Comments by "Lawrence D’Oliveiro" (@lawrencedoliveiro9104) on "THIS 1936 Paper Theorized the FIRST Computer EVER, by Alan Turing" video.

  1. Turing also published a groundbreaking paper in an entirely different field, namely biology. He was considering the issue of how the amorphous mass of cells making up a fertilized embryo can suddenly decide that this is its “front” and this is its “back” and that is “the left side” and that is “the right side”.
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  2. 7:51 Church and his student Kleene did some interesting work with the λ-calculus. For example, they showed how mathematical paradoxes (like Russell’s paradox) could be represented by expressions that could be manipulated logically without the whole world collapsing about your ears. Mathematicians go to great lengths to try to ensure that their theories are free of paradoxes. But I think λ-calculus shows how you can tame the paradox and not be afraid of it.
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  3. 6:18 Worth making something very clear here: the program (call it D, the “deciding program”) that decides whether a given program (call it P, the “problem program”) will terminate for input data I is taking both P and I as input data. In other words, a program is input data to another program! This is a key point about the nature of the Turing machine, and also of all our electronic digital computers: programs and data are both represented using the same set of symbols that can be stored in the memory of the machine. The only difference between the two is, a stream of symbols becomes a “program” only because you point the CPU at the start of that stream and say “run this as a program”.
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  4. 0:14 Also worth watching, if you like the dramatization approach, is a BBC TV movie about Turing from 1996, called Breaking The Code . This was based on a stage play from 1986.
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  5. 4:06 Gödel’s name sounds more like “guh-del” then “goo-del”.
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  6. Yeah, but Turing’s tape was erasable.
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  7. 5:20 That “which implies” part has not actually been proven. It’s called the “Church-Turing thesis”, and the mathematical term for it is a “conjecture”. It seems to be true, as far as we can tell, in all the examples so far, but, as for the general case, we can’t be sure either way.
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