Creating The Simple Math of Everything

by Matt_Simpson 2 min read20th Jul 200928 comments

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Eliezer once proposed an Idea for a book, The Simple Math of Everything.  The basic idea is to compile articles on the basic mathematics of a wide variety of fields, but nothing too complicated.

Not Jacobean matrices for frequency-dependent gene selection; just Haldane's calculation of time to fixation.  Not quantum physics; just the wave equation for sound in air.  Not the maximum entropy solution using Lagrange Multipliers; just Bayes's Rule.

Now, writing a book is a pretty daunting task.  Luckily brian_jaress had the idea of creating an index of links to already available online articles.  XFrequentist pointed out that something like this has been done before over at Evolving Thoughts.  This initially discourage me, but it eventually helped me refine what I thought the index should be.  A key characteristic of Eliezer's idea is that it should be worthwhile for someone who doesn't know the material to read the entire index.  Many of the links at evolving thoughts point to rather narrow topics that might not be very interesting to a generalist.  Also there is just plain a ton of stuff to read over there - at least 100 articles.

So we should come up with some basic criteria for the articles.  Here is what I suggest (let me know what you think):

  1. The index must be short: say 10 - 20 links.  Or rather, the core of the index must be short.  We can have longer lists of narrower and more in depth articles for people who want to get into more detail about, say, quantum physics or economic growth.  But these should be separate from the main index.
  2. Each article must meet minimum requirements in terms of how interesting the topic is and how important it is. Remember, this is an index for the reader to gain a general understanding of many fields
  3. The article must include some math - at minimum, some basic algebra.  Calculus is good as long as it significantly adds to the article.  In fact, this should probably be the basic rule for all additions of complex math.  Modularization also helps - i.e., if the relatively complicated math is in a clearly visible section that can be skipped without losing anything significant from the rest of the article, it should be ok.
This list of criteria isn't meant to be exhaustive either.  If there is anything you guys think should be added, by all means, suggest it and we can debate it.  Also, an article shouldn't have to perfectly fit our criteria in order to qualify for the index, as long as it's at least close and is an improvement over what we have in its place.
I should also mention that there is no problem with linking to Lesswrong.  So if you see major problem with the article we have on, say, the ideal gas law, then write a better version.  If we gradually replace offsite links to LW links, we could even publish an ebook or something.
We should also hash out exactly which topics deserve to be represented, and furthermore the number of topics.  I'll suggest some from the fields I'm most familiar with (you should do the same):
  • Baye's Rule
  • Supply and Demand (probably with effects of price controls, incidence of tax, etc., and limitations)
  • Economic Growth (Solow Growth model with limitations/implications)

If you do happen to come across something worth considering for the index, by all means, update the wiki.  (a good place to start looking would be at Evolving Thoughts...)  Perhaps we should add a section to the wiki for articles that we think are worth consideration so we can differentiate them from the main list.  What thoughts do you have (about all of this)?

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