It might as well be my own hand on the madman’s lever—and yet, while I grieve for all innocents, my soul is at peace, insofar as it’s ever been at peace about anything.
Psychopath.
It might as well be my own hand on the madman’s lever—and yet, while I grieve for all innocents, my soul is at peace, insofar as it’s ever been at peace about anything.
Psychopath.
Gödel makes everyone weep. For tears of joy, my top pick is still Doug Hofstadter’s Gödel, Escher, Bach, which is suitable for undergraduates. Another strong classic is Raymond Smullyan’s To Mock a Mockingbird. Both of these dead-trees are worth it; I personally find myself cracking them open regularly for citations, quotes, and insights. For tears of frustration, the best way to fully understand the numerical machinery is Peter Smith’s An Introduction to Gödel’s Theorems, freely available online. These books are still receiving new editions, but any edition should suffice. If the goal is merely to ensure that the student can diagonalize, then the student can directly read Bill Lawvere’s 1968 paper Diagonal arguments & Cartesian closed categories with undergraduate category theory, but in any case they should also read Noson Yanofsky’s 2003 expository paper A universal approach to self-referential paradoxes, incompleteness & fixed points. The easiest options are at the beginning of the paragraph and the hardest ones are at the end; nonetheless any option will cover Cantor, Russell, Gödel, Turing, Tarski, and the essentials of diagonalization.
I don’t know what to do about stuff like the Complexity Zoo. Their veterinarian is Greg Kuberberg, a decent guy who draws lots of diagrams. I took some photos myself when I last visited. But obviously it’s not an ideal situation for the best-known encyclopedia to be run by Aaronson and Habryka.
And hardly run, at that: this changelog is all spam. Tsk, tsk.
They don’t even try to catch the page spammers? Ow god. (the account creation is hard to do something about, but the page spammers is just bad, in this case it is also bad because all the new accounts end with 4 numbers). Less than the bare minimum.
(how are the very online, worried about robots killing everybody, have enough time to write book sized blogposts, so bad at this, when I was active trying to maintain a wiki I checked the recent changes somewhat regularly, for shame).
Give me admin rights Scott, I can keep the toxic elements off
myyour wiki.The very unscientific sampling I did just now suggests that those complexity classes which Wikipedia covers, it covers better than the Zoo does anything. Of course, the Zoo has room for #P/lowpoly and LOGWANK and all the other classes that are attested in one paper apiece.
See so the wiki should link, or even cache/include the oages from wikipedia that are better easy to do in mediawiki.
Make me an admin Scott, I know mediawiki, and I can be trusted. Honest.
MediaWiki does not seem like the right tool for this job, if one were starting from scratch. It’s… a lot of infrastructure for a small number of pages that will be changed very sporadically by a small number of people.
Hey, it looks like our very own corbin started the “complexity class” page at the nLab! Maybe we should flesh that out. (I started their page for the number 24 but am not very active at all.)
Yeah sadly my knowledge of recent research on complexity classes is almost non-existent and before that I was not the greatest at it in university.
Sometimes the required writing style for nLab is a little restrictive. It’s not a good place to dump a bunch of info. Kind of opposite that, I also beefed up the esolangs list of complexity classes a while ago; it’s limited in scope and audience too, but folks usually find that style more accessible.
I’m so jealous that you started the page for 24! I’ve only worked on niche topics and meanwhile you’ve got the most important numerology in all of combinatorics. I still need to rewrite that Jim Carrey movie 23 to be about 24; it’s on my list.
I copied this over to the recommendations thread for actual-science versions of things that the Sequences gesture incompetently at.