Mathematics as Reality (Introduction)

One of the most interesting and provocative ideas to emerge from the intersection of mathematics, philosophy, and physics is the proposal, by MIT cosmologist Max Tegmark, that our universe is a mathematical structure.  Everyone knows that mathematics is indispensable for understanding our universe, but the Mathematical Universe Hypothesis (MUH) says something rather more remarkable.  Two of the most salient questions in all of philosophy are:

(1) Why is there something rather than nothing?

(2) Why is mathematics so effective in describing reality as we know it?

The profundity of these questions is quickly made manifest upon the slightest reflection.  MUH is an ambitious, albeit ingenious, solution to the inherent problems raised in these two questions.  It postulates that reality is mathematics in a very real and well-defined sense; more specifically, physical existence equals mathematical existence. One might describe such a view as a form of radical Platonism or, equally, a mathematical version of modal realism.  In fact, these are the very descriptions employed by Tegmark himself.  As such, MUH answers (1) because it entails that there really is no such thing as an ontological nullity or universal negation.  Something necessarily exists, namely all possible mathematical structures, which Tegmark refers to as the Mathematical Ensemble or Level IV Multiverse.  It also answers (2) by making it trivial.  Certainly, if reality is mathematics, then science is merely the endeavor of uncovering how our particular mathematical system operates or behaves.

Now, as a mathematician, this suggestion resonates with me and isn’t so hard to imagine being the case.  For most people, however, MUH probably sounds outlandish at best, if not incoherent!  After all, what could it possibly mean for reality to be mathematics?  You mean, the chair I’m sitting on is no different than the equations I write down when doing my math homework?

I grant that, at first sight, the idea seems a bit absurd; but  the fog begins to lift, I think, upon a reflection of what mathematics really is.  It is my hope to explore, and clarify, this most fascinating idea in a series of posts.  Included in this investigation will be an incorporation of Douglas Hofstadter’s ideas espoused in his landmark work, Gödel, Escher, Bach: an Eternal Golden Braid, which, I believe, specifically fleshes out Tegmark’s notion of a Self-Aware Sub-Structure (SAS).  On Tegmark’s (and presumably Hofstadter’s) view, a human would be an example of a SAS.  Hofstadter, however, uses the terminology “strange loops” or “tangled hierarchies”.

These posts are primarily for my own benefit, to engage these ideas and to deepen my understanding.  But for anyone who might be reading this blog, I hope that what I write is both interesting and enlightening.  Of course, if I totally botch something or if clarification is needed or if there are other ideas that would be interesting to fit in, please feel free to contribute and participate in the comments.  Happy reading.