is the universe a mathematical structure?

Quantum physics can predict the behaviour of particles and energy to an extraordinary degree. Quantum Electrodynamics, for example, predicts a value for the electromagnetic fine structure constant which is so accurate that we have not been able to find a difference between the predicted value and the real value despite measuring to 14 decimal points (the measurements are difficult!)

The point of this is that the result of the most precise measurements we have ever made can be predicted using some math, without needing to do the actual measurement.

This is because the universe is mathematical in nature. There is nothing in the universe which we don’t have a formula for.

A co-worker retorted “what about the soul?” Treating that like the serious question she intended it to be, even thoughts and so-called “free will” can be predicted using math. Thoughts are determined by processes in the brain involving chemistry and electricity; both of which are well understood and predictable.

We have artificial neural networks which work similar to the brain. While they sometimes do things that we don’t immediately understand and which look like thought, we can examine the weights and synapses of the network and break every thought and decision right down to the 1s and 0s that they’re made of.

Just because we don’t understand how something works, doesn’t mean that it’s magic. The brain is not magic. Each tiny part of the brain works in very precise and predictable ways, and the thoughts and decisions that we call “free will” emerge from the billions of neural firings that happen every second (13 billion per second! There are 86,000,000,000 neurons in the brain, and they all fire on average about .15 times per second).

Everything that happens in the universe is predictable by math.

Even the universe itself, devoid of all matter and energy, is still a mathematical structure. Why are there exactly three space dimensions? An answer can be found in a theory called “Causal Dynamic Triangulation“, which describes how exactly three dimensions of space can arise from a set of mathematical rules involving triangles. The theory is more accepted than the alternative highly-regarded “loop quantum gravity” theory, because it produces exact measurements between points (impossible in LQG), and because it describes space both for Planck-scale measurements (the smallest possible), and for astronomical scales as well.

The fact that everything in the universe is predictable with math, even space itself, allows the possibility that you can create a single equation that predicts absolutely everything that can happen.

And if you run that calculation? You would be able to pick a precise date and time, and tell exactly what the state of the universe is on that time (or at least, you would know the most likely layout – quantum mechanics is very precise but also fuzzy).

This is regardless of so-called “free will”. Everything is predictable, including thoughts, if you have enough starting information.

It gets weird now: if everything, including thoughts, can be predicted using a single (probably very complex) formula or algorithm, then how do you know that you are real?

I mean, if everything you do is simply a result of an algorithm following its steps one by one, as physics shows us, then are you anything more than just a bunch of variables in that algorithm?

And if so, then is there a difference between the algorithm running for real in some super-computer somewhere, as people like Elon Musk suggest, or running in potential simply because every mathematical algorithm that can exist must have results whether the algorithm is run or not?

Personally, I’m in the latter camp for a number of reasons:
1. If the universe is running in a super-computer somewhere, is the super computer real or running inside a simulation of its own?
2. The eternal question “why is there something rather than nothing” is solved forever if there really is nothing and everything we see is simply a shared simulation running in potential but not in “reality”.
3. It also helps explain another related issue – is there exactly one universe? No, there are infinite universes, for each possible result of this universal algorithm, and every single one of them “exists” is a result, even if they are not “real”.
4. What is reality? When he heard the idea that nothing is “real” and that reality is subjective (immaterialism), Samuel Johnson famously kicked a rock hard and shouted “I refute it thus!”. However, that’s not a refutation – in a universe where you and I share a hallucination, everything in that hallucination is real to us, whether the objects are objectively real or not.

A very welcome bonus to the idea that the universe is mathematical in nature, is the possibility that it leads to personal immortality, through the idea of quantum immortality.

Is the Universe made of math?

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

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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.