20th January, 2011.

E-infinity communication No. 74

NAMING E-INFINITY:

Some aphorisms, quotations and remarkable historical events connected to the science of the infinite transfinite set theory and the theory of dimensions as well as the relation to religion and God.

1. In the beginning was the word and the word was with God and the word was God (The Gospel according to St. John, first verse).

2. “I have no need for this hypothesis”: This was the answer of Laplace to Napoleon’s question about why God did not appear in his work.

3. Philosophy is a battle against the bewitchment of our intelligence by means of language. (Wittgenstein – Philosophical Investigation).

4. Heisenberg “discontinuous” quantum mechanics was a giant leap forwards. Schrödinger’s continuity illusion of his differential equation was effectively a step backwards. (Mohamed El Naschie rephrasing words of A. Connes).

5. Not how the world is is the mystical but that it is. (Wittgenstein – Tractatus).

6. The name that can be named is not the eternal name. (Tao Te Ching).

7. In a fractal spacetime setting we must replace differentiation and integration with Weyl- Suslin scaling. In E-infinity the main scaling as well as the main renormalization semi group is the golden mean scaling and the golden mean renormalization group of M. Feigenbaum. (Mohamed El Naschie about E-infinity).

8. Dimension is a scale dependent phenomenon. (B.G. Sidharth about fractal spacetime).

9. Neither K. Gödel’s proof of the consistency of the continuum hypothesis with the axioms of set theory, nor mine of its independence from them was the final answer….but I think there is no answer other than the answer that it is undecidable. (P. Cohen).

10. The Cantor space c is the unique up to homeomorphism perfect non-empty compact, zero-dimensional space. (Text book definition of the Cantor space 2 to the power of Baire space used by El Naschie in E-infinity).

11. E-infinity theory is a weighted Borel hierarchy. (El Naschie following an idea due to J.A. Wheeler).

12. In Batz we walked by the sea …. It was there that Pavel Urysohn wrote his famous paper on countable connected Hausdorff spaces …. On August 17 out for another swim …. Urysohn was catapulted by a wave directly onto the rocks …. Urysohn was buried in Batz-sur-Mer… (Prof. Pavel Alexandrov remembering Pavel Urysohn, the discoverer (or inventor) of the transfinite deductive theory of dimensions and that the empty set has a topological dimension equal minus one ( ̶ 1)).

13. The Moscow School of Mathematics founded by Egorov and Luzin is one of the most important sources of information and inspiration for E-infinity theory of high energy physics. On the deep level of trying to understand quantum mechanics it is at best misguided and at worse childish and naïve to make a separation between mathematics and physics. (Mohamed El Naschie in one of his recent lectures 2009-2010).

14. For my work the most important members of the Russian (Moscow School of Mathematics) are Urysohn, Kolmogorov, Suslin, Gel’fand, Arnold, Alexandrov, Shinchin, Pontryagin and Sinai. (Mohamed El Naschie 2009).

15. Prof. Pavel Florensky was convinced that the nineteenth century was an intellectual disaster …. because of the concept of ‘continuity’ …. because of the strength of differential calculus with many practical application problems that could not be solved this way were ignored – essentially discontinuous phenomena (such as quantum mechanics). Florensky (member of the Moscow School of Mathematics) wanted to restore discontinuity to its rightful place in the “Weltanschaung”. (Graham-Kantor-El Naschie 2010).

16. Everything visible is connected to the invisible … the sensible to the nonsensible. Perhaps the thinkable to the unthinkable. (Novalis – fragment).

17. Anaxagoras conceived the infinite in the same way as Anaximander. He called the infinite (Apeiron) which is the primodal mixture of chaos. (P. Zellini).

18. von Neumann’s formulation of the question was adopted by Kurt Gödel. There, as in E- infinity, we distinguish between set and class. (Mohamed El Naschie).

19. In E-infinity we solve a measure problem by summing over infinitely many but countable Cantor sets. However every Cantor set has uncountably infinitely many points. That is how we arrive at finite expression for a completely wild situation as far as computations are concerned. (Mohamed El Naschie 2009).

20. If we went back to the most perfect image of the word soaring to the level of an invisible being, it would mean recalling the Hindu Vāc. In E-infinity the VAK is the vague attractor of Kolmogorov which is conjectured by R. Thom to be the stationary states of quantum mechanics and used by Mohamed El Naschie to calculate the mass spectrum of elementary high energy particles. The Logos of the Greeks is analogous to the Hindu Vāc. (P. Zellini and Mohamed El Naschie).

21. There is strictly speaking no such thing as mathematical proof. (G.H. Hardy).

22. It is obvious then that the mathematical problem of the infinite is automatically projected into the moral sphere …. This is clear in the work of F. Nietzsche and R. Musil. (P. Zellini and Mohamed El Naschie).

23. My fuzzy K3 as well as all the transfinitely corrected Betti numbers, Euler invariant and instanton numbers and curvatures as well as invariant dimensions are intuitive extensions of cohomology to the theory of fiber bundles. Without knowing, not being a mathematician, I extended cohomology in the same way as Grothendieck and Atiyah extended cohomology using K-theory. In other words my K3 and all the fuzzy manifolds are a product of a non-declared K-theory which was christened transfinite E-infinity theory. (Mohamed El Naschie 2010).

E-infinity Group.