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Say we imagined a mathematical model so detailed that it completely describes a universe like our own. Now if we simulated such a universe on a futuristic supercomputer then obviously the beings inside will exist in a sense. On the other hand if we don't ever simulate the model, and in fact there are an infinite number of possible abstract universes, then do the beings inside these abstract universes exist? Do you think we are possibly only abstract mathematical existence ourselves?

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    I've heard the proposal before by a mathematician but I don't understand it. Mathematical models are developed by modeling something else: If you model the travel of a particle by distance = rate * time, you establish some numerical principles to explain how to use this equation, and then observe reality to check that it models reality well. If existence is a mathematical model, what would you check it against? Mathematical models are the mental constructs of humans, so it seems unintelligible to me that existence would be a mathematical model, which is a thing in the mind of a human.
    – Addem
    Commented Apr 2, 2014 at 20:47
  • @Addem You're describing the broad field of physics, and possibly other sciences that use math. I think mathematics may be more universal than just in our heads. Maybe beings outside our observable universe also do similar mathematics. Commented Apr 2, 2014 at 21:00
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    @EnjoysMath, we can certainly mistake dreams for reality--and I can even make sense of, and debate about, the proposal that all of reality "is a dream". I take that to be a loose and poetic way of saying that our perceptions do not stand in a relationship to an object that is in existentially independent of but responsible for those perceptions. That seems like a well-formed (but dubious) proposal to me. But I don't know what it is for a mathematical structure to exist independent of its conception by thinking creatures.
    – Addem
    Commented Apr 3, 2014 at 1:57
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    This is essentially Pythagoras's view. More recently Max Tegmark has advocated this view in his "Mathematical Universe Hypothesis."
    – Geremia
    Commented Apr 3, 2014 at 17:42
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    This is a good critical review of notion as a scientific hypothesis. scottaaronson.com/blog/?p=1753 Commented Apr 5, 2014 at 2:30

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My answer would be yes, the universe could be simply a mathematical abstraction.

Why? Because I have never heard about a proof that refutes your question (title). In fact, I've read in magazines -- a very long time ago (when the movie Matrix was popular) -- that we cannot refute the hypothesis that we live inside a simulation.

In other words: "the universe could be simply a mathematical abstraction" is a valid hypothesis. Today, we are unable to disprove it.


Regarding your other question (body - "can we create our own simulation?"): my answer would be no.

It has to do with the fact that it is computationally and physically impossible to run a simulation -- complete, perfect, lossless, bit precise -- of our universe from inside our universe (please someone verify that sentence, as I'm not 100% sure about that, it's just vague memory).

I'll quote myself (curiously, I've written down the following a few days ago):

The simulated beings will never have enough computational power to run a complete and perfect simulation like the simulation inside which they live.

Again, I might be completely wrong. But if I'm not wrong, I'll be very happy because I like that quote (I've written it down for a reason :)

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  • Obviously no one here is a computer programmer. There is no way to produce such a simulation without bugs! Therefore, finding bugs could be our only way to know if we live in one. In 'Matrix' bugs were Deja Vus...
    – Natxo
    Commented Apr 4, 2014 at 11:58
  • The question is not the bugs, but whether or not it is actually possible (in terms of having enough computational power) to simulate a universe from inside of it (like a recursive simulation :P)
    – feelthhis
    Commented Apr 4, 2014 at 14:51
  • I did not say anything about a simulation. I said "abstract mathematical existence", meaning you don't need to simulate it, it just is. Commented Dec 19, 2021 at 4:06
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You don't even need to go so far as a futuristic supercomputer-powered universe simulation to get the idea that maybe we're all just bits of code living in an artificial realm.

Video games today include NPCs that interact with players (and eachother) based only on what that object can "sense", and interact with their virtual environment in novel ways to satisfy programmed "needs" (think SIMs going to the bathroom, or FPS NPCs running for health power ups when at low HP).

Now advance those kinds of behaviors a couple of generations. You could have NPCs with no direct access to information beyond that which their "senses" bring in, and not necessarily aware of their artificial status.

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  • How can you say that one thing is artificial, and so the "gods / beings" outside must the real thing. It's either all fake or it's all real. Commented Dec 19, 2021 at 4:08

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