In case someone doesn't already know it, here is Conway's Game of Life simulated in Conway's Game of Life:
Previous discussion: https://news.ycombinator.com/item?id=24323011
My question: does anybody know what the ratio of trade-off between time and space is for Hashlife? I haven't been able to find anything from my searches.
But if you have 640 kilobytes memory (ought to be enough for anyone), that means your cache will have 2^640000 entries.
When transforming to game of life every bit of memory becomes many cells in the grid, so the requirements for that would be even worse.
But this doesn't let you magically mine bitcoin in fast-forward, because in order to mine bitcoin, you need to insert random bytes into your block and keep changing them until you get lucky and find a hash that starts with a certain number of zeroes. This effectively guarantees that you aren't going to have cached computation snippets that are big enough to skip any meaningful amount of work.
At best, you might be able to fast-forward at the instruction level granularity, at which point you might as well be mining on your CPU.
> Hashlife can take the same length of time to compute from generation N to generation 2N for any large enough N - it has logarithmic complexity.
If 2N takes as much time as N, then 4N takes as much time as N, and so 8N takes as much as N, and so... (for any large enough N). This seems to indicate--asymptotically--constant time, not logarithmic.
It’s reminiscent of what it feels like to dig deeply into a metabolic or reproductive process in a cell and be overcome with the sheer complexity of it, then look at the back of your hand and realize it’s all happening right there, now.
Basically it feels a bit like life.
Even if the real world has a creator (or is a simulation), my money would be on it being impossible for the creator to know what is going to happen. Life would be the simulation.
All of this is happening in my body right now so i can type these letters: WTF
once you look at microbiology you cannot unsee that it looks just like a massive, complicated stochasticaly-driven computer
Every time I go down this rabbit hole I get re-convinced of panspermia. Maybe when I retire I'll study enough statistics and molecular biology to try to get my head around it. Or by then we'll be talking to aliens and the question will be moot.
I've read Wolfram claim this, but as a conjecture, iirc. Is there a formal proof that in order to predict life patterns we essentially need to run the cellular automaton?
Oddly beautiful seeing it run too. And the gliders flowing around put me in mind a bit of the ants that run Pratchett's Hex.
I probably could do it, understanding all the parts implies that. Eventually. Just not in a reasonable amount of time, and perhaps not as neatly.
I believe it to be a system based on collision-based computing .
My hunch is this: Matter and Energy have a duality that is analogous to code and data. Einstein likened the speed of light to the speed of information. Wolfram/Toffoli/Fredkin or well, any other Cellular Automata specialist, studied the rate of propagation in CA, Lyapunov exponents. 
Now it seems to me, that if we can create a digital system which provides for code <-> data duality analogous to Mass–energy equivalence , then we should be able to get stable structures that hold data, and stable processes that process data. I have tried for many years on and off with various CAs. Many of the CAs have been unconventional, like cells containing arrays of particles, particles being objects rather than simple numbers or enum types. And CAs based on reals or complex numbers or associated vector fields.
https://github.com/churchofthought/HexagonalComplexAutomata (WebGL 2.0)
https://github.com/churchofthought/Grautamaton (WebGL 2.0)
Example of a Complex-valued Cellular Automata based on Sandpile dynamics
Big Bang (video): https://photos.app.goo.gl/K7fovThbvatpmGQy5
End result (image): https://photos.app.goo.gl/n5amaqn8ZLVocn1Z6
This doesn't mean the patterns would visually look like cells and membranes though...
without any spoilers there are literally tens of books out there that explore this very same idea. (some of them hard scifi)
I would counter your question by asking, isn't your comment here practically and intellectually useless?
We need more than that.
We need breathing, pissing, shitting, fighting, and sex.
We do not know how ‘soup of chemistry’ does information processing. (e.g. biology)
The more it looks like soup, the more we might be able to intuit how to tackle things that are unbounded in complexity. E.g. how do millions of cells coordinate growth to make a new organ/repair and then stop, what are the chemical initial conditions that generate this complex orchestra, what tells it to stop, can we speak that language if we knew it?
With computer in GOL you have GOL which will do the pattern transformations.
If you say it's not pebbles then imagine a mechanical computer built out of them. Provide some kinetic energy and rocks begin to compute just as the silicon in your computer begins to compute when you put electrical energy into it.
For any passerbys