Optimization Concepts in the Game of Life

A good source for the technology available in the Game of Life is the draft of Nathaniel Johnston and Dave Greene's new book "Conway’s Game of Life: Mathematics and Construction".

Is microCOVID "badness" superlinear?

The if the probabilities of catching COVID on two occasions are x and y, the the probability of catching it at least once is 1 - (1 - x)(1 - y) which equals x + y - xy. So if x and y are large enough for xy to be significant, then splitting is better because even though catching it the second time will increase your viral load, it's not going to make it twice as bad as it already was.

Agency in Conway’s Game of Life

The link still works for me. Perhaps you must first become a member of that discord? Invite link: https://discord.gg/nZ9JV5Be (valid for 7 days)

Agency in Conway’s Game of Life

The weird thing is that there are two metrics involved: information can propagate through a nonempty universe at 1 cell per generation in the sense of the l_infinity metric, but it can only propagate into empty space at 1/2 a cell per generation in the sense of the l_1 metric.


Agency in Conway’s Game of Life

You're probably right, but I can think of the following points.

Its rule is more complicated than Life's, so its worse as an example of emergent complexity from simple rules (which was Conway's original motivation).

It's also a harder location to demonstrate self replication. Any self replicator in Critters would have to be fed with some food source.

Agency in Conway’s Game of Life

Yeah, although probably you'd want to include a 'buffer' at the edge of the region to protect the entity from gliders thrown out from the surroundings. A 1,000,000 cell thick border filled randomly with blocks at 0.1% density would do the job.

Agency in Conway’s Game of Life

This is very much a heuristic, but good enough in this case.

Suppose we want to know how many times we expect to see a pattern with n cells in a random field of area A. Ignoring edge effects, there are A different offsets at which the pattern could appear. Each of these has a 1/2^n chance of being the pattern. So we expect at least one copy of the pattern if n < log_2(A).

In this case the area is (10^60)^2, so we expect patterns of size up to 398.631. In other words, we expect the ash to contain any pattern you can fit in a 20 by 20 box.

Agency in Conway’s Game of Life

The glider moves at c/4 diagonally, while the c/2 ships move horizontally. A c/2 ship moving right and then down will reach its destination at the same time the c/4 glider does. In fact, gliders travel at the empty space speed limit.

Agency in Conway’s Game of Life

Most glider guns in random ash will immediately be destroyed by the chaos they cause. Those that don't will eventually reach an eater which will neutralise them. But yes, such things could pose a nasty surprise for any AI trying to clean up the ash. When it removes the eater it will suddenly have a glider stream coming towards it! But this doesn't prove it's impossible to clear up the ash.

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