This states that given a population of n elements, let n1, n2, n3, …,nk be positive integers such that n1 + n2 + n3 + … + nk = n. Then there are precisely N = n!/n1! n2!n3!…nk! ways of partitioning the population into k subpopulations of sizes n1, n2, n3, …,nk, respectively. Note that this is a generalization of the binomial theorem. Furthermore, the order of the subpopulations matters as for example can be shown by the progression of cracks appearing in a mirror. Let say the first crack divides the mirror into two partitions stretching from 0 to infinity. Then succeeding cracks can only partition these two existing cracks since crack cannot cross over other existing cracks. This would then imply that the big bang is a binary crack operation, in the sense that the birth of the universe was initiated by two crack partitions during the first crack of dawn.
A crack appearing in space-time would most likely and separately divides the time domain into past and future and the space domain into two hyperbolic sheets of positive and negative curvature.


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