Bit from it. Mathematical Clarification by Michael Alexeevich Popov

Gennady,

Doubters may suggest that in comparison with energy conservation law, Hawking's 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( 2005 )) can be violated ? Moreover, there is no such thing as physical measurement of bits of thermal information in physics .

( copy of comment for Gennady Gorelik )

Dear Helmut,

I have some doubts on 'In physics everything is basically bi-polar energy '? As is known, Levi-Strauss, founder of French structuralism ,showed that the whole structure of primitive thought is binary as well. However, tendency to operate with binary counters in all situations in physics could be understood also as taking simplification seriously ?

( copy of comment for H.A.von Schweizer )

Dear Jan,

my remark :

Shannon and Other Structuralisms

In comparison with Wheeler Structuralism ( 0-1 structure underpins all of our data and all our sciences ) and Category Structuralism ( by Roman Jakobson, Levi-Strauss, Burbaki, Abramsky and Coecke ) where the universals of human culture exist only at the level of structure,'culinary triangles' or other intuitive ordered things ; Shannon bits mathematics is pure mathematics. Shannon mathematical assumption is based on elementary algebra of common logarithm logax, where the logarithm of x to the base 2 is defined by the equation y = log2 x. This definition is of course applicable only when y is RATIONAL NUMBER. Beyond Shannon rational bits there exists new world of real, irrational, imaginary and complex bits, the world of Weierstrass theorem and the world of real lines contained infinitely many imaginary bits.

Thus, it could be difficult to find real differences between Wheeler binarism and Alternative Gospel of structures , indeed. In fact, similarity between Wheeler and Topos Gospel by Doring & Isham philosophies are obvious.

(Copy of comment for Jan Durham ).

Michel,

I count myself fortunate to find your recent arXiv articles on Riemann conjecture and its quantum simulations.I try to make something similar but merely in the context of post - quantum cryptology. My initial result ( published in 1999 in France )is connected with introduction of periodic perfect numbers(Bull Sci math 1999,123,29-31),hence, new definitions of prime number theorem, cubic groups and quantum one-way function( Cryptology ePrint Archive, 653/2010 ) are arising. I had found that your attempt to formulate Riemann hypothesis as a property of the low temperature Kubo-Martin-Schwinger states is very original. Your last articles also suggest that beyond very popular Wheeler delusion there exist new world of unknown mathematics and unexpected physics.

best

Michael

Michel,

P e r f e c t s. It's correct. But it is only a beginning of mystery- Plato ( Euler who made reference to this puzzling place in Republic ) predicted an existence of merely three perfect periodic numbers at all, Ramanujan ( note books ) developed more general technoque using similar assumption and recieved somothing fundamentally different ( he had surprisingly quantum "taste").My new definition of "perfectness" in Bul Sci math is based on elementary proof of impossibility of Euler odd perfect numbers as well.

C u b i c ( already sent ) One - way function in cryptology is another definition of P is not NP solution.

R H . An attempt of Latorre-like superposition of all odds ( 2013 )in quantum computations of pi(x) and the Mangoldt's function.

Best

Dear Akinbo,

Shannon was a mathematician and it is logical to follow his context ( not Wheeler brave speculations ) to understand bit.

In arithmetic we start from the positive integers ( 1,2,3,4,5,6,...) and from the ideas of addition, multiplication,substraction and division. It is easy to test that these operations are not always possible ( 4 - 29, 5 - 7, 2 - 8, 4/29,5/7,... etc )unless we admot new kind of integers ( negative numbers, or more generally, rational numbers )If we include root extraction and the solution of equations, we can find some operations are not possible also unless we admit a new kind of numbers. Mathematicians had found that the extraction of the square root - 1 is not possible unless we go further and admit the complex numbers ( as is known, following mathematicians Einstein, Heisenberg and Schrodinger introduced the square root of - 1 in physics ).Thus,it is practical and productive everywhere ( even philosopher Immanuel Kant made an attempt to introduce negative numbers in philosophy ...)

Complex numbers are sometimes called imaginary.Complex number is not number in the same sense as a rational number ( used by Shannon for bits )It is a pair of numbers (x,y), united symbolically in the form z = x + yi . Hence, it is easy to see, that when y = 0 we say that z is real ( special term for 'post-rational numbers' ), correspondingly, when x = 0 then z is pure imaginary.

Next step.

let ax + by +c = 0 be an equation with complex numbers ( coefficients ). If we give x any concrete complex value , we can find the value of y. Set of pairs of real and complex values of x and y which satisfy the equation is called imaginary straight line, the pairs of them usually are called imaginary points and are said to lie on the line. When x and y are real, the point is called a real point; correspondingly, when a, b, c are all real, the line is defined as real line.etc Hence, we can easy deduce answers for questions 2 and 3.

Dear Than,

I suppose that Physics as a science tries to establish truth but not poetics and political sense of argument.R.Feynman also suggested that physicists have a way of avoiding the politics and subjective tastes in science : if you have an apparatus which is capable of telling how many bits of information given thermal energy ( "termal information" )must contain in the terms of physical measurement, then you can say scientifically about entity information, indeed. Because there is no such thing as physical measurement of the bits of thermal information, then 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 )) and its consequences might be considered, unfortunately,as popular illusion.

respectfully

Michael

Dear Antony,

Thank you for high rank. Let me imagine a continuation of your n-dimensionality logical game. If rational n-dimensionality ( n = -1,0,1,2,3 and we assume that n is rational number ) is accepted ( i.e. there is a mathematical proof ) we can go further and we may admit a new kind of possible dimensionality, expressed by the square root -1 and complex numbers ( why not ? Einstein and Hawking use the square root - 1 as an imaginary time / complex time variable u in physics ).Hence, new unexpected physical generalizations are deduced.

( copy of my comment for Antony Ryan by 1 Aug 2013 )