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.

Mathematical Universe

For the last few hundred years, we have been able to gradually pin down exactly how everything in the universe works, right down to a very small group of equations.

What that means is that everything in the universe can be predicted using math (either exactly, or statistically).

Philosophically, there is no difference at all between a mathematical description of you observing the universe, and the real you observing the universe. How could you tell which is “real”, when everything that happens in “reality” can be predicted by just doing the math? Is there a difference between a mathematical universe and a “real” universe?

In a way, this means that we are all like NPCs (non-player characters) in a computer game, all of us convinced that we are real and that the world we inhabit is real, when in fact, the entire game and ourselves are being simulated in a universe-encompassing machine.

In reality’s case, what is this universe-encompassing machine? Well, math can be worked out on a computer, on paper, or in your head, and if done correctly, it will always come up with the same answers. Math is objective – it doesn’t rely on a medium. It doesn’t need the paper in order to be correct – it just is.

Consider the sequence (1, 2, 3, 4, …) for example – the next number is 5, no matter whether we compute it or not.

Even incredibly complex equations obey the same objective law – if you consider an equation that predicts the position of every particle in the universe in one second – this equation will have an answer whether it is calculated or not.

All equations exist in potential. This means that the equation “x+y-z” has just as much reality as the sequence “1, 2, 3, 4, …”, and therefore the answers to those equations also all exist in potential.

This means that every possible universe exists as a mathematical potential, and because there is no discernible difference between “reality” and a simulated universe (for people inside those universes), it means that every single universe, that you can describe mathematically, exists.

And by extension, every universe in which you survive the present and the near and far futures, also exists.

black holes and baby universes

Yesterday, I was talking to some of my students at the Coolest Projects seminar in Dublin, and we ended up discussing Nikodem Poplawski’s idea that all black holes contain universes, and how that leads to there being infinite universes, and therefore we are all immortal (due to quantum immortality).

In Newton’s classical mechanics, the more mass there is in a volume, the stronger the gravity is near that volume.

However, if each black hole contains a universe, and then recursively contains its own black holes and therefore further universes and black holes (turtles all the way down!), then that means that each black hole can potentially contain infinite mass, and so Newton’s math suggests that the gravity of black holes is infinite in strength.

But it’s not. We know this because if it was, there would be nothing outside black holes – it would all be sucked in.

So how can a black hole contain potentially infinite mass, and yet not exude infinite gravitational attraction?

The solution lies in the speed of gravity.

If the sun was to suddenly vanish from our solar system, then the Earth would continue to orbit the space where it was for 8 minutes, because gravity waves take time to propagate across space.

If a black hole creates its own space inside itself, due to the huge pressure and friction, then gravity from the absolute center (for example), takes longer to get to the outside because it has more space to traverse.

We know from our own observations that this universe is expanding. If all universes within black holes are created by the expansion of space, then it is possible that the space is created at such a speed that gravity cannot travel from one side of the hole through the center to the other side, because the space expands so fast that it simply never gets there.

We know as well that in our own universe, there is no such thing as empty space. Virtual particles appear and disappear all the time. It makes sense that sometimes these virtual particles will appear, separate, and sometimes not recombine and vanish. Sometimes, matter (and therefore mass) will appear out of nothing.

And so, the inside of a black hole will create its own space, alone with its own new matter, seeding a new universe.

So how does this all tie in with immortality?

The number of possible configurations of energy/mass in a universe depends on the size of that universe. Space is made of nodes and lines connecting the nodes. There is no “distance” between the nodes. “Distance” and “size” are measured by literally counting the nodes and lines.

Because space is quantised, anything that is in space must be located on a specific node. This means that if there are three nodes, for example, then a point particle can only exist in one of three places. This in turn means that if you have four universes, each composed of three nodes (in the same configuration for simplicity) and one point particle, then at least two of those universes must be exactly the same.

The same principle means that if you have larger universes and more particles, there is still a limit to how many universes you can have before two of them must be exactly the same.

For example, if there are 4 nodes (again, configured similarly for simplicity) and 2 point particles, there are only 16 unique configurations (4+4*3). If there are 3 point particles, there are 40 unique configurations (4+4*3+4*3*2).

In the first case, if there are 17 universes, at least two are exactly the same. In the second, if there are 41 universes, at least two are exactly the same.

No matter how large the universe gets, there is still a number that equates to how many possible configurations it can be in. If more than that number of universes exist, then there are duplicates.

If all black holes contain universes, and there are then recursive universes and black holes, then there are infinite universes, and therefore there are infinite duplicates of universes.

This means that there are infinite universes which are exact copies of this universe, including copies of you, which have your exact history, memories, and thoughts.

If there is a chance that you will die tonight, there are some universes where you will die, but you will only be aware of those in which you survive.

And therefore, black holes and baby universes, lead to a kind of multiverse immortality.

the multiverse and immortality

I was reading a bit about Nikodem Poplawski’s theory of black holes and baby universes, and thought I might expand on how that can lead to a kind of multiverse immortality (or quantum immortality, even though this is not a quantum multiverse idea).

The general belief is that black holes are “infinitely” dense, which suggests that anything that goes too close to one is stretched (spaghettified), and then torn apart by tidal forces, leading to an eventual crush once inside the hole proper.

Nikodem’s idea is that it is impossible to make matter infinitely dense, as the torsion forces the matter to expand, even while gravity is forcing it to collapse. Eventually, the pressure becomes so high that the contained matter essentially explodes, even though from the outside, we would see no such thing.

The explosion manifests on the inside of the black hole as a Big Bang, from which is born a new universe. This may seem unintuitive, but I think what he’s suggesting is that the explosion forces the creation of space itself. Imagine a TARDIS’s interior exploding into being, inside a normal police box, for example. From the outside, we see nothing. On the inside, we see a whole universe born and growing.

How this leads towards immortality is that if every black hole can have a universe inside it, as Nikodem suggests, and each universe is can have black holes inside them, then there are a potential infinite number of universes.

If there are infinite universes, then every possible configuration of matter can be found somewhere, and will also be repeated somewhere. Since the universe we are in is definitely a “possible configuration of matter”, then that means that there are infinite copies of this universe contained throughout the universe, either directly inside its black holes, or inside black holes contained in the black holes (etc). In other words, the universe is infinite in this idea, but in a “nested” kind of way.

If there are infinite copies of this universe, then there will also be a universe for ever possible choice we make, or every random event. So, if you were to have a stroke tomorrow and die, there will also be infinite universes where you don’t, and since your identity is ultimately physical in nature, “you” will survive in those and will not even remember that “you” had a stroke.

What does it look like at the edge of the universe?

In an article at Forbes, Ethan Siegel walked us through a general overview of the history of the universe. His point boiled down to a simple fact: there is no edge to the universe, because the universe is infinite in size. In his words:

the Universe itself isn’t finite in volume; it’s only the observable part that’s finite

The whole premise is similar to the question “when I stand on a 30 meter hill, I can see for miles around – what does it look like at the horizon?”

The short answer is “the same”. The horizon is not the edge of the world. It is simply as far as you can see in that direction (19.6km) before the world curves away from your sight. If you were to stand at a point on the horizon, then you would see that the world looks pretty much the same as around the hill you were on. Roads, fields, rivers. All the same. And in the same direction, you would see a horizon, 19.6km away…

The same is true of the universe. The “edge” of the universe that we see is stretched away visibly into nothing 46.6bly (billion light years) away, but if you were to magically move yourself to any point on the edge of the visible universe, you would see that you are in an area that looks pretty much the same – surrounded by gases, stars, galaxies. And in the same direction, you would be able to see a further 46.6bly to yet another “edge”.

The difference between the two stories here is that the world is curved, so it really is finite in size. This is how the horizon happens in the first place. But, in the universe’s case, space is not curved, as far as we can see. It just goes on, and on, and on, without limit.

So, there really is no edge to the universe. The idea is a misunderstanding, just like the idea that the horizon is the edge of the world.