[AntonioLao]

The shape of things to come or the shape that was or the shape that is could be the motto of another Millennium Problem worthy of a $1M prize money. The most abstract among the seven problems, its technical name is known as the Hodge Conjecture. It is a question about the topology of complex mathematical objects build up from simple topological building blocks called algebraic cycles of algebraic geometry (or algebraic variety).

A simpler conjecture would then be that each algebraic cycle is equivalent to a square singular symmetric Hadamard matrix whose mathematical dimension of complexity is functionally related to the number of elements of the matrix. For a matrix of four elements its dimension is two. For a matrix of nine elements its dimension is three. For a matrix of sixteen elements its dimension is four, so on and so forth. On the other hand, nonsingular nonsymmetric two dimensional matrices are equivalent to Pauli spin matrices of quantum mechanics. Nonsingular nonsymmetric four dimensional matrices are equivalent to the metric tensors of general relativity. Dirac matrices are also equivalent to the nonsingular semisymmetric four dimensional algebraic variety of algebraic cycles formed from fractal dimension of two elements spinors. Fractal is not the same as fractional. All these topological structures share a common characteristic. That is the existence of some elements that are complex and imaginary numbers. However, Hadamard matrices contain only integer rational numbers of positive and negative unity: {1, -1}.