> Turing says that a certain space, the space of all compact subsets of [0,1]^2 endowed with the metric "integral of minimal distance required to transform {1 ink at each point of P1} u {infinite amount of ink at (2, 0)} into {1 ink at each point of P2} u {infinite amount of ink at (2,0)}", is conditionally-compact. How is that related to the article's argument?
This is not obvious, I think. The article has moved away from Turing's "integral of the distance we have to transfer ink", instead using "maximum distance we have to transfer any ink", and I don't have a great intuition for whether this is a legit transformation of the argument. (I'm sure both proofs are correct, but it's not obvious to me that they are the same proof.)
