The present short note points out a most interesting and quite unexpected connection between the number of distinct knot as a function of their crossing number and exceptional Lie groups and Stein space hierarchies. It is found that the... more
The present short note points out a most interesting and quite unexpected connection between the number of distinct knot as a function of their crossing number and exceptional Lie groups and Stein space hierarchies. It is found that the crossing number 7 plays the role of threshold similar to 4 and 5 in E-infinity theory and for the 11 crossing the number of distinct knots is very close to4α¯0+1=548+1=549,where α¯0=137 is the inverse integer electromagnetic fine structure constant. This is particularly intriguing in view of a similar relation pertinent to the 17 two and three Stein spaces where the total dimension is∑117Stein=5α¯0+1=685+1=686,as well as the sum of the eight exceptional Lie symmetry groups∑i=18|Ei|=4α¯0=548.The slight discrepancy of one is explained in both cases by the inclusion of El Naschie’s transfinite corrections leading to∑i=18|Ei|=(4)(137+k0)=548.328157and∑i=117Stein=(5)(137+k0)=685.41097,where ko=ϕ5(1−φ5) and φ=5-1/2.
