- solid — the category
FinSet, a sack of wheat , a bag of marbles; atoms; axiom of choice; individuation. The urelemente or wheat-kernels are interchangeable although they’re technically distinct. Yet I can pick out just one and it has a mass.
- liquid — continuity; probability mass; Lewis’ gunky line; Geoff Hellman; the pre-modern, “continuous” idea of water; Urs Schreiber; Yoshihiro Maruyama; John L Bell
- gas — Lebesgue measure theory; sizing Wiener processes or other things in other “smooth” categories; here I mean again the pre-atomic vision of gas: in some sense it has constant mass, but it might be so de-pressurised that there’s not much in some sub-chamber, and the mass might even be so dispersed not only can you not pick out atoms and expect them to have a size (so each point of probability density has “zero” chance of happening), but you might need a “significant pocket” of gas before you get the volume—and unlike liquid, the gas’ volume might confuse you without some “pressure”-like concept “squeezing” the stuff to constrain the notion of volume.
Posts tagged with imagination
The spirit of mathematics is not captured by spending 3 hours solving 20 look-alike homework problems. Mathematics is thinking, comparing, analyzing, inventing, and understanding.
The main point is not quantity or speed—the main point is quality of thought.
A rock pile ceases to be a rock pile the moment a single man contemplates it, bearing within him the image of a cathedral.
Antoine de Saint-Exupéry
But there were also more profound features, which took me a long time even to notice, because they are so at odds with modern experience that neither New Guineans nor I could even articulate them. Each of us took some aspects of our lifestyle for granted and couldn’t conceive of an alternative.
Those other New Guinea features included the non-existence of “friendship” (associating with someone just because you like them), a much greater awareness of rare hazards, war as an omnipresent reality, morality in a world without judicial recourse, and a vital role of very old people. …
Many of my experiences in New Guinea have been intense—a sudden encounter at night with a wild man, the prolonged agony of a nearly-fatal boat accident, one broken little stick in the forest warning us that nomads might be about to catch us as trespassers …
Jared Diamond, The World Before Yesterday