You call it numerology, I call you mathematical illiteratology

14th December, 2010.
E-infinity communication No. 58
You call it numerology, I call you mathematical illiteratology

Let us take one really obvious example for what we would like to illustrate here, namely how intricate the role played by number theory in physics could be and how hasty judgment could put one in an embarrassing situation. Academics in general are judgmental but mathematical physicists should not be no matter how senior they are because at a certain very deep level mostly connected to quantum mechanics rather than general relativity there is no real difference between ‘pure mathematics’ and ‘pure physics’. At this deep level as Prof. El Naschie stressed in one of his lectures, one should not relay on ‘common sense’ which he calls ‘the logic of savages’ following Lord B. Russler. The only thing one can rely on is the most stringent form of logic as in transfinite set theory and K-theory or inspiration from God or such higher instance. Such inspiration is hard to come by and cannot be depended upon in a regular way. The example we will give here is taken from Table No. 6, page 658 of the paper “On a class of general theories for high energy particle physics”, published in CS&F, (2006), pp. 649-668 by M.S. El Naschie. The table is labeled “The number 42 in mathematics and physics – A short survey”.
The importance of 42 is that it is 10 times the expectation Hausdorff dimension of E-infinity spacetime when we take the integer part only and is also equal to the inverse coupling constant of non-super symmetric grand unification of all fundamental forces excluding gravity. The first number of the list is the third Bernoulli number. I remember that one notable scientist protested against such unmotivated connection and obvious numerology. Others went as far as calling on a French scientist very close to Mohamed El Naschie and becoming impolite about this playing with numbers. One in particular who is as self confident as he is ignorant called it ‘alchemy’ although modern physics has long shown that the dream of alchemists of changing copper into gold is in principle correct because the basic building blocks are the same, namely elementary particles. Deep mathematical contemplation coupled with a great deal of knowledge of mathematical and physical facts shows that a relation between all Bernoulli numbers and quantum mechanics is by no means outlandish nor numerology or number coincidence. For instance the function guessed initially by Max Planck for his black body radiation which marked the beginning of quantum theory was a complex function involving many hidden things such as the Bernoulli numbers. That is how Planck arrived at a constant which he later called h and which we know as the Planck constant in order to obtain dimensionless numbers from physical quantities with dimension. Even more general than that, we have to recall that the Bernoulli numbers originally come from the function of integers and are thus related to K-theory topics such as the Riemann-Roch index used by C. Castro and M.S. El Naschie in E-infinity theory as well as the Atiyeh-Singer index used in topological quantum field theory of Witten. Finally for this communication, they are related to the Gauss-Bonnet theorem which El Naschie was able to generalize for a fractal Cantorian geometry and find the curvature of spacetime as a topological invariant exactly equal to the square root of the sum of all two and three Stein spaces which is in turn exactly equal to (5) multiplied with the inverse of the electromagnetic fine structure constant 137. Taking the square root of 685.4101966 we find the said curvature, namely 26 + k = 26.18033989 which is the inverse coupling constant of the super symmetric unification of all fundamental forces including gravity. Consequently 685.4101966 may be seen as a numerical potential or a Lagrangian and using Weyl-Suslin scaling as a substitute for calculus, a great deal of information of physical relevance may be obtained with an unheard of simplicity and elegance.
So in the end, the joke is on those who think they are very witty and spend most of their time making silly jokes on other people instead of spending their time on something useful. For this reason, and although he can be very witty when he wants to be, El Naschie as well as most of his colleagues and friends keep a great distance from making fun of other people’s work or personality. Trying to be witty most of the time is a clear sign of poverty of intellect and personality.
E-infinity Group

Relevant literature:
1. Curvature, Lagrangian and holonomy of Cantorian-fractal spacetime, Chaos, Solitons & Fractals, Vol. 41(4), (2009), p. 2163-2167.
2. Deriving the largest expected number of elementary particles in the standard model from the maximal compact subgroup H of the exceptional Lie group E7(-5), Chaos, Solitons & Fractals, Vol. 38(4), (2008), p. 956-961.
3. Derivation of the Euler characteristic and the curvature of Cantorian-fractal spacetime using Nash Euclidean embedding and the universal Menger sponge, Chaos, Solitons & Fractals, Vol. 41(5), (2009), p. 2394-2398.