Mathematical Proof Debunks Idea the Universe Is a Computer Simulation

> Arithmetic expressiveness; LQG can internally model the natural numbers with their basic operations. This is important as quantum gravity should reproduce calculations used for amplitudes, curvature scalars, entropy, etc in appropriate limits. Both string theory [34, 37] and LQG [35, 38] satisfy this by reproducing GR and QM in appropriate limits

Here the citations are four entire books. How am I supposed to very that LQG can model N with that?

Godel then latches onto that to create an alphabet of the symbols which then are mapped to numbers; thus formulas are even bigger numbers, and derivations are even bigger bigger numbers. So for any statements there should be a derivation that prove the statement is true or a derivation that proves the statement is false. Of course most statements will be false, but even then there will be a derivation showing so.

Then Godel does some clever manipulation to show that there will be some statements for which there can be no such derivation in either way. But that does not need the physics theory to express things about itself. It only requires to be mathematically complex enough (it'd be weird if a theory of everything was simpler than Robinson Arithmetic) and that it has rules of derivation of its statements (ie, that mechanical math can be applied to deduce the truth of the matter from the first principles of the theory).

Of course, the actual undecidable godel number and the associated physical proposition would be immensely complex. But that is only cause nobody has tried to improve on Godel's methodology of assigning numbers to propositions. He used what was simpler, prime factorization, cause it was easy to reason about, but results in astronomical numbers. But there is no reason a better, less explosive way of encoding propositions could be found that made an undecidible Godel number to be translated into something comprehensible.

But this is largely unnecessary; Godel proof forces the mathematical system to speak about itself and then abuses this reflection to create a contradiction. It means the system is not complete, that there are statements in the system that cannot be proven from its first principles and derivation rules; the fact that the one Godel showed to exist is self referential does not mean all the undecidable propositions _are_ self referential. There well could be other, non self referential undecidable propositions, that could very well have a comprehensible physical interpretation.

And, regardless of the universe being a simulation or not, the physical theory will ultimately need to deal with this incompleteness.

But, making proofs about the capabilities of the exact types of computation we currently use can still be interesting.

I think it is worse hypothesis than even Drake's equation - there, at least we know all factors, we just have no idea what their value is and with sample size of 1, the current uncertainly is like 40+ orders of magnitude. That still brings us closer to "is there inteligent life in universe" answer than we ever got with "is this universe a simulation".

It doesn't make obvious sense to waste such vast amount of energy for absolutely no purpose that we can observe: surely you could add a grain of doubt in your absolute statements no ?

The universe is probably nothing very interesting, and reality depressingly obvious once we figure it out. It's like all these astrological sky maps they were doing to predict the mood of the gods above, before we realized we were a rock turning around an hydrogen ball, itself turning around the galactic center, completely non-special, like every other block of rock out there.

Being in a simulation is just a way for you to replace god with a machine equivalent. You want a purpose, a father figure, an observer and a designer. Sadly, I think you and I are as precious as an ant, completely not part of any simulation, having no purpose and barely any effect on the universe. We're here because we could and we'll disappear because we must, with barely a blip, while everything in the universe is turning around senselessly.