This article in WaPo fills me with rage.
Unsurprisingly, the blogs are all over this, which assuages my fury somewhat. SciAm blog notes that, on a national level, abandoning math education will cripple the competitiveness of our labor force on the international market. Pharyngula notes that, from a selfish perspective, an individual student who abandons math is closing off a whole array of potentially fulfilling (and lucrative) options for one's personal growth and career. And M. Yglesias probably has the most cutting reply:
Less esoterically, there's simply no way you can write about the budget, or tax policy, or Social Security, or whether or not the health care system suffers from too much "adverse selection" unless you understand some math. You can't really write about anything sensibly unless you grasp the difference between a one percent change in something and a one percentage point change or whether or not 100 milion dollars is a lot of money relative to the size of the federal budget or the American GDP. Sadly, Cohen is more-or-less correct to say that an inability to grasp these kinds of mathematical concepts does not, in practice, seem to impede one's career as a political journalist in contemporary America. But that says a lot more about the poor state of journalism than it does about the value of algebra.
Part of the problem with our national press corps is that most journalists are just stupid. Contrast the coverage of the Federal budget with the coverage of Cheney shooting someone in the face. One reason the latter's been covered more effectively than the former is that journalists are too dumb to figure out the budget (and too lazy to spend the effort to do so), but any idiot can understand somebody getting shot in the face. Hence, any idiot can be a journalist, a state of affairs that Cohen wishes to preserve, for transparently self-serving reasons, and in spite of the terrifying consequences for society.
I also want to comment on the following paragraph:
Gabriela, sooner or later someone's going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers. Writing is the highest form of reasoning. This is a fact. Algebra is not. The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence. I can cite Shelly, whose last name will not be mentioned, who aced algebra but when called to the board in geography class, located the Sahara Desert right where the Gobi usually is. She was off by a whole continent.
By writing this paragraph, Cohen confirms once again that he is a fucking moron. Nobody actually capable of thinking clearly could write the above paragraph, because it contains two extremely bad errors of reasoning. First, it confuses memorization skills with reasoning skills --- note how Cohen denigrates mathematically inclined children specifically for not having memorized geographical or historical facts. Second, it makes the following implication: "There exist children who excel at math, but do poorly in most other subjects; therefore English is a higher form of reasoning than math." But consider the converse statement: "There exist children who excel in English, but do poorly in most other subjects; therefore math is a higher form of reasoning than English." An obligation falls to Cohen either to deny the premise of the latter (which is untenable: there are children who excel in English but do poorly in most other subjects), or differentiate it from the former claim. Of course, Cohen does neither, because he can't see his own glaring error of reasoning. (Or else he can, but he doesn't admit it, which makes him a con artist rather than a fool.)
This leads me to my next point, which is the intrinsic ludicrousness of the claim that writing is the highest form of reasoning. I love writing and I love reading, but no finer device was ever invented for deception, obfuscation, sloppy thinking, and straight-up nonsense than natural language. The proof of this is Cohen's column, which is a mile-high pile of crap, but is written in a sufficiently entertaining style that many readers will not be put out by the glaring errors of fact and reasoning within it.
People who study reasoning --- i.e., logicians --- rapidly abandon natural language and develop formalized notation using algebraic rules. (Note that "algebraic" here denotes something broader than high school algebra.) In formal logical systems, one is forced to state one's premises and rules of inference explicitly; and, given an explicit enough derivation for a conclusion, one can usually determine via syntactic inspection alone whether the reasoning is valid. The tools of formal logic are so useful that non-logicians in philosophy have adopted aspects of them more generally. In fact, formalizing Cohen's argument above would make it immediately clear how silly it was.
And, of course, formal logic forms the foundation of computer science as well. Incidentally, as a computer scientist, I can state definitively that Cohen's claim that computers cannot reason "even a little bit" is utterly bogus. Friends of mine have written software with greater reasoning abilities than your average Washington Post columnist (which, granted, is not a very high bar).
Natural language is a useful tool, but its highest virtues are as a system for coordinating action, performing social grooming, and producing aesthetic effects. As a tool of reasoning it's deeply flawed, although it certainly has its place.
Finally, I want to say one further thing about learning and effort in general. Everything worth doing has its difficult spots. I am currently working on a very large proof, and it's a major struggle for me to focus and make forward progress. (Hence the blogging.) From observing myself and the grad students around me for over six years, I have found that the factor that really distinguishes people who achieve great things from people who don't is their ability to exert productive effort continuously through those difficult patches. For grad students, I am probably around the median in this respect; peers of mine who got tenure-track offers at top-35 research universities are almost certainly above the median; peers of mine who dropped out of grad school are probably below the median. The same holds at all levels of ability and achievement.
And when you're in a rough patch, a variety of factors can help you through it. One of those factors is social pressure. If you create a climate in which it is simply accepted that plenty of people "can't do math" and that math is "useless" then --- guess what? --- you will increase the fraction of people who give up as soon as they hit a rough patch. They will sit down to do their homework, stare at the problems, and when they come to a hard passage in the problem, they will give up, rather than exercising their ingenuity. To the extent that society accepts and promotes the utterances of jokers like Cohen, students will be encouraged to do exactly this. For this reason, it is not only stupid, but actually evil for the Post to publish Cohen's writing. But then, blithely promulgating stupidity and evil is pretty much par for the course for the Op-Ed page of a major American newspaper.
p.s. A while ago, I proposed an alternative that would improve our national Op-Ed pages immensely. Of course, nothing like that proposal will ever come to pass, because journalism's a corrupt old-boy network where a long career cranking journalistic prose on deadline puts you first in line for the cushy columnist jobs.
Algebra is important. (I wonder how anyone could disagree with that?)ReplyDelete
One should not, however, be too quick to draw an absolute distinction between reasoning and memorization skills. The ability to retain large amounts of information is very much affected by how effectively one is able to see webs of relationships between otherwise disconnected facts. This is different than rote memorization ability, which is more like being able to memorize long strings of random numbers. A good memory is one sign of a well ordered mind that is able to effectively deal with large amounts of (often very messy and contradictory) information without becoming paralyzed.
Thus, one could say that a good memory is, more often than not, evidence for what I would choose to call certain effective habits of mental hygiene. This is not quite the same thing as "reasoning ability", though certainly reasoning is involved as well.
The most annoying thing about the press is how they are perpetually confusing the essential with the trivial, as if they had no way of conceiving when one thing was more important than another. Everything is reported is the same breathless, hyperbolic style. Even if they knew about and could use formally correct logical methods, one feels they would probably end up getting bogged down in inessential details as a valid logical method is no guarantee of a sound result.
In other words, their minds are simply disordered. I feel this is more than just a symptom of lacking acquintance with the tools of logic (which are necessary but not sufficient), as logic only provides transcendental truths from which it is difficult, if not sometimes impossible, to reach the world of actuality.
Excellent write-up. I linked you here. Cohen doesn't know what he's talking about, and it's quite clear that he doesn't know the first thing about reasoning or logic.ReplyDelete
"Writing is the highest form of reasoning" was indeed moronic. But high school algebra doesn't deserve that title either. When I took abstract algebra, it was like night and day. (I am currently in a master's program in CS) (Colleague!)ReplyDelete