# 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)?

• mak­ing a gen­eral primer on “the story of what hu­mans un­der­stand thus far” with bias to­wards those con­cepts that have the broad­est ap­pli­ca­bil­ity is one of my goals.

Areas to cover: ther­mo­dy­nam­ics, fo­cus­ing on en­tropy. nat­u­ral se­lec­tion. sup­ply and de­mand. bayesian statis­tics, fo­cus­ing on how the sci­en­tific method is a sub­set of bayesian rea­son­ing. a primer on pri­mate sig­nal­ing and group dy­nam­ics. a “just so” sto­ries ver­sion of the list of com­mon fal­la­cies and the list of cog­ni­tive bi­ases available on sites like wikipe­dia.

in fact, in­clude just so sto­ries for ev­ery con­cept listed. of course even­tu­ally the in­tended tar­get should re­al­ize “just so” sto­ries don’t count as ev­i­dence, but the pre­sen­ta­tion will help in­tro­duce ev­ery­thing to a broader au­di­ence and also make it more ac­cessible to chil­dren.

oh and the ba­sics of game the­ory.

• 22 Jul 2009 0:41 UTC
2 points

Make sure to in­clude some­thing about Big-O no­ta­tion; I’m always sur­prised at how lit­tle it’s gen­er­al­ized be­yond al­gorithms.

• Huh? It’s already be­yond. :-) Big-O no­ta­tion is about the be­hav­ior of func­tions as their ar­gu­ment goes to some limit. Some­times the func­tion of in­ter­est is the run­ning time or space re­quire­ment of an al­gorithm, some­times it’s some­thing else, like the asymp­totic of a sum.

• In what way can Big-O no­ta­tion be gen­er­al­ized be­yond al­gorithms? Per­haps it would be use­ful to define ‘Big-O no­ta­tion’ and ‘al­gorithm’.

• Choice Un­der Uncer­tainty (Is this suit­able?)

• (Non-co­op­er­a­tive) Game Theory

• This may be some­what tan­gen­tial, but a bit of graph the­ory would do won­ders, es­pe­cially the­ory re­lated to rec­og­niz­ing de­cep­tive or mis­lead­ing graphs.

• Care­ful. The term “graph the­ory” is usu­ally used to re­fer to a spe­cific branch of math­e­mat­ics which I don’t think you’re refer­ring to.

• My mis­take, I was refer­ring to the Ed­ward Tufte stuff. Thank you for cor­rect­ing me.

• As I sug­gested in the last post on this topic: ex­am­ples.

They don’t even have to be se­ri­ous ex­am­ples, but ex­am­ples of how one might use the ba­sic math, and hope­fully ex­am­ples that are easy to fol­low but not an ob­vi­ous us­age. For ex­am­ple, the time-to-ge­netic-fix­a­tion ex­am­ple might be: you have 20 friends, half of whom have a pet rock. How many years un­til pet rocks have drifted into ex­tinc­tion etc.

• Why re-in­vent the wheel this has already been done if I un­der­stand cor­rectly for ex­am­ple in a bit of a more spe­cific case “Fun­da­men­tal For­mu­las of Physics”.

• “Fun­da­men­tal For­mu­las of Physics” is just a list of for­mu­las with­out much ex­pla­na­tion.

• has some­thing this gen­eral been done already? We’re talk­ing ev­ery­thing from physics to com­puter sci­ence to eco­nomics. It’s the sim­ple math of ev­ery­thing. If you show me, I’ll be­lieve you, but for now I re­main skep­ti­cal.

• A page named “ba­sic maths”, ex­plain­ing “es­sen­tial” con­cepts would be great. I don’t know if it is pos­si­ble, but i would want the ex­pla­na­tions to be the­o­ret­i­cal—the way eliezer ex­plains bayes, ba­si­cally some­thing for the gen­er­al­ists who can’t learn maths by look­ing at equa­tions!!

• Thirded. What should be es­sen­tial? Alge­bra and some ba­sic calcu­lus? Any­thing more?

• Yes, and prob­a­bly a de­tailed prob­a­bil­ity les­son. I was very good at maths in high school, but now af­ter 10 years af­ter high­school, i have to­tally lost touch. Though i still know the con­cepts, i get a bit lost when peo­ple start talk­ing in “p” terms out of nowhere. I would like to fol­low ev­ery­thing.

• Se­conded, with the caveat that it’s called “Ba­sic Math”. Or to com­pro­mise, “Ba­sic Math­e­mat­ics”.

• I re­al­ise it should be ba­sic “math”. For some strange rea­son al­most 99% of peo­ple here in in­dia say maths. We are taught by teach­ers as maths. Peo­ple in­vari­ably say I like maths, not math. Its just so in­grained by now that i wrote that in spite of know­ing that its “math”. Prob­a­bly a thing like your com­ment is what my brain was wait­ing for, it would be more “brainy” be­fore writ­ing maths again :)

• There is no right or wrong about the mat­ter, only con­ven­tion. In Bri­tain, In­dia, and many other places, the con­ven­tional ab­bre­vi­a­tion is maths. In the United States, it is math.

But thomblake’s sug­ges­tion of “Ba­sic Math­e­mat­ics” at least sidesteps hav­ing to choose.

• In the spirit of com­pro­mise, I sug­gest “Ba­sic Math­e­matic”, the one op­tion that noone likes. (Ever looked up where the ab­bre­vi­a­tion “UTC” came from?)

• thanks for tel­lin that. I should have looked up be­fore say­ing that

• Ok, I have to be hon­est this en­tire idea makes me cringe, it seems a bit to much like a cheap get out of learn­ing the math idea. Maybe I am bi­ased be­cause I ac­tu­ally am a math­e­mat­i­cian but these kind of ideas I think are dan­ger­ous since you take away an im­por­tant bar of ad­mis­sion to fields like physics. If you don’t un­der­stand why the math is an im­por­tant bar of ad­mis­sion look at the google groups physics group.

To be hon­est I think some­one would be bet­ter off spend­ing their time learn­ing calcu­lus at min­i­mum then try­ing to read this kind of gen­eral overview. I think what is likely to hap­pen is that ei­ther the math will be to sim­ple and mud­dles the field to the point of be­ing use­less or its so com­plex that no­body can fol­low it. A good case and point you can un­der­stand quan­tum physics if you un­der­stand alge­bra but your go­ing to be hope­less in a dis­cus­sion about it with­out un­der­stand­ing things like the differ­en­tial equa­tions. Of course there are other fields which you have to know the math, from some of my own ex­pe­rience, fluid me­chan­ics.

For my own part I think re­quired math should in­clude at min­i­mum: Ad­vanced Calcu­lus (not that “calcu­lus class” you took in high school it doesn’t count) Differ­en­tial Equa­tions Lin­ear Alge­bra Ab­stract Alge­bra Set The­ory (ba­sic at least) Num­ber Theory

I think with these you prob­a­bly can figure a lot of the more com­plex math out.

I am sure I am leav­ing a cou­ple out but you get the idea.

• While I also don’t see the point in the en­ter­prise, and think many of the spe­cific sug­ges­tions mis­guided, you mis­in­ter­pret its in­tent. Read the origi­nal post for an ex­pla­na­tion. The point isn’t to learn math “in a sim­ple form”, but to ex­plain some of the most im­por­tant facts about the world with at least a bit of math­e­mat­i­cal rigor and ex­pres­sive power.

• Oh I get it. I would make the same point ei­ther way es­pe­cially when the idea comes from a non math per­son. When­ever a non math per­son says this kind of thing it should make any­one who has done their due dili­gence cringe.

If you can’t do the math so for the physics if par­tial differ­en­tial equa­tions are be­yond you then you shouldn’t be talk­ing about physics. There are many fields where know­ing the “drop-dead” math is not suffi­cient to qual­ify one to talk about it.

Now I know you will all vote me down, I am rock­ing the boat.

• Do you ex­pect a per­son to end up worth off as a re­sult of learn­ing about some sub­ject to less than cer­tain level of de­tail? If it’s bet­ter to learn a lit­tle than not at all, it’s prob­a­bly bet­ter to learn a few facts writ­ten in math than no facts writ­ten in math at all. It seems that you have to agree with one or the other.