The Tao of
Mathematics

Modern physics then, is built on quick-sand. But what of pure mathematics? Russel’s paradox put paid to mathematics based on logic. Indeed as Gödel showed there is no complete and consistent set of axioms for all mathematics. Mathematics too is therefore built on quick-sand.

The problem however goes deeper than that. We use mathematics to model the universe but we don’t consider if the universe can be modeled by mathematics. We take that as a given, but it certainly does not follow.

Remember earlier when discussing the Schrödinger’s cat thought experiment we quietly introduced this concept of a random number. If R represents a random number and R1 represents another random number then R is both identical to and not identical to R1.

It turns out that although mathematics can be used to describe the universe in terms of ideal constructs such as sets and numbers, it’s not the language the universe can be fully expressed in. Think of the lizard creatures we evolved from. Did they understand algebra? Did they even understand symbolic representations such as 1+1=2. Clearly not. Could they even imagine it? Clearly not. Our level of understanding of the universe is akin to theirs.

I can hope that maybe we are not as distant. Maybe it is more akin to trying to describe the color blue to a blind person. Try as you might there is no substitute for the sense of sight to truly know what a color is. We are simply not capable of understanding what replaces a mathematics of symbols and functions. We can conjecture, like the blind person that there is a description of the universe based on concepts we can not truly grasp with our limited intelligence: Randomness, infinities, and paradoxes.