There are two enduring internet-subjects on which if any negative criticism appears, no matter how slight, can be counted on to generate tea-cup furies.
The first is Apple computer. For example, question the hubris of Steve Jobs, who last week introduced Apple’s tablet under a looming picture of a stone-carrying Moses descending Sinai, and legions of fanboys will descend upon your site and explain to you just how stupid you are, and why you will always be so since you cannot comprehend the simple logic of how the Israelites would have spent 50% less time wandering had they only been presented their Commandments via the iPad. (In colour!)
It used to be that any negative press of Ron Paul or Obama would produce the same attacks of splenetic fever. But Ron Paul is long dead (so I’ve heard) and the growing perception is that Obama has read from one teleprompter too many.
So we are left with Ayn Rand. Daniel knew the danger going in, which is why he took pains to present ideas of Rand’s which he thought were true. The first: “[S]he was among the first to appreciate that the notion of collective rights (a mirror image of racial discrimination) would ‘disintegrate a country into an institutionalized civil war of pressure groups, each fighting for legislative favors and special privileges at the expense of one another.'”
This was an empirical prediction which experienced has verified, and is therefore true, but not yet universally acknowledged.
Daniels also recommends “her observation that ‘Even if it were proved…that the incidence of men of potentially superior brain power is greater among the members of certain races than among the members of others, it would still tell us nothing about any given individual and it would be irrelevant to one’s judgment of him.'”
This is a (comforting) statement of philosophy and is false. Further, any statistician knows that it is false.
Suppose there are two group, M and N. And to avoid emotion, suppose M and N represent the sales (in dollars) of two rival products. The statement that the evidence shows the “incidence of…superior brain power is greater among the members of” a certain group is translated into “the evidence is that the probability of group M having higher sales than group N is greater than 50%.”
Writing this in traditional notion (for those comfortable with this) gives
Pr( Sales[M] > Sales[N] | Our Evidence) > 0.5).
Another way to state this is that if you had to guess which product, M or N, would have greater sales, you would maximize your chance of confirming your guess by saying “M.” This does not, of course, prove that the sales of M will be greater. N can still beat M.
Rand would say that the evidence that it is probable that M > N “would still tell us nothing about any given individual and it would be irrelevant to one’s judgment of him.” Here there is only one individual per group (just the sales M and N), but knowing who that individual is tells us something about that individual and is not irrelevant to our judgment of him.
You might object that Rand obviously meant more than one individual per group. So suppose sales of M and N are generated by salesmen. That is, M has a host of salesmen hawking it and so does N. The number of salesmen in each group need not be equal.
Our equivalent evidence is that the salesmen in M sell more than do the salesmen in N. That is, given this evidence, the probability that a salesperson from M outperforms a salesperson from N is greater than 50%. Notationally,
Pr( Individual[M] > Individual[N] | Our Evidence) > 0.5).
If all—pay attention to this “all”—we knew about the two individuals in front of us is that one sold M and the other sold N, then this would tell us something about these given individuals.
Our knowledge of what group these individuals belonged to would be relevant to our judgment of them. Our judgment is that, given the evidence we have of the two people in front of us, the guy that sold M is probably a better salesman than the guy who sold N.
This, again, does not prove guy M is better than guy N. We could learn new evidence that changes our perception: for example, guy M is drunk.
But in general, Rand’s statement is logically false.
Be careful to understand what we proved. We did not prove that, in comparing different groups of humans, there will be measurable differences. Whether or not there are is an empirical, and not a logical, question. This is what statistics is all about.
What we did prove was that if those differences are real, then that information would be relevant to judgments about members in different groups.