A comment which woke me from my long nap:

” What areas of mathematics or technical knowledge would you consider necessary for a hedgie analyst or academic researcher in economics /pol science /anthropology / history? I’m not interested in bits, bolts, DNA or mechanical things, but would like to apply more rigor to social, business and economic problems. “

Simple answer: statistics (and ideas in probability). Not the baby stats rubbish where they give you a recipe and hope for the best. Not even the stuff they teach you in an experimental physics course: real statistics, like they use on Wall Street to make money.

If you want to be bleeding edge, or do some exploration on your own, there are interesting results in information theory and machine learning which can help you, but what will help you more than this is a deep understanding of plain old statistics. Frequentist, Bayesian, Topological; whatever: just learn some stats to the point where you understand how they work, what they’re good for and where they break down.

My formal training was in physics, where, generally speaking, statistical sophistication is fairly low. Physicists have the luxury of being able to construct experiments where the observation of one or two photons or some preposterously small amount of torque on a magnetometer is meaningful. Pretty much nobody but physicists have this luxury.

Physicists no longer have this luxury for the most interesting problems these days. Unfortunately nobody told them, which is why physics has been languishing in the swamplands, with “physicists” working on non falsifiable noodle theory, cosmology and writing software for computer architectures which will probably never exist. I think it was Kelvin who said, “in science there is only physics, all the rest is stamp collecting.” When Kelvin said it, this was true: because nobody had bothered to invent statistics yet. Physics was the only real Baconian science.

Now, we have statistics. A flawed quasi-mathematical technique which is effectively how we know anything about everything that isn’t pre-1950s physics. Yes, yes, Disraeli and Mark Twain said there are “lies, damn lies and statistics.” He should have said, “bad statistics” -but that’s all there was in those days. Before we had the adding machine, statistics was the purview of Gauss and people who mostly were not doing it right.

Guys like Fisher, Pearson (both of them), Kolmogorov, Neyman, de Finetti, Jeffreys, Savage, Cramer and the lot are as important to our understanding of the world as Heisenberg and Darwin. Indeed, at this point I would go so far as to say that statistics invented in the 1930s is arguably more important than physics done in the 1930s. Most of the useful new knowledge of the last 60 years is directly attributable to such men. They don’t get enough respect.

Doing statistics well is the essence of all useful social science. As you probably have noticed, most social science is not done well. Much of social “science” isn’t very scientific; it’s often merely ideological gorp. The statistics used in the social sciences (and biological sciences and drug discovery and …) is abused preposterously to the point where they appear to be mathematical and methodological jokes rather than results which must be taken seriously. If social sciences took themselves seriously, they would be sciences rather than shaggy dog stories.

Consider psychology: according to a recent Science article, the majority of results of a sample of psychology papers can’t be reproduced. Let that sink in for a moment: more than half the results of these psychology papers are anecdotes. Part of this is because the researchers in that field are quacks and morons. Part of it is because they are evil quacks and morons. I sit in a cafe which is near the UC Berkeley psychology building, and often overhear conversations by professors, grad students and post-docs from this place. Once in a while I overhear something intelligent and salubrious. For example, I was grateful to overhear a conversation about this paper a few months ago.

However, I have often heard learned psychology department dunderheads stating what the result of their paper will be, and instructing their underlings to mine the data for p-values. I suppose they may have thought themselves speaking over the heads of the rabble, since nobody else from their department was visible. Mind you, they did this in a public place, in a town which is filled to the nostrils with people with training in rigorous subjects, like, you know, me, the buxom Russian girl reading Dirac in the corner, the options trader eating a sandwich, and the girl pouring the coffee, who is studying mathematics. This indicates to me that such people are so abysmally stupid and unaware of their own deficiencies, they couldn’t achieve a scientific result if they actually tried to do so. Have a click on this link for the UCB psychology department: at least two people on this list are cretinous scientific frauds. If the Science paper mentioned above is a representative sample, most of them are.

Should I ever strike it rich enough to endow a foundation, I would pay legions of trained statisticians to go through the literature and eviscerate the mountains of bad “research” and arrive at the truth. If Universities were interested in advancing human knowledge, rather than advancing a tenured circle jerk which fields a football team, they’d fund entire departments of people who do nothing but act as Inquisitors about their research findings. Meanwhile I will have to content myself with instigating ambitious young people to arm themselves with the best statistical weapons they can muster, and go forth to slay dragons.

It can be done, and at this point, it can be good for your career. Examples here, here and here. There is plenty of bullshit out there, and as Thucydides (also worth a look for young social scientists) said, “the society that separates its scholars from its warriors will have its thinking done by cowards, and its fighting by fools” so get to work!