Creating The Simple Math of Everything

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)?