I want to bet on this, but since I don't know the person who asked the question personally and science is so complicated, I'm not sure if I can trust him to resolve this objectively based on a rough literature search that he does. This is not something currently measurable, and other things that are much more measurable (for example, economic theories) are something that many reasonable people disagree on. I wonder if there is a more objective measure of resolution that would draw in more participants to the market.

Arbitrage opportunity between this market and https://manifold.markets/IsakRindebk/are-we-living-in-a-simulation-80f1073c1d2c

Are We Living in a simulation?

48% chance. The idea that we might be living in a simulation is a topic of philosophical debate and speculation. There's no definitive evidence one way or the other, so it remains an open question without a conclusive answer.

@Dfe2f There is not, actually, an arbitrage.

We are living in a simulation constructed by our brain, with some correspondences with some parts of reality.
This would be true that we are inside a computer or not.

I will bite. Mostly because I would love to talk to Mira about this.

This is going to sound ridiculous, but I know a proof that we can’t be in a simulation. One part is that we can’t simulate hard random.

Specifically for Mira, even if we are embedded in a larger universe, that larger universe would not be a simulation.

@PC Take every single object in the universe with quantum state and tensor it all together into an absolutely massive but constant size matrix representing the quantum state of everything. It evolves deterministically using Schrodinger's Equation, using constant FLOPs. There will have to be a correction for general relativity, but otherwise there is no randomness and the execution time does not depend on the contents of said universe.

If I understand your argument, it's something like "Our universe contains randomness. Turing machines cannot compute a random number. So our universe is not a classical simulation similarly to how executions of large quantum algorithms are evidence against a classical simulation."

Unfortunately, any quantum circuit with a "measurement" operator can always be rewritten to have the measurement at the end. It's the "Deferred Measurement Principle". Assuming it holds when physics is unified, any randomness in quantum experiments can be deferred to the end of the universe as it deterministically calculates a probability distribution.

A deterministic universe that takes constant memory and constant FLOPs to simulate. Not as compelling an argument.

@Mira Let me try to understand your argument. So, "Deferred Measurement Principle" is one where delaying measurements until the end of a computation won't affect the probability distribution of outcomes. And this does not violate the fact that measurement will collapse the probability space. And thus, you believe that hard random is possible?

@PC If I proved that this is not hard random, would you believe that we are not in a simulation?

@PC what is "hard random" in this context? Google was not helpful.

@MartinRandall oh, not that different than true randomness

@PC I'm not sure that we could prove whether true randomness exists. A CSPRNG cannot be distinguished from true random in polynomial time. Additionally the base randomness of our universe is on a very small scale that we can't accurately measure.

Also simulators with a source of true randomness can use some of it to provide true randomness to their simulations. The same randomness can be used in many simulations so they need not run out.

@MartinRandall who says there is such a thing as true randomness anyway

If it's a simulation, it's not a classical computer because if "P != BQP" it would be quite strange for "base reality" to be taking exponential slowdowns whenever you factor integers or something.

If it's running on a quantum computer, then you have to ask: "Does the no-cloning theorem and similar carry over to nested universes' qubits?". Probably - and then our universe's data is 'owned' by our universe and not by base reality, since they can't clone it.

A simulation that can't be saved or forked is not really a simulation. Though it may be embedded inside a larger universe(maybe we're in the inside of a black hole).

@Mira Why assume that the external universe has similar physics at all? We could create consciousness in Minecraft, but their physics experiments would turn up very different answers to ours.

@IsaacKing It's not physics, it's computation. Minecraft worlds can't factor integers any faster than we can, regardless of the different physics.

If P != BQP, a Minecraft world executing a quantum algorithm with exponential speedup on a large input is evidence against it being a simulation on anything computationally equivalent to a classical computer.

@Mira Minecraft doesn't have quantum effects, so they'd be limited to classical computation, and wouldn't be able to derive the fact that the outer universe has something better.

@IsaacKing That's true. But in our universe, in 2019, Google announced "quantum supremacy" on 53 qubits.

Google claimed that their Sycamore processor performed a specific quantum calculation in 200 seconds that would have taken the most powerful supercomputers over 10,000 years to accomplish.

So imagine that, but scaled up. Even if base reality has 10^1000 times more compute than any of our computers, we could stress their systems by just adding a couple thousand qubits. Completion of the calculation is evidence against us being in a (classical) simulation.

There's some debate on this particular experiment. I think somebody actually did the calculation on a massive supercomputer a couple years later. But if you get the details right, and if somebody mathematically proves P != BQP, the same idea should apply to a future experiment.

@Mira The simulators just might have access to a halting oracle.

@Mira Maybe they just have vastly more time on their hands than we'd expect.

Related: https://manifold.markets/IsaacKing/how-will-the-universe-end

How will the universe end?

Resolves once there's a strong scientific consensus on the answer, or a consensus that we can't know the answer until it happens. In the latter case, I'll resolve with equal probability to all the options that haven't been ruled out. Duplicate answers will be ignored, only the first to be submitted counts.

I'd personally give this this <5% odds. One major reason is that most conceptions of "simulation" are rather specific to how we understand simulations. It's easy for me to imagine we're not in "base reality", but there could be many reasons for this - I assume that most we either haven't thought of, or couldn't even be able to understand.

@OzzieGooen There is also a question about what is even meant by "base reality" and whether there is such a thing.

But I think by "simulation" they mean something like a program running on something like computers created by beings that look and feel very much like human beings.

And in that sense it is near 100% certainty we are not in a simulation, the same way it is near 100% certainty I am not a "brain in a vat."

@DavidBolin how can you be so sure about the brain in a vat, given you essentially are in fact a brain in a human shaped vat

@Odoacre In the literal sense, it is completely certain I am not a brain in a vat, because "vat" refers to a particular sort of thing that I am not inside, and "brain" refers to something inside me, not to me.

But I was not even discussing the literal sense. The sense it could true is something like "in a metaphysical sense, I am a brain in a vat, namely there is a world outside this world, and in that outer world, relationships between things are such that they call me a brain in a vat, and there are things that stand to other things like brains stand to things in this world, and things that stand to other things in that world like vats do in this world."

And in that sense, there is no way to know for sure I am not a brain in a vat. But it is extremely improbable simply because it is an extremely detailed account of an outer world unknown to us; it is improbable in the same way that Scientology is improbable.