Implications of Sarkovskii and El Naschie’s number theoretical theorem for physics

13th December, 2010.
E-infinity communication No. 57

Implications of Sarkovskii and El Naschie’s number theoretical theorem for physics

In 1975 the American J. York (one of the members of the Honorary Editorial Board of Chaos, Solitons & Fractals) and his student Li wrote a paper entitled “Period Three Implies Chaos” which was one of the most important and influential papers which helped establish chaos as a field of research in engineering and physics. However the same theorem of J. York who gave the science of chaos its name was already discovered in 1964 in number theory by the Russian mathematician Sarkovskii as explained for instance in the excellent book of H.G. Schuster “Deterministic Chaos”, published by VCH, Weinheim, Germany (1989). This shows the importance of number theory in physics which should be understood as the foundation of mathematics just like set theory and therefore the foundation of physics. It should not be understood as playing with the golden mean or number acrobatics (there is nothing called number acrobatics at all) or numerology as some (truly silly) people sometimes say. There is another very important example of a theorem in number theory given by El Naschie in 1998 with deep physical connections to much of the work on spacetime physics. The paper in question is “Four as the expectation value of the set of all positive integers and the geometry of four manifolds”, published in CS&F, Vol 9(9), (1998), pp. 1625-1629. The paper may be found in the E-infinity free of charge published papers (open access) or Elsevier’s Science Direct.
E-infinity Group.