Bit from it. Mathematical Clarification by Michael Alexeevich Popov

Peter,

My later reading of your essay showed an importance of following passages :

> " Binary based mathematics relies on the Law of the Excluded Middle between assigned symbols 0,1, A,B, or yes/no for waves".

"Time itself is a special case. The concept time is a human invention to describe change, often confused with the physical evidence of emissions from 'clocks'".

< refinement . When Albert Einstein extended physically accepted list of arithmetical operations so as to include the extraction of the square root of minus 1 in his theory of imaginary time (SR), he admitted the complex numbers and new theory of time. Thus, if we find that some equations of higher degree used in physics are insoluble by aid of complex numbers now, we can go further and admit new math. Hence, new time theory can be connected with new mathematics of non-integer dimensionality spacetime. In 1986 quantum theorists Karl Svozil and Anton Zeilinger proposed that the notion of the dimension of spacetime could be based on"philosophical" measure-theoretic concepts ( admitting the possibility of noninteger dimensions , like 4 - έ ). They introduced in fact an operational dimension which is smaller than the idealized Housdorff dimension. However, they intuitively extended their list of accepted arithmetical operations so as to include the solution of higher equations.Thus,we might to be led to the consideration of numbers of another types in order to introduce complex dimensionality and new time theory, taking technically.

http://www.worldscientific.com/doi/abs/10.1142/S0217751X86000368

Peter

(technical addition )

' Binary based mathematics relies on the Law of the Excluded Middle between assigned symbols 0,1, A,B, or yes/no for waves'.

Refinement. May be philosophically in the terms of analytical tradition, it is correct, however, mathematically speaking, it is a kind of Wheeler simplification. Indeed, we cannot say that Weirstrass theorem relies on the Law of the Excluded Middle. Technically, in alternative proof of Weirstrass theorem, we divide some interval into two equal parts, when one at least contain infinitely many points. Proceeding in this way we can define a sequence of intervals each of which is a half of its predecessor, and each of which contains infinitely many points. Hence, ideas of points of accumulations, Dedekind theorem, sections of the real numbers into left-hand class / right-hand class, etc. Thus, Wheeler yes/no logic must have limited sense and actual binary mathe-matics is more complicated.

( Copy of my comment for Peter Jackson by 5 Aug 2013 )

Dear Amazigh,

Thank you for your visit.

Some your observations :

'... the duality was obvious to the Egyptians, Greeks, etc.. , And especially the Chinese...

For me the question is quite different : why we do not have yet flushed the irrefutable arguments that prove that the universe is binary, dualistic...

Today, Einstein's relativity is well understood in the physical domain. It explains very well the two points of view of two people moving relative to each other...

Finally, I would like to conjecture that:

-The first principle that governs the universe is Duality. The principle of conservation has come after. Give the same interest to duality that to motion, and things will better.

-We know matter is dual as well as the light is. So if duality is everywhere, how to recognize this fact, as we did for the motion ?

-The Duality is the common language by excellence, the integral link between all the elements of nature, the machine code of the universe '

may suggest some analogies with field findings of structural anthropologists. In particular,French anthropologist Levi-Strauss made reference to 353 duality based different myths in order to prove that the human brain does have a tendency to operate with binary oppositions in all sorts of situations. This result is foundation of structural anthropology and semantic algebra of myths today. However, the sceptics were right as well, because human brain can operate in other ways also. Thus, a fully satisfactory model of the human mind would contain many unknown features which do not occur merely in digital computers. I suppose you can improve your structural linguistic analysis of oppositions by Jakobson's technique based on conjecture that ' in all the languages of the world the complex systems of oppositions between the phonemes are no more than a multi-directional elaboration of a more complex system which is common to all, namely the contrast between consonant and vowel, which through the working of double opposition between compact and diffuse, acute and grave...'

with the best wishes

Michael

Dear Sreenath,

Thank you for your visit.

Because it is physical forum, may I ask you merely one very strange question : How we can make physical measurement of the bits of taking universal information seriously in reality ?

Dear Wang,

My later comment, sorry :

When you proposed that 'one day a more complete theory should unify all the three basic concepts Matter-Energy-Information ' , you probably made an assumption that the law of information conservation in future physics is quite possible.

But, sceptics may suggest that in comparison with energy conservation law , Hawking -like law of information conservation (The information remains firmly in our universe. Thus, if you jump into a black hole, your mass energy will be returned to our universe but in a mangled form which contains the information about what you were like but in a state where it can not be easily recognized.( Hawking, 2005 )) can be violated ? Moreover, speaking exactly, there is no such thing as physical measurement of bits of thermal information or generally - universal information in physics.

Best

Michael

Dear Sreenath,

It would be almost impossible to predict another result.Rank is less important but pleasure to participate in global self organized anthropological experiment is beyond any expectations.It is very rare event.Indeed.

Respectfully

Michael