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ERRATA: • The "Church-Turing Thesis" is different from the "Church-Turing Theorem". The "theorem" is the claim which I discussed in the video- namely, that the Turing machine and lambda calculus are equally powerful. The "thesis" is the informal claim that the two of these systems are a sufficient formalization which capture the idea of "arbitrary computation". • I claimed in the end of the video that this was the first example of animated visual lambda expressions. Paul Brauner has some videos here: • Lambda Diagrams . I probably should have chosen my words more carefully- I meant animating the interpolation between two consecutive terms during beta reduction! • It seems that both lisp and rust blur the line between functional and imperative programming more than I realized, so take that chart at the end with a grain of salt! JOIN OUR DISCORD! / discord Support us! 2swap: / 2swap 6884: https://ko-fi.com/iam6884 Sources and Links: Tromp's Diagrams, showcased throughout the video: https://tromp.github.io/cl/diagrams.html At 4:28, a number of visualizations for the Lambda Calculus were shown. These include: (Top Left) David C Keenan's Graphical Notation for the Lambda Calculus: https://dkeenan.com/Lambda/ (Top Center) A notation I found on Robin Piedeleu's site, but which is likely much older: https://piedeleu.com/posts/diagrammat... (Top Right) de Brujin indices: https://en.wikipedia.org/wiki/De_Brui... (Bottom Left) Vex (Wayne Citrin, Richard Hall, Benjamin Zorn): https://www.researchgate.net/publicat... (Bottom Right) Visual Lambda Calculus (Viktor Massalõgin): https://bntr.planet.ee/lambda/work/vi... / https://github.com/bntre/visual-lambda Lecture Notes on the Lambda Calculus (book): https://www.amazon.com/Lecture-Notes-... 6884's Music: https://6884.bandcamp.com/ This video was rendered using SwapTube! https://github.com/2swap/swaptube Oh, also, this is my first time using auto-dubbed tracks. I am VERY IRRITATED to have to use this... I happen to speak a few languages on the list and I would have preferred to dub it myself. As far as I can tell, I as a creator am not even given the opportunity to do so. If anyone else knows of a way, please comment :) Also, let me know if the AI dub in your language is particularly poor.