Let's say you decided a best way to achieve some goal is to create a simulation. You'll almost certainly have to balance:

  • The accuracy of the simulation, i.e. how well it describes some "real" conditions you intend to model.
  • The cost of preparing and running the simulation, e.g. the necessary computing resources.

Note that this is true regardless of the purpose and complexity of the simulation - be it weather modelling, or a civ-like computer game.

Consider a following assumption:

We live in a simulation created by some entities who had the dilemma described above and they decided perfect accuracy is not necessary.

This gives us a sort-of-an-answer to the question "what is behind the laws of physics?": they are approximations of some other laws that would be harder to compute. Therefore, maybe we could try to devise:

  • the "true" laws that govern the thing our world is modelling
  • the "accuracy metric" for the simulation

and observe how they together lead to the laws of physics we see?

I know and understand how speculative this is. Nevertheless, I find this really interesting. So, the question: is there any literature approaching the simulation hypothesis from this direction? Anything I could read?

EDIT: The meaning of the "simulation" in this context differs - I think - from the default. In this POV, the world we live in is the "hardware" built with a purpose of simulating something even more complex. In other words, there is no question e.g. "how they simulate our quantum mechanics" but rather "why implement quantum mechanics the way they did".

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Applied to our world[1], it implies that the entities that are simulating us have access to a more powerful form of computation than quantum computers. Quantum mechanics is thought to be extremely hard to simulate on a classical computer, which means that either our simulators have access to powerful quantum computers, or an even more powerful form of computation.

[1] specifically, quantum mechanics and BQP != BPP, which could be overturned by a better theory of physics or a breakthrough in complexity theory, respectively.

I don't think this answer is in any way related to my question.

This is my fault, because I didn't explain what I exactly mean by the "simulation", and the meaning is different than the most popular one. Details in EDIT in the main post.

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I don't know quantum mechanics, but your back-of-the-envelope logic seems a little suspicious to me.  The Earth is not an isolated system. It's being influenced by gravitational pulls from little bits of matter all over the universe. So wouldn't a reverse simulation of Earth also require you to simulate things outside of Earth?
Seems like you are trying to revert entropy. I suspect there are no simple solutions; and probably no solutions at all. If we are lucky, we will find a way to recreate the minds without having to revert everything (perhaps constraints like "the dead mind was homo sapiens" will sufficiently reduce the search space). Still no idea how specifically. From my perspective, this belongs to category "once we have a friendly superhuman AI, we can ask it to solve the problem".
2the gears to ascension1y
I think ability to recover minds is actually going to be a key component of the AI safety objective when we find it. we need to figure out how to define what we want to not be lost to thermal noise. I see there as being two key levels to safety: don't forget, and keep fueling. a just barely safe AI would freeze all of humanity forever but preserve practical reversibility of that action, a truly safe ai would also preserve our aesthetic influence on new burn, a highly safe ai would minimize its own burn and give us a fair ratio of the ongoing burn. I don't think any sort of data augmented constraint search will ever be able to know exactly what weather was happening in the middle of the Pacific Ocean at 3:00 p.m. the day before Newton's apple - fluid physics is far too chaotic, I don't think any physical system can ever collect all the fragments of that event and put them back together. and we probably will never be able to know most of what was going through newton's mind a few hours before the apple; though we might be able to constrain to a fairly narrow probability distribution. and knowing precisely, beyond what can be guessed by roleplaying the era, what was happening in the mind of arbitrary humans 100k years ago, is super extra not happening ever. that said, I think much of the form of what those minds experienced is possible to constrain by estimating enough boundary conditions (estimate of genetics, resource availability, weather distribution, etc) that we may be able to approximate it. but I don't think archeology will ever be able to reach perfect recovery. unless silent watcher aliens have been here for a while recording everything. if there are supermoral superintelligences, they had better have deployed archeology time capsule drones to every planet for exactly this reason!