Deeper than primes

[epix]

In other words epix you are wrong because according to traditional mathematics |R| is a size (or magnitude) of collection of objects (0-dimensional elements, in this case), which is smaller than the size (or magnitude) of a 1-dimensional element, where Dimension is the property "of the same kind" that enables the comparison.

Your claim lacks citation, which is a necessary addendum in your case, coz your interpretation of what the "traditional math" says is known to result in aggravated assault on the power set -- just to mentioned one instance where you completely lost your analytic footing.

You completely lack the necessary terminology to describe the relationships that you think exist. "Magnitude of real numbers" in connection with the size or cardinality of R simply doesn't exist in the traditional math terminology, yet you use the term to "repeat" what the traditional math says, which is a strong indicative of you not comprehending the story that the traditional math tells.

The cardinality of R and the cardinality of its subsets A and B as codomains is independent of the magnitude or length of line segments, as you can see below.

You just claim that rabbit can run faster than dormi completely oblivious to the fact that dormi doesn't exist.

 

[doronshadmi]

“A = True” was your own assertion Doron which means that “AB AND A or A AND AB” simply (and strictly) evaluates to “AB”

A = True
B = False

AB = True/False superposition, or in other words, AB is non-strict.

Since input AB is non-strict , then AB AND A or AB AND A output is non-strict, where the commutativity of AND connective has no influence on the non-strict property of the output.

It is very simple, yet you can't get it.

 

[doronshadmi]

Your claim lacks citation, which is a necessary addendum in your case, coz your interpretation of what the "traditional math" says is known to result in aggravated assault on the power set -- just to mentioned one instance where you completely lost your analytic footing.

You completely lack the necessary terminology to describe the relationships that you think exist. "Magnitude of real numbers" in connection with the size or cardinality of R simply doesn't exist in the traditional math terminology, yet you use the term to "repeat" what the traditional math says, which is a strong indicative of you not comprehending the story that the traditional math tells.

The cardinality of R and the cardinality of its subsets A and B as codomains is independent of the magnitude or length of line segments, as you can see below.

[qimg]http://img684.imageshack.us/img684/8067/injectbiject.png[/qimg]

You just claim that rabbit can run faster than dormi completely oblivious to the fact that dormi doesn't exist.

Only your second diagram is relevant, and it is equivalent to the following diagram:

Sets A,B,C,D, ... etc. have the same cardinality (which is the size of a given set), which is |R| points and yet the size of the 1-dimensional elements is different exactly because |R| < |1-dimensional element| = the power of the continuum.

In other words, a set of |R| points does not have the power of the continuum, and one understands it only if he\she does not ignore the non-locality of 1-dimensional element under line\points co-existence (where a point is the minimal existing local element, and a line is the minimal existing non-local element, where no set of points has the property of non-local element).

 

[epix]

A = True
B = False

AB = True/False superposition, or in other words, AB is non-strict.

Since input AB is non-strict , then AB AND A or AB AND A output is non-strict, where the commutativity of AND connective has no influence on the non-strict property of the output.

It is very simple, yet you can't get it.

Very simple? Show a shade of mercy for Lord's wisdom, coz you took it to the heights only a few dare to climb:

The superposition calculus is a calculus for reasoning in equational first-order logic. It has been developed in the early 1990s and combines concepts from first-order resolution with ordering-based equality handling as developed in the context of (unfailing) Knuth-Bendix completion. It can be seen as a generalization of either resolution (to equational logic) or unfailing completion (to full clausal logic). As most first-order calculi, superposition tries to show the unsatisfiability of a set of first-order clauses, i.e. it performs proofs by refutation. Superposition is refutation-complete — given unlimited resources and a fair derivation strategy, every unsatisfiable clause set can eventually be proved to be unsatisfiable.

As of 2007, most of the (state-of-the-art) theorem provers for first-order logic are based on superposition (e.g. the E equational theorem prover), although only a few implement the pure calculus.

http://en.wikipedia.org/wiki/Superposition_calculus

Is the variable AB some union of mutually exclusive statements? Can you substitute AB with an example so the output given by the conjunction AND could be demonstrated by using an applicable example? I give you an example of the example:

The law of superposition (or the principle of superposition) is a key axiom based on observations of natural history that is a foundational principle of sedimentary stratigraphy and so of other geology dependent natural sciences:

“ Sedimentary layers are deposited in a time sequence, with the oldest on the bottom and the youngest on the top. ”

The law was formulated in the 17th century by the Danish scientist Nicolas Steno.

http://en.wikipedia.org/wiki/Law_of_superposition

So like A=bottom and B=top. According to the pre-traditional logic, deposits accumulate from the bottom to the top. If AB = bottomtop, then according to
"AB AND A or AB AND A," which btw redefines the function of the coordinate conjunction "or", the output is non-strict. What is a non-strict output when you feed the beast with bottomtop AND bottom?


"No honey, don't spit the seed of the fruit, for nothing would spring in the organ we share with the squirrels."
Eve

 

[epix]

Only your second diagram is relevant, and it is equivalent to the following diagram:

[qimg]http://farm7.static.flickr.com/6007/5876056051_22cd25ac8b_b.jpg[/qimg]

Sets A,B,C,D, ... etc. have the same cardinality (which is the size of a given set), which is |R| points and yet the size of the 1-dimensional elements is different exactly because |R| < |1-dimensional element| = the power of the continuum.

In other words, a set of |R| points does not have the power of the continuum, and one understands it only if he\she does not ignore the non-locality of 1-dimensional element under line\points co-existence (where a point is the minimal existing local element, and a line is the minimal existing non-local element, where no set of points has the property of non-local element).

Your interpretation of "relevancy" doesn't allow you to make any basic comparison. What exactly is "the power of the continuum?" You just can't grasp the proof that the size of sets is independent of the magnitude and the position of the medium they are organized in. There is a bijection between

1234567 and 1 2 3 4 5 6 7

but ________ is shorter than _______________

If R doesn't have "the power of the continuum," then what does? Why don't you demonstrate the power of the continuum without using undefined, coined terms of yours?

 

[doronshadmi]

Your interpretation of "relevancy" doesn't allow you to make any basic comparison.

Wrong epix. Your interpretation of "relevancy" doesn't allow you to make any basic comparison between the power of collection of local elements, and the power of the continuum, which is non-local.

What exactly is "the power of the continuum?"

The non-locality of the considered element.

You just can't grasp the proof that the size of sets is independent of the magnitude and the position of the medium they are organized in.

Wrong again epix.

The size of sets does not have the power of the continuum, simply because a collection of |R| objects of 0 size each is always less than the power of non-locality.

There is a bijection between

1234567 and 1 2 3 4 5 6 7

but ________ is shorter than _______________

Your example is irrelevant since your collection does not have |R| objects of 0 size each, along the line segments.

If R doesn't have "the power of the continuum," then what does? Why don't you demonstrate the power of the continuum without using undefined, coined terms of yours?

Why you are closed under the concept of collection, which its power is always less than the power of non-local element?

 

[doronshadmi]

Very simple? Show a shade of mercy for Lord's wisdom, coz you took it to the heights only a few dare to climb:

http://en.wikipedia.org/wiki/Superposition_calculus

Is the variable AB some union of mutually exclusive statements? Can you substitute AB with an example so the output given by the conjunction AND could be demonstrated by using an applicable example? I give you an example of the example:

http://en.wikipedia.org/wiki/Law_of_superposition

So like A=bottom and B=top. According to the pre-traditional logic, deposits accumulate from the bottom to the top. If AB = bottomtop, then according to
"AB AND A or AB AND A," which btw redefines the function of the coordinate conjunction "or", the output is non-strict. What is a non-strict output when you feed the beast with bottomtop AND bottom?


"No honey, don't spit the seed of the fruit, for nothing would spring in the organ we share with the squirrels."
Eve

By using your example, AB means that "A=bottom and B=top" is indeterminate so we can't determine if it is "bottom", "top" or some intermediate state between them. Because of this non-determination AB is not a contradiction.

Contradiction, in this case, is the result of forcing determination on the indeterminate.

AB is exactly the simultaneity of more than one option in parallel, which is intermediate and called by me superposition.

 

[epix]

AB is exactly the simultaneity of more than one option in parallel, which is intermediate and called by me superposition.

The major prophets who got the chance to contribute to the Bible with their visions were lucky that you were not born in antiquity. Yet, at the same time, you can't imagine what to substitute the variables A and B with. That makes you something like a false prophet and that's the other reason why there is no Book of Doron.

Suppose that A=false prophet and B=not false prophet, coz you've already made false/truth assignment to A and B. So what does your AB AND A --> A imply? I'm curious how your insight differs from the traditional view and treatment of the relationship between A and B:

For an equation describing a physical phenomenon, the superposition principle states that a combination of solutions to a linear equation is also a solution of it. When this is true the equation is said to obey the superposition principle. Thus if functions f1, f2 and f3 each solve the linear equation ψ, then ψ=c1f1+c2f2+c3f3 would also be a solution, in which each c is a coefficient. For example, the electrical field due to a distribution of charged particles can be described by the sum of the contributions of the individual particles.

Similarly, probability theory states that the probability of an event can be described by a combination of the probabilities of certain specific other events (see Mathematical treatment). For example, the probability of flipping two coins (coin A and coin B) and having at least one land head-up can be expressed as the sum of the probabilities for three specific events: coin A heads with B tails, coin A heads with B heads, and coin A tails with B heads. In this case the probability could be expressed as:

P(heads > = 1) = P(AnotB) + P(AandB) + P(BnotA)
or even:

P(heads > = 1) = 1 − P(notAnotB)

(Note the commutativity of P(AnotB) and P(BnotA). Like if you commute from A to B and back from B to A going along the straight line, the distance travelled is the same.)

Coin tossing doesn't have to be parallel -- a sequential toss delivers head/tail result as well -- according to the "traditional math." Explain the difference in your parallel-only stipulation and don't forget to provide the example for the union of A and B, which is AB according to your prophecy... I mean a vision... I mean whatever it is.

 

[The Man]

A = True
B = False

AB = True/False superposition, or in other words, AB is non-strict.

Since input AB is non-strict , then AB AND A or AB AND A output is non-strict, where the commutativity of AND connective has no influence on the non-strict property of the output.

It is very simple, yet you can't get it.

Again since “A = True” “then AB AND A or AB AND A” simply and strictly evaluates to just your “AB”. It is very simple yet you just deliberately refuse to accept it.

 

[The Man]

By using your example, AB means that "A=bottom and B=top" is indeterminate so we can't determine if it is "bottom", "top" or some intermediate state between them. Because of this non-determination AB is not a contradiction.

Contradiction, in this case, is the result of forcing determination on the indeterminate.

AB is exactly the simultaneity of more than one option in parallel, which is intermediate and called by me superposition.

So why not just call it what you claim it to be, ‘indeterminate’, as opposed to continuing calling it what you specifically claim it is not, a superposition? Unless your intent is simply to try to deliberately deceive? Perhaps it is because, as already noted before, being indeterminate is exactly what makes a variable, well, variable and in order for you to pretend that you’ve come up with something new you have to pretend your ‘indeterminate’ is something even you claim it is not, a superposition.

 

[epix]

Again since “A = True” “then AB AND A or AB AND A” simply and strictly evaluates to just your “AB”. It is very simple yet you just deliberately refuse to accept it.

Do you find any justification to the above case where the grammatical conjuction "or" separates two identical clauses?

I initially set AB = 10 following Doron's assignment A=true=1 and B=false=0 and wound up with input

10 AND 0

There are tables that determine the "traditional" single-digit binary inputs, but I couldn't find any with multiple digit input. So I tried the alternative where the input is triangular,

1
...AND 0
0

to evaluate the relationship separately as

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

and that lineup returned 00=FalseFalse=BB.

What did you use to decode Doron's ciphergoulash to come up with AB?

 

[epix]

Only your second diagram is relevant, and it is equivalent to the following diagram:

[qimg]http://farm7.static.flickr.com/6007/5876056051_22cd25ac8b_b.jpg[/qimg]

The equivalency doesn't exist, only some similarity. Your diagram is not a convincing rendition. The length of the horizontal lines may be the same. See why.

 

[The Man]

Do you find any justification to the above case where the grammatical conjuction "or" separates two identical clauses?

Yes, because both of those clauses still evaluate the same.

I initially set AB = 10 following Doron's assignment A=true=1 and B=false=0 and wound up with input

10 AND 0

There are tables that determine the "traditional" single-digit binary inputs, but I couldn't find any with multiple digit input. So I tried the alternative where the input is triangular,

1
...AND 0
0

to evaluate the relationship separately as

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

and that lineup returned 00=FalseFalse=BB.

What did you use to decode Doron's ciphergoulash to come up with AB?

“AB”, as everything else is superfluous.

That’s the real rub of it epix, it doesn’t matter what Doron wants to call his variable, it is still a variable. That “A=TRUE” simply means that the result of any variable you “AND” with his “A” (in whatever order for those variables) is just going to be that variable (the “…AND A” or “A AND…” just becomes superfluous). Just as any variable you “AND” with “FALSE” (His “B”) is always going to result in “FALSE” (so the “AB AND…” or “…AND AB” just becomes superfluous).

 

[epix]

Yes, because both of those clauses still evaluate the same.

Are you saying that the or in Dorons, "Since input AB is non-strict , then AB AND A or AB AND A output is non-strict, where the commutativity of AND connective has no influence on the non-strict property of the output, was actually meant to be upper-case OR, the logical connective; and not lower-case or, the coordinating conjunction? I don't think there are too many people who would separate a single option by saying, Let's go to the movies or to the movies.

“AB”, as everything else is superfluous.

That’s the real rub of it epix, it doesn’t matter what Doron wants to call his variable, it is still a variable. That “A=TRUE” simply means that the result of any variable you “AND” with his “A” (in whatever order for those variables) is just going to be that variable (the “…AND A” or “A AND…” just becomes superfluous). Just as any variable you “AND” with “FALSE” (His “B”) is always going to result in “FALSE” (so the “AB AND…” or “…AND AB” just becomes superfluous).

If the lower-case "or" is functional, then "AB AND A or AB AND A" results in two different inputs which are related by AND, like "movies or theater," for example. But what kind of clue is there to separate the case when the ANDed inputs are identical to each other?

AB AND A = movie
AB AND A = theater

I didn't go that far though and just tried to figure the output for AB AND A when A=True and B=False.

 

[doronshadmi]

The major prophets who got the chance to contribute to the Bible with their visions were lucky that you were not born in antiquity. Yet, at the same time, you can't imagine what to substitute the variables A and B with. That makes you something like a false prophet and that's the other reason why there is no Book of Doron.

Suppose that A=false prophet and B=not false prophet, coz you've already made false/truth assignment to A and B. So what does your AB AND A --> A imply? I'm curious how your insight differs from the traditional view and treatment of the relationship between A and B:


(Note the commutativity of P(AnotB) and P(BnotA). Like if you commute from A to B and back from B to A going along the straight line, the distance travelled is the same.)

Coin tossing doesn't have to be parallel -- a sequential toss delivers head/tail result as well -- according to the "traditional math." Explain the difference in your parallel-only stipulation and don't forget to provide the example for the union of A and B, which is AB according to your prophecy... I mean a vision... I mean whatever it is.

Your reply has nothing to do with http://www.internationalskeptics.com/forums/showpost.php?p=7318785&postcount=15807 .

You are still closed inside the traditional box, which can't comprehend mathematical objects line Uncertainty x Redundancy Distinction-Trees.

 

[doronshadmi]

Again since “A = True” “then AB AND A or AB AND A” simply and strictly evaluates to just your “AB”. It is very simple yet you just deliberately refuse to accept it.

Wrong The Man.

You simply refuse to deal with the fact that the commutativity of AND connective has no influence on the output, which is determined by the property of the input.

Since the input in the case of AB AND A or A AND AB is non-strict, so is the output.

Your limited reasoning can't comprehend, for example, http://www.internationalskeptics.com/forums/showpost.php?p=7318785&postcount=15807.

Your weak and limited reasoning is clearly seen by this kind of poor and limited reply:

"AB" is not some strict name of a variable.

You can call it whatever you want Doron, it changes nothing.

"AB" is superposition of variables, which has no clear determination.

Sure it does it has the clear determination that it is not a superposition of anything. Since your “superposition” emphatically and by your own assertion does not involve the principle of superposition.

 

[doronshadmi]

The equivalency doesn't exist,

Wrong. They are equivalent.

 

[epix]

Your reply has nothing to do with http://www.internationalskeptics.com/forums/showpost.php?p=7318785&postcount=15807 .

Your usage of "superposition" in your logical schemes got nothing to do with the meaning of the word.

You are still closed inside the traditional box, which can't comprehend mathematical objects line Uncertainty x Redundancy Distinction-Trees.

Red und ancy ist inction?

You got redundant D in your statement -- a "superposition" of German, English and Gibberish.

 

[doronshadmi]

Your usage of "superposition" in your logical schemes got nothing to do with the meaning of the word.

Wrong.

It adds parallel existence of the considered values that is resulted by non-determination, which becomes explicit by symmetry's break.

Take, for example, the 2-Uncertainty x 2-Redundancy Distinction-Tree:

(AB,AB) (AB,A)  (AB,B)  (AB)    (A,A)   (B,B)   (A,B)   (A)     (B)     ()

A * *   A * *   A * .   A * .   A * *   A . .   A * .   A * .   A . .   A . .
  | |     | |     | |     | |     | |     | |     | |     | |     | |     | |
B *_*   B *_.   B *_*   B *_.   B ._.   B *_*   B ._*   B ._.   B *_.   B ._.

(2,2) = (AB,AB)
(2,1) = (AB,A),(AB,B)
(2,0)=  (AB)
(1,1) = (A,A),(B,B),(A,B)
(1,0)=  (A),(B)
(0,0)=  ()

Any appearance of that tree is called Distinction State (DS), where any DS is under a structure called Frame (F), for example: (AB ,B ) is a DS that is under (2,1) F. The order in each DS or F has no significance (similar to {a,b}={b,a}) but any DS is the basis of any possible order (similar to the concept of Set as being the basis of permutations).

 

[epix]

Wrong. They are equivalent.

Lines which are parallel and lines which are not parallel are not equivalent. That's why God drew an arrow => below the exit sign so both fruity loops knew which way is out of Paradise.

= are parallel and mean "equals to"

> or < are not parallel and mean "greater than" or "less than"



Btw, Paradise or Garden of Eden are both mythical names. The place has been always called Fenway Park by the local fowl in the air.

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