Recommended reading for new rationalists

27 XFrequentist 09 July 2009 07:47PM

This has been discussed in passing several times, but I thought it might be worthwhile to collect a list of recommended reading for new members and/or aspiring rationalists. There's probably going to be plenty of overlap with the SingInst reading list, but I think the purposes of the two are sufficiently distinct that a separate list is appropriate.

Some requests:

  • A list of blog posts can be collected at another point in spacetime; for now, please stick to books, book sections, or essays1.
  • Please post a single suggestion per comment, so upvoting can determine the final list for the eternal fame of wikihood.
  • Please limit yourself to no more than 3-5 suggestions. We could probably all think of dozens, try and think what would actually be the best for the purposes of this site.
  • Please only suggest an entry if you've read it. Judgement Under Uncertainty, while certain to make the list, should be put there by someone who has invested the time and waded through it (i.e. someone other than me).
  • Please say why you're suggesting it. What did you learn from it? What is its specific relevance to rationality? (ETA)

 Happy posting!

PS - Is there a "New Readers Start Here" page, or something similar (aside from "About")? I seem to remember someone talking about one, but I can't find it.

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Formalized math: dream vs reality

12 cousin_it 09 July 2009 08:51PM

(Disclaimer: this post is intended as an enthusiastic introduction to a topic I knew absolutely nothing about till yesterday. Correct me harshly as needed.)

We programmers like to instantly pigeonhole problems as "trivial" and "impossible". The AI-Box has been proposed as candidate for the simplest "impossible" problem. Today I'd like to talk about a genuinely hard problem that many people quickly file as "trivial": formalizing mathematics. Not as in, teach the computer to devise and prove novel conjectures. More like, type in a proof for some simple mathematical fact, e.g. the irrationality of the square root of 2, and get the computer to verify it.

Now, if you're unfamiliar with the entire field, what's your best guess as to the length of the proof? I'll grant you the generous assumption that the verifier already has an extensive library of axioms, lemmas and theorems in elementary math, just not this particular fact. Can you do it in one line? Two lines? (Here's a one-liner for humans: when p/q is in lowest terms, p2/q2 is also in lowest terms and hence cannot reduce to 2.)

While knowledgeable readers chuckle to themselves and the rest frantically calibrate, I will take a moment to talk about the dream...

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