muzik wrote:3c/14 is a pretty weirdly common speed. There's a pi wave that travels at that speed diagonally, pulsars replicate at that speed, and this block moved at that speed... yet we still have no spaceship.

You can get that block to move at quite a few possible speeds in that general neighborhood -- it's only likely to have a 3 in it because the block moves three steps diagonally per two gliders. I don't think that really adds much to the weirdly-common count...! And pulsars move at 3c/15, don't they? -- as in the

p15 pre-pulsar spaceship. And that's orthogonally not diagonally, so that would be the start of a different count anyway.

The lack of a spaceship seems not too surprising at all, considering that period 14 spaceships

are maybe a thousand times harder to find than period 13 spaceships,

which are maybe a thousand times harder to find than period 12 spaceships,

which are maybe a thousand times harder to find than period 11 spaceships,

which are maybe a thousand times harder to find than period 10 spaceships,

which are maybe a thousand times harder to find than period 9 spaceships,

which are maybe a thousand times harder to find than period 8 spaceships,

which are maybe a thousand times harder to find than period 7 spaceships,

which are currently (

spaghetti monster) taking maybe a month of CPU time to run a successful search.

[I'm practicing saying this in different ways, to see if one way helps build intuition better than another. Apologies if you've heard it all before.]

"A thousand" may be a serious underestimate, but it wouldn't really matter if it were an overestimate. And it's perfectly possible that there may happen to be very tiny spaceships for some of those speeds, but it doesn't change the general pattern.

The Exponential Wall
If there's no lucky tiny spaceship, then the number of unknown bits to be searched goes up linearly, so the size of the search problem goes up exponentially... roughly speaking. To us CPU-limited humans, an exponential curve like this looks like a wall at any given time -- and the only effect of Moore's Law (a much gentler exponential curve than my hypothesized factor of a thousand) is to gradually move where the wall is.

Right now the wall seems to be around period 8. Most likely we could already move the wall beyond period 8 by setting a high-performance computing cluster to work on a c/8 or 3c/8 search or whatever, for a month or two, or otherwise setting up a distributed computing project. But then N*c/9 would still look just as hard to reach as N*c/8 does now. This has serious implications for N*c/10, let alone N*c/14.

Wild Random Speculations
As soon as a lucky 3c/14 spaceship pops up, with some handy sparks or a nice little sparky tagalong, then suddenly the odds get much better of adding in support for known waves that travel at the same speed, just the same as happened with the spaghetti monster spaceship.

But it's hard to argue that the existence of the pi-wave makes the hypothetical existence of a tiny spaceship any more likely. To support the same speed in a limited area, it will probably need a completely unrelated mechanism for movement.