They argue that the universe isn’t mathematically computable, and therefore not possible to simulate. It’s not about physical computers.
We know there’s a class of ”uncomputable problems” for which there’s no algorithm (most well known is halting problem). If the universe rely on any of these uncomputable problems, then no computer - no matter how advanced it is - can simulate the universe. Something else other than pure computation is needed.
However, their argument rely on that ”quantum gravity” is what makes the universe uncomputable. I’m not sure how valid this statement is.
Going to circle back around on uncomputible in “our” version of reality. I mean it’s kind of lazy in its way but it seems like the possibility that the “real” universe is a fundamentally different kind of place throws out most if not all methods for “proving” it’s not. I’m not even a fan of the matrix theory but still, to acknowledge it.
When someone claims something isn’t computable, it is instantantly sus, especially from math nerds and not compsci nerds. Imagine the universe is indeed uncomputable, but each measurement is. The number of measurements you’d need to sim (at various scales/resolutions) is vastly smaller than the universe as a whole. This is morally equivalent to occlusion pruning in 3D games. If you aren’t looking at it, it isn’t being rendered.
When it comes to theory of computability, you don’t need to account for optimization techniques. No need to consider the practicality of getting an answer from the algorithm, like how long it takes or how much memory it requires. Either you can get an answer in finite amount of time, or you can not.
But I agree it’s sus when it comes to making such strong statements about the compatibility of the reality. I don’t trust this paper makes all the right assumptions.
However, their argument rely on that ”quantum gravity” is what makes the universe uncomputable. I’m not sure how valid this statement is.
Here is the assumption the authors use that brings quantum gravity into the proof:
As we do not have a fully consistent theory of quantum gravity, several different axiomatic
systems have been proposed to model quantum gravity [26–32]. In all these programs, it
is assumed a candidate theory of quantum gravity is encoded as a computational formal
system
F_QG = {L_QG, ΣQG, R_alg} .
I interpret their assumption to mean that describing quantum gravity in this way is how it would be defined as a formal computational system. This is the approach that all of the other leading theories (String Theory, Loop Quantum Gravity) have taken, which have failed to provide a fully consistent and complete description of gravity. I think the proof is saying that non-computational components can be incorporated into a fully consistent and complete formal system and so taking a non-computational approach to quantum gravity would then incorporate gravity into the formal system thereby completing the theory of everything.
Does that make sense? I am not a logician by any extent and I have no idea how robust this proof really is. I do think the bold claims the authors are making deserve heavy scrutiny, but I am not the one to provide that scrutiny.
I have no idea either. I feel like I have some surface understanding of what they want to achieve, but I’m completely lost as soon it gets any deeper than that.
They argue that the universe isn’t mathematically computable, and therefore not possible to simulate. It’s not about physical computers.
We know there’s a class of ”uncomputable problems” for which there’s no algorithm (most well known is halting problem). If the universe rely on any of these uncomputable problems, then no computer - no matter how advanced it is - can simulate the universe. Something else other than pure computation is needed.
However, their argument rely on that ”quantum gravity” is what makes the universe uncomputable. I’m not sure how valid this statement is.
Going to circle back around on uncomputible in “our” version of reality. I mean it’s kind of lazy in its way but it seems like the possibility that the “real” universe is a fundamentally different kind of place throws out most if not all methods for “proving” it’s not. I’m not even a fan of the matrix theory but still, to acknowledge it.
When someone claims something isn’t computable, it is instantantly sus, especially from math nerds and not compsci nerds. Imagine the universe is indeed uncomputable, but each measurement is. The number of measurements you’d need to sim (at various scales/resolutions) is vastly smaller than the universe as a whole. This is morally equivalent to occlusion pruning in 3D games. If you aren’t looking at it, it isn’t being rendered.
When it comes to theory of computability, you don’t need to account for optimization techniques. No need to consider the practicality of getting an answer from the algorithm, like how long it takes or how much memory it requires. Either you can get an answer in finite amount of time, or you can not.
But I agree it’s sus when it comes to making such strong statements about the compatibility of the reality. I don’t trust this paper makes all the right assumptions.
Here is the assumption the authors use that brings quantum gravity into the proof:
I interpret their assumption to mean that describing quantum gravity in this way is how it would be defined as a formal computational system. This is the approach that all of the other leading theories (String Theory, Loop Quantum Gravity) have taken, which have failed to provide a fully consistent and complete description of gravity. I think the proof is saying that non-computational components can be incorporated into a fully consistent and complete formal system and so taking a non-computational approach to quantum gravity would then incorporate gravity into the formal system thereby completing the theory of everything.
Does that make sense? I am not a logician by any extent and I have no idea how robust this proof really is. I do think the bold claims the authors are making deserve heavy scrutiny, but I am not the one to provide that scrutiny.
I have no idea either. I feel like I have some surface understanding of what they want to achieve, but I’m completely lost as soon it gets any deeper than that.