This is bad, because the resource fraction for the true class goes to 0 as we increase the number of classes.
I think this is an important point you make, but… you seem to be looking at r/n as both n and r go to infinity, which makes my brain hurt. Whether this is a problem seems to depend on how fast r and n go to infinity, as if, for instance, r=n^2 then as n goes to infinity, ri/r goes to 0 and ri goes to infinity. If an increase in physical resources leads to a greater than linear increase in concept space (due to having more processing power) then this would become problematic.
Also I am confused because at first C1 is described as the “central concept of chocolate” the concept most probable to represent actual chocolate, and later C1 is described as the “true class” as if the mode of a probability distribution has probability 1.
I think this is an important point you make, but… you seem to be looking at r/n as both n and r go to infinity, which makes my brain hurt. Whether this is a problem seems to depend on how fast r and n go to infinity, as if, for instance, r=n^2 then as n goes to infinity, ri/r goes to 0 and ri goes to infinity. If an increase in physical resources leads to a greater than linear increase in concept space (due to having more processing power) then this would become problematic.
Also I am confused because at first C1 is described as the “central concept of chocolate” the concept most probable to represent actual chocolate, and later C1 is described as the “true class” as if the mode of a probability distribution has probability 1.
Fixed the sloppy terminology about the central / true concept, thanks for pointing it out!
See Addendum on asymptotics in the post.