Antipasti (VIII)

Yet more toothsome morsels, to whet your appetite.

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What men are poets  who can speak of Jupiter as if he were like a man,  but if he is an immense spinning sphere of methane and ammonia  must be silent?

 Ifyou have a space with enough structure to keep things apart which ought to be, and if the space itself is not too huge, then you can define a distance between any pair of elements. The function that specifies this distance  is called the “metric”…

Once you know a metric exists, there are all kinds of consequences.  You can use that knowledge to work backward  and deduce things about manifold topology, without knowing the exact metric

Though the superficial similarity of the quantum case and the U.M.T.   doesn’thold up,  there does appear to be a rather arresting analogy with post-Chomskyan linguistics.

A metric space can be a very odd object.  It may fail to have almost any property one can think of.

Reverse narrative always struck me as a dubious device, as it is no way to tell a moral story (morality requires causality, and an onward-unfolding free will); but it’s a superb way to explore epistemology.