What if life arose in Conway's Game of Life?

This is a question that I've been thinking about off and on for a while, and I think it's a really interesting one. If I had an extra career's worth of time that I could do whatever I wanted with, I can easily imagine spending it on this! I really hope that I can make progress on it one day.

For now, I guess I'll write a few blog posts. I'd like to write a longer essay eventually, and this seems like a good way to write it out piece-by-piece.

A note on philosophy of blog-posting: I could spend a lot of time explaining or linking to Conway's Game of Life, the history of people thinking about life arising in Life, and all the nice progress that's been made lately (check out these forums, the Gemini "replicator", and Golly), but that's not much fun for me. So, I won't! Sorry, essay etiquette.

A spacefiller ("Max") found in 1995

Here are the thoughts about life in Life that I think it makes sense to explain first:

Fundamental laws, higher-level laws, and simulations

Life's rules can be thought of as being like the laws of physics. However, as far as we know, living organisms under our laws of physics only arise at scales orders of magnitude larger than the scale of the most "natural" entities under our laws of physics, and function mostly on the higher-level laws of chemistry and thermodynamics. That could be true for Life, too -- maybe the smallest organisms are astronomically large, and function mostly on higher-level laws that we've yet to find. (What could these laws be? I'd love to know!) However, for the purposes of this post, I'll be assuming that life in Life isn't like this, and functions on scales where the rules of Life are relevant. I think at least some of my arguments will apply at any scale, but I'm not sure.

An interesting sub-possibility is that "life" in Life occurs most frequently within simulations run on computers that naturally occur in Life, instead of in the "basement" laws -- for example, maybe it's easier to build a computer in Life that simulates our own laws of physics (which eventually give rise to life, at least in some cases) than it is to build a functional organism under Life's rules. Again, I'll assume that this isn't true, but it'd be pretty neat if we could show that it was!

Cosmology

I'm interested in when life "naturally" arises. However, Life's rules don't specify a start state, and so there's no built-in "cosmology". The setting that seems most natural to me is to start out with a random setting of each cell in an infinite plane to On or Off, with p being a "cosmological constant" that determines the probability of a cell starting On. (Maybe intelligent organisms will later be able to experimentally determine p by examining their world?) Since different p values may be more hospitable to life than others, I'd also like to let p vary gradually over the infinite plane, sort of like the different physical constants in the level-2 Tegmark multiverse.

A not-atypical view of a small region with a random starting configuration

What is life anyway?

I'm going with a pretty basic definition:

In Conway's Game of Life, a region of cells is alive if, when placed in some "reasonably natural" environment, produce two or more copies of itself.

You'll note that this definition is imprecise. I'm also leaving out some other common criteria like homeostasis, metabolism, and growth, because I think they might look quite different in Life than they do in our physics.

Abiogenesis

...just a teaser! I'll get to this next in another post.