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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 ou

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.
  - GistNoesis 4y ago
    What matters are the function properties, which you can get by running the function. One important property is how much compute and memory do you need to run the function. Which induce an order on functions. If we assume our current state is the result of an execution of a function currently being run, we can learn plenty of things. For example we may infer the source code of the function being run. If this source code happens to be sampled from a simple class of function, this would be strong evidence that we are indeed being evaluated. The classical example is the constants of the universe being fine-tuned for life. Presumably universes that are uninteresting get simulated very quickly, therefore if the upper universe is running a search for interesting universes, it would spend most of its computation time (and therefore our current state is most likely to be sampled) from an universe that require more computation, aka near the edge of chaos, where life thrive. This kind of inductive reasoning may provide strong evidence for the hypothesis. For example we could be in a quine universe : A universe that can run inside itself the source code that created it and be able to observe itself and match its own past to its simulation. Being inside such a universe would be strong evidence for the simulation hypothesis.
    - jstanley 4y ago
      I think we're still talking past each other. You're talking about the state being a "result of an execution". But you don't need the execution! All of our observations are part of the function. You only need to execute it if you want to find out what is inside it from outside. For anyone inside the universe, your experience is the same regardless of whether or not the function is evaluated. In fact it is impossible to determine whether or not the function has been evaluated. That would be like a sum that gives a different answer when you evaluate it compared to when you just think about it.

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.
- GistNoesis 4y ago
  What matters are the function properties, which you can get by running the function. One important property is how much compute and memory do you need to run the function. Which induce an order on functions. If we assume our current state is the result of an execution of a function currently being run, we can learn plenty of things. For example we may infer the source code of the function being run. If this source code happens to be sampled from a simple class of function, this would be strong evidence that we are indeed being evaluated. The classical example is the constants of the universe being fine-tuned for life. Presumably universes that are uninteresting get simulated very quickly, therefore if the upper universe is running a search for interesting universes, it would spend most of its computation time (and therefore our current state is most likely to be sampled) from an universe that require more computation, aka near the edge of chaos, where life thrive. This kind of inductive reasoning may provide strong evidence for the hypothesis. For example we could be in a quine universe : A universe that can run inside itself the source code that created it and be able to observe itself and match its own past to its simulation. Being inside such a universe would be strong evidence for the simulation hypothesis.
  - jstanley 4y ago
    I think we're still talking past each other. You're talking about the state being a "result of an execution". But you don't need the execution! All of our observations are part of the function. You only need to execute it if you want to find out what is inside it from outside. For anyone inside the universe, your experience is the same regardless of whether or not the function is evaluated. In fact it is impossible to determine whether or not the function has been evaluated. That would be like a sum that gives a different answer when you evaluate it compared to when you just think about it.