Deeper than primes

[zooterkin]

1/3, which is a local number.

Are you actually unable or unwilling to perform the division? Or do you just not like the result you get when you do?

 

[realpaladin]

While I agree that Doron has much in common with the attitudes of Intuitionistc schools of Mathematics,
Unlike them he does assert the existance of more than just a potential infinity.

In his approach Actual Infinity is Non-Locality, Potential Infinity is of Locality.

In my opinion, what's crucial with Doron is the Non-Local/Local Interaction (or "linkage" as it's currently called.)
What he's been asserting about 1/3 not equalling .3333333333...........
in Organic Mathematics follows from his Redundancy/Uncertainty structure of Organic Numbers as seen, but not necessarily directly perceived in his Direct Perception .pdf.

Chicken or egg? I'm not certain.
But as it stands now, everything rests on the Non-Local/Local framwork.

Apathia, I have no single problem with his OM paradigm if he would not attribute these 'signs of grandeur' to it.

that ⅓ ≈ 0.33 (recurrent) is nothing new and it is being dealt with in mathematics.

That is where the ≈ symbol comes from.

His 'linkage' is a simply a more cumbersome and verbal way (simply substituting symbols for words does not make it any less verbal) to do with OM what math has been doing for ages.

What he does is simply putting on extra constraints so it matches perception.

But as you should be aware, perception is always but a subset of the full faculties of the mind.

Proof: imagination is not a perception. It can be forced to make it look like it is, but it is not.

For example: I could image infinity as a Möbius ring, with numbers never overwriting each other but just matching my local viewpoint and travelling distance from my starting point. That way I also have a 'local/non-local' linkage and potential and actual infinity.
This way, I could talk about infinity sizes in 'cycles on the ring'.
But it is only imagination and of little use, because it *needs* that extra constraint of the Möbius ring.

Now, it was you who mentioned TM, right? If you check Vedic Mathematics, then you will find that they use Sutra's to give you the 'direct perception' of an algorithm that works very fast for doing certain calculations.

But the big(!) difference with Doron is that they have addenda that use real rigorous proofs in mathematics to explain why the Sutra's hold true for any case.

But not only Vedic 'Math' is different, Abacus Math as well: http://www.streetdirectory.com/trav...ences_between_abacus_math_and_vedic_math.html

There are lots of different ways to do things.

And if Doron just sees that his way of doing things is more like Vedic Math, i.e. doing nothing new with mathematics, but finding, for some, easier to work with methods, then he could finally try to finalise it.

OM will simply not be the unification of Discreet and Continuous Maths.

It has no new insights in math!

He merely insists on calling existing answers by different names. Like using the 'greater than' symbol for saying the same as lim(x).

Or stating that the transmutation of a rational number into a real number will not yield the exact result.

Or stating that a point has less than 1 dimension.

Or saying 'no amount of 0-dim can fill up a 1-dim', meaning infinity.

So while I am happy for you that you can use his ways of talking for your own mental imagery, it is nothing new for people really using math.

 

[!Kaggen]

The more I think about this epic thread, Doron's posting history elsewhere, and his geocities library, the more I am convinced it all distills down to one simple issue: The basic concept of infinity. Doron does not understand it; he continually fights with it.

Part of the battle comes from him treating things as active processes. 0.999... cannot simply exist as a complete entity; it must be an on-going sequence of events, adding more 9's to the end, never to be finished. As such, it can never quite reach its destination, unity.

The process view creates the conflict, and from there he invents things or adapts things he misunderstands to resolve the conflict. 0.999... isn't 1, so there must be some difference between the two. Let's call it 0.000...1. Doron has reinvented infinitesimals. Infinitesimals fail for lack of numerical consistency, but Doron covers by declaring his infinitesimal to not be a number.

The whole local/non-local aspect of things is part of this invention to cover inconsistency. It sounds sciency, and look how easy it is to just declare 0.999... to be a non-local number and thus free it from the constraints imposed by "standard mathematics."


If I am correct in this, it would explain the difficulty people like Apathia have had trying to explore the philosophic underpinnings of some of the topics Doron has raised. Doron doesn't have any philosophic underpinnings for his local/non-local views; they are just things he has backed into to cover his misunderstanding of infinity.

I stand corrected!
As I said before Doron is exploring epistemology using mathematical concepts without realizing his mathematical concepts require an epistemology as they are obviously different to standard mathematical concepts. Therefore Doron needs to first develop a clear epistemology otherwise he and the mathematical logicians here will constantly talk cross-purposes.
Developing a concept of infinity can help to develop an epistemology as many philosophers have pointed out.
I still say that exploring an epistemology which allows for more mobile concepts to deal with difficulties standard math comes up against in life sciences, which is what Doron is aiming at, is best done by exploring Projective Geometry.
It is much more fundamental than any specific Geometry or Algebra since it has the minimum of axioms and excludes compass constructions.
It also has a well defined and simple concept of infinity and resulting principle of duality (non-local, local) which is intuitive enough to be useful.
It even has practical applications, wow!

 

[!Kaggen]

Apathia, I have no single problem with his OM paradigm if he would not attribute these 'signs of grandeur' to it.

that ⅓ ≈ 0.33 (recurrent) is nothing new and it is being dealt with in mathematics.

That is where the ≈ symbol comes from.

His 'linkage' is a simply a more cumbersome and verbal way (simply substituting symbols for words does not make it any less verbal) to do with OM what math has been doing for ages.

What he does is simply putting on extra constraints so it matches perception.

But as you should be aware, perception is always but a subset of the full faculties of the mind.

Proof: imagination is not a perception. It can be forced to make it look like it is, but it is not.

For example: I could image infinity as a Möbius ring, with numbers never overwriting each other but just matching my local viewpoint and travelling distance from my starting point. That way I also have a 'local/non-local' linkage and potential and actual infinity.
This way, I could talk about infinity sizes in 'cycles on the ring'.
But it is only imagination and of little use, because it *needs* that extra constraint of the Möbius ring.

Now, it was you who mentioned TM, right? If you check Vedic Mathematics, then you will find that they use Sutra's to give you the 'direct perception' of an algorithm that works very fast for doing certain calculations.

But the big(!) difference with Doron is that they have addenda that use real rigorous proofs in mathematics to explain why the Sutra's hold true for any case.

But not only Vedic 'Math' is different, Abacus Math as well: http://www.streetdirectory.com/trav...ences_between_abacus_math_and_vedic_math.html

There are lots of different ways to do things.

And if Doron just sees that his way of doing things is more like Vedic Math, i.e. doing nothing new with mathematics, but finding, for some, easier to work with methods, then he could finally try to finalise it.

OM will simply not be the unification of Discreet and Continuous Maths.

It has no new insights in math!

He merely insists on calling existing answers by different names. Like using the 'greater than' symbol for saying the same as lim(x).

Or stating that the transmutation of a rational number into a real number will not yield the exact result.

Or stating that a point has less than 1 dimension.

Or saying 'no amount of 0-dim can fill up a 1-dim', meaning infinity.

So while I am happy for you that you can use his ways of talking for your own mental imagery, it is nothing new for people really using math.

I disagree with your statement that "imagination is not a perception".
A percept can also be a concept which is perceived.
Memory being a good example.
When you recall something you previously perceived you are not perceiving what you actually perceived then (the exact same electric stimulation's in the brain), but the imaginative re-construction of what you perceived i.e. a concept. That does not mean it is no less real otherwise we would need to always look at something in order to "truly" remember it.

 

[realpaladin]

I disagree with your statement that "imagination is not a perception".
A percept can also be a concept which is perceived.
Memory being a good example.
When you recall something you previously perceived you are not perceiving what you actually perceived then (the exact same electric stimulation's in the brain), but the imaginative re-construction of what you perceived i.e. a concept. That does not mean it is no less real otherwise we would need to always look at something in order to "truly" remember it.

Hmmm, this suggests you subscribe to the (old) school of 'memory is a rolodex' system.

But in fact, memory is more complicated than that.

I would like to direct you to the excellent site of Mr. Wiseman: www.quirkology.com where you can test yourself and 'perceive' that your perception, memory recollection and imagination are but a small subset of what your brain really does.

I have made Doron do one of these experiments, the results speak for themselves.

Even when taken as the, now outdated, notion that perception is our input-system, it can, by mere definition of it being not the whole, but a part through which we perceive, never substitute for the knowledge that we construct by reasoning.

There is a succinct difference between wisdom (problem solving by remodelling experience), intelligence (problem solving by inference of abstract building blocks and their properties) and 'being clever' (my language leaves me in the lurch again. Solving problems by 'reverse engineering' the properties and relinking them again).

It is easy for people to fall into the trap that 'perception is everything' because it is the thing that is most obvious to us.

Hence Doron's insistence on 'atomicity'.

But since science has progressed a lot since the popsci documentary's were made, it has become clear that perception is a muddled, reconstructed and duct-taped performance at best.

The biggest problem discussing perception with others is that with the right redefinition I can even make 'a trip to the mall, buying a pack of condoms, going home and getting laid' fall under the one word 'perception'.

Perception is neither math nor is it physics.

Perception is a conglomerate of different processes that mean different things to different entities (species, machines, people).

So unless you would start out with a clear definition of what perception means in this case, it is all but a bunch of vague woo.

To help matters along:

My definition of perception is but the entry of signals from nerve endings to the brain. When that signal is modelled into an object (without the connotations, history and relations) the perception ends. Processing begins.
(this is an abridged version)

 

[!Kaggen]

Hmmm, this suggests you subscribe to the (old) school of 'memory is a rolodex' system.

But in fact, memory is more complicated than that.

I would like to direct you to the excellent site of Mr. Wiseman: www.quirkology.com where you can test yourself and 'perceive' that your perception, memory recollection and imagination are but a small subset of what your brain really does.

I have made Doron do one of these experiments, the results speak for themselves.

Even when taken as the, now outdated, notion that perception is our input-system, it can, by mere definition of it being not the whole, but a part through which we perceive, never substitute for the knowledge that we construct by reasoning.

There is a succinct difference between wisdom (problem solving by remodelling experience), intelligence (problem solving by inference of abstract building blocks and their properties) and 'being clever' (my language leaves me in the lurch again. Solving problems by 'reverse engineering' the properties and relinking them again).

It is easy for people to fall into the trap that 'perception is everything' because it is the thing that is most obvious to us.

Hence Doron's insistence on 'atomicity'.

But since science has progressed a lot since the popsci documentary's were made, it has become clear that perception is a muddled, reconstructed and duct-taped performance at best.

The biggest problem discussing perception with others is that with the right redefinition I can even make 'a trip to the mall, buying a pack of condoms, going home and getting laid' fall under the one word 'perception'.

Perception is neither math nor is it physics.

Perception is a conglomerate of different processes that mean different things to different entities (species, machines, people).

So unless you would start out with a clear definition of what perception means in this case, it is all but a bunch of vague woo.

To help matters along:

My definition of perception is but the entry of signals from nerve endings to the brain. When that signal is modelled into an object (without the connotations, history and relations) the perception ends. Processing begins.
(this is an abridged version)

Thanks for the link I will explore.

I am not sure what you mean by perception not being math or science since you come to your definition of perception by means of math and science.

Or are you saying (using your definition of perception) perception cannot be perceived only reasoned.

The question then is, is reasoning primary and independent of perception which it defines in retrospect? or are we going in circles if we use your definition of perception.

 

[realpaladin]

Thanks for the link I will explore.

I am not sure what you mean by perception not being math or science since you come to your definition of perception by means of math and science.

Or are you saying (using your definition of perception) perception cannot be perceived only reasoned.

The question then is, is reasoning primary and independent of perception which it defines in retrospect? or are we going in circles if we use your definition of perception.

Well, I apologize for being not clear:

'Perceiving is not reasoning' and 'Perception is not math or science' but 'Math or science can explain perception' is more like:

'All men are goind to die. Socrates is a man. Socrates is going to die.' does not mean 'All men are Socrates'.

I am saying that perception in my definition ends at the moment the nerve-endings and their respective counterpart in the brain have given the brain a signal that is different from the normal noise of signals so that the brain can work with it.

And yes, perception *is* defined in retrospect. There are numerous experiments that can prove this to you (you will find a couple of those on Mr. Wisemans site).

The simplest one is that you 'perceive' continuous reality even though the frequency of your vision processing is around 25 Hertz (I believe, might be wrong here).

A cool trick to make you realise this is the following: Find a clock with a second hand on it. Stare at something that is not the clock, and do not have the clock in your field of vision.
Then suddenly turn to the clock and watch the second hand. You will notice that the first second takes longer than all the following seconds.

But I suspect that people like Doron want to define 'percept' as 'it is immediately obvious'.

And I can not accept that.

 

[!Kaggen]

Well, I apologize for being not clear:

'Perceiving is not reasoning' and 'Perception is not math or science' but 'Math or science can explain perception' is more like:

'All men are goind to die. Socrates is a man. Socrates is going to die.' does not mean 'All men are Socrates'.

I am saying that perception in my definition ends at the moment the nerve-endings and their respective counterpart in the brain have given the brain a signal that is different from the normal noise of signals so that the brain can work with it.

And yes, perception *is* defined in retrospect. There are numerous experiments that can prove this to you (you will find a couple of those on Mr. Wisemans site).

The simplest one is that you 'perceive' continuous reality even though the frequency of your vision processing is around 25 Hertz (I believe, might be wrong here).

A cool trick to make you realise this is the following: Find a clock with a second hand on it. Stare at something that is not the clock, and do not have the clock in your field of vision.
Then suddenly turn to the clock and watch the second hand. You will notice that the first second takes longer than all the following seconds.

But I suspect that people like Doron want to define 'percept' as 'it is immediately obvious'.

And I can not accept that.

Your analogy of 'Perceiving is not reasoning' and 'Perception is not math or science' but 'Math or science can explain perception' is more like:

with Socrates, mortality and men

Should go more like this. All men not immortal. All men are not Socrates. Socrates is a man.


Unless reasoning is math and science in which case.All men are not immortal. All men are not Socrates. Socrates is a mortal man.


In both cases I do not see how this relates to perception as defined by where nerve impulses end and their counterparts in the brain begin.

In vision the optic nerves transmit separate quadrants of the visual field which is also inverted from each retina.
2 quadrants from each retina are transmitted to the upper gyrus in the left occipital lobe and 2 quadrants from each retina are transmitted to the upper gyrus in the right occipital lobe. The other 4 are transmitted to the lower gyrus of the left and right occipital lobe in the same way. In other words 2 quandrants from each retina have there signals transmitted to the opposite side of the brain (left/right retina to right/left occipital lobe).
Thus 8 different signals are transmitted to the brain, but we are only conscious of 4 from one retina (right one in right-handed people). The other 4 are suppressed from consciousness and processed further for depth perception. The conscious 4 signals are then scattered around the brain for further processing.

So does all the optic nerve information from all 8 quadrants of the retina translate to perception or only 4. If we could project the optic nerve signals onto a projector screen the image would not resemble the original visual field. We would need to re-work the signals so as to get the image to resemble the original visual field. Specifically the depth perception which is not implicit in the image on the retina.

Furthermore the signals are then further dissected within the brain so that much of the whole picture is now "scattered" for processing . There has been no evidence to suggest that the "scattered" processed signals are ever "re-united" in a specific brain location to be interpreted.

On another note where would you say the perceptions end with someone who has synaethesia (http://en.wikipedia.org/wiki/Synaesthesia)?

 

[Apathia]

So while I am happy for you that you can use his ways of talking for your own mental imagery, it is nothing new for people really using math.

You are happy for me too early in the game.
I can understand what the Organic Numbres are supposed to represent, but I don't yet see how they become an ethical utiliity.

And my jaws fall just as far to the floor as yours when Doron's OM doesn't seem to be able to divide one by three, and must make the fractional expression a "local number" while the decimal expression must be a "non-local number."

As for the language of my own spirituality, I find that in literature and poetry.

 

[doronshadmi]

The Part of the battle comes from him treating things as active processes. 0.999... cannot simply exist as a complete entity

There is no processes here. 0.999...[base 10] is exactly a non-local number.

The problem is in the mind of any one that can't get non-locality as a fundametal building-block in addition to Locality.

Here it is:

At the beginning of the 20th century there were two major revolutions in Physics, when STR [1], GRT [2] and QM first aired their views. These theories provided better explanations to physical anomalies both in macro and the micro scales. Still at the beginning of the 21th century there is no simple and straightforward theory that naturally links between the macro and the micro scales. Nevertheless both macro and micro frameworks have changed their attitudes about the researcher as a significant factor of the researched framework. Nowadays the researcher is no longer considered as a "pure" observer of the results, and the researcher's possible influences on the results are not unconditionally ignored. Also properties like Uncertainty, Redundancy and Randomness etc … are more and more understood as essentials of the researched space.

In 1935 the EPR thought experiment was published [3], and since then it leads an approach that disagrees with the probabilistic interpretations of physical theories and experimental results. EPR original aim was to show that QM's probabilistic interpretations enable non-local phenomena that allow information's transfer faster than the speed of light (which is an essential constant of Einstein's SRT and GRT). Actual physical experiments [4], mostly based on Bell [5] and Bohm [6] thought experiments, have shown non-local phenomena at the QM micro scale, but until these days there is no agreement about Bell and Bohm thought experiments, and there is no agreement about the experimental results that are based on them, including disagreements about their technical validity and\or their interpretations. It has to be stressed that at the basis of both experimental and theoretical frameworks there is the mathematical language, and some scholars believe that a better understanding of that language can put these mentioned problems in a new light. These voices can be added to the vision of "One Mathematics" [7] which its aim is to find a common base ground for many mathematical branches under a one organic approach [8], which enables better linkage among them.

Here are some suggested principles that may fulfill these goals (more details will be given soon):

1. Atomic self state is a realm that has no sub-realms, for example: {} is Atomic self state.

2. In order to be expressed beyond the non-expressible atomic self state, we need at least two realms that are linked with each other without derived from each other.

3. Non-locality and Locality are exactly two realms that if linked with each other, enable any possible realm (abstract or not) that is beyond the non-expressible self atomic state. For example, Distance, Division, Scale, Size or any possible measured terms, are all based on Non-locality\Locality Linkage.

4. A line is the minimal representation of Non-locality and a point is the minimal representation of Locality.

5. The linkage between Non-locality and Locality defines a Distinction-Tree, where its Y-axis is used in order to measure the Uncertainty of its elements and its X-axis is used in order to measure the Redundancy of its elements.

For example, the 2-Uncertainty x 2-Redundancy Distinction-Tree is:

(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, but any DS is the basis of any possible order. As for Non-locality and Locality linkage, it can be introduced, for example, by the ratio between different dimensions, as follows:

n=1 to ∞
k= 0 to n-1

Any n-dim is non-local with respect to any amount of k-dim elements because: given n-dim element, there are infinitely many k-dim elements on it such that k-dimA ≠ k-dimB ≠ k-dimC …, where ≠ is an example of n-dim domain, which is not covered by any k-dim element. If some claims against this assertion then he has to avoid ≠. But then there is at most one and only one k-dim element on the n-dim element. By carefully investigate the dimensions' example it is discovered that ≠ is equivalent to n-dim that is used as a differentiator between more than one k-dim on it, no matter what id each k-dim has. We distinguish between the state of "many" (whether it is finitely many or infinitely many) and the state of the one (n-dim state > many k-dims state) by ignoring the id of each k-dim (expressed as k-dim ≠ k-dim ≠ k-dim …).

For example: k-dim ≠ k-dim ≠ k-dim has cardinality 3, whether the k-dims are distinguishable or not. By extending the cardinality to ∞ , we still find ≠ as a projection of n-dim, which is used as a differentiator between more than one k-dim on it. At the moment that the Organic paradigm is understood, then, for example: 0.999…[base 10] < 1 exactly by 0.000…1 , where the "…1" of "0.000…1" is equivalent to ≠ as a projection of n-dim between non-finite amount of 0.9(≠) + 0.09(≠) + 0.009(≠) + … k-dims and 1 n-dim (no amount of many k-dims, whether they are distinct or not, is n-dim). As we all know 0.999…[based 10] is currently considered as a numeral of number 1. This is not the case by the Organic paradigm, where 0.999…[based 10] is considered as a non-local number and 1 is considered as local number of "0.999…[base 10] < 1" expression.

These examples can be used without loss of generality in many mathematical branches, and this generalization actually provides a non-trivial way for "One Mathematics", which we call "The Organic Unity of The Mathematical Science" [9].


Organism means that any possible expression exists at-once together with the entire expressions, such that each expression enables the non-trivial further developments of any other expression. It means that we have a dynamic environment that is based on invariant principles, which actually expressed by dynamic changes.

In order to lift up things (to develop them) we simultaneously have stability AND changeability in a one framework ("Give me a place to stand on, and I will move the Earth", Archimedes of Syracuse). As for Distinction as a main principle, we are using it as follows:

Organic Numbers (ON) is a number system that is based on DS.

We do not need more than A and B in order to introduce the entire ON system.

1) AB represents the Uncertain state of Distinction of an element under ON.

2) A,B represents the clear id state of Distinction under ON.

3) A,A represents the Redundant state of Distinction under ON.

(1)(2)(3) itself can be represented as ABC ; A,B,C ; A,A,A cases of ON3.

The main idea is to reduce things into a single structure (a one organism), for example: we need 3 2-dim structures in order to represent the 6 permutations of (A,B,C) structure:

A *  .  .                                                                               
  |  |  |                                                                               
B .  *  . = (A,B,C) , (C,B,A)                                                           
  |  |  |                                                                               
C .__.__*                                                                               
                                                                                        
                                                                                        
A .  *  .                                                                               
  |  |  |                                                                               
B *  .  . = (B,A,C) , (C,A,B)                                                           
  |  |  |                                                                               
C .__.__*                                                                               
                                                                                        
                                                                                        
A *  .  .                                                                               
  |  |  |                                                                               
B .  .  * = (A,C,B) , (B,C,A)                                                           
  |  |  |                                                                               
C .__*__.

But (A,B,C) case is reducible into 3-dim 3-Uncertainty x 3-Redundancy organism:
[qimg]http://www.geocities.com/complementarytheory/ABC.jpg[/qimg]
So the A,B,C ids can be picked in any wished order, under the same ON.

ZFC set theory (which is used as the basis of many mathematical branches) uses only A,B as the general case of Distinction, while ON are based on a generalization of Distinction (as shown in pages 2 and 3). Furthermore, since ON are the results of Non-locality\Locality linkage, where this linkage is a one "Tree of knowledge", then the researcher and the researched are organs of a one organism. Currently the organic approach is not at the core of the mathematical science. On the contrary, any discovered\invented linkage between some given mathematical branches is considered as an unexpected event of this science, and we argue that this arbitrary paradigm has to be developed into the organic view of the mathematical science. We believe that this is the right way to unify the abstract and the non-abstract realms into a one fruitful and dynamically developed body of scientific knowledge, where researcher\researched linkage is not unconditionally ignored.


[1] Einstein Albert: On the Electrodynamics of Moving Bodies, Annalen der Physik,
17:891, June 30, 1905 (English translation by W. Perrett and G.B. Jeffery).

[2] Einstein Albert (1915): "Die Feldgleichungen der Gravitation (The Field Equations of
Gravitation)", Koniglich Preussische Akademie der Wissenschaften: 844–847.

[3] Einstein, Podolsky, Rosen: Can Quantum-Mechanical Description of
Physical Reality Be Considered Complete? Phys. Rev. 47, 777 - 780 (1935).

[4] Aspect Alain: Experimental Tests of Realistic Local Theories via Bell's Theorem,
Phys. Rev. Lett. 47, 460 (1981).

[5] J. S. Bell, On the Einstein Podolsky Rosen Paradox, Physics 1, 195 (1964).

[6] Bohm David (1952). "A Suggested Interpretation of the Quantum Theory in Terms of
"Hidden Variables" I". Physical Review 85: 166–179

[7] L. Lovasz: One Mathematics http://www.cs.elte.hu/~lovasz/berlin.pdf .

[8] Moshe Klein, Doron Shadmi: Organic Mathematics, International Journal of Pure and
Applied Mathematics, volume 49 No. 3 2008, 329-340
http://www.geocities.com/complementarytheory/IJPAM-OM.pdf .

[9] Hilbert David: Mathematical Problems, Bulletin of The American
Mathematical Society, Volume 37. Number 4, Pages 407-436, S 0273-
0979(00)00881-8.

 

[doronshadmi]

Structure is not a “Buiding-block” it is what you have after you put two or more building-blocks or parts together.

No, Structure in its simplest form is something that is not defined by or made of other structures.

You are talking about the complex result of the linkage of two atomic types (Non-locality and locality) that enable any complex realm without being complex themselves.

It has to be stressed that no Complexity (abstract or not) is possible if the atomic self state does not refers to itself and enables the simplest expressible realm of Non-locality and Locality, that if linked enable Complexity, in the first place.

The Man, it can be understood only by direct perception, so as long as you get "Structure" at the verbal level, you don't get it.

 

[doronshadmi]

You are happy for me too early in the game.
I can understand what the Organic Numbres are supposed to represent, but I don't yet see how they become an ethical utiliity.

Very simple.

At the moment that the researcher and the researched are organs of a one realm by direct perception, any action cannot be but a reinforcement of the linkage between the Simple (atomic) and Complex (expressible) aspects of a one realm.

Organic Numbers are the exact reduction of that one realm, where this redaction totally exposes that realm be striping it from any complicated mystical or verbal-based maneuvers.

As this is done by direct perception of the one realm, any aware organ of that realm naturally uses Ethics and Logics at the basis of any of its actions (abstract or not) as a natural organ of a one realm.

 

[doronshadmi]

The whole local/non-local aspect of things is part of this invention to cover inconsistency. It sounds sciency, and look how easy it is to just declare 0.999... to be a non-local number and thus free it from the constraints imposed by "standard mathematics."

If "consistency" means that no change is possible at the core of the mathematical science, and any mathematical activity must be done upon the agreed core, then you are right jsfisher.

In my work I clearly show that by using direct perception at the core of that science, fundamental verbal-based agreements are changeable.

It does not mean at all that these changes are inconsistent. It simply means that fundamental verbal-based agreements are changeable if direct perception is used at the core of the mathematical science.

One of these changes shows that 0.999...[base 10] is not a numeral of number 1, but it is a legitimate number that has non-local properties that local number 1 does not have.

The difference between non-local numbers and local numbers open a new mathematical universe for further research, where the "standard mathematics" universe is some organ of it.

As long as one does his best in order to avoid any change at the verbal-based agreed core of the mathematical science, there is no use to communicate with him on these issues.

As about "Incompleteness", by using direct perception one immediately understands that "Completeness" is the non-expressible Atomic self state.

Again, Incompleteness is exactly the complex result of the linkage of two atomic types (Non-locality and locality) that enable any complex realm without being complex themselves.

It has to be stressed that no Complexity (abstract or not) is possible if the atomic self state does not refers to itself and enables the simplest expressible realm of Non-locality and Locality, that if linked enable Complexity, in the first place.

Complexity is exactly the result of the inability of the expressed to fully express the atomic state that enables it, in the first place, and this incomplete ability is exactly the openness of any anti-entropic system (as written in post #1 ( http://www.internationalskeptics.com/forums/showpost.php?p=4083359&postcount=1 ) of that thread).

 

[doronshadmi]

As long as you don't disagree with me by using direct perception as the basis of your reasoning, there is no use to continue to discuss on these issues.

 

[jsfisher]

There is no processes here. 0.999...[base 10] is exactly a non-local number.

The problem is in the mind of any one that can't get non-locality as a fundametal building-block in addition to Locality.

It is just something you made up. And it is something you are unable to define or describe. It is an imaginary invention on your part, and totally unnecessary.

Mathematics functions fine without it. With it, it falls into contradiction and inconsistency, and it does that with no actual application to demonstrate any advantage.

 

[jsfisher]

If "consistency" means that no change is possible at the core of the mathematical science, and any mathematical activity must be done upon the agreed core, then you are right jsfisher.

It doesn't, but I still am.

 

[doronshadmi]

Or can Doron tell me what the smallest distance is between two 0-dim elements?

I say it is lim(0).

The smallest distance between two 0-dim elements > 0-dim element.

The smallest distance between two 0-dim elements = 1-dim element.

As you see, this is a structural difference that stands and the basis of the concept of Distance.

In other words, Structure is the Building-block of Distance, Division, Scale or any other possible change.

You need two tomato's, I need one tomatoe...

No realpaladin you are using Two.

One is called 0-dim element.

The other is called lim(0) , which is not 0-dim element.

Just don't tell us that lim(0) is not an element, but it is a collection of infinitely many 0-dim elements.

If you do that, you immediately need to show how infinitely many 0-dim elements are not "smashed" into a one 0-dim element, in the first place.

Let me give you a clue, do you know what ≠ between any pair of your non-finite collection of 0-dim elements means?

( and no, ≠ is not a non-finite collection of 0-dim elements between these arbitrary pair of 0-dim elements, because by using this assertion you are in a non-finite regression, and then you must agree that this non-finite regression is actually a proof that no collection of 0-dim elements can fully cover a 1-dim element, and then surprise surprise you have two tomatoes, called 0-dim and 1-dim ).

 

[doronshadmi]

It is just something you made up. And it is something you are unable to define or describe. It is an imaginary invention on your part, and totally unnecessary.

Mathematics functions fine without it. With it, it falls into contradiction and inconsistency, and it does that with no actual application to demonstrate any advantage.

No, it is your failure to get Mathematics by using direct perception.

Mathematics has nothing to do with your failure and your inability to get ON as a demonstration of actual applicative advantage.

All you care is to save the verbal-based agreements of your community.

 

[doronshadmi]

It doesn't, but I still am.

No you don't, because you have no direct perception about the disscused subject.

 

[doronshadmi]

jsfisher,

From day 1 you are here for one and only one purpose, which is: to do your best in order to not change any fundamental verbal-based agreement of your community.

I used your stiffness (which you call by mistake consistency) for further refinement of some verbal-based expressions of OM.

Now what is needed is to find scholars with opened minds to new fundamental notions and changes, and OM will start to air its view more and more day by day, until the verbal-based expression will be exactly what it is, some expression of direct perception.