Science Book Club – Episode 12
Nature has not only some mathematical properties but only mathematical properties.
The basic theme of the book is I want to encourage us all to think big, because we humans have again and again and again underestimated not only the size of our cosmos, realising that everything we thought existed was just a small part of a much grander structure like a planet, a solar system, a galaxy, a universe and maybe even a hierarchy of parallel universes, but we’ve also repeatedly underestimated the power of our human minds to understand our cosmos and, through technology, even improve it. And it’s really interesting to ask why is it that we’ve been able to figure out so much more than the cavemen ever thought that, you know, their minds were capable of. Partly it’s, of course, just cause, you know, the human mind is much more complex and awesome than we thought; the most complicated object we’ve discovered so far in our entire universe is the human brain. But I think there’s more to it, I think another reason why we’ve underestimated our ability to understand is cause we’ve discovered that, um, gradually nature has all these mathematical clues and patterns and regularities hidden in it which us humans have been able to uncover with experiments and mathematical equations. So tapping into these regularities, they will be able to predict our future better and figure out what kind of technologies will work. And this is pretty uncontroversial, it’s a pretty old idea going back all the way to Pythagoras, who said that numbers rule our universe, and Galileo, who said that our universe was like a book written in the language of mathematics, but where it gets really controversial is when you ask: what does this really mean?
I explore in my book, The Mathematical Universe, a whole range of possibilities from people who think this means nothing, or it’s just some kind of fluke we should be grateful for, to the possibility that it really means something very profound: that nature might actually be mathematical in a very fundamental sense. The most extreme idea I explore is something called the mathematical universe hypothesis – that nature has not only some mathematical properties but only mathematical properties – and that sounds pretty loony at first when you just look around, it doesn’t look very mathematical at all around here. But if you look more closely as a physicist, of course you realise that everything here is made of these elementary particles like quarks and electrons, and what properties does an electron actually have? It doesn’t have a smell or a colour or a texture or any of these non-mathematical properties we associate with stuff, the only properties an electron has are properties like minus one, one half, one, and we scientists have come up with geeky names for these properties like electric charge and spin and lepton number; an electron doesn’t care what we call these things, the only properties it has are these mathematical properties, these numbers. It’s a purely mathematical object in a sense that it has no non-mathematical properties and, as far as we can tell from the Large Hadron Collider and other physics experiments, the same goes for all the other particles that make up absolutely everything in our space here.
What about space itself? What property does it have? It has the property “three”, you know, the largest number of fingers I can put that are perpendicular to one another. Again, we have a nerdy name for this, we call it dimensionality, but space doesn’t care what we call it: the property is three. Einstein realised space also had some other properties called topology and curvature but they’re also mathematical properties. So if you take seriously the idea that both stuff in space and space itself are purely mathematical then it doesn’t sound quite as insane any more, this idea that I’m talking about, that maybe everything is purely mathematical.