Deeper than primes

[jsfisher]

Please see http://www.internationalskeptics.com/forums/showpost.php?p=5932683&postcount=9814 .

...which doesn't answer any of my questions. How about you just address them directly, point by point.

 

[Apathia]

Items in "Parallel" have cardinality is we deal with finite size, but the identity of each element is uncertain.

I am completely lost again.

So, actually items in "Parallel" are counted in quantity, but serial bridging emliminates quantity?

Bridging does not collect, but eliminates?

Parallel items, apart from bridging and linkage have no identity, or uncertain identity.
But bridging gives them identity by a process of elimination?


Ok, maybe this:
Items in "Parallel" can be counted under the generality of items, but they don't have an identity under which the could be counted as members of a common class.

 

[Apathia]

I asked:

How do you indicate in a formula when a number is at the element level or when it is at the collection level?

The considered mathematical structure is k-Uncertainty x k-Redundancy tree, where its Y-axis (a given branch of the given tree) is used in order to measure the Uncertainty of its elements, and its X-axis (of the given tree) is used in order to measure the Redundancy of its elements.

"In a formula"

So you draw the Redundancy/Uncertainty Matrix and try to figure if that number is a cardinal or an ordinal on it?

Why does this always evaporate into nothing?

If numbers in "Parallel," prior to collection, prior to any seriality, prior to a common identity to gather them into a countable set, are quantites,

The matrix loses any meaning.
There's a puff of smoke, and when it clears, there's nothing there at all.

 

[The Man]

Excellent questions, let us improve it.

Thanks, but how about just answering the questions directly.

EDIT:

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

x is an element.

Definition 1: Identity is a property of x, which allows its recognition.

For example x=A , x=B

Again

Would x=AB be a different “Identity” than x=A or x=B? Would it be a union of those two 'identities'?

Would x=AA be different than x=A?

Definition 2: If x has more than a single identity, then x is called Uncertain.

For example x=AB

AB would be a “single identity” unless both AB represents a collection of “identities” or as asked before a union of two collections of “identities” represented by A and B respectively.

Definition 3: Redundancy is a duplication of single or uncertain identities, in a given collection.

For example (A,A) , (B,B) , (AB,AB)

This would seem to be indicating that AB is a different “identity” than A or B thus (AB,A,B) would have no redundancy.

And seems to be supported by this assertion…

As you see Uncertainty is at the level of the element (a given branch of the given tree), where Redundancy is at the level of the collection (the given tree).

x=A or x=B would be ‘certain’ while x=AB would be ‘uncertain’ by your ascriptions thus as ‘certainty’ would be a different ‘property’ from ‘uncertainty’ those “id”s, would be different.




No need to simply keep repeating your previous posts or variations on it until we establish the meanings and application of your definitions. Actually answering the questions ask directly would be a start.

 

[doronshadmi]

So, actually items in "Parallel" are counted in quantity, but serial bridging emliminates quantity?

No, serial bridging has simply 1-Uncertainy x 1-Redundancy of any n-Uncertainy x n-Redundancy, where n = 2 to ∞

 

[doronshadmi]

This would seem to be indicating that AB is a different “identity” than A or B thus (AB,A,B) would have no redundancy.

(AB,A,B) is a DS under F (2,1,1) of 3-Uncertainy x 3-Redundancy tree:

(1,1,2) =                                        
(A,A,AB),(A,A,AC),(A,A,BC)                       
(B,B,AB),(B,B,AC),(B,B,BC)                       
(A,B,AB),(A,B,AC),(A,B,BC)                       
(A,C,AB),(A,C,AC),(A,C,BC)
(B,C,AB),(B,C,AC),(B,C,BC)

k = 0 to n, where n is some natural number.

Again, the considered mathematical structure is k-Uncertainty x k-Redundancy tree, where its Y-axis (a given branch of the given tree) is used in order to measure the Uncertainty of its elements, and its X-axis (of the given tree) is used in order to measure the Redundancy of its elements.

It does not mean that X-axis or Y-axis of a given k-Uncertainty x k-Redundancy tree must have Uncertainty or Redundancy > 1

For example, please see DS of F (1,1,1) under 3-Uncertainy x 3-Redundancy tree:

(1,1,1) = 
(A,A,A),(B,B,B),(C,C,C)
(A,A,B),(A,A,C),(B,B,A)
(B,B,C),(C,C,A),(C,C,B)
(A,B,C)


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

 

[jsfisher]

(AB,A,B) is a DS under F (2,1,1) of 3-Uncertainy x 3-Redundancy tree:

(1,1,2) =                                        
(A,A,AB),(A,A,AC),(A,A,BC)                       
(B,B,AB),(B,B,AC),(B,B,BC)                       
(A,B,AB),(A,B,AC),(A,B,BC)                       
(A,C,AB),(A,C,AC),(A,C,BC)                       
(B,C,AB),(B,C,AC),(B,C,BC)

So, in addition to avoiding even the simplest of questions, doron is dyslexic? By the way, (C,C,AC) sends hugs and kisses and apologizes for missing this great unveiling.

 

[The Man]

(AB,A,B) is a DS under F (2,1,1) of 3-Uncertainy x 3-Redundancy tree:

(1,1,2) =                                        
(A,A,AB),(A,A,AC),(A,A,BC)                       
(B,B,AB),(B,B,AC),(B,B,BC)                       
(A,B,AB),(A,B,AC),(A,B,BC)                       
(A,C,AB),(A,C,AC),(A,C,BC)                       
(B,C,AB),(B,C,AC),(B,C,BC)

Again

Would x=AB be a different “Identity” than x=A or x=B? Would it be a union of those two 'identities'?

Would x=AA be different than x=A?

Again

x=A or x=B would be ‘certain’ while x=AB would be ‘uncertain’ by your ascriptions thus as ‘certainty’ would be a different ‘property’ from ‘uncertainty’ those “id”s, would be different.

Again

No need to simply keep repeating your previous posts or variations on it until we establish the meanings and application of your definitions. Actually answering the questions ask directly would be a start.

If you can not directly answer some simple and direct questions about your “definitions” without simply referring to your subsequent nonsense then we must conclude that your “definitions” are in fact meaningless and only serve as a contrivance on your part for you to simply tout that subsequent nonsense.

 

[The Man]

So, in addition to avoiding even the simplest of questions, doron is dyslexic? By the way, (C,C,AC) sends hugs and kisses and apologizes for missing this great unveiling.

(C,C,AB) and (C,C,BC) would have also sent their regards, but were too uncertain and felt it would be redundant.

 

[jsfisher]

(C,C,AB) and (C,C,BC) would have also sent their regards, but were too uncertain and felt it would be redundant.

I know. This, by the way, is more or less a repeat of a tangent doron flew off on about a year ago. The tangent ended poorly for Moshe.

 

[doronshadmi]

Again,


(AB,A,B) is a DS under F (2,1,1) of 3-Uncertainy x 3-Redundancy tree ( (C,C,AB),(C,C,AC),(C,C,BC) where added, thanks):

(1,1,2) =                                        
(A,A,AB),(A,A,AC),(A,A,BC)                       
(B,B,AB),(B,B,AC),(B,B,BC)
(C,C,AB),(C,C,AC),(C,C,BC)                       
(A,B,AB),(A,B,AC),(A,B,BC)                       
(A,C,AB),(A,C,AC),(A,C,BC)
(B,C,AB),(B,C,AC),(B,C,BC)

k = 0 to n, where n is some natural number.

Again, the considered mathematical structure is k-Uncertainty x k-Redundancy tree, where its Y-axis (a given branch of the given tree) is used in order to measure the Uncertainty of its elements, and its X-axis (of the given tree) is used in order to measure the Redundancy of its elements.

It does not mean that X-axis or Y-axis of a given k-Uncertainty x k-Redundancy tree must have Uncertainty or Redundancy > 1

For example, please see DS of F (1,1,1) under 3-Uncertainy x 3-Redundancy tree:

(1,1,1) = 
(A,A,A),(B,B,B),(C,C,C)
(A,A,B),(A,A,C),(B,B,A)
(B,B,C),(C,C,A),(C,C,B)
(A,B,C)


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

 

[doronshadmi]

I know. This, by the way, is more or less a repeat of a tangent doron flew off on about a year ago. The tangent ended poorly for Moshe.

k = 0 to n, where n is some natural number.

You are missing the point here, the main principle here is the k-Uncertainty x k-Redundancy tree, which first needs a general formula to know how many DS there are under a given k-Uncertainty x k-Redundancy tree.

The next stage is to find some algorithm that defines the structure of each DS of some k-Uncertainty x k-Redundancy tree, where the general quantitative formula is some part of that algorithm.

I explicitly wrote in http://www.internationalskeptics.com/forums/showpost.php?p=5932683&postcount=9814 this:

Maybe I have missed something in 3x3 , so a general formula of k=0 to n (where n is some natural number) actually points out that more cases must be defined in a given k-Uncertainty x k-Redundancy tree.

 

[jsfisher]

k = 0 to n, where n is some natural number.

This is a non sequitur.

You are missing the point here....

No, not really. The Man and I would like you to actually read, comprehend, then respond to our posts, though. Your concerns cannot be addressed until you first clear up the ambiguity and lack of meaning in your definitions.

Can we start there, please?

 

[Apathia]

"Element Level"
Collection Level"

It's certainly important to be able to distinguish these levels, isn't it?
Or there's just no point in Organic Numbers as a new mathematics.

So, I've got my three copper pennies.

Let's just assume I've already done the Memory/Object Linkage and the Local/Non-Local Linkage.
I'm concerned with Redundancy/Uncertainty, Element/Collection, and Element/Relation here.

Now I'm saying three pennies, because though they set on my desk in "Parallel" as unique items without a clear class identity to identify them as of a common class that I can count three elements of ...
Well, we've already said they have the quantity three.

Three on the element level, but not three on the collection level, because they have not been collected into three pennies with a redundant identity.

Stop!

We've already done the deed.
Speaking of the quantity three, it is already assumed we have identified all of them as pennies, so collecting them into the same class with a redundant ID of Penny and an amount of 3.

Quantity (how many) always assumes a collection.
The redundancy may be no more than object,
but count the objects and you have collected.

an "element" may be a unique item. but talk of one element and it's a collection of one.

So then why the asparagus introduce the act of collection after you have already claimed the results of collecting?

You speak of the element level as if it were a special, unrecognized state.
But then give elements quantity.
Not just ordinality. You claim quantity foo elements in the element level.

So it's an empty distinction.

Or are you trying to say that collection pertains to a special act of collection in addition to the background one.

So there are three oranges in the bowl on the kitchen table.
This is the collection level.
But on the element level, there are the oranges outside the bowl:
all the oranges in Orange County.

But do I need some special matrix to tell me the difference between what's in the bowl and what's in countless orchards in California?
(Never mind Florida and Valencia.)

What we normally do is specify the common class or location of the quantity.
Sure we can trivially say there are three oranges in the bowl and two on the table.
But these are both simple quantities that as quantities are all on the same level of quantity.
We don't have to keep an account of everywhere and everywhat and all the different groupings that may be going on.
We just specify what items of what collection we are counting.

Why do you have to make of this some special twist of mind that you think requires "hidden assumptions" and a new kind of "magnitude?"
Or a distinction between an Element Quantity and a Collection Quantity.
There's no real distinction.

Is there a problem here with manipulating classes and specifying sets?
That seems to fit not allowing a set to be complete because one has to tally up every possible thing that isn't as member of it,
but is
in the ambiguity of uncertainty.

I say, ambiguity is great in poetry,
but I don't want it in my bank account.

 

[doronshadmi]

Ok let us try this version:

k = 0 to n, where n is a natural number.

General description:

The considered mathematical structure is k-Uncertainty x k-Redundancy tree, where its Y-axis (a given branch of the given tree) is used in order to measure the Uncertainty (if > 1) of its branches, and its X-axis (of the given tree) is used in order to measure the Redundancy (if > 1) of its branches.

Some definitions:

x is a branch of k-Uncertainty x k-Redundancy tree as follows:

Definition 1: Identity is x recognition with respect to itself.

Definition 2: Superposition is a simultaneous identity of x with respect to itself.

Definition 3: Non-superposition of identities allows certain x recognition with respect to itself.

Example: x=A , x=B

Definition 4: Superposition of identities does not allow certain x recognition with respect to itself.

Example: x=AB

Definition 5: Redundancy is a duplication of certain or uncertain identities, with respect to a given tree.

For example (A,A) , (B,B) , (AB,AB)


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


Here are the detailed example of k=0 to 2:

0x0

(0)=()



1x1                                        
                                           
A * .                                        
                                           
(1) = (A)
(0) = ()

                                          
                                 
2X2

(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) = ()

As you see Uncertainty is at the level of the a given branch of the given tree, where Redundancy is at the level of the given tree.

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}).

From the following definitions and examples x=AA is impossible, because AA is not a superposition of x with respect to itself.

 

[Apathia]

Ok let us try this version:

k = 0 to n, where n is a natural number.

General description:

The considered mathematical structure is k-Uncertainty x k-Redundancy tree, where its Y-axis (a given branch of the given tree) is used in order to measure the Uncertainty (if > 1) of its branches, and its X-axis (of the given tree) is used in order to measure the Redundancy (if > 1) of its branches.

Some definitions:

x is a branch of k-Uncertainty x k-Redundancy tree as follows:

Definition 1: Identity is x recognition with respect to itself.

Definition 2: Superposition is a simultaneous identity of x with respect to itself.

Definition 3: Non-superposition of identities allows certain x recognition with respect to itself.

Example: x=A , x=B

Definition 4: Superposition of identities does not allow certain x recognition with respect to itself.

Example: x=AB

Definition 5: Redundancy is a duplication of certain or uncertain identities, with respect to a given tree.

For example (A,A) , (B,B) , (AB,AB)


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


Here are the detailed example of k=0 to 2:

0x0

(0)=()



1x1                                        
                                           
A * .                                        
                                           
(1) = (A)
(0) = ()

                                          
                                 
2X2

(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) = ()

As you see Uncertainty is at the level of the a given branch of the given tree, where Redundancy is at the level of the given tree.

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}).

From the following definitions and examples x=AA is impossible, because AA is not a superposition of x with respect to itself.

This morning I find myself back at "beginner's mind,"
meaning in this case clueless.

For one, I really don't have any idea now what "Identity" means in the Doron context.
The above strengthens my feeling that none of these words mean what I would take them to mean.

I'm not making any real progress understanding Doron as presenting a coherent idea.
Once I think I've gotten clarity about some point, it's soon lost in statements that undo it.

It'd snakes and ladders again.
I've landed on another snake square instead of a ladder one. and I'm back to square one.

As usual I'll just go back offstsge and watch the surrealistic specticle till something moves me to post again.

 

[jsfisher]

This morning I find myself back at "beginner's mind,"
meaning in this case clueless.

For one, I really don't have any idea now what "Identity" means in the Doron context.
The above strengthens my feeling that none of these words mean what I would take them to mean.

I'm not making any real progress understanding Doron as presenting a coherent idea.
Once I think I've gotten clarity about some point, it's soon lost in statements that undo it.

It'd snakes and ladders again.
I've landed on another snake square instead of a ladder one. and I'm back to square one.

As usual I'll just go back offstsge and watch the surrealistic specticle till something moves me to post again.

We have been over this territory before. Not necessarily these specifics, but the same territory. Those menorah diagrams of his (for lack of a better name for them) are at the center of his thinking, and once again he is trying to reverse-engineer a foundation for them that somehow makes them significant.

His goal is significance, not clarity. For Doron, making up important-sounding names is sufficient to define something. As a result, his definitions each fail. He'll fix them by recycling the very same or similar definition after substituting new words for old. He never understands why his definition continues to fail.

We see this already. His first set of important-sounding labels was identity, uncertain, and redundant. (He used "copy", too, but that really wasn't all that important-sounding.) Just recently he has drifted every so slightly to identity, superposition, and redundancy. He has also convinced himself "recognition with respect to itself" means something.

The word-shift will continue for a while, then Doron will return to his "you don't get it" mode.

Unfortunately, most of what Doron has to offer is either completely wrong or completely trivial. (His menorah diagrams fall into the later category.) Honest attempts to explore Doron's version of Mathematics with him quickly reveal the lack of significance and lack of correctness in so much of what he posts. He cannot accept that, and so he doesn't.

 

[The Man]

Ok let us try this version:

k = 0 to n, where n is a natural number.

General description:

The considered mathematical structure is k-Uncertainty x k-Redundancy tree, where its Y-axis (a given branch of the given tree) is used in order to measure the Uncertainty (if > 1) of its branches, and its X-axis (of the given tree) is used in order to measure the Redundancy (if > 1) of its branches.

Some definitions:

x is a branch of k-Uncertainty x k-Redundancy tree as follows:

Definition 1: Identity is x recognition with respect to itself.

What is “recognition with respect to itself”? If you mean “Identity” is some representation that we can recognize, then just say so.

Definition 2: Superposition is a simultaneous identity of x with respect to itself.

Superposition is a linier addition so "Superposition" as “a simultaneous identity of x with respect to itself” would be x+x, 2x or xx if addition is assumed between the “x” representations or ‘identities’ in your "Superposition" notation.

Definition 3: Non-superposition of identities allows certain x recognition with respect to itself.

Example: x=A , x=B]

So x=A and x=B are “certain” while x=AB is not? That does not coincide with AB being a superposition as A+B would be as certain as A and B. You seem to be confusing superposition for uncertainty as to whether x is A or B.

Definition 4: Superposition of identities does not allow certain x recognition with respect to itself.

Example: x=AB

See above, superposition is specifically a linear addition (as you have been told before). For example 6 can be a superposition of 3 and 3, 4 and 2 or 7 and -1, so on and so forth. As you give the elements of the superposition, A and B in this case, and claim they are “certain” then their superposition is certain as A+B, or AB in your apparent "Superposition" notation.

Definition 5: Redundancy is a duplication of certain or uncertain identities, with respect to a given tree.

For example (A,A) , (B,B) , (AB,AB)

Given your assertion that AB is a superposition of A and B it would not be the same "Identity" as A or B. Thus there would be no redundant "Identity" in (A,B,AB). Perhaps you are including the individual ’identities’ of the “Superposition” in your ‘redundant’ consideration. So (A,B,AB) would be one “Redundancy” and (A,B,AB) would be another. Making the total “Redundancy” of (A,B,AB) equal to 2. However that would also make (AA,BB) redundant by the same amount.


Also as you assert x=A to be certain as well as x=B to be certain then AB (as their superposition) would be certain. Again you seem to be confusing (and I think deliberately) superposition to infer that you simply do not know whether x=A or x=B in your AB “Superposition” notation.

To try and explain the actual quantum mechanics (and superposition principle) that I think you are basing your confusion on: A state vector can be considered to be comprised of two or more state vectors in superposition, the resulting state vector is the sum of those individual state vectors.


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

The net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.

We have been over all of this before Doron, but for some reason you continue to go around in circles. Perhaps you simply can not remember what was addressed before, but I can assure you that we do.

<preceding uncertain and redundant nonsense snipped>


From the following definitions and examples x=AA is impossible, because AA is not a superposition of x with respect to itself.

AA (in your notation) is specifically a “superposition of x with respect to itself”, when x=A. Nothing in your above given “definitions” restricts that and in fact your given…

Definition 2: Superposition is a simultaneous identity of x with respect to itself.

specificaly requires it, as noted above.

 

[Apathia]

Those menorah diagrams of his (for lack of a better name for them)

They do look like that.
As an esoteric system of symbols, I see Doron's OM as having a strong kinship with the Kabbalah.

My recent mistake has been to again expect it to be itellectually or logically coherant, when it's actual purpose is in ambiguity, and as you say, "Significance."

 

[doronshadmi]

For one, I really don't have any idea now what "Identity" means in the Doron context.

The above strengthens my feeling that none of these words mean what I would take them to mean.

I believe you think so because I said that self-state has no identity at all.

But by definition 1, identity is exactly the recognition of branch x with respect to that has no identity at all, exactly as some color is identified with respect to transparency (not any color).