New mathematical framework reshapes debate over simulation hypothesis

> The big riddle of Universe is, how

A lot of people are more interested in the Why of the Universe than the How, though.

How is an implementation detail, Why is "profound". At least that's how I think most people look at it.

Someone did another 'Kleene-Turing' on the whole issue with "the origin"?

bad bad not good.

This all assumes there's no computation beyond a Turing machine, right? Therefore, this assumes reality is a simulation on a finite set of rationals?

So, as long as one believes in continuum, this is just toying around?

Konrad Zuse was a German pioneer in computing, best known for building the Z3 in 1941—the world's first functional programmable digital computer. Later in his career, he explored profound philosophical and theoretical ideas about the nature of the universe. Rechnender Raum (literally "Computing Space" or "Calculating Space") is the title of his groundbreaking 1969 book (published in the series Schriften zur Datenverarbeitung). In it, Zuse proposed that the entire universe operates as a vast discrete computational process, akin to a giant cellular automaton. He argued that physical laws and reality itself emerge from digital, step-by-step computations on a grid of discrete "cells" in space, rather than from continuous analog processes as traditionally assumed in physics. This idea challenged the prevailing view of continuous physical laws and laid the foundation for what we now call digital physics, pancomputationalism, or the simulation hypothesis (the notion that reality might be a computation, possibly running on some underlying "computer"). Zuse's work is widely regarded as the first formal proposal of digital physics, predating similar ideas by others like Edward Fredkin or Stephen Wolfram.

The problem of computers is the problem of time : How to obtain a consistent causal chain !

The classical naive way of obtaining a consistent causal chain, is to put the links one after the other following the order defined by the simulation time.

The funnier question is : can it be done another way ? With the advance of generative AI, and things like diffusion model it's proven that it's possible theoretically (universal distribution approximation). It's not so much simulating a timeline, but more sampling the whole timeline while enforcing its physics-law self-consistency from both directions of the causal graph.

In toy models like game of life, we can even have recursivity of simulation : https://news.ycombinator.com/item?id=33978978 unlike section 7.3 of this paper where the computers of the lower simulations are started in ordered-time

In other toy model you can diffusion-model learn and map the chaotic distribution of all possible three-body problem trajectories.

Although sampling can be simulated, the efficient way of doing it necessitate to explore all the possible universes simultaneously like in QM (which we can do by only exploring a finite number of them while bounding the neighbor universe region according to the question we are trying to answer using the Lipschitz continuity property).

Sampling allows you to bound maximal computational usage and be sure to reach your end-time target, but at the risk of not being perfectly physically consistent. Whereas simulating present the risk of the lower simulations siphoning the computational resources and preventing the simulation time to reach its end-time target, but what you could compute is guaranteed consistent.

Sampled bottled universe are ideal for answering question like how many years must a universe have before life can emerge, while simulated bottled universe are like a box of chocolate, you never know what you are going to get.

The question being can you tell which bottle you are currently in, and which bottle would you rather get.