Here’s a question.
Why does the universe exist?
Why is there something rather than nothing?
I’ve never heard even a half-convincing answer to this question.
Until now.
—
Stephen Wolfram claims to have an explanation for the existence of the universe.
Here it is in a nutshell.
Why does the universe exist?
If Wolfram Physics is right, and the universe is a hypergraph, then the question becomes: “Why does the hypergraph exist?”
And that’s like asking why the number 7 exists...
...except that the number 7 doesn’t give rise to conscious beings able to appreciate its existence, whereas the hypergraph does.
Let me break that down.
Do numbers count?
Let’s start with the number 7.
It’s an odd place to start, but it’s a prime example of something that exists independently of the universe.
I’m holding up 7 fingers.
My 7 fingers exist in the universe.
But the number 7 exists independently of the existence of my 7 fingers.
Imagine we lived in a universe in which there weren’t 7 of anything, in which there were 6 of some things, and 8 of other things, but there just happened not to be 7 of anything.
In this universe, we’d still be able to conceive of the number 7. It’s a mathematical concept that exists independently of whether it applies to anything in the universe.
If you doubt that, let’s use a higher number. I can conceive of the number 88,510, for example, even though I have no idea whether there are 88,510 of anything in our universe. (If, by some freakish chance, you happen to be holding up 88,510 fingers right now, let me know.)
If you still doubt it, let’s use an even higher number. I can conceive of the number 10 to the power of 10 to the power of 10 to the power of 10 to the power of 10 to the power of 10 to the power of 10, for example, even though there might not be that number of anything in the universe, and, indeed, my calculator breaks if I try to enter such an enormous number. (Again, if, by some freakish chance, you happen to be holding up that number of fingers right now, let me know.)
I can conceive of these numbers, but it really doesn’t matter whether I do. After all, I didn’t just bring the number 88,510 into existence by conceiving of it. It was always the number between 88,509 and 88,511, whether I thought of it or not. I didn’t just bring the number 10 to the power of 10 to the power of 10 to the power of 10 to the power of 10 to the power of 10 to the power of 10 into existence by thinking of it or talking about it. These numbers really don’t care whether or not I, or anyone else, think of them or talk about them.
Numbers like the number 7 are mathematical concepts that exist independently of me, independently of anyone, independently of the universe.
Palpable
Let’s be a little more precise here.
What does it mean to say that the number 7 exists?
I know what it means to say that my fingers exist. It means that they exist in the material realm, the one I’m in right now and can reliably report really is here. I can reach out and touch my fingers.
But it means something different to say that the number 7 exists.
It doesn’t mean that it exists in the material realm.
At best, numbers exist only in an abstract, Platonic realm.
You can’t reach out and touch the number 7, in the same way as I can reach out and touch my fingers.
Let’s keep this in mind as we consider the rest of Stephen Wolfram’s explanation for the existence of the universe.
Population of the Platonic realm
Numbers aren’t the only things that exist independently of the universe.
Shapes, such as circles...
...and spheres...
...exist in the same abstract, Platonic realm, regardless of whether anything in the universe is truly circular or spherical.
Indeed, any number of mathematical concepts – sets, lattices, tensors, fields, hypergraphs, and so on – exist in this way, independently of the universe.
And why stop at hypergraphs? Hypergraph rewriting rules are mathematical concepts too:
Such rules, if they’re repeatedly applied to a hypergraph, cause it to evolve in complex ways. If these rules are mathematical concepts, then they, too, exist in the same way as the number 7 exists, independently of the universe.
It doesn’t matter whether hypergraphs and hypergraph rewriting rules apply to anything in the universe.
It doesn’t matter whether we conceive of hypergraphs and hypergraph rewriting rules, whether we think of them, whether we talk about them.
Hypergraphs that evolve through the application of rules exist in the same way as the number 7 exists, independently of the universe, independently of any conscious beings who might think of them or talk about them.
The universe is a hypergraph
Which brings us to Wolfram Physics.
Stephen Wolfram, Jonathan Gorard and others have been exploring the possibility that the universe might be modelled by a hypergraph.
According to Wolfram Physics, the universe is a hypergraph that evolves through the application of hypergraph rewriting rules:
How can a hypergraph model space, time, matter and everything else in the universe?
Well, that’s what The Last Theory is all about. Take a look at my other articles, and you’ll find yourself enthralled, as I am, by this new, computational approach to physics.
But wait a minute.
I’ve said that hypergraphs that evolve through the application of rules exist independently of the universe, independently of any conscious beings who might think of them or talk about them.
And I’ve just said that, according to Wolfram Physics, the universe is a hypergraph that evolves through the application of rules.
If both these things are true, then the universe exists.
The one thing I can’t be confused about
If we accept this proof that the universe exists, we have to concede that it only proves that universe exists in the same way as the number 7 exists, in the abstract, Platonic realm.
But is that really the answer we’re looking for?
Earlier, I made a distinction between the abstract, Platonic realm in which numbers, spheres and hypergraphs exist, and the material realm in which I can reach out and touch my fingers.
When we’re asking: “Why does the universe exist?” surely we’re not asking: “Why does the universe exist in the abstract, Platonic realm?”
Surely what we’re asking is: “Why does the universe exist in the material realm?”
Who cares whether the universe exists in the way a circle or a sphere exists, in some abstract, Platonic realm?
What I care about is why the universe exists in the way my fingers exist, in a way that I can reach out and touch, in the material realm, the one I’m in right now and can reliably report really is here.
But let’s dig a little deeper.
What do I mean when I say that I’m looking at the universe right now and can reliably report that it really is here?
What do I mean when I say that I can reach out and touch it?
For all I know we might be living in a simulation. (For all you simulationists out there, don’t get too excited, I’m not saying that we are living in a simulation, I’m just saying that we might be living in a simulation.) For all I know, when I reach out and touch my fingers, the simulation might be carefully feeding me the sensations I would feel if my fingers were real.
Still, there’s one thing I do know. I’m conscious. Even if we were living in a simulation, it wouldn’t work if I didn’t have a conscious mind to feed the sensations into.
I might be confused about everything else, but not about this: it feels like something to be me.
I can be sure that I’m conscious, even if I’m not sure whether my fingers are real or simulated.
Which means that I can be sure that some sort of universe exists, with my consciousness in it, no matter how deeply confused I might be about everything else in that universe.
That’s all I’m really saying when I say that the universe exists in the material realm: that I’m conscious of some sort of universe.
Different realms
So here’s where we’re at.
Hypergraphs that evolve through the application of rules exist in the abstract, Platonic realm.
According to Wolfram Physics, the universe is a hypergraph that evolves through the application of rules.
Space, time, matter and everything else in the universe all arise from the evolving hypergraph.
And when I say space, time, matter and everything else in the universe, that includes my fingers, my mind and my consciousness.
My consciousness arises from the hypergraph, just as my fingers and my mind arise from the hypergraph, just as space, time, matter and everything else in the universe arise from the hypergraph.
Space exists in the same way as the hypergraph exists, since the hypergraph is space.
Matter exists in the same way as the hypergraph exists, since particles of matter are persistent tangles in the hypergraph.
My fingers exist in the same way as the hypergraph exists, since a series of very specific persistent tangles in the hypergraph are my fingers.
My mind exists in the same way as the hypergraph exists, since another series of very specific persistent tangles in the hypergraph are my mind.
My consciousness, too, exists in the same way as the hypergraph exists.
But the hypergraph, like all hypergraphs that evolve through the application of rules, exists in the abstract, Platonic realm.
If my consciousness exists in the same way as the hypergraph exists, and the hypergraph exists in the abstract, Platonic realm, then my consciousness, too, exists in the abstract, Platonic realm.
Now’s a good time to remember that the only evidence I have that the universe exists in the material realm comes from my consciousness... which, we’ve just concluded, exists in the abstract, Platonic realm.
So maybe I’m wrong to make a distinction between the abstract, Platonic realm in which numbers, spheres and hypergraphs exist, and the material realm in which I can reach out and touch my fingers.
Maybe they’re the same place.
Maybe space, time, matter and everything else in the universe, including my fingers, my mind and my consciousness, exist in this one place, call it the abstract, Platonic realm, call it the material realm, either way.
Who cares whether a circle or a sphere exists in the abstract, Platonic realm.
There’s no one there to notice.
But who cares whether a hypergraph that evolves through the application of rules exists in the abstract, Platonic realm?
Well, if the evolving hypergraph gives rise to space, time and matter, our fingers, our minds and our consciousness, then there is someone there to notice.
We are there to notice.
Occam’s objection
So what do you think?
Do you accept Stephen Wolfram’s argument that we exist in the same abstract, Platonic realm as the number 7?
Do you think that explains the existence of the universe?
I confess I’m not convinced.
Here are my objections.
1. Wolfram’s argument assumes that the universe is a hypergraph. That’s a pretty bold assumption. Even if Wolfram Physics evolves into the most precise, most complete theory of physics ever – better than quantum mechanics, better general relativity, better than particle physics – I still wouldn’t say that the universe is a hypergraph, only that the hypergraph is a good model of the universe. I like Jonathan Gorard’s agnosticism as to the reality of the hypergraph. It’s a model. Maybe it’s real. Maybe not. We’ll never know.
2. Wolfram’s argument also assumes that the number 7 exists. Even with all my provisos about its existing only in an abstract, Platonic realm, this, too, is a pretty bold assumption. Philosophers have been arguing for millenia about whether numbers exist and, if they do, in what sense they exist. If the existence of the universe relies on something as tenuous as the existence of the number 7, then the existence of the universe, too, seems pretty tenuous.
3. If Wolfram’s argument proves that a universe based on a hypergraph that evolves through the application of rules exists, then it proves that a universe based on every other imaginable mathematical concept that evolves through every other imaginable computational paradigm exists too. That’s an awful lot of universes. Admittedly, the only ones anyone cares about are those that give rise to consciousness, but if the hypergraph and rules can give rise to consciousness, then I find it hard to believe that there aren’t other mathematical concepts and computational paradigms that can do the same. Swallowing the existence of all these other universes seems something of an affront to Occam.
Why does the universe exist?
One more time, then...
Why does the universe exist?
If Wolfram Physics is right, and the universe is a hypergraph, then the question becomes: “Why does the hypergraph exist?”
And that’s like asking why the number 7 exists...
...except that the number 7 doesn’t give rise to conscious beings able to appreciate its existence, whereas the hypergraph does.
Are you convinced by Stephen Wolfram’s explanation?
Let me know!