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This is not so far off as one might think. You see, a lot of people believe in the simulation hypothesis. And sequential hash computation, aka proof of work, me

This is not so far off as one might think. You see, a lot of people believe in the simulation hypothesis. And sequential hash computation, aka proof of work, means that even from inside the simulation we can be assured by math, that the upper computer running the simulation has done the work. One might argue that the universe is doing much more computation every instant, but it's not so evident because of compression (for example algorithm like Hashlife). There are numerical shortcuts as anyone that has written a numerical simulation knows. For example you can simulate a black hole that may one time have been entire galaxies by just a few numbers (its mass, momentum, and spin). Proof of work, give us an upper bound on the computation available to us. The question is what is going to happen when we cross this bound. I like to call it Numerical Biological Instability : when you write big enough simulations you have to take into account for the emergence of unwanted sub-computations that may end-up stealing all your computation cycles. And I like the idea of NBI being one possible solution to the Fermi Paradox : We are the first advanced civilization because there can't be multiple advanced civilizations because as soon as we suck-up all the available computation the simulation speed crawl to a stop. And given that we can see to the edges of the universe with telescopes, it's not easy to put computational limits on parts of the universe without leaving observable traces. And given that computational power tend to follow exponential growth. Only universes with a single advanced pre-singularity civilization tend to be simulated.

jstanley 4y ago
I don't think this is quite right. If our universe can be simulated, then the simulation is just computing a (complicated) mathematical function. If all of our observations are emergent effects of the mathematical function, then our observations are exactly the same regardless of whether there is an "upper layer" actually computing the function. Imagine writing a simulation of a point mass following a parabolic arc under the influence of gravity: the path of the mass is the same regardless of whether you run the simulation or not. It would be the same for our universe. If it is possible to describe mathematically, then you don't need to run the simulation in order for the contents of the universe to experience themselves existing. The simplest explanation is that there is no uppermost layer, it's all just mathematics. See also https://en.wikipedia.org/wiki/Our_Mathematical_Universe https://en.wikipedia.org/wiki/Our_Mathematical_Universe
- GistNoesis 4y ago
  There is something Wolfram would call computational irreducibility (related to the Halting Problem), which means even though the simulation is just a deterministic mathematical function, to know what happens in it you must run the code, and that may require lot of memory and compute along the way even if the universe ends in an heat death. In fact universe is probably stored by a seed (42), along something like 10 lines of definition, and 100 line of code would be enough to implement it in a naive version (Physicists sell tee-shirts with some pseudo version of it). Morpheus would say : "There's a difference between knowing the path and walking the path..."
  - jstanley 4y ago
    For someone outside the universe to know what happens in it, they must run the code. For someone inside the universe, their observations are just part of the function. To know the millionth digit of pi you have to calculate it, but the digit is the same regardless.
- unyttigfjelltol 4y ago
  I think there's a subtler point in the parent comment, that is whenever we observe different parts of the universe we are collapsing its quantum wave function, which would have large consequences for any would-be simulation. https://physics.stackexchange.com/questions/43406/what-constitutes-an-observation-measurement-in-qm https://physics.stackexchange.com/questions/43406/what-const...
- karmakaze 4y ago
  There's no reason that the upper layer isn't cheating. Very much like we do in video games where we use approximations or even better work backward from a result and (re)write history. Even all our memories could be altered to make us believe any history or facts as desired. There's too much freedom to be able make strong conclusions.
  - jstanley 4y ago
    There doesn't have to be an upper layer at all. Everything you can possibly observe is determined by merely specifying the function. You have no way to determine whether or not the function is being evaluated anywhere. It wouldn't make any difference.
florbnit 4y ago
> because there can't be multiple advanced civilizations because as soon as we suck-up all the available computation the simulation speed crawl to a stop. If our reality is a simulation. It doesn’t matter how fast the “computer” is running. We could be living inside a grid of rocks in a gigantic dessert being pushed around slowly by an immortal turtle according to rule 30. How would it matter for us as we are living in the simulation and our relative time is always one second second per second, even if it takes a billion years for the turtle to rearrange the rocks to compute that second. So there is no way to “drain the simulation of resources”, unless we figure out a way to kill the turtle, but that’s not likely to be possible, since we’re just patterns in the rocks.
- GistNoesis 4y ago
  What would be happening to us isn't the point. (Simulation would just stop, we would just cease to exist without even being aware of it, (not so dissimilar to the video/short story of the article). The point is showing there is no paradox, because our current situation is quite normal. The point is if the upper computer has a constant simulation budget, then our universe maximum age (perceptible duration for us) is the time it takes for the first civilization to reach the singularity. The upper computer won't ever be able to simulate behind this horizon. Which means that if we sample our universe at random among simulated universes, it is very likely that we won't observe advanced aliens because all the possible simulated universes by construction only contain one advanced civilization, and therefore there is no paradox. (There could eventually be multiple civilizations but time-frames of their technological explosions have to overlap very precisely (100 years out of 15 billions) so it's very unlikely, and because of Moore's law most of the computational load will be spent on the one with the biggest exponential)
yencabulator 4y ago
> And sequential hash computation, aka proof of work, means that even from inside the simulation we can be assured by math, that the upper computer running the simulation has done the work. Actually, perhaps not. Your senses and memory are part of the simulation. There is no need for the PoW math to actually take place, just that you believe it has.
- GistNoesis 4y ago
  You can check the proof manually if you need convincing. (Or you can invent ways to check that your computer is computing correctly). I'm inclined to believe computation did happen, because otherwise you get theories like super-determinism, where consistency is really dubious. And the way to make them consistent in a robust way involve playing an adversarial lying game against agents from inside the simulation, which favors greatly the agents inside the simulation and therefore is even more computationally expensive than just doing the computation. But even just taking a picture of a night sky and trying to infer the history, is very consistent with some computations happening according to fixed rules.

jstanley 4y ago

I don't think this is quite right. If our universe can be simulated, then the simulation is just computing a (complicated) mathematical function. If all of our observations are emergent effects of the mathematical function, then our observations are exactly the same regardless of whether there is an "upper layer" actually computing the function. Imagine writing a simulation of a point mass following a parabolic arc under the influence of gravity: the path of the mass is the same regardless of whether you run the simulation or not. It would be the same for our universe. If it is possible to describe mathematically, then you don't need to run the simulation in order for the contents of the universe to experience themselves existing. The simplest explanation is that there is no uppermost layer, it's all just mathematics. See also https://en.wikipedia.org/wiki/Our_Mathematical_Universe https://en.wikipedia.org/wiki/Our_Mathematical_Universe

GistNoesis 4y ago
There is something Wolfram would call computational irreducibility (related to the Halting Problem), which means even though the simulation is just a deterministic mathematical function, to know what happens in it you must run the code, and that may require lot of memory and compute along the way even if the universe ends in an heat death. In fact universe is probably stored by a seed (42), along something like 10 lines of definition, and 100 line of code would be enough to implement it in a naive version (Physicists sell tee-shirts with some pseudo version of it). Morpheus would say : "There's a difference between knowing the path and walking the path..."
- jstanley 4y ago
  For someone outside the universe to know what happens in it, they must run the code. For someone inside the universe, their observations are just part of the function. To know the millionth digit of pi you have to calculate it, but the digit is the same regardless.
unyttigfjelltol 4y ago
I think there's a subtler point in the parent comment, that is whenever we observe different parts of the universe we are collapsing its quantum wave function, which would have large consequences for any would-be simulation. https://physics.stackexchange.com/questions/43406/what-constitutes-an-observation-measurement-in-qm https://physics.stackexchange.com/questions/43406/what-const...
karmakaze 4y ago
There's no reason that the upper layer isn't cheating. Very much like we do in video games where we use approximations or even better work backward from a result and (re)write history. Even all our memories could be altered to make us believe any history or facts as desired. There's too much freedom to be able make strong conclusions.
- jstanley 4y ago
  There doesn't have to be an upper layer at all. Everything you can possibly observe is determined by merely specifying the function. You have no way to determine whether or not the function is being evaluated anywhere. It wouldn't make any difference.

florbnit 4y ago

> because there can't be multiple advanced civilizations because as soon as we suck-up all the available computation the simulation speed crawl to a stop. If our reality is a simulation. It doesn’t matter how fast the “computer” is running. We could be living inside a grid of rocks in a gigantic dessert being pushed around slowly by an immortal turtle according to rule 30. How would it matter for us as we are living in the simulation and our relative time is always one second second per second, even if it takes a billion years for the turtle to rearrange the rocks to compute that second. So there is no way to “drain the simulation of resources”, unless we figure out a way to kill the turtle, but that’s not likely to be possible, since we’re just patterns in the rocks.

GistNoesis 4y ago
What would be happening to us isn't the point. (Simulation would just stop, we would just cease to exist without even being aware of it, (not so dissimilar to the video/short story of the article). The point is showing there is no paradox, because our current situation is quite normal. The point is if the upper computer has a constant simulation budget, then our universe maximum age (perceptible duration for us) is the time it takes for the first civilization to reach the singularity. The upper computer won't ever be able to simulate behind this horizon. Which means that if we sample our universe at random among simulated universes, it is very likely that we won't observe advanced aliens because all the possible simulated universes by construction only contain one advanced civilization, and therefore there is no paradox. (There could eventually be multiple civilizations but time-frames of their technological explosions have to overlap very precisely (100 years out of 15 billions) so it's very unlikely, and because of Moore's law most of the computational load will be spent on the one with the biggest exponential)

yencabulator 4y ago

> And sequential hash computation, aka proof of work, means that even from inside the simulation we can be assured by math, that the upper computer running the simulation has done the work. Actually, perhaps not. Your senses and memory are part of the simulation. There is no need for the PoW math to actually take place, just that you believe it has.

GistNoesis 4y ago
You can check the proof manually if you need convincing. (Or you can invent ways to check that your computer is computing correctly). I'm inclined to believe computation did happen, because otherwise you get theories like super-determinism, where consistency is really dubious. And the way to make them consistent in a robust way involve playing an adversarial lying game against agents from inside the simulation, which favors greatly the agents inside the simulation and therefore is even more computationally expensive than just doing the computation. But even just taking a picture of a night sky and trying to infer the history, is very consistent with some computations happening according to fixed rules.