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QC (in Berlin 7/29-???)

@QiaochuYuan

related to this, i've observed a funny pattern with respect to godel's incompleteness theorem specifically that the better someone understands the technical details behind it, the less philosophical or metaphysical significance they assign it

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David Chapman

@Meaningness

· Jan 24

How the foundational crises in math and physics a century ago undermined confidence in social institutions, leading—via the anti-rational New Age and Evangelical movements—to our current chaotic dysfunctions. https://meaningness.com/collapse-of-rational-certainty…

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4:48 AM · Feb 2, 2022·Twitter Web App

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QC (in Berlin 7/29-???)

@QiaochuYuan

·

Feb 2

Replying to

@QiaochuYuan

i guess personally i'm just used to it, like yes there's this eldritch horror at the bottom of mathematics that makes a mockery of our attempts to be absolutely certain of anything, and... it's just not a big deal! regular math works just fine anyway, so does everything else

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QC (in Berlin 7/29-???)

@QiaochuYuan

·

Feb 2

i do think the proof is worth understanding if only as good mental training. i'm not sure in what exactly but it's something like "thinking using multiple levels of reference." my favorite explanation of incompleteness is scott aaronson's here: https://scottaaronson.com/democritus/lec3.html…

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QC (in Berlin 7/29-???)

@QiaochuYuan

·

Feb 2

also separately y'all might have fun learning more about the historical context of the foundational crisis in mathematics. it must've been a weird time to live through https://en.wikipedia.org/wiki/Foundations_of_mathematics#Foundational_crisis…

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QC (in Berlin 7/29-???)

@QiaochuYuan

· Feb 2

Replying to @JakeOrthwein

it's really a shame to learn this material without the historical context of the crisis in foundations and what a big deal it seemed like at the time. logicomix is the closest thing i know of to a really dramatic presentation: https://amazon.com/Logicomix-search-truth-Apostolos-Doxiadis/dp/1596914521…

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QC (in Berlin 7/29-???)

@QiaochuYuan

·

Feb 2

i've been informed that forrest landry apparently finds the incompleteness theorem (or some generalization of it that i don't understand) deeply significant but i can't make heads or tails of it yet https://mflb.com/uvsm_8/ict_dialog_5.html…

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Matt "" Olson

@arachnocapital2

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Feb 2

Replying to

@QiaochuYuan

it me over the course of reading GEB and working through Negel and Newman's "Goedel's Proof" I went from a sense of cosmic wonder to "wow, that's a great fucking trick, nice work"

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af

@araknofennisti

·

Feb 2

Would you recommend that book?

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af

@araknofennisti

·

Feb 2

Replying to

@QiaochuYuan

The same goes for the whole “math is the universal language of the universe” vs “math is a thing humans came up with, and can alter to get useful and interesting results”

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Matjaž Leonardis

@MatjazLeonardis

·

Feb 2

Replying to

@QiaochuYuan

I have the exact same experience. Eventually you start asking Qs like: Why would you expect some random system of statements to be complete (no system with two models ever is)? Why could all truth about naturals be captured in a finite number of statements? Why this language? Etc

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QC (in Berlin 7/29-???)

@QiaochuYuan

·

Feb 2

another possible angle is to be like "well first-order logic just isn't that great then" (second-order PA has the natural numbers as a unique model)

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acidshill

@acidshill

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Feb 2

Replying to

@QiaochuYuan

yea i’ve never really got why people assign such significance to ‘sometimes there are true things you can’t prove with the information you have’ or ‘a system can’t show itself to be consistent’

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