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I think Stephen at least dares to ask the question. Here is a little thought-experiment on the Nature of Time. You take the three body problem and you pick an
by GistNoesis 2y ago
I think Stephen at least dares to ask the question.
Here is a little thought-experiment on the Nature of Time.
You take the three body problem and you pick an initial condition and generate the trajectory of the three body from 0 to T by integrating through time with some numerical scheme like Runge-Kutta.
Now you do it again, and again, generating each time a "universe" of three-body trajectories. Doing so allows you to build a dataset of physically realist three-body trajectories.
And now the kicker : You train a diffusion model on this (potentially infinite synthetic) dataset. Once trained, to build a "universe" (aka 3-body trajectories) you only need to sample from this diffusion model. There is no more need to integrate through time. Past, present and future inside the universe just fold themselves into place in order to make sure the universe follows the time-evolution constraint.
When working numerically, both these schemes can theoretically be as accurate as desired (error smaller than any chosen epsilon), although the diffusion model seems to potentially necessitate more memory in toy model, it's not evident as the universe is stored in a compressed fashion which necessitate less memory when the universe is no longer a toy model.
The underlying question I perceive from Stephen works are is whether it's more efficient computationally to explore all possible universes simultaneously in which case time is a mere constraint you have to solve, or to generate each universe independently stepping through internal time.
Although it may seems to be the same (our perception only having access to a slice of the multiverse), as in the end you get in both cases a physically consistent universe, the nature of the sampling process change the distribution of possible states. It also opens the possibility of shifting across various universes, not that we would be physically aware of (the previous universe and future universe), but we would benefit by experiencing a "better" universe. It's the same vibe of ideas which states that our universe has been fine-tuned for life to be possible.