# Organic mathematics

1. Mar 28, 2004

### moshek

Organic mathematic (*)
Mathematical experiment to solve
the 6 th' problem of Hilbert

"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 1900)

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.

realty - imagination
object - subject

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

----------------------------------------------------------
Intelligent life (*)

Planet Mar's was connected twice to the search of man for intelligent life. First was the effort to understand the retrograde movement of mars on the background of the night sky. second was a mistake that identify cannel on is face done by other culture. maybe there is connection between mars to the search of life in the area of mathematics.
Thousand year's ago people observed that mars is going sometime in the opposite direction relative to the stars. Mars is moving slowly on the background of the night sky so you can distingue the different every day, suddenly he stand and then start to go in the opposite direction. Then he stop again and continue his regular direction.
For explaining this strange movement the astronomer invented complex system of wheels so that earth is in the center . the most complicate system was invented by Talmy and it included 12 wheels. But 400 year's ago Copernicus invent a new revolutionary idea so that put the sun in the center of the world and not the planet earth. In this observation the explanation to the movement of mar's became very simple and it base on some interaction of movement between mar's and earth. This is how the science revolution started and it was with many hard struggle. The follower of Copernicus, Galilo and Newoton base the science way of thinking by a development of a new suitable mathematics.
The top of this way of thinking bring in the 20 century to the development of two central theory: Relativity and Quantum theory. These two theory's change the way man understood himself in the world. We are not passive observer in the phenomena , and we have some active part that base on the interaction that between us and the world. Is there a way to establish similar principle in the rational area of mathematics? By first looking it look that there is no way for doing this. The world of mathematics seems to be absolute and exist without man. But from the other side we know that here is today some need to develop a new looking to mathematics that can bring to more understanding of the relation between mathematics and the world of phenomena. This was express in the lecture of Alein Connes who develop 20 year's ago Non commutative Geometry, and consider as one of the leading mathematician in the world today. "… we need today a new understanding in mathematics that it's source is not necessarily come from logic but more on the geometry." This end the last lecture in the conference "100 to Hilbert" . This conference was to point another famous lecture of Hilbert in Paris in 1900. Hilbert end his lecture by drawing a vision to discover an organic unity of mathematics.
A Common looking on those two important conference like two eye's, one took place in Paris and the other in Los-angels, with a different of 100 year's in time arise the question if and how is moving mathematics , like mars, on the background of the culture of mankind. This is how arise the problem that not solved yet , of the inherent hidden connection between mathematics and the real world. But like the observation of Copernicus that aloud us to put the Sun in the center of our world and by this to understand more simply the interaction between the earth and mar's, we can point to a third eye's that solved the mathematical problem. The new common center of mathematics and physic is the discovery of the organic unity of mathematics , intelligent life.

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

(*) was publish at December 2000 in the booklet "100 to Hilbert" Tel-Hai Academy.

Last edited: Apr 12, 2004
2. Mar 28, 2004

### Organic

Dear Moshek,

I think the main point here is that mathematicians cannot be just observers of their results, but a full participators that determinate each result by using a flexible language, that can be changed during use, and can change the cognition's depth of the person who using this language.

We have found that this is exactly what is going in Quantum Mechanics where
the user has to determine the research limits because of the duality of the Quantum elements.

It means that this mutual influence between a mathematician and the language that he uses, has to be based on some logical system that can be a comprehensive method that can support this cognition-language dynamic relationships, which is totally different way that leaves behind the platonic realm point of view.

I suggest Complementary Logic as this comprehensive method:

http://www.geocities.com/complementarytheory/BFC.pdf

Yours,

Organic

Last edited: Mar 28, 2004
3. Mar 28, 2004

### moshek

Dear Organic:

Thank you for your respond and opinion about my paper "Organic mathematics" !

I wrote it few years ago and Share it during the conference "100 to Hilbert" that take place at U.C.L.A august 2000. Recently I discover Wittgenstein opinion about the possibility to create new mathematics by using the Klein bottle geometry. So you can read I wrote about it in my paper. I decide that today it is the right time to publish it here to share with other the discovery, and to got there opinions.

Your new theory about Numbers is the local size of my theory and the relation between local and global property is essential in any concept in mathematics or as you named it complementary theory.

I am sure that this is going to be a very long Voyger but we must start at some point..

My Best whishes
Moshek

Last edited: Mar 28, 2004
4. Apr 10, 2004

### moshek

For mathematics

I thank Lorentz for puting the poem in his new thread which was moved from mathematics to philosopy . The editing that was dond by my friend John and i thank him for doing that.

FOR MATHEMATICS

The current Big Bang
Is a real glory!
The Milky-Way is all around us
And was created with our Solar System.

'Everything is a number'
Said Pythagoras
As he was hearing
The Music of the Spheres.

But there were many dark waters
Which covered the head of Hippasus
After he discovered
The Secret of Irrationality.

Maybe Euclid hid the narratives
Of the Protection of the Axioms
Of the Parallels
When he established his own mathematics.

While Newton calculated
The end of the world,
Leibnitz -- with the monads -- believed
A unitary language must exist.

Goethe could see in the word
The generic type,
But did not like or know
True mathematics.

Hilbert remained
Deeply misunderstood
With his list of 23 problems
and organic unity.

A. Connes with his theory
Of non-communicative geometry
Of 100 to Hilbert, ended up
With a new understanding.

M. Athiya, in his index
And K theory
Discussed it all
As some enigma.

The vision of J. Stuart
Shared the flexibility
Of the nature of numbers
In his epilogue.

Wittgenstein says
We should be aliens
To see properly
In the bottle of Klein.

From the top of the mountain
Of the Rieman hypothesis
We can see another mountain, an analogue,
And hear its Sixth Symphony.

Einstein performed the actual
First step of a child
When he asked how we
Measure a length.

Only when we see the world
Like children again
Will we count once more
From the beginning: 1. 2. 3.

Moshe Klein 10.4.04

Last edited: Apr 12, 2004