The Functional Form of Intelligence

Interesting post by James Flynn at Cato Unbound on the subject of intelligence. Here’s the part I found most enlightening:

Two twins raised apart, thanks to having slightly better genes than average, would both get into increasingly privileged environments. Both would get more teacher attention, would be encouraged to do more homework, would get into a top stream, and by adulthood, they would both be far above average. Moreover, thanks to their identical genes, their environmental histories would be very similar. Their identical genes were getting all of the credit for the combination of identical genes plus nearly identical enriching environmental factors! The environmental factors were not feeble at all: they just tended to be similar for identical twins when raised apart, which made them look feeble.

Now, Flynn’s spin on this is that, in essence, the twin studies have led us to overestimate the importance of genetics in intelligence. But I would put it differently: it may not be mathematically meaningful to talk about the percentage contributions to intelligence of genetics and environment. Why not? The attempt to apportion percentage credit to each factor assumes that the total has a linear form something like this:

IQ = aX + bY

where X is genetics and Y is environment (I’m simplifying a lot here, in order to focus on just one complication). But if one effect of genetic intelligence is to attract more environmental resources because those resources will likely generate a higher return, then the function may look more like this:

IQ = aX + bY + cXY

The interactive term cXY, which captures the greater return from environment given a better genetic endowment, makes it literally nonsensical to ask what percentage of intelligence is due to each factor. Some part of intelligence cannot be attributed to either one, but must be attributed to both. Now, you could look at that equation and say, “Okay, but we could apportion cXY to factors X and Y by assigning them a/(a+b) and b/(a+b) of the credit respectively.” The problem with that approach becomes apparent when you consider this functional form:

IQ = aX + cXY

Here, using the apportionment strategy just described would result in saying environment makes no contribution at all to intelligence – when clearly it does. More complex functional forms would raise even more formidable barriers to apportioning the credit for intelligence to different sources.

I made a closely related point, in an entirely different context, here.