The Simple Math of Everything

I am not a pro­fes­sional evolu­tion­ary biol­o­gist. I only know a few equa­tions, very sim­ple ones by com­par­i­son to what can be found in any text­book on evolu­tion­ary the­ory with math, and on one mem­o­rable oc­ca­sion I used one in­cor­rectly. For me to pub­lish an ar­ti­cle in a highly tech­ni­cal ev-bio jour­nal would be as im­pos­si­ble as cor­po­ra­tions evolv­ing. And yet when I’m deal­ing with al­most any­one who’s not a pro­fes­sional evolu­tion­ary biol­o­gist…

It seems to me that there’s a sub­stan­tial ad­van­tage in know­ing the drop-dead ba­sic fun­da­men­tal em­bar­rass­ingly sim­ple math­e­mat­ics in as many differ­ent sub­jects as you can man­age. Not, nec­es­sar­ily, the high-falutin’ com­pli­cated damn math that ap­pears in the lat­est jour­nal ar­ti­cles. Not un­less you plan to be­come a pro­fes­sional in the field. But for peo­ple who can read calcu­lus, and some­times just plain alge­bra, the drop-dead ba­sic math­e­mat­ics of a field may not take that long to learn. And it’s likely to change your out­look on life more than the math-free pop­u­lariza­tions or the highly tech­ni­cal math.

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.

The Sim­ple Math of Every­thing, writ­ten for peo­ple who are good at math, might not be all that weighty a vol­ume. How long does it take to ex­plain Bayes’s Rule to some­one who’s good at math? Damn would I like to buy that book and send it back in time to my 16-year-old self. But there’s no way I have time to write this book, so I’m toss­ing the idea out there.

Even in read­ing pop­u­lar works on sci­ence, there is yet power. You don’t want to end up like those poor souls in that re­cent in­ter­view (I couldn’t Google) where a well-known sci­en­tist in field XYZ thinks the uni­verse is 100 billion years old. But it seems to me that there’s sub­stan­tially more power in push­ing un­til you en­counter some ba­sic math. Not com­pli­cated math, just ba­sic math. F=ma is too sim­ple, though. You should take the high­est low-hang­ing fruit you can reach.

Yes, there are sci­ences whose soul is not in their math, yet which are nonethe­less in­cred­ibly im­por­tant and en­light­en­ing. Evolu­tion­ary psy­chol­ogy, for ex­am­ple. But even there, if you kept push­ing un­til you en­coun­tered equa­tions, you would be well-served by that heuris­tic, even if the equa­tions didn’t seem all that en­light­en­ing com­pared to the ba­sic re­sults.

I re­mem­ber when I fi­nally picked up and started read­ing through my copy of the Feyn­man Lec­tures on Physics, even though I couldn’t think of any re­al­is­tic ex­cuse for how this was go­ing to help my AI work, be­cause I just got fed up with not know­ing physics. And—you can guess how this story ends—it gave me a new way of look­ing at the world, which all my ear­lier read­ing in pop­u­lar physics (in­clud­ing Feyn­man’s QED) hadn’t done. Did that help in­spire my AI re­search? Hell yes. (Though it’s a good thing I stud­ied neu­ro­science, evolu­tion­ary psy­chol­ogy, evolu­tion­ary biol­ogy, Bayes, and physics in that or­der—physics alone would have been ter­rible in­spira­tion for AI re­search.)

In academia (or so I am given to un­der­stand) there’s a huge pres­sure to spe­cial­ize, to push your un­der­stand­ing of one sub­ject all the way out to the fron­tier of the lat­est jour­nal ar­ti­cles, so that you can write your own jour­nal ar­ti­cles and get tenure. Well, one may cer­tainly have to learn the far math of one field, but why avoid the sim­ple math of oth­ers? Is it too em­bar­rass­ing to learn just a lit­tle math, and then stop? Is there an un­writ­ten rule which says that once you start learn­ing any math, you are obli­gated to finish it all? Could that be why the prac­tice isn’t more com­mon?

I know that I’m much more em­bar­rassed to know a few sim­ple equa­tions of physics, than I was to know only pop­u­lar physics. It feels wronger to know a few sim­ple equa­tions of evolu­tion­ary biol­ogy than to know only qual­i­ta­tive evolu­tion­ary biol­ogy. Even men­tion­ing how use­ful it’s been seems wrong, as if I’m boast­ing about some­thing that no one should boast about. It feels like I’m a dilet­tante—but how would I be dilet­ting less if I hadn’t stud­ied even the sim­ple math?