The universe is its own simulation

Years ago, I read Candide by Voltaire. In the foreword it was mentioned that Voltaire wrote it in a few days as a rebuttal to Leibniz’s claim that the we live in the best possible universe.

The novel was bad. Indeed, it felt like it had been written in a few days. But I don’t hold that against Voltaire (He, after all, said the wittiest saying of them all – “A witty saying proves nothing”). I can imagine his mind space after reading Leibniz’s claim: Leibniz, my man, did you even look around!

The universe we live in is bad. There is a lot of pain in here, and a lot of suffering. I am yet to find a rational argument against the problem of evil. I don’t care too much about rationality, I feel it has very obvious limits, but I haven’t experienced any experiential understanding that’d explain the existence of evil either yet, so I can see myself in Voltaire’s mind space. Leibniz, brother, there is a lot of bad stuff going on, how can you go about asserting that this is the best things can be.

And that novel is basically a rant coming from this mind space. It’s not a great novel, because it isn’t, it’s just an exasperated rant (The tldr of the novel is that a lot of bad things happen to characters in it, thus showing the absurdity of the claim that the world is good. Interestingly, at the end the characters do find themselves in a safe, good place, but being human they can't stand being still there either).

Now, I’ve always felt a bit puzzled about why did Leibniz make that claim. He is a great mathematician, why would he claim something so dumb. I’ve never bothered to read his actual claim though, I must confess. I felt reading it would be a bore, and I just assumed it was an application of mathematics to an area it wasn’t applicable to.

Definitions. Words have different meanings in the minds of different people. We’ll come back to this.

Years ago, I think before I’d read Candide, I had had the sudden realisation that the universe is its own simulation. I remember the exact moment - sitting in an autorickshaw on a wonderful sunny afternoon as it sputtered along a curvy tree spotted Gachibowli road.

It’s difficult to talk about this, because I don’t know if there is anything much more to say about it: The universe is its own simulation, that's just it. The statement has a self-sufficient self-explanatory factual quality in my mind.

I realise though that maybe these words have a different structure in your vector space than they have in mine, so what I'm saying might not be apparent to everyone. I guess I could rephrase it as

“any 1:1 simulation that we build of the universe will be at least as complex as the universe if we are to retain full fidelity”,

and

“to whatever end it is running to, teleological or otherwise, can only be computed by simulating it in its full fullness”.

Sometimes I think it is a trite observation.

Note that I’m not saying our universe, I’m referring to the universe. This is one of the reasons why I find simulation hypotheses (that we’re living in a simulation) quite uninteresting - in doesn’t really matter, because even if we are, then there is a (possibly infinitely regressing) universe that contains our simulation, so we can think about the properties of that ur universe. The universe.

A few days ago, I realised how these two things are related.

Leibniz was claiming the same thing!

The misunderstanding arises because of the use of best. I think it might’ve been a translation thing, the word that Leibniz might’ve intended was perfect.

But even perfect has a positive valence to it, so it is not still not the perfect fit. Here, he was using the word perfect in the sense of, say, a crystal, which has a perfect lattice structure. The sense he was using it doesn’t have implication of good or lack thereof attached to it. It is only an observation about its mechanics, and in that sense the universe is perfect - it is the best simulation of itself that could be.

Why does this matter? Well, I don’t think it is does unless you’re philosophising. I am, so it made me happy to see two different long standing threads click together, in that satisfying click of unison. For all I know, I still might be putting words in Leibniz’s mouth, but that’s fine, in my thoughts that who Leibniz can be until someday I know better.

Practically, this had made me reconsider the various claims about God that I’ve come across being made by mathematicians. It is a surprisingly common thing, especially for established mathematicians in their later years (or maybe that’s when they have the courage to publish such claims), to make “proofs” about God, say of her existence or lack thereof etc., or of the properties God must possess.

I used to dismiss these as kooky, but now I realise for some of them it could just be me misapprehending the definitions of the terms under consideration.

Separately, I’ve also come to realise that mathematics is separate from, and more than, rationality. This is a slow burner, it becomes more apparent the more I understand category theory. So all my misgivings about rationality don’t really apply to mathematics. Maths is about structure, about the relationships between objects. Rationality is a just a limited view of viewing the world that coincides with how a lot of mathematical truths are discovered, but category theoretical discoveries can be made without rationality (and indeed, I would imagine that most interesting math is done this way).

So combined - that mathematicians proving things about, say, God, might be using God in a very different sense than the theistic one, and - that mathematics is more than just rationality - open a whole new universe of thought for me. Hopefully, I’ll see you there.