Maths in the dock for design.

How Did Mathematics Come to be Woven Into the Fabric of Reality?

Posted by Barry Arrington

We all learned pi in school in the context of circles.  Pi is the ratio of a circle’s circumference to its diameter.  It is an irrational number approximated by 3.14.

It turns out that pi shows up all over the place, not just in circles.  Here is just one instance.  Take a piece of paper and a stick.  Draw several lines along the paper so that the lines are the length of the stick from each other.  Then randomly drop the stick on the paper.  The probability that the stick will land so that it cuts a line is exactly 2/pi, or about 64%.  If one were to perform millions of trials, one could use the results to perform a very precise calculation of the value of pi without ever considering its relation to circles.

This is just one of many places pi pops up in reality, and pi is just one of several mathematical constants that appear to be woven into the fabric of the universe. One mathematician likened it to looking out over a mountain range, where the bases of the mountains are shrouded in fog, and the symbol for pi is etched into the top of each mountain – one intuitively knows that it is all connected at some basic level even if one has no idea why.

What are we to make of what physicist Eugene Wigner called the “unreasonable effectiveness of mathematics” in describing reality?  The word “unreasonable” makes sense only in the context of expectations.  If one expects the mathematical structure of the universe to be elegant and beautiful, the fact that it turns out to be elegant and beautiful is not unreasonable at all.  It is only unreasonable if one approaches it from the perspective of the metaphysical materialist.  In his universe reality consists of nothing but particles in motion randomly bumping into each other.  In that universe there is no reason to expect any underlying mathematical order, no reason to expect mountain tops etched with pi to pop up all over the place, and no reason to suspect that those mountain tops are connected by a unifying order at the base.

Given materialist premises, none of this makes the slightest bit of sense.  It is just a brute fact.  It cannot be denied or explained.  Yet there it is.

MIT cosmologist Max Tegmark has a theory.  He says consider a character in a computer game (let’s call him Mario) that is so complex and sophisticated that he is able to achieve consciousness.  If Mario were to begin exploring his environment, he would find a lot of mathematical connections.  And if continued to explore, Mario would ultimately find that his entire world is mathematical at its roots.  Tegmark believes we live in a universe that is not just described by mathematics; he believes that mathematics defines all of reality, just as the reality of Mario’s computer game world is defined by mathematics.

Here is the interesting part.  Tegmark makes no design inference.  (He is a multiverse fanatic).  This is astounding.  All he needs to do is take his own analogy one step further.  Why is Mario’s computer game world connected mathematically?  Obviously, it is because that mathematical structure was 
imposed on the game by the game designer.

Why is the universe we live in connected by an unreasonably beautiful, elegant and effective mathematical structure?  Come on Max.  You are a smart guy.  I know you can figure it out.