Nov 17, 2007
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?