Deeper than primes

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Organic Mathematics

Dear Doron,

Here is the paper which I wrote in 2000 for the conference "100 to Hilbert" in U.C.L.A university. I think it come from what you name as direct perception. Anyhow the tree of distinctions is a tremendous development Since it create a real praxis of OM.

So the next step can be to develop an application to OM !!!

Your
Moshe





Organic mathematics
Mathematical experiment to solve
the 6 th 'problem of hilbert

Moshe Klein

"The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfill this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples"
. D.Hilbert


Organic mathematics is an extension of the ordinary language of math with the observation of the human act of creating math. An inspiration for this observation can come from the last sentences of David Hilbert's lecture in Paris in 1900.


1. Socrates
The ordinary math is based on logical rules, and the famous "modus ponenS " :
1.All man are to die @ 2.Socrates is a man ---imply----- 3. Socrates will die
Many of the structures in math are based on this rule. But from Socrates himself WE have learnt the famous sentence

I know that I don’t know

This illogical contradiction made Socrates himself to be someone who will remain forever in man's conscience.

2. Hilbert
. 2,500 years after Socrates, David Hilbert made one of the most important lectures ever made. Leading the mathematitian community he declared a list of 23 open problems. In term of Socrates Hilbert modified it to :

I know what I don't know

It made his lecture influential and inspired the math community to try and solve his problems.

3. Goedel

One of the problems of Hilbert ( the 2nd problem) was after the success made on Geometry was to find the compatibility of the arithmetical axioms. 30 years later Goedel proved that aritmetic is incomplete and therefore it is impossible to fulfill Hilbert's task. He described a mathematical sentence in arithmetic that declares.

I can't be proven

As the 2 nd problem, most of the problems in Hilbert's list have been solved during the past century. One of the few that are still open , is the 6 th problem.

4. The 6 th problem


The 6 th problem of Hilbert was about a mathematical treatment of the axioms of physics:
" the investigation on the foundation of geometry suggest the problem : to treat in the same manner, by means of axioms, those physical sciences in which mathematics plays an important part ; in the first rank are the theory of probabilities and mechanics

Hilbert in his lecture

This is the willing to establish the right connection between mathematics and physics. Since mathematicians themselves belong to the physical world the 6 th problem is the only problem in the list , that has an organic quality, since a solution to the problem should be replaced by organic quality , as a solution to the problem contains inherently the formulation of the problem itself. Similar to the invention of calculus we need to develop a new language that emphasizes not just the value of a mathematical result but also the way that it changes. So we need to find a way to immerge those two aspects of math and the real world.


5. Organic mathematics
The Klein bottle invented by Felix Klein, is a mathematical model that demonstrates the quality of merging two opposite sides. The two different sides look separates only from the local point of view but from the global point of view the are one. Using this ability , an organic mathematics language should make the bridge between 3 polarities.


But We know that this ability as the model of Klein bottle can be reached only in the 4 th dimension. by an observation on what can't be observed in infinite we reach the goal :
I can be observed

But differ from Goedel steps we deal with the relation between math and the physical world. So , Instead of logical @ arithmetical sequence as goedel did , we need to find an environment to make physical@mathematical an experience in the effort to solved the 6 th problem of Hilbert . Since I belive that today there is no one Hilbert but many of him . A nice homage to Hilbert will be a common effort to solve one of his problems during the 6 days of the conference "100 to Hilbert".

Moshe klein (interacts) Amos Granit
 
Last edited:
http://www.geocities.com/complementarytheory/OMDP.pdf

The words get in the way for me.
They block the view.
So excuse me Doron, I have to go about this in a different way of speaking.

First I'm going to hold off talking about number for a bit.
There's a notion to be got first before I can make that application.
I'll call it "differentiation."

Indulge me a bit. This subject requires speaking of an altered state of consciousness. Some of you will know what I’m speaking of right away. Others will use your imaginations.

Earlier in our travels with Doron, I thought this was crucial to his meaning.
But his reply was negative so I canned it.
But it's obvious to me now that this is the place to start.

Sometimes I'm able to just let my mind drop away. No drugs necessary. Just a relaxation.
And when I do so, I find what my senses perceive to be a single seamless whole. There's no differentiating of objects, even of my self. What was exclusively of me is no longer separate. No inside, no outside.

This can only be described metaphorically.
There is sound, but there is a vast Silence.
There is multicolored light, but a deep Darkness.

Mystical literature gives it many names.
The Void
The Unborn
The Tao

This state doesn't last long.
Differentiation begins to set in.
Individual patterns get singled out
And finally I back to the world of objects.

On the way back there is a place to linger,
A place more of us have been and can relate to.

Again, it's important to note that when one is in "Unitary Consciousness,"
"Samadhi," or whatever you call it, the senses are working as usual.
It's not some empty blank slate before you.
It's just that there's no differentiation of individual things.
Everything is just a single seamless whole, and not even a one thing.
There is no object.

Once I'm back too business as usual, my perception has been cleft into innumerable, individual objects, separate from each other, associated in classes or types.

There's a stage between, though, that is also a common place in our usual consciousness.
I'll get to that in a moment, but first a little Doron.

Doron uses this _____________ to represent the seamless, undifferentiated whole.
And this . for an object differentiated from the whole.

Now watch out!
Forget mathematical points and lines.
What we are looking at here isn't sign but symbol.
Seeing how Doron is going to attempt to use these mathematically depends first on not seeing them as mathematical objects.

________________ Represents Non-Local Consciousness, the state of undifferentiation.
There's no locality in it. Every thing is everywhere. (no things).
Too call it "Non-Local" misses the mark, because there isn't any locality.
There is only locality, boundaries, and grouping when a differentiation is made.

. represents Local Consciousness.
That's the consciousness of innumerable, individual objects broken off from each other.

There are two ways of seeing there, but just those two aren't alone.

We single out objects from the whole, but we also focus on features of the whole.
I'm sitting in meditation and Ii look up to see my bonsai in the window.
It's still seamlessly integral to all of my perception, and is not an object as such, but it is the feature of my focus, and becomes the center of my attention. It's like it’s the foremost feature of reality.
And as it is more differentiated, it becomes The One that illuminates all else.
The Bonsai is still not a separate object. It remains integral to the whole "organism," as Doron would put it. Or it is the Heart of the organism.

More often we regard persons this way when we are giving them our full attention in listening and sharing. In such moments of encounter, they aren't objects to us. Not objects of any agenda or classification.

It's a situation of consciousness where they are in one aspect local for us and in another, non-local.
They are here, present, but their presence contains all else.
(And if you have not experienced this, I grieve for you.)

So we have The Void that is Full _______________________
and objects . . . . scattered about.

But we also have singular encounters in the Non-Local.
They stand in their own light as non-local to any classification and prior to classification.

Once we've differentiated into separate objects, we begin to group them.
It's then we can count them as sharing or being local to a given class.

We then have objects in localities . geographic and collective.

Now to Doron's Organic Numbers.
Doron intends that number can partake of or show these modes of consciousness as well.

So, as I've written in previous posts, the Organic Number Three is not merely 3 local elements added together.
There could be three foci undifferentiated from the whole and therefore not separate objects to be added up. In which case the count or how many is One or each one One in its own right, at its own focus of attention.
(This is more nuanced than "Redundancy.")
Or there could be two that are differentiated into countables, while one remains it's own man.
The Organic Number Three is meant to represent these Non-Local-Local circumstances.
You have the "Parallel potentials of 3 and the "Serial" potentials of 3.
The fractal tree of Redundancy and Uncertaintiy is meant to represent these potentials.
(Though it's too easy for a person to take it that the Parallels simply represent object elements outside a count. And take it that their non-locality is simply another location.)

Too much in one post, but ...

Doron's mathematical application of the __________________ symbol makes it the line of an infinite fullness of number.
Once you break it up into number objects in local fragments, once you have the discrete, differentiated, mathematical objects, add them up forever, but all the king' horses and all the king's men will not put infinity back together again.
You can't get to infinity from local objects.
You have to begin the other way, from Non-Locality, from infinity back to the finite.
 
Apathia said:
http://www.geocities.com/complementarytheory/OMDP.pdf

The words get in the way for me.
They block the view.
So excuse me Doron, I have to go about this in a different way of speaking.

First I'm going to hold off talking about number for a bit.
There's a notion to be got first before I can make that application.
I'll call it "differentiation."

Indulge me a bit. This subject requires speaking of an altered state of consciousness. Some of you will know what I’m speaking of right away. Others will use your imaginations.

Earlier in our travels with Doron, I thought this was crucial to his meaning.
But his reply was negative so I canned it.
But it's obvious to me now that this is the place to start.

Sometimes I'm able to just let my mind drop away. No drugs necessary. Just a relaxation.
And when I do so, I find what my senses perceive to be a single seamless whole. There's no differentiating of objects, even of my self. What was exclusively of me is no longer separate. No inside, no outside.

This can only be described metaphorically.
There is sound, but there is a vast Silence.
There is multicolored light, but a deep Darkness.

Mystical literature gives it many names.
The Void
The Unborn
The Tao

This state doesn't last long.
Differentiation begins to set in.
Individual patterns get singled out
And finally I back to the world of objects.

On the way back there is a place to linger,
A place more of us have been and can relate to.

Again, it's important to note that when one is in "Unitary Consciousness,"
"Samadhi," or whatever you call it, the senses are working as usual.
It's not some empty blank slate before you.
It's just that there's no differentiation of individual things.
Everything is just a single seamless whole, and not even a one thing.
There is no object.

Once I'm back too business as usual, my perception has been cleft into innumerable, individual objects, separate from each other, associated in classes or types.

There's a stage between, though, that is also a common place in our usual consciousness.
I'll get to that in a moment, but first a little Doron.

Doron uses this _____________ to represent the seamless, undifferentiated whole.
And this . for an object differentiated from the whole.

Now watch out!
Forget mathematical points and lines.
What we are looking at here isn't sign but symbol.
Seeing how Doron is going to attempt to use these mathematically depends first on not seeing them as mathematical objects.

________________ Represents Non-Local Consciousness, the state of undifferentiation.
There's no locality in it. Every thing is everywhere. (no things).
Too call it "Non-Local" misses the mark, because there isn't any locality.
There is only locality, boundaries, and grouping when a differentiation is made.

. represents Local Consciousness.
That's the consciousness of innumerable, individual objects broken off from each other.

There are two ways of seeing there, but just those two aren't alone.

We single out objects from the whole, but we also focus on features of the whole.
I'm sitting in meditation and Ii look up to see my bonsai in the window.
It's still seamlessly integral to all of my perception, and is not an object as such, but it is the feature of my focus, and becomes the center of my attention. It's like it’s the foremost feature of reality.
And as it is more differentiated, it becomes The One that illuminates all else.
The Bonsai is still not a separate object. It remains integral to the whole "organism," as Doron would put it. Or it is the Heart of the organism.

More often we regard persons this way when we are giving them our full attention in listening and sharing. In such moments of encounter, they aren't objects to us. Not objects of any agenda or classification.

It's a situation of consciousness where they are in one aspect local for us and in another, non-local.
They are here, present, but their presence contains all else.
(And if you have not experienced this, I grieve for you.)

So we have The Void that is Full _______________________
and objects . . . . scattered about.

But we also have singular encounters in the Non-Local.
They stand in their own light as non-local to any classification and prior to classification.

Once we've differentiated into separate objects, we begin to group them.
It's then we can count them as sharing or being local to a given class.

We then have objects in localities . geographic and collective.

Now to Doron's Organic Numbers.
Doron intends that number can partake of or show these modes of consciousness as well.

So, as I've written in previous posts, the Organic Number Three is not merely 3 local elements added together.
There could be three foci undifferentiated from the whole and therefore not separate objects to be added up. In which case the count or how many is One or each one One in its own right, at its own focus of attention.
(This is more nuanced than "Redundancy.")
Or there could be two that are differentiated into countables, while one remains it's own man.
The Organic Number Three is meant to represent these Non-Local-Local circumstances.
You have the "Parallel potentials of 3 and the "Serial" potentials of 3.
The fractal tree of Redundancy and Uncertaintiy is meant to represent these potentials.
(Though it's too easy for a person to take it that the Parallels simply represent object elements outside a count. And take it that their non-locality is simply another location.)

Too much in one post, but ...

Doron's mathematical application of the __________________ symbol makes it the line of an infinite fullness of number.
Once you break it up into number objects in local fragments, once you have the discrete, differentiated, mathematical objects, add them up forever, but all the king' horses and all the king's men will not put infinity back together again.
You can't get to infinity from local objects.
You have to begin the other way, from Non-Locality, from infinity back to the finite.
Click to expand...

Aphatia,

I send you my love.
 
MosheKlein said:
Dear Doron,

Here is the paper which I wrote in 2000 for the conference "100 to Hilbert" in U.C.L.A university. I think it come from what you name as direct perception. Anyhow the tree of distinctions is a tremendous development Since it create a real praxis of OM.

So the next step can be to develop an application to OM !!!

Your
Moshe





Organic mathematics
Mathematical experiment to solve
the 6 th 'problem of hilbert

Moshe Klein

"The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfill this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples"
. D.Hilbert


Organic mathematics is an extension of the ordinary language of math with the observation of the human act of creating math. An inspiration for this observation can come from the last sentences of David Hilbert's lecture in Paris in 1900.


1. Socrates
The ordinary math is based on logical rules, and the famous "modus ponenS " :
1.All man are to die @ 2.Socrates is a man ---imply----- 3. Socrates will die
Many of the structures in math are based on this rule. But from Socrates himself WE have learnt the famous sentence

I know that I don’t know

This illogical contradiction made Socrates himself to be someone who will remain forever in man's conscience.

2. Hilbert
. 2,500 years after Socrates, David Hilbert made one of the most important lectures ever made. Leading the mathematitian community he declared a list of 23 open problems. In term of Socrates Hilbert modified it to :

I know what I don't know

It made his lecture influential and inspired the math community to try and solve his problems.

3. Goedel

One of the problems of Hilbert ( the 2nd problem) was after the success made on Geometry was to find the compatibility of the arithmetical axioms. 30 years later Goedel proved that aritmetic is incomplete and therefore it is impossible to fulfill Hilbert's task. He described a mathematical sentence in arithmetic that declares.

I can't be proven

As the 2 nd problem, most of the problems in Hilbert's list have been solved during the past century. One of the few that are still open , is the 6 th problem.

4. The 6 th problem


The 6 th problem of Hilbert was about a mathematical treatment of the axioms of physics:
" the investigation on the foundation of geometry suggest the problem : to treat in the same manner, by means of axioms, those physical sciences in which mathematics plays an important part ; in the first rank are the theory of probabilities and mechanics

Hilbert in his lecture

This is the willing to establish the right connection between mathematics and physics. Since mathematicians themselves belong to the physical world the 6 th problem is the only problem in the list , that has an organic quality, since a solution to the problem should be replaced by organic quality , as a solution to the problem contains inherently the formulation of the problem itself. Similar to the invention of calculus we need to develop a new language that emphasizes not just the value of a mathematical result but also the way that it changes. So we need to find a way to immerge those two aspects of math and the real world.


5. Organic mathematics
The Klein bottle invented by Felix Klein, is a mathematical model that demonstrates the quality of merging two opposite sides. The two different sides look separates only from the local point of view but from the global point of view the are one. Using this ability , an organic mathematics language should make the bridge between 3 polarities.


But We know that this ability as the model of Klein bottle can be reached only in the 4 th dimension. by an observation on what can't be observed in infinite we reach the goal :
I can be observed

But differ from Goedel steps we deal with the relation between math and the physical world. So , Instead of logical @ arithmetical sequence as goedel did , we need to find an environment to make physical@mathematical an experience in the effort to solved the 6 th problem of Hilbert . Since I belive that today there is no one Hilbert but many of him . A nice homage to Hilbert will be a common effort to solve one of his problems during the 6 days of the conference "100 to Hilbert".

Moshe klein (interacts) Amos Granit
Click to expand...



Thank you Moshe,

After 9 years it is reduced into n-Uncertainty x n-Redundancy tree to start with.
 
Last edited:
Apathia said:
Mystical literature gives it many names.
The Void
The Unborn
The Tao
Click to expand...
It has seemed to me for some time that the 'Direct Perception' idea has been lifted from Eastern philosophies of completeness and holism - the sarvakarajnata (the quality of knowing things as they are) of Buddhism seems a particularly close match.

I have been wondering why Doron hasn't made any reference to these roots.
 
Aphatia said:
This state doesn't last long.
Differentiation begins to set in.
Individual patterns get singled out
And finally I back to the world of objects.
Click to expand...



Direct Perception training analogy:

There is a technique to get a stable color of a cloth.

It goes like this:

We have a white cloth.

Let us say that we wish to get an orange cloth, so in order to get it
we repeat on these steps:

1) We take the cloth and dipping it in orange color.

2) We take the cloth and expose it to any possible weather conditions like sun light, wind, rain, snow, whatever …

3) As a result most of the orange color is washed out from the cloth, but we take it and return to step 1.


After several loops we get a colored stable orange cloth.


So is the case of Direct perception awareness.

During an appropriate training we are able to be Direct perception awareness beside any possible mental activity, such that no mental activity blocks Direct perception awareness in our daily life.
 
Last edited:
doronshadmi said:
Thank you Moshe,

After 9 years it is reduced into n-Uncertainty x n-Redundancy tree to start with.
Click to expand...

yes I agree with you.
Today this is a very clear praxis of Organic Mathematics.
And this is a contribution of Jfisher to the process of clearing
On = 1,2,3,9,24,76,236,... is not important anymore !!
 
Last edited:
MosheKlein said:
yes I agree with you.
Today this is a very clear praxis of Organic Mathematics.
And this is a contribution of Jfisher to the process of clearing
On = 1,2,3,9,24,76,236,... is not important anymore !!
Click to expand...

Moshe 1,2,3,9,24,76,236,... was never important.

Furthermore, it is nothing but a quantitative serial result of ON's partial case.

This partial case is used only as an example of Non-locality\Locality linkage.


It looks important to you exactly because you were trained to get Math as serial quantitative space by the western academic system, and this is exactly where jsfisher and you fail to get OM and ON.

Your intuition was for many years beyond the western academic system, but after n-Uncertainty x n-Redundancy Tree is available, you have a truly formal tool to play with, which is more rigorous than any verbal-based formality (which is the only formal environment that jsfisher gets, at this stage).


I have asked jsfisher to add his name to OM's Acknowledgements but he refused.

In second thought I prefer him as OM's critics, he is dong a great job in this position.
 
Last edited:
doronshadmi said:
Please demostrate exactly how ordering distinctions is not one of the cases of that tree.

You can use 2-Uncertainty x 2-Redundancy tree:
Code: 
2X2                                             
                                                
(AB,AB) (AB,A)  (AB,B)  (A,A)   (B,B)   (A,B)   
                                                
A * *   A * *   A * .   A * *   A . .   A * .   
  | |     | |     | |     | |     | |     | |   
B *_*   B *_.   B *_*   B ._.   B *_*   B ._*   
                                                
(2,2) = (AB,AB)                                 
(2,1) = (AB,A),(AB,B)                           
(1,1) = (A,A),(B,B),(A,B)
Click to expand...

Why should I bother when you demonstrate it so effectively yourself?

doronshadmi said:
How, for example, (A,B) excludes ordering distinctions ?

For example, let us take (A,B,C) case of 3-Uncertainty x 3-Redundancy tree:

Code: 
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 .__*__.

The tree is there, all you have to do is to play with it.
Click to expand...


By setting (B,A,C) equal to (C,A, B) you are claiming that a reversal in order is not a distinction in your notions that you claim are specifically about distinctions. Similarly although you now claim your tree has the ability to make certain ordering distinction like (A,B,C) is distinguishable from (B,A,C) (apparently from where you place the “*”s) those particular distinctions are not distinctly included in your ‘On’ calculations.

Play with your tree or what ever you want to call it all you want. Until you included ordering distinctions in your ‘On’ calculation then you are excluding ordering distinctions for your notions you claim are based on, well, distinction.
 
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