Functional Abstraction

And the Failures of Esoterism

Mathematics is by far humankind’s most abstract, if not outright artificial, construct. Fundamental arithmetic, algebra, and to a certain extent even calculus are all defined on the unnatural parameters of an arbitrary base-ten number system, with arbitrary symbols and arbitrary notations. As children we are led to accept this construct as fact, groundless but somehow representative of real world phenomena; the symbolic representation of division, reduction, and duplication which we evidence daily.

But the power of higher level mathematics is the ability to breach the limitations of the imaginable: herein we find evidence to the incredible imaginative and speculative capabilities of the mind. The mathematical world, as one which has never and never will tangibly exist, is a realm of idealities; a rigorous but self-deluding universe composed of our everyday algebraic interactions extrapolated to a pompous degree. It is a realm where continuity is abundant despite our existence in a universe of quantization; a realm where we all understand the notion of “a point” despite the impossibility of its physical existence. Math is a level of consciousness divorced from the physical nature constituting that consciousness.

But this is entirely too spiritual an emotion: for mathematics is not a religion. It proclaims no ethical values nor proposes any behavior to its followers. It is neither moral nor immoral, but amoral - and indeed, foolish is the mathematician who claims he can live his life by the proofs he recounts. The abstraction of math and the objectification of the physical world are antithetical; they cannot be reconciled to a method of action. Instead, mathematics is more closely defined in philosophical terms. We innately accept notions such as the strictly one-dimensional, two-dimensional, the line, the plane; all are in fact imaginary. However, it is because these notions have some ideological counterpart in the real world (i.e. we can imagine a sheet of paper to be a plane, or a string to be a line, even though both representations necessitates the three-dimensionality of matter) that we commonly have no difficulty in grasping the purely abstract quality of their description. Mathematics is then a manner of thinking, but not a prescription for living.

So what then, concisely, is mathematics? It is irreducible and universal symbolism. It occasionally represents actuality, but often lingers in a theoretical framework too dense to give it inherent value. Mathematics will never be more valuable than any other body of theory; it is incomparable, and to attempt to use its formulaic rigor and necessity of proof would annihilate most other categories. The case is simply this: because mathematics is entirely of our own making, because it does not deal with reality as such, it is easy for us to demand of it an unnatural degree of proof. But to demand the same of the humanities, or sociology, or even the science of biology is to impose a completely foreign design upon a completely foreign subject matter. The quest for mathematical rigor would sooner reduce everything to the equation than leave ambiguity where it need exist.

Indeed, it is this incredible otherworldly quality to higher level mathematics which jeopardizes its applicability and pushes math to the brink of utter esoterism. Because of its abstraction, its dense and elusive symbolism, such highly theoretical math is at once profound and effectively useless. Like any brand of esoteric knowledge, mathematics will never be valuable to humankind until it attempts to reintegrate itself into the accessible body of human knowledge; not the hermetic fascination of academics. It must be the job of mathematicians to display the functionality of their work to the world, for they have long since made the laymen’s access to it impenetrable. As the link between the theoretical and the actual is rebuilt, so too will the public interest in mathematics.