Thinking about discontinuous jumps: So, improving a search algorithm from order n squared to order n log(n) is a discontinuous jump. It appears to be a jump in speed...

However, using an improved algorithm to search a space of possible designs, plans or theorems an order of magnitude faster could seem indistinguishable from a jump in quality.

Reducing error rates seems like an improvement in quality, yet it may be possible to reduce error rates, for example, by running more trials of an experiment. Here, speed seems to have produced quality.

Going the other way around, switching a clinical trial from a frequentist design to an adaptive Bayesian design seems like an improvement in quality-yet the frequentist trial can be made just as valid if we make more trials. An apparent improvement in quality is overcome by speed.