A,A,A…) form ) of a given quantity.

The various aspects of your discourse still don't fit seamlessly together but are disjointed with words that have sometimes contradictory meanings and are presented as a whole only by means of equivocation.

I'll take it then that one feature of this chaos is that Organic Mathematics seeks to present numbers that have indefinite or not yet decided qunatities.
The Organic Number "3" is not necessarily the traditional quantity three, but may be 2, 1, or 0 by traditional reckoning. And is simultainiously all those values.

Traditionally number counts items of a defined common class of items.
OM seeks to have number include items that aren't of the given class.
So in its attempt at "non-locality" a sack of a dozen potatoes isn't the quantity 12.
The actual Organic Number of this situation is ...
Well, that can't be known.
It must be a very large figure, because it must include all the potatoes that haven't been sacked, all the Mr. Potato Head toys, all the potato pancakes in the IHOP, tomatoes (The are also members of the Nightshade Family), and this just can't stop.

But you might reply to me that "non-local" items in "parallel" as opposed to "serial" aren't "quantities (how many)." And I'm off because I'm not distingushing between the "element" and the "collective" levels.
I really hope you don't go that way, because it is a blatant contradiction of what you have claimed elsewhere.

 

[Apathia]

I think I get the overall picture now, certainly the intent of OM.
It's only confusing when I, or anyone, looks to closely, especially with a mathematical eye.

If one uses Organic Numbers, (s)he will see beyond the boundaries of ordinary set membership, to include the myriad of things that aren't being caged by that set or any set. And even the conventional members of a set can be regarded as liberated from its confinement while still granted the privileges of membership.

There is a view to quality that transcends a mere quantitative sum.

The result of a calculation involving a mathematical formula is not the last word, since it is only a special case of Organic Number.

Using Organic Numbers, the boundaries of analytic and discursive thinking are broken through to the realm of free association.

And there are more spiritual values intended in OM than I have time to talk about this evening.

The natural question is
How do you use an Organic Number?

Sure you can use the serial aspect of it in the ordinary way.
But it's meant for more, right?

Attempting formulas and calculations with it is getting "serial" only.
Trying to calculate all that is non-locally present and included in ones target of discourse, is cumbersome beyond measure.

Counting with Organic Numbers is an unimaginable exercise.

So how does one use the expanded value of an organic number?

But my mistake here is again looking at the matter too closely.
The diagrams of OM are meant to be seen from a distance.
Like the kind of distance where I saw the relation between the symbolic intent of the Redundancy/Uncertainty diagrams and that Escher print of the staircases.

The use is not making a formula can calculate the fictitious hidden variables of quantum behavior, but its almost kabbalah-like diagrams and its Yin/Yang approach are symbolic of Transcendence.

Doron you can show me mistaken simply by showing us how an organic number is used in a mathematical way.

I don't mean a loose resemblance to waves and particles or an odd version of the Lorentz contraction.
I mean a Doron Transformation using OM that results in actionable intelligence or objective results.

Or show us exactly how OM is a mirror of the workings of intuition and non-linear thinking.

But maybe that would be asking to look to closely.

Maybe just how one uses OM as a ritual of transcendent thinking.

Oh, it's not meant for the TM stuff?
It's just meant to include an uncertainty and "fog" to set membership?

Well, show us how that's done.

 

[epix]

Contradiction is 0000 and Tautology is 1111.

This is heavy, just burying tensor calculus into a pile of triviality.

Let's try again.

A) 0000 = "a set of identical digits"
B) 1111 = "a set of identical digits not identical to (A)"

Tautology: "a needless repetition of an idea, statement, or word"
http://www.merriam-webster.com/dictionary/tautology

If the cardinality of (A) is 4 and the cardinality of (B) is 4 as well, then under that condition, (A) = (B). But if the 0's in (A) and the 1's in (B) repeat 4 times, and "TAUTOLOGY" <> "CONTRADICTION," then a contradiction emerges: due to the definition of tautology, both sets cannot have the same cardinal number. The error-free version is then

Contradiction is 0000 and Tautology is 1111111111111....

until someone says that there have been just enough 1's, and no further repetition is needed.