tildedave · HackerTrans

3 года назадdiscuss

This book is the reason I was able to pass my computer architecture exams in grad school. Just lugged the 800 page monstrosity around an entire semester and read it every chance I could. A really wonderful book ... I should get a recent copy and re-read it again.

tildedave

5 лет назадdiscuss

Kevin Conrad has a more in-depth paper on this at roughly the same maturity level, also motivated by Feynman's story: https://kconrad.math.uconn.edu/blurbs/analysis/diffunderint....

tildedave

6 лет назадdiscuss

The continuum hypothesis is more like Euclid's parallel postulate than a Gödel sentence - assuming ZFC consistent there are models with CH true and CH false (the cardinality of the continuum doesn't have to be the first uncountable cardinal).

Everything gets qualified with "assuming ZFC consistent" or "assuming Peano consistent" because any inconsistent theory proves any statement. More of a proof technicality than anything too profound.

There is a construction of a model of Peano arithmetic, so it is consistent, as long as you accept the system used in the proof: https://en.wikipedia.org/wiki/Gentzen%27s_consistency_proof

Not sure if this sheds light on the parent commentator's question ... the terminology can be quite tricky.

tildedave

6 лет назадdiscuss

As someone who took a number of mathetical logic classes between undergrad/graduate I always found this Gödel-sentence argument on the face-laughable, since the logical inconsistency was so easy to repair. My favorite critique of this was Hans Moravec's dialogue between Penrose and a robot AI, having resurrected his brain long past humanity's extinction: http://www.calculemus.org/MathUniversalis/NS/10/10moravec.ht...

tildedave

6 лет назадdiscuss

Not a historian, but _Why the West Rules - For Now_ by Ian Morris was a good read. Covers the sweep of world history with the audacious goal of quantifying human development at all moments in history. It mainly focuses on the west (starting in the Mesopotamian region) and the east (starting in the area surrounding the Yellow river) and addresses questions like "why didn't China discover America" (basically - too far away). You might also find it interesting!

tildedave

6 лет назадdiscuss

Sorry to point you to more references, but the AskHistorians subreddit has a pretty good survey of views on the issue. https://www.reddit.com/r/AskHistorians/search?q=zinn&restric...

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