1. A computer implementing a nondeterministic Turing machine, the nondeterministic Turing machine comprising: a knowledgebase containing data representing a plurality of objects, data representing a plurality of classes, and data representing relationships between the plurality of objects and the plurality of classes; an induction module comprising means for generating data representing a concept represented by a plurality of inputs representing the plurality of objects and for storing the data representing the concept in the knowledgebase; a deduction module for retrieving, from the knowledgebase, data representing a class containing an object represented by an input to the deduction module; a reduction module for retrieving, from the knowledgebase, data representing an object which is a member of a class represented by an input to the reduction module; a cognitive logic unit adapted to: ( 1 ) store data representing a product P in the knowledgebase as a spatial binary number having a first plurality of spatial binary bits; ( 2 ) create and store a mapping of the first plurality of spatial binary bits to x, y, and z dimensions in a first repeating pattern in the knowledgebase; ( 3 ) obtain a complement C of the product P, wherein the complement C includes a second plurality of spatial binary bits; wherein C=1 n 2 −P; wherein B is equal to the number of bits in P; wherein n=(B/2) if B is even; wherein n=(B+1)/2 if B is odd; wherein 1 n 2 is a binary number of length n consisting solely of ls; ( 4 ) create and store a mapping of the second plurality of spatial binary bits to the x, y, and z dimensions in a second repeating pattern; ( 5 ) construct an empty diagonal form representation of partial products of a first and second factor of the product P; ( 6 ) recursively fill the diagonal form representation with a third plurality of spatial binary bits based on the product P and a divider D; and ( 7 ) identify the first and second factor of the product P based on the filled diagonal form representation; wherein the data representing the plurality of objects represent the plurality of objects in the form of three-dimensional representations of a fourth plurality of spatial binary bits; and wherein the data representing the plurality of classes represent the plurality of classes in the form of three-dimensional representations of a fifth plurality of spatial binary bits; wherein the plurality of inputs and a current state of the nondeterministic Turing machine does not determine at least one of: (1) the data representing the class, and (2) the data representing the object; wherein each of the first, second, third, fourth, and fifth pluralities of spatial binary bits has a value selected from the set consisting of −1 and +1.