Would Aliens Understand Lambda Calculus
summary
Argues lambda calculus may be invented not discovered and supports that with philosophy of mathematics and cognitive science, not just romance. Shows Curry–Howard correspondence as a sociologically tuned fit (cartesian closed categories, intuitionistic proofs, specific lambda variants), connects evaluation to embodied container schema and beta reduction as a directed, irreversible operation, and tests plausibility against concrete alien examples (Arrival, Solaris, chaotic gas-cloud) to show which embodied experiences would or would not produce lambda-style reasoning.
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chapters (34)
- 0:00Intro
- 1:26Twitter discussion
- 2:10Random books
- 2:44Platonism
- 4:08The Romans of Mathematics
- 5:09The Social Process
- 7:33Culture
- 8:30Hilbert
- 9:59Where mathematics comes from
- 11:11Cognitive science of mathematics
- 11:30Metaphors
- 12:57Derivatives
- 13:41Mathematical Concepts
- 18:31Cognitive Science
- 19:30Curie Howard Lambic Correspondence
- 20:06Lambda Calculus
- 20:49Is there something deep
- 21:03Category proofs
- 21:53Program verification
- 22:35Perspective
- 23:05Evolutionary Fit
- 24:14Cultural Background
- 25:22Mathematical Network
- 26:02Cognitive Scientists
- 27:44The Quest
- 28:15Romance of Mathematics
- 29:12Cognitive Science Aspects
- 29:28Container Schema
- 32:26Reduction
- 32:53Direction
- 34:59Solaris
- 36:02Gaseous Aliens
- 36:57Star Trek Aliens
- 38:41Directionality
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