Greg Cochran continues to be one of my current favorite reads. I learned something entirely new to me, the breeder's equation, from his recent post of the same name.
R = h2 S.
R is the response to selection, S is the selection differential, and h2 is the narrow-sense heritability. This is the workhorse equation for quantitative genetics. The selective differential S, is the difference between the population mean and the mean of the parental population (some subset of the total population).
In an aside, Greg also explained regression to the mean using the breeder's equation. I hadn't truly understood what regression to the mean meant until I saw Greg's explanation. Greg is a physicist who went into evolutionary biology, so it isn't surprising to me that I find his point of view readily comprehensible.
The comments on Greg's blog are also very informative, although truth be told sometimes I just browse the comment threads for Greg's smackdown on some poor soul. There were a lot of good links in the comments, and some books I wish I had time to read. Greg and Bruce Charlton have the opportunity to exchange words on the recent Victorian reaction time data, needless to say, Greg is not impressed.
Where it really gets interesting, is when Greg brings up an objection to a decline in intelligence that I also thought of: with that big of a drop, you would see a complete collapse of intellectual endeavour at the highest levels, by which Greg means math and physics. Bruce rejoined: of course it has! Greg's rebuttal was scoffing, Bruce's counter equally scoffing, and ultimately Greg fell back on the argument from authority: Bruce is ignorant of the current state of math and physics, and so cannot really assess them as well as Greg can.
I've pondered whether the rate of intellectual discovery is slowing, but the data I looked at was patent filings and other technological items rather than science per se. Recently, I also suggested there is something intellectually barren about the twentieth century compared to the rest of modernity, especially in the way the guiding lights of Western Civilization seem frozen in time.
Yet for all that, I side with Greg here. Bruce has never struck me as a very quantitative thinker, so I think Greg's accusation is largely correct. Also, despite it's reputed fallaciousness, I think the argument from authority is perfectly appropriate when assessing a question of this type. Greg really is better placed than Bruce to assess math and physics, because he understands these subjects better.
I think the one way Bruce's argument still has force is the way in which science is becoming disconnected from technology and society. The early modern scientists were all about useful inventions, in contrast with the ancient and medieval scientists who were more interested in knowledge for its own sake. Science seems to be trending back towards the knowledge for its own sake model, and as a consequence most people are less interested. When Bruce says,
"I suppose this is hard to settle – but to an outsider, a collapse in the highest levels of physics has very obviously happened, since the quality of the best modern physicists seems qualitatively *much* inferior to those of, say, 100 years ago – or, to put it another way, the supply of geniuses has almost completely dried-up. Maths looks much the same – but I don’t know so much about it."
What I really hear is: scientists of 2013 are less famous than scientists of 1913. Sure, there are TED talks, but nobody is lining up to hear Faraday's lectures on electricity any longer. Now it is Malcom Gladwell. Nobody really thinks Gladwell is part of the leading edge of science himself. Part of the problem here is modern physics and mathematics are way over the public's heads'. I can almost hear Bruce's rebuttal here, but I think the problem is the work has gotten much more abstract over the last two centuries, so much so that it hard for non-specialist scientists to truly understand. Faraday or Maxwell or Darwin have a far wider audience, because their work is both simpler and broader. Greg suggested to Bruce that he study the Princeton Companion to Mathematics, and then they could discuss the subject fruitfully.
I am far from Greg's level, but I don't have any doubt that both mathematics and physics have progressed in impressive ways, on their own terms. What this has not done, however, is given us flying cars. So, no one cares. Science has abandoned it's Baconian roots for an older Aristolielian set of roots, but no one seems to have noticed yet. Plus, nobody really knows what Aristotle actually said anymore, but that is a different post.