The Eternal Doorman

38:41 See Pupina Plomer on the Children of Llullaillaco . Subscribe to Pupina Plomer . 

See Doomsday: Friday, 13 November, A.D. 2026. At this date human population will approach infinity if it grows as it has grown in the last two millenia by Heinz von Foerster, Patricia M. Mora and Larry Amiot. Subscribe to Anton Petrov .

I was recently told that it's unreasonable to expect anybody to read more than 500 words on any subject. Is that true? I often read more than 500 words, especially of books. But if I have to explain what words like epistemology and ontology mean as well, then that doesn't leave many words left. The best part of this lecture of Searle's is at 23:24 . I get into detail, with some examples from the 80s explicitly citing Searle in this post:  John Searle's Chinese Room Argument . One way to save words is to leave it up to the reader to look things up themselves, but very often they don't do that, even when you provide links for them to click: I suppose that's because links just lead to more words! See Collaborative Mathematics . Subscribe to Philosophy Overdose . 

You can read notes on Martin-Löf's lecture given in Padua in 1980 here:  Giovanni Sambin's notes on Per Martin-Löf's Intuitionistic Type Theory . My comment : 40:32 Thorsten "You only need the notion of a type... Then I can explain a proposition,..." I remember when you did that a few weeks ago , and you explained it, but did anybody actually understand your explanation? I know I didn't! 30:38 On intensional and extensional theories and "running them in parallel". I wonder how far you could get by modelling functions with bijections between pairs, i.e. permutations on graphs. I did something like this once in the iterative construction I described in this post:  Brady Haran interview with Terence Tao . It produced some very interesting constructions full of amazing symmetries. See also  Category Theory May Actually be a Disease  and Emma Tye on Martin-Löf Type Theory . What I did was construct something like a closure operator on an abstract algeb...

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They were Inca human sacrifices made in the late fifteenth century. See  Children of Llullaillaco . In 1999 the almost perfectly preserved remains of these three children were discovered near the summit of the volcano. Since 2007 they have been exhibited in a specially constructed museum in Salta, Argentina. Descendents of these people still maintain the beliefs in the mountain deities to whom these sacrifices were made, ... Subscribe to Pupina Plomer . 

You really need these in computer science, chemistry, biology, physics and every other subject, because the potential for abuse by corporate, military-industrial power structures is enormous. See  Brady Haran Interview with Hugo Duminil-Copin  and  Brady Haran interview with Terence Tao .  Subscribe to  SAIR . 

See https://msp.cis.strath.ac.uk/msp101.html  I wish I had read this description of it before, because now it makes a heck of a lot more sense!  The simply-typed lambda calculus (STLC) gives us a nice Curry-Howard correspondence with propositional logic by treating the function arrow of STLC as implication. From this we can compute proofs as programs. But a natural question is then: what about predicate logics instead of propositional? Martin-Löf Type Theory (or Intuitionistic Type Theory) is a type theory based on predicate logic, with type constructions representing existentially quantified variables (Sigma) and universally quantified variables (Pi). We can also construct inductively defined families - W-types - as well-founded trees. Note that Martin-Löf's original paper was inconsistent due to having the type-in-type paradox, and that he later introduced a predicative version with universe hierarchies. In this introduction, we assume knowledge of the STLC and natural-deduc...

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