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jdh.hamkins.org | ||
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reportofanimals.com
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| | | | | DISCLAIMER: This is an essay I wrote for my Masters degree in 2023, part of a series I will be putting on this site to get me started. While I have changed some of my views and found new lines of inquiry since I wrote this, I feel there is value in it and after... | |
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scottaaronson.blog
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| | | | | In Michael Sipser's Introduction to the Theory of Computation textbook, he has one Platonically perfect homework exercise, so perfect that I can reconstruct it from memory despite not having opened the book for over a decade. It goes like this: Let f:{0,1}*?{0,1} be the constant 1 function if God exists, or the constant 0 function... | |
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scottaaronson.blog
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| | | | | (Thanks to Amit Sahai for spurring me to write this post!) The Background We all remember Gödel's First Incompleteness Theorem from kindergarten. This is the thing that, given a formal system F, constructs a sentence G(F) that's a mathematical encoding of "This sentence is not provable in F." If F proves G(F), then F proves... | |
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cre8math.com
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| | | This might sound like an odd question -- most students seem to think so when I ask it. The reason it sounds a little strange is that most students -- even when I taught at a magnet STEM high school -- think there's just one type of geometry: Euclidean geometry. This isn't surprising given the... | ||
