There is a set A such that, given any set x, x is not a member of A.

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