Saturday, November 12, 2005

The myth of #1

Humans are not well-ordered

Mathematics is good stuff. I would never deny that. Still, mathematical ideas sometimes intrude where they do not belong. (See, for example, my earlier post on Who owns mathematics?) The responsible mathematician will not hesitate to point out when it occurs.

The recent (and continuing) controversy over the vacancies on the U.S. Supreme Court has resurrected the persistent myth of number one, this time in the guise of "the best man for the job." Some commentators criticized the suggestion that a woman should be appointed to succeed Sandra Day O'Connor. ("You can't trust women," said Rush, "Give me a straightforward, honest speaking man any day.") Fortunately, except for unregenerate troglodytes like the aforementioned Rush, most people at least express a preference for the "best man or woman" for the job, or perhaps just "the best person." This notion is full of hot air, and I would like to deflate it.

In mathematics we sometimes talk about "well-ordered sets." A set S is well-ordered if every nonempty subset contains a minimal element. The classic example is the natural numbers: {1, 2, 3, 4, ...}. If the subset is finite, then the subset also has a maximal element. The population of humans on planet earth is finite, so it would have a maximal element if only it could be well-ordered.

We understand the ordering of the natural numbers because we can quickly discern which of two numbers is larger. Unfortunately, we then generalize from numbers to people with expressions like "the smartest," "the richest," and "the best qualified." We might think that Stephen Hawking must be the smartest, and there is good evidence that Bill Gates is the richest, but how are we to determine the most qualified person for a given job? There is no clear ordering criterion for such cases. In fact, we should expect that there would be a number of fully qualified individuals, although they might have diverse qualifications, any one of whom could fill the bill perfectly well. For example, if we're talking about Supreme Court nominees (as we were, you may recall), then presumably some weight would be given to courtroom experience. On other other hand, a lack of courtroom experience might be offset by participation in legislative service, giving the prospective nominee knowledge and sensitivity to legislative intent. Many other factors can be brought in, variously weighted and balanced. The notion of "best" is insupportable.

Personal best

I am reminded when a nephew expressed his dismay that university admission standards might prevent his enrollment in favor of "less qualified" minorities. I fear that I was not sympathetic to my nephew's plight and explained that it was entirely appropriate for admissions officers to consider many factors in their decisions. It was not my experience that any unqualified applicants were being admitted, but the successful candidates were selected for many different reasons, including grade point averages, Scholastic Aptitude Test scores, letters of recommendation, athletic prowess, personal essays, legacies, and records of having overcome disadvantaged childhoods and limited educational opportunities.

My nephew was of the well-ordering school. He believed that one could rank the applicants from best to worst, after which one should then begin admitting students from the top of the list down, continuing until the university's capacity for students was exhausted. It sounded neat and tidy and so very defensible as a rational system. However, I pressed him to explain his ranking system. He told me that admissions should be based on grade point averages. I demurred. Some schools give easy grades and their students would be unfairly advantaged over those who attended more rigorous institutions. For the sake of argument, I recommended SAT scores as a preferable criterion, since SAT scores were nationally normed and independent of individual schools. My nephew could not agree with this at all. Further inquiry established that he had an excellent high school GPA but his SATs were merely good, not spectacular. This was clear evidence to him that SATs were not as good a measure of student ability as GPAs. Can you blame him? I sure don't. But I disagree with him.

By the way, you need not be unduly concerned over the fate of my nephew. Lucky for him, the California State University was not too fixated on SAT scores and he enrolled at one of its best campuses. He subsequently discovered that the University of California was also willing to admit him.

A corollary

The myth of #1 stalks us in many guises. One common form prompts people to criticize those whose priorities differ from their own. For example, many pets were separated from their owners in the confusion of the hurricane Katrina disaster in Louisiana and Mississippi. People who contributed to animal shelters and to efforts to reunite pets with their families were told that this was a foolish use of relief dollars when there were also children who were separated from their parents. Aren't children more important than pets?

At first, this seems an easy question to answer. Very few people would argue that cats and dogs should have priority over human children. But the myth of #1 suggests that higher priority issues must be resolved before lower priority issues can be addressed. The reality is very different. Even if the "highest" priority can be unambiguously identified, it is extremely unlikely ever to be fully resolved. To insist on dealing only with #1 until it is settled, while #2 etcetera languish, is to guarantee that #2 and the others will forever be neglected. One parody of the myth goes like this: "How can I even think of mowing the lawn when there is so much hunger in the world?"

The simplest response to the myth of #1 is to continue to make your own personal judgment of priorities. You then devote as much time, effort, or money as you can afford to those at the top, progressing as far down the priority list as you can reasonably go. You may, of course, feel that your #1 priority will absorb all of your effort or charity, and that is your right. However, don't let the myth of #1 cause you to cast aspersions at those who spread their efforts more broadly. After all, your #1 may be their #3, and it will be getting at least some attention from them.


Anonymous said...

Isn't it more to the point to say that humans aren't *totally ordered* by intelligence?

Zeno said...

Do you mean because they could be equal in intelligence? Sure, I suppose so. But that could also be construed as a failure of the usual ranking mechanisms for not having enough decimal places. My larger point would be that intelligence measures are difficult to defend as constructs that gauge any intrinsic human quality, so they should be used with great restraint. Would we even think we "knew" what IQ is supposedly measuring if the "I" weren't in its name?

Thanks a lot for your comment.

Eyes Open said...

PLEASE put animals and pets HIGHER up on your personal lists.
SEE why here -

(this blog is not making ANY $$ from your visit - just honest pics and links to rescue orgs STILL saving hell-ravaged pets and animals in New Horrorleans)

Awareness + Action = Ideal

Anonymous said...

I meant that it is not necessarily possible to compare the intelligence of two individuals at all... Since what we call intelligence refers to many different properties, even if it is sometimes possible to compare intelligence so that person A is more intelligent than Person D, and B and C are somewhere in between, it might be impossible to comparatively rank the intelligence of B and C. Hence, intelligence is not only not well ordered, but more to the point, is not totally ordered.

Zeno said...

I meant that it is not necessarily possible to compare the intelligence of two individuals at all.

Thanks, Anonymous, for clarifying your point. I agree.

blog said...

And extending Anonymous's point a little further; even if it is possible to compare the intelligence of two people, it may be impossible to put three people in order. In voting systems, there's Arrow's Theorem, which may have a parallel in intelligence measures.

For example, it may be true that A is more intelligent than B, B is more intelligent than C, and C is more intelligent than A - if you struggle with this idea, think about "Rock, Paper, Scissors", where Rock beats Paper, Paper beats Scissors, yet Scissors beat Rock.