Yes. Whereas in L_inf, they are the same speed. This is exactly the argument I was trying to make. That we want a metric that considers the glider to be faster than the c/4 orthogonal space ship since the glider never takes any longer than the c/4 orthogonal space ship to reach any particular location, and frequently gets there much faster.Mats wrote:I'm sorry but I'm still having problems understanding your argument. After substitution you get: "the glider's travel is always less than or equal to the c/4 ortogonal spaceship's travel time." In L_1 the glider is faster than a c/4 ortogonal spaceship.quintopia wrote:Substitute "a c/4 orthogonal spaceship" for every occurrence of LWSS and it should make more sense.

*facepalm* You're the one that claimed your metric was based on a norm of some sort by calling it "L_'not quite infinity but very large'"Mats wrote:Why would you need a normed space to sort spaceship speeds?quintopia wrote:makes absolutely no sense. L_p is a set of normed spaces. There is no norm that satisfies your lexicographical ordering.

However, I will give you this: there is a norm that gives lexicographical ordering if you're willing to allow it to be a surreal-valued function.

In any case, which property of a norm is it that you think is not necessary to give a sensible measurement of distances travelled?

Yes of course we are only concerned with the behavior of spaceships in empty space, but I'm not sure why it matters that a glider could not travel to (0,x) in a vacuum: when discussing speeds of patterns, we can, without loss of generality, pause the simulation, rotate the pattern by 90 degrees, and restart the simulation. This takes zero generations, and, in a sensible metric, would not affect the total distance traveled, so the final speed calculation will still be reliable. In all the L_p-normed spaces, this property holds.HartmutHolzwart wrote:it's the fastest velocity in empty space. Btw. a glider could not change its direction in empty space and would never get to (0,2x).