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Prime Number and Cosmical Number

Published online by Cambridge University Press:  14 March 2022

Robert S. Hartman
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Extract

The conformity of mathematics and physics has so far been taken for granted. Philosophical explanations of that fundamental fact have never been satisfactory, mathematical explanations never had been attempted. In the following a fundamental theorem for the conformity of mathematics and physics will be demonstrated.

Mathematics can be defined as the science of Number, physics as the science of Matter. The elementary constituents of mathematics are the prime numbers, those of matter the particles, particularly protons and electrons. The only essential property of these elements as such is their existence, given within a given complex or space. Their fundamental relation is their distribution within their respective spaces. The theorem of the distribution of primes in the arithmetical series of numbers is the fundamental theorem of mathematics. The fundamental theorem of physics would be a theorem of the distribution of particles in geometrical space. If it were shown that both theorems were equal, the essential conformity of mathematics and physics would be mathematically demonstrated.

Type
Technical Scientific Section
Information
Philosophy of Science , Volume 9 , Issue 2 , April 1942 , pp. 190 - 196
Copyright
Copyright © Philosophy of Science Association 1942

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References

1 New York: The Macmillan Company, 1939, page 170.

2 Cambridge: At the University Press, 1936, page 272.

3 McVittie, Cosmological Theory, London: Methuen and Co., Ltd., 1937, page 9. There also following quotations.

4 Aslrophys. J. 74, 43, 1931. Proc. Nat. Acad. Sci. Philad. 15, 168, 1929; 20, 264, 1934.

5 Astrophys. J. 84, 158 and 270, 1936.

6 The exact value of N depends on that of v. The exact value of v is 792.614, the exact value of R 6.76965 · 1026.

7 Astronomy and Cosmogony, Cambridge: At the University Press, 1929, page 4.

8 The exact value of log V depends, like that of N, of the value V, or v. For v = 792.614 log V = 13.697752. The factor a is of no importance in this connection. If it were taken as 1.00000 log V would be 13.696292.

9 Page 358 ff. There also following quotations.

10 Italics mine.