Yesterday, I was looking through the Android playstore, looking for a casual game to play while waiting for sleep.

*image: is nature fractal?*

One of the games I looked at was called something like “Solar System Creator”. A comment in it struck me. It said something like “This would be so much better if the math was more realistic”.

I presume the author meant how planets (particularly Mercury) follow Einsteinian gravity instead of Newtonian, but it there was a point in there that I think the author missed.

Before Newton figured out his gravitation formulas, people believed that everything fell to their “natural level” at a constant speed. Newton then showed that things are attracted to each other at speeds relating to their mass and the distance between them. Einstein went further and showed that the mass of objects affected the space surrounding the objects, which in turn affected the distance between things.

As each explanation of gravity got more realistic, the mathematical formulas became more sophisticated, but also much more accurate.

One thing can be said about math that cannot be said about anything else I can think of – it is absolute. If a formula says “this is so”, then you can be very sure that “this is so”. Math is either correct, or you’ve made a mistake.

Physics has math at its core. In fact, you could say that all of physics, and all of science, really, is a way to figure out what are the mathematics behind reality. Each leap in understanding in physics is simply a formula which more accurately models reality.

Based on this, there is an inevitable conclusion – that the universe is mathematical, and that we simply don’t know all the rules yet.

At the moment, there is a conflict between General Relativity and Quantum Mechanics. In the future, this will be resolved (the Grand Unified Theorem). But will we then know all the mathematics that rules the universe?

We can’t say. Science is done by checking the math, figuring out if reality doesn’t quite match what the math says, and then refining the math model you’re making. Even if the math matches what we see exactly, that doesn’t mean that there isn’t yet another substrate hidden under it all. General Relativity is more accurate than Classical Mechanics, whether you know about Mercury’s motion (etc) or not. It is possible that there is something that is yet more accurate than the Grand Unified Theorem.

Either way, it can’t be escaped that even if people don’t admit it out loud, the universe is made of math.

I mean that quite literally.

I was reading a blog recently that I thought had a catchy name – “selfaware patterns“. Both words in there deserve to be examined closely.

When we create artificial intelligence in computers, we mostly use a model called an “artificial neural network“. This is a pattern of inputs and weights formed into a lattice. When data is fed into the inputs, math happens (I’d like to also say “magic happens”), and the outputs give us values that depend on the layout of the network. We can copy the lattice from one computer to another, or save it and revive it later. This “pattern” of neural network could be considered to be a specific identity at a specific time.

“Self-aware” is a word we’ve been struggling with for centuries – why are we conscious? What does it really mean? In philosophy, there is a difference between consciousness and self-awareness, but the common understanding is that they mean the same thing. By examining myself, I find that the “I” that is conscious is only part of my brain. I’m not aware of all the muscle movements that go into typing on this laptop, for example, but I am aware of the thoughts that lead them.

A huge philosophical problem is the question of how do we know that other people are self-aware? You could ask them, and they could say “Yes, I am conscious”, but how do you know that they are not programmed to do so?

Non-player characters in computer games are getting more and more sophisticated, and will soon be indistinguishable from “real” people, in that they believe their world is real, they interact with each other, and they act semi-randomly. Just like real people. What if one of them was to one day say “I think I’m real”? Can you say that this NPC is conscious and self-aware? Can you say for a fact that it is not?

Self-awareness is an every-day example of the “No True Scotsman” fallacy. If someone says “I am self-aware”, you cannot be sure that they are wrong.

Some day very soon, we will have artificially intelligent “conscious patterns”, and soon after, “self-aware patterns”, in our computers, and we won’t think the idea is strange.

But the idea opens us up to another one – what if we, ourselves, are self-aware patterns?

If the entire universe is mathematical, then we are also mathematical. We are patterns. And yet we are also conscious. This means that our very identities can be encoded as mathematical values. Inputs and weights.

Remember what I said about neural networks being patterns that can be copied to other computers or saved and revived at later times.

If this is indeed a mathematical universe, then it is possible that there are an infinite number of other mathematical universes, each as “real” as this. And there may be infinite copies of your own “unique” identity, living out a life in another universe, totally unaware of this one.

What happens if you die here but don’t die there?

Well, imagine it from the point of view of a computer game character that you “save” every now and then, and if something disastrous happens, you “restore” from the last save point. This is pretty much the same as what we’re saying here.

In the computer game scenario, you stop considering the dead version of the character – as far as you are concerned, the living version in the currently active game is the only “real” one. The fact that this version was restored from a saved copy doesn’t make it any less real, and in fact, the character itself is not “aware” that it is a copy.

If you were to die suddenly in this universe, and there are infinite other universes, there will be at least one where you survive. The analogy is obvious – by surviving in that universe, you survive. As simple as that.

Is the universe made of math? You’d better hope it is! Because a mathematical universe could literally save your life some day.

Thanks for the link! Interesting post.

I do think we are self aware patterns, which is why I chose that name. Our patterns are composed of neurons and synapses, or dropping down a layer, of DNA, RNA, proteins, and lipids, or going further down, of atoms, subatomic particles, fields, branes, or whatever the base layer of reality is, if there is a base layer; it may be structure all the way down.

But rather than say that the universe is mathematics, I prefer to say that the mathematics are the universe. The reason is that what we observed in the universe seemed to drive mathematical developments, such as geometry, algebra, and calculus. As I indicated in the post, I’m a mathematical empiricist these days.