This is Part 4 in a series on the mathematical universe hypothesis. Check out Parts 1, 2, and 3.
Well, kind of. Like I said at the beginning, I’m not really keen on the idea of the mathematical universe. My own personal biggest objection stems from the whole point of occam’s razor: make things as simple as possible. And that sounds nice as you’re removing baggage to arrive at a universe made of math, but then to explain reality (which is a rather large undertaking) you have to start adding things back IN, like a multiverse, like the anthropic principle, like the restriction to simple-enough mathematical structures.
I dunno, that seems to me like baggage of a different kind.
Besides, simple doesn’t always mean correct. Good old Willy Occam proposed his razor as a guide to approaching thinking, not as a be-all-end-all decider of rightness. Look, physics in the 19th century was a heck of a lot simpler than physics in the 21st century. We had gravity, electromagnetism, and, like, heat. That was it. Now we have quantum this and superconducting that and oh hello there’s the Higgs boson. Is 19th century physics correct because it’s simpler?
I sure hope not.
There are plenty of other objections to the mathematical universe.
Here’s one: we can concoct ALL SORTS of weird particles, forces, properties of nature. Things that violate no known laws of physics, things that by all rights SHOULD exist in the universe, but…don’t. But if the universe is made of math, why don’t these things exist, even when they could? Who gets to decide what’s in our corner of the multiverse and what’s not?
And hey, let’s go back to Godel. Us humans can see above the math. We can point to statements and say “oh wow that true” even though the mathematical system has no way of proving it within itself. So if we’re just made of math (and, if Tegmark is right, made of the simpler kind of math that avoids paradoxes and whatnot), how are we able to see above the system that we’re made of? Shouldn’t the math that is our universe also be responsible for all the math that we come up with? How can the math we write down be more complex than the math that the universe is made of?
Tegmark says that we can debate this all day long, but in the end it comes down to evidence. He argues that if we DO find a theory of everything, then that’s a clue that we live in a mathematical universe? I mean, I suppose, but also it could mean a bunch of other things, which is why this isn’t that much of a physical theory.
In the end, whether you think this is a valid approach or not comes down to what you think of math. Not, like, your personal opinion of it based on 5th grade multiplication tables. But how REAL you think math is.
2500 years ago in ancient Greece, the cult of Pythagoras believed that “all is number”, that by studying geometry and arithmetic they could arrive at divine truth. Things like the Pythagorean theorem were studied – no, worshipped – as mystical revelations. Like I said, the nerdiest cult in history.
People today still debate whether math is DISCOVERED or if its INVENTED. If it’s discovered, then math already exists. 2+2=4 whether or not there are any rocks hanging around or people to count them. The circumference of a circle is still 2piradius, whether or not there are any actual circles. If you believe that math already exists, and we’re just uncovering pieces of that hidden reality, then you might be willing to believe that math itself is reality.
But maybe math is invented. Tegmark calls so much our subjective experience of the world baggage. But maybe math is baggage too. Maybe we created it to solve real-world problems, like figuring out when the river would flood again or how many seeds to plant this year or how much I should trade my cow for. And maybe the fact that math works so well is an illusion of its own: if you wear math-colored glasses, then the universe looks a lot like math. But there’s so much to reality that can’t be explained by physics, math, or even science. And that even if we did have a theory of everything, we couldn’t use it to describe the sensation of the color orange or the feeling of grief.
Different folks have different takes on these kinds of questions. And whether you like the mathematical universe or not, these questions are very powerful, because they challenge us to ask, well, what the heck it is we think we’re doing here.
Let me leave you with one more incomplete metaphor. Does Hamlet exist? Sure, yes, of course, you can download a copy of it right now. But if you destroyed all copies, burned every page, would it still exist? What if Shakespeare never happened? What if he never wrote it down? Does Hamlet still exist in the space of all possible combinations of words? The answer is year, kinda, sorta, but also not really. But it took someone like Shakespeare to pluck that particular combination out and make them real in a different way?
Stephen Hawking said it best when he asked, “What is it that breathes fire into the equations and makes a universe for them to describe?”
Maybe there is no fire. Maybe it’s god. Maybe it’s you and me. My answer?
Maybe just in the asking we are doing everything that the universe requires of us.
