Invariant Quotes (4 quotes)
Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant in what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a²-b² but was floored because the examiner unkindly asked for the factors of p²q².
Historical science is not worse, more restricted, or less capable of achieving firm conclusions because experiment, prediction, and subsumption under invariant laws of nature do not represent its usual working methods. The sciences of history use a different mode of explanation, rooted in the comparative and observational richness in our data. We cannot see a past event directly, but science is usually based on inference, not unvarnished observation (you dont see electrons, gravity, or black holes either).
In science there is and will remain a Platonic element which could not be taken away without ruining it. Among the infinite diversity of singular phenomena science can only look for invariants.
One evening at a Joint Summer Research Congerence in the early 1990s Nicholai Reshetikhin and I [David Yetter] button-holed Flato, and explained at length Shums coherence theorem and the role of categories in quantum knot invariants. Flato was persistently dismissive of categories as a mere language. I retired for the evening, leaving Reshetikhin and Flato to the discussion. At the next mornings session, Flato tapped me on the shoulder, and, giving a thumbs-up sign, whispered, Hey! Viva les categories! These new ones, the braided monoidal ones.