Tag Archives: Stefan Banach

Space

The word ‘space’ has acquired several meanings, which is what you would expect of such a sexy, primitive, metaphorically rich, eminently repurposeable concept. Outer space, of course, is where cosmonauts, Hubble telescopes, television satellites, and aliens reside. It’s ℝ³, or … Continue reading

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Nonterminating decimals do not make sense.

The Banach-Tarski paradox proves how f#cked up the real numbers are. Logical peculiarities confuse our intuitions about “length”, “density”, “volume”, etc. within the continuum (ℝ) of nonterminating decimals. Which is why Measure Theory is a graduate-level mathematics course. These peculiarities … Continue reading

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mms://velblod2.ijs.si:80/v002/08/baajzm56lyuqznmadeotndh5gi6xkxxw.wmv New logics. File this under Mathematics of argumentation, truth, validity, and propositions. Minute 11:30 “We have certain proof-theoretic intuitions about valid ways of reasoning. And we have other model-theoretic intuitions about what can be true. And we want those to … Continue reading

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