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What would you say are the top ten theorems of Life?

Probably #1 is that no spaceship can go above speed (M,N)/2(M+N) for M and N pos. integers.

2. That life can do universal computations

3. That orphans exist

I would go with: there exist a spaceship of any valid speed and direction i.e. any speed slower than (M,N)/2(M+N).

simsim314 wrote:I would go with: there exist a spaceship of any valid speed and direction i.e. any speed slower than (M,N)/2(M+N).

Has that actually been proven? Plus, aren't speeds equal to (M,N)/2(M+N) an open question in any case?

simsim314 wrote:I would go with: there exist a spaceship of any valid speed and direction i.e. any speed slower than (M,N)/2(M+N).

I think your wording is ambiguous there. Certainly there exists a ship for any speed strictly slower than (M,N)/2(M+N) (and that is an amazing theorem!), but apart from c/2 and (1,1)c/4 we don't know whether any ships with exactly that speed exist.

Macbi wrote:but apart from c/2 and (1,1)c/4 we don't know whether any ships with exactly that speed exist.

Good point. Interesting enough - no natural nor constructable ship with this property exists, or has been proven to exist.

A for awesome wrote:Has that actually been proven?

Proven yes, by a theoretical construction (actually I've found several ways to construct a universal ship). But no actual construction was made yet...

#4. There are no period-3 phoenixes.
#5. The Block is the only (finite) still life where all cells have three neighbors.

Bullet51 wrote:#4. There are no period-3 phoenixes.

I thought it was proven that there were no p3 phoenices.

AforAmpere wrote:

Bullet51 wrote:#4. There are no period-3 phoenixes.

I thought it was proven that there were no p3 phoenices.

Exactly, this is why this is in the Theorems thread and not Unsolved Conjectures.