Category theory in El Naschie’s E-infinity

19th January, 2011.
E-infinity communication No. 72

Category theory in El Naschie’s E-infinity

Category is mentioned explicitly in connection with ribbon category in El Naschie’s important paper on quantum groups. Utilizing results connected to tensor categories he arrives at a quantum dimension which takes the exact value of 4 when q is set equal to the inverse of the golden mean. The theory is strongly connected to knot theory, Hopf algebra and of course tangle category. The close connection to noncommutative geometry and E-infinity becomes trivially obvious when setting the Eigenvalue q = ½ in El Naschie’s expectation value of the Hausdorff dimension which is identical to A. Connes’ noncommutative dimension and finding that the dimension in this case is exactly 4 which corresponds to exactly 4 for the quantum dimension provided q = ½ is replaced by q equal to the inverse golden mean. The duality between the two dimensions becomes apparent when one realizes that for q equal the golden mean the noncommutativity Hausdorff dimension becomes equal to the famous dimension of an infinitely fractal four dimensional space, namely 4.23606799. This situation is explained in detail in “Quantum groups and Hamiltonian sets on a nuclear spacetime Cantorian manifold”, CS&F, Vol. 10(7), (1999), pp. 1251-1256. In general however El Naschie does not make explicit reference to to n-categories nor its coffee shop direct by Dr. J. Baez. The fact is E-infinity results are all obtained by elementary methods but could have been obtained using categories theory. It is also a fact that Prof. El Naschie did not refer to many relevant papers in category theory which may have ignited the unprecedented anger of Dr. John Baez of Riverside University, California. In fact we in E-infinity feel that we should consider n-categories in future despite the claim of some that it is simply too abstract to be physics. This is a claim which we do not accept in principle because at the deep level of trying to understand the building blocks of nature and figure out the meaning of the quantum, any separation between physics and mathematics is artificial and in general mathematical, logical reasoning is paramount.
E-infinity Group.