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Serguey Shilov

The Chronicle. Definitions of the Megascience
     Notes on fields of W. Heisenberg's 
"Physics and philosophy"
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3. Mechanics of time. Space of mathematics.
The law of prime numbers as the general field theory

Heisenberg wrote: "All things are numbers" is a sentence attributed to Pyphagoras. The only mathematical 
forms available at that time were such geometric forms as the regular solids or the triangles which form their surface. In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical form, but of a mach more complicated nature. ... Modern science, however, has from its 
beginning in the sixteenth and seventeenth centuries started from the dynamic problem. The constant 
element in physics since Newton is not a configuration or a geometrical form, but a dynamic low. The 
equation of motion hold at all times, it is in this sense eternal, whereas the geometrical forms, like the orbits, 
are changing. Therefore, the mathematical forms that represent the elementary particles will be solutions 
of some eternal law of motion for matter.  
Actually this is a problem which has not yet been solved. The fundamental law of motion for matter is not 
yet known and therefore it is not yet possible to derive mathematically the properties of the elementary 
particles from such a law. But theoretical physics in its present state seems to be not very far from this goal 
and we can at least say what kind of law we have to expect. The final equation of motion for matter will probably be some quantized nonlinear wave equation for a wave field of operators that simply represents 
matter, not any specified kind of waves or particles. This wave equation will probably be equivalent 
to rather complicated sets of integral equations, which have "Eigenvalues" and "Eigensolutions", as mathematicians call it. These Eigensolutions will finally represent the elementary particles; they are the mathematical forms which shall replace the regular solids of the Pyphagoreans. We might mention here that 
these "Eigensolutions" will follow from the fundamental equation for matter by mach the same mathematical process by which the harmonic vibrations of the     Pyphagorean string follow from the differential equation 
of the string. 
If we follow the Pyphagorean line of thought we may hope that the fundamental law of motion will turn out 
as a mathematically simple law, so simple as it hoped to find as far back as Plato. It is difficult to give any 
good argument for this hope for simplicity - except the fact that it has hitherto always been possible to write 
the fundamental equations in physics in simple mathematical forms. This fact fits in with the Pyphagorean 
religion, and many physicists share their belief in this respect, but no convincing argument has yet been given 
to show that it must be so. (End of quotation.) 

The chronicle uncovers the foundations of mathematics problem in the following way: the mathematics is 
the pure theory of space. If the physical time is uncovered as temperature in its original physical sense, the 
problem of measuring in the physics is uncovered consequently as the creative function of space, i. e. as mathematics. The mathematics is the measurement of physics. A fundamental problem of the Chronicle is 
the problem of time measurement. The time measurement is a sole essence of physical process, as far as 
the process has mathematical form. The time measurement is physics of formulas, strategy of universalization 
of "divisions" of the modern physics. The space is a reality which arises as the outcome of time measurement. 
The time measurement is the dynamic and static function of time, a function of time. 
The time measurement is a theory of number. The time measurement - Time the reversible, the recurring, 
the multidirectional - is a theory of number. The classical thermodynamics, keeping the problems of time in shade, has resulted in generating of nonequilibrium thermodynamics, i. e. statistical physics. The statistical physics within the framework of a reflection of physical knowledge program can be reduced to the 
problems of the foundations of mathematics. The program of the Chronicle brings us closely to the 
development of the foundations of mathematics as to that field of knowledge where the basic problems of 
physical knowledge are solved. 
More particularly, program of the reflection of mathematics is necessary. The strategy of the present 
program supposes re-definition, or, more clearly speaking, definition, determination of number. The state 
of mathematical knowledge is characterized by the same problems as state of physical one. We notice here 
the same forestalling development of "divisions" of mathematics in relation to a state of development of the foundations of mathematics. Actually, the present-day symbiosis of physics and mathematics also leads to radical re-thinking of basic concepts used in mathematics, among which the most fundamental value has 
the concept of number. 
The number is the basic subject of physical knowledge. Physics studies number. Physics studies effects originating in connection with the existence of number. The number is the form of existence of time in 
nature, while temperature is the content of existence of time in nature. The number is the actual subject of physics. Number is a wave and particle simultaneously. The number is an actual object, the element of time; 
a thing, subject of time which, from the point of view  of the researcher, is both wave and particle. The 
number, thus, is a thing realizing oscillatory and undulatory processes. The number radiates. It is the 
problem of modern physics: the object which realizes the physical process as such, physical process, 
which explicitly and in detail is investigated in divisions of physics has not been defined. The Chronicle 
defines this object as a number, number of a numerical series, as an object which concretely existing in 
time, from time, by force of time; object which has all variety of qualities uncovered in divisions of modern physics. 
Basic foundation of the mechanics of time (chronicle) is the following: the number is a concrete moment, 
i. e. an outcome of making of a certain amount of space by certain force of time. That is the formula of 
number. The form of existence of a number is oscillation (harmonic oscillations, mechanical harmonic 
oscillations, free harmonic oscillations in an electrical oscillatory circuit, relaxation and forced oscillations). 
The real theory of number arises as radical criticism of quantum mechanics. The quantum mechanics 
develops as speculative physical knowledge around true, but not realized subject of physical knowledge. 
The quantum physics has closest approached than other divisions of physics to true, but not explicit 
object of modern physics, to number. But physics has stopped in front of it and generates phantasmagoric constructions of "nominal" quarks. 
Heisenberg's principle of uncertainty, concerned with a problem of a measurability in the physics, on the assumption of sequential thought means circumstance developed in this text: sole and basic matter of all 
divisions

of modern physics is number as such, its reality, "behaviour", law (laws) of its genesis and 
structure, interaction among numbers. There is no other reality of modern physics in the aggregate of its divisions, but number in itself. 
The real object of the physics is number. The chronicle is a theory of number. Mathematical aspect of 
numbers corresponds to divisions of the physics. There is nothing in concrete division of physics but the 
study of concrete properties of a certain sort of numbers as chronosystems. The natural numbers, integers, 
prime numbers, fractions, positive and negative numbers, rational numbers and irrational numbers are 
types of unification of chronosystems. 
The space consists of numbers. Exclusively actual infinity of numerical series (denumerable infinity) as 
such is space in itself. The relation of actual numbers is the definition of gravitation. 
Solely actual infinity of a numerical series is "field". An infinite numerical series is the consistence of 
"nature", it is process of time as matter of any realization. The universal and concrete number is a reality disappearing under the name "solid" in the classical mechanics. There is only number. The interior relations 
of a numerical series form transparent space of the physics. The quantum physics (mechanics) disappears 
in the theory of number. The new theory of number is the unified theory of physical interactions in which distinctions of the divisions of physics become substantive. The number is "velocity", "acceleration", 
"impulse", "momentum", "energy", "thermal motion", "work", "fluctuation", "electric field", "electric charge", "electric current", "dielectric", "semi-conductor", "plasma", "magnetic field", "atom", "induction", 
"oscillation", "wave", "radiation of heat", "photon", "radio-activity", "fundamental interactions of ultimate particles". The number is a primary subject of physics and coincides with the essence of mathematics. The number is being of time in the form of space. "T" (linear time) of the physics' formulas, is, undoubtedly, a turnover variable, but nevertheless should be interpreted as real function, as outcome of transformations. 
Even in case of the formula of a velocity as the relation of distance to time it is necessary to understand that 
just the time (even linear time) is produced in this process, and what is required for this purpose is concrete velocity and distance which are formed and become possible by virtue of necessity of making certain linear amount of time. 
All physical experiments are experiments "inside" of numerical series, are experiments with concrete 
numbers, experiments in the field of interaction of numbers, experiments basing upon actual infinity of one 
but really existing numerical series. 
The general theory of number is the general field theory. The physical field is an nfinite numerical series of 
various types of numbers. For that simple reason, that there are various kinds or qualities of numbers, i.e. 
natural numbers, integers, prime numbers, fractions, positive and negative numbers, rational numbers and irrational numbers. In other words, a numerical series incorporates qualitative distinctions of physical 
processes, is present by a transparence and interchangeability of all physical processes. There is no nature investigated by physics, except a numerical series as such, unique and infinite. Distinction of number types 
is a genuine physical reality of physical processes presented in divisions of modern physics. The distinction 
of number types is the actual form of distinction of physical interactions and of kinds of physical substance. 
The formula of a general field theory is the law of prime numbers. The various types of numbers are that concrete reality which are situated beyond "types of a substance" investigated in divisions of physics. 
The prime numbers are a fundamental reality - foundation of physical processes - fixing indestructible, indissoluble connection between time and heat. The law of prime numbers is the plain fact of existence of 
an infinite amount of prime numbers, of "solids as generators of gravitation" which in traditional 
mathematical sense is nothing but the Fermat theorem heuristic (clear) proving. The mathematics speak 
about the Great Fermat theorem in such a way: "There are no such four numbers which would satisfy to the equation: ?n + ?n = zn ["n" here is exponent], where: n > 2; x, y, z are positive integers. Trying to solve the problem of the "great Fermat theorem", it is necessary to answer a question: "And what do we, in fact, 
search?" If the answer is casual numerical coincidences, then it is necessary to calculate regularities of 
power numerical series according to general numerical series. But such approach can not give the crucial 
answer to the problem: "Why is it impossible nevertheless to divide a cube by other two cubes, and why 
is it impossible in general to divide number in a power above second by other two numbers of the same 
power?" As it is well known, it is possible to seek out many pairs of integers which sum total of second 
power as well is some of integer's second power. You may find as much such numbers as necessary. But 
try to seek similar examples for the third power. You will not discover any! You will experience the 
complete failure in the search of an example for fourth, fifth and other higher power. That is the "great proposition of Fermat". It states that equation xn+yn=zn has no positive integer solutions". 
The fundamental formula of the Chronicle is the formula of space: "The great Fermat theorem is the physical formula of space". 
The space as a concrete infinity of a numerical series is subordinated to the Law of the Great Fermat 
theorem. The concrete infinity of prime numbers of a numerical series (the Law of prime numbers) is the 
Great Fermat theorem proving. The Law of prime numbers is the physical formula of time. Thus, the 
fundamental formula of the Chronicle - the formula of a general field theory - states: "The Great Fermat 
theorem proving is the law of prime numbers". It is the fundamental formula of the mechanics of time. 
This formula is a mathematical equivalent of the concept of time - "Heat is Time. Time is Heat". 
The types of numbers reflect all variety of physical processes and are the investigated form of this variety. 
Types of numbers, instead of "nominal laws", mythical and archaic "forces" of interactions, form a priori 
structure of any physical research. 
The great Fermat theorem uncovers structure of real infinite numerical series, whose genesis out of time is uncovered in the fact of existence of an infinite amount of prime numbers. The divisibility of number is a 
concrete physical essence of physical process. Indivisible, prime number is the last genuine object of 
physics. The law of prime numbers - the Great Fermat theorem - is the law of creation of the world, of 
the nature in its pure, primordial aspect. 
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