Yes, GoL physics is simpler than Real Life physics.

RL follows quantum mechanics. As far as we know, its state cannot be recorded perfectly.

GoL is a Turing Machine. Its state can be recorded perfectly.

RL follows relativity. There is no equivalent in GoL.

Hashlife gives a method to compute GoL boards faster than processing each cell, and gives an exact answer. There is no equivalent for RL. At best there are probabilistic predictions. (There might be a 1E-50000 chance that the Sun won't rise tomorrow because all of the atoms in the Sun fuse at the same time and it blows up.)

I don't think we do know that. Maybe relativity and quantum mechanics are still 10 layers of complicated structures up from a far simpler ruleset.

> RL follows relativity. There is no equivalent in GoL

Of course there is an equivalent of relativity! There's a fixed, ultimate speed-limit (i.e. c) of once-cell/time-step. It is not possible to transmit information faster than this in GoL.

You can have C without relativity. There are no relative reference frames in GoL. Reactions only work at specific absolute speeds, and most of them only work at absolute speed 0.

Relativity can exist in an absolute environment like GoL if you consider the momentum of the quantum vacuum virtual particles. Look it up :-)

Seriously guys. Downvotes for talking about digital physics? Sad me.

https://en.wikipedia.org/wiki/Superfluid_vacuum_theory#Relat...

"Relativistic quantum field theory"

Downvotes for asking whether we're certain of some rather ignorant assumptions. -4 for me.

Um, my first comment was just referring to the fact that in an absolutely framed turing-complete environment. One can sprout a quantum vacuum full of constant noise, ie. constant producing and annihilating structures(analagous to virtual particles.)

This is already experimentally observed in our own universe. Quantum noise exists in vacuums.

If you look at C in GoL as the fastest an actual black square can propagate, then of course you'll validate your naive assumptions that our universe could never be digitally replicated by GoL. But if you take the idea of implementing a primordial sea of quantum noise, and looking at the GoL board not as physical particles directly, but as a deeper construct. Then you can actually replicate relativity.

http://arxiv.org/pdf/physics/9902034.pdf

> (There might be a 1E-50000 chance that the Sun won't rise tomorrow because all of the atoms in the Sun fuse at the same time and it blows up.)

To estimate probability of an event you must have a sample were both have occurred, to provide a probability for something like the Sun not rising tomorrow is pure non-sense.

You can easily calculate the probability of flipping heads a million times in a row, even though this also has never happened.

Because we have sampled all states of the hypothetical quarter, and are constricting many, many values concerned with flipping.

The same can't be said for the atoms in the sun.

We have complete, verified descriptions of what the possible states look like. You can predict precisely how long it will take a cannonball to fall to the ground (at least in a vacuum), even if you've never dropped it from exactly that particular height before.

"Precise" - to within some tolerance. At some point you reach the uncertainty limits allowed by quantum mechanics.

You also have to make an arbitrary decision about when the cannonball touches the ground. How much interaction is needed between the atoms of the cannonball and ground before you say there's contact?

These issues don't exist in the GoL universe.

We are sure that Game of Life physics is simpler than Real Life _chemistry_. There, fixed that for you.

It also helps that we GoL comes with the capacity to instantiate the universe in any configuration we wish, rather than being forced to coerce it into that state from scratch.

Not from scratch, but from inside!

Inside? Tell me what the outside is, then :)

Outside the Game of Life is easy to tell.

Outside the universe ain't. But even though, I can confidently say that we are definitely inside.

But does it make sense to even talk about inside and outside then when talking about the universe?

It makes about as much as uncountable infinite numbers. I can say everything in the universe is within a countably infinite distance of me. Thus, anything an uncountable infinite distance from me is outside the universe.

Not a very tangible idea, but not useless of purpose of reasoning about the affairs of things.

It's a bit of an abuse of notation. Talking about the inside definitely makes sense. (Talking about the outside is a bit like talking about the empty set.)

Yes. Real Life physics has been proven to be either nonlocal or nondeterministic (Bell inequalities). Life physics is both local and deterministic.