My High School Math Teacher Was A Space Alien!

I am fascinated -- I have long been fascinated -- that the same person can be smart in some ways and stupid in others.

If I were a scientist with an adequate research budget, I would probably want to study human intelligence just to find out what I could about that one unexpected fact. (Of course, if I were a scientist and I had an adequate research budget, that, too, would be an unexpected fact.)  How can the same person be both smart and stupid?

I don't know a reliable answer to that question, but I do think many of us -- perhaps even most of us -- more or less fit the description of being smart in some ways and stupid in others.  And those of us who do not fit that description seem more often stupid in everything than smart in everything.

I'm aware of Gardner's Theory of Multiple Intelligences. And his theory would seem to explain why the same person can be smart in some ways and stupid in other ways.  Yet, so far as I know, Gardner's theory is as yet unsupported by much in the way of hard evidence.  Consequently, I remain an agnostic about it.

Often, when I think of the people in my life who have most deeply -- some might say "most traumatically" -- impressed me as smart in some ways and stupid in others, I think of my high school math teacher, Mr. B.

No one -- not even I -- questioned Mr. B's competence as a mathematician.  I will submit, however, that Mr. B, despite his smarts in math, was twenty years ahead of his time in some kinds of stupid.

I had Mr. B as a teacher in the early 1970s.  William F. Buckley was alive, and Buckley was frequently a very smart man.  He also had the clout to be the intellectual guardian of the Republican Party.  That is, if he decided someone or some group was too stupid to fit in as a Republican, Buckley would use his considerable influence to exile them from the Party.  The Republicans have no one like him today. Today,. the crazies have become the Party.

The John Birch Society was one of the groups Buckley succeeded in kicking out of the Party.  The "Birchers" believed -- in the way stupid people fanatically believe things -- all sorts of nonsense.  For instance, they thought Dwight D. Eisenhower was a willing tool of the Soviet Union and a deliberate traitor to America.  Buckley thought the Birchers were in danger of sliding into fascism.  Perhaps he was right.

My math teacher subscribed to the John Birch Society, and perhaps to other Radical Right organizations as well. We knew whenever he had received in the mail another one of their newsletters -- he would put aside teaching mathematics for the day and instead lecture us on themes that were rarely enough heard in the early 1970s outside of certain circles.

I can still recall a few of his more memorable pronouncements: "Pollution never killed anyone".  "Martin Luther King, Jr. was a Communist out to destroy America. Don't let anyone tell you different."  "The Soviets will invade us any year now. Maybe any day now."  "Women don't need equal rights.  Men do!  Women are smarter than men."  "Negroes are shameless whiners. They haven't been discriminated against since the end of the Civil War."

I am a strong believer in the notion that, although everyone has a right to his or her opinions, not all opinions are created equal.  Some opinions are forged of sound logic and a weight of evidence.  Some other opinions are forged of logical fallacies and bullshit.  Many people believe that differences of opinion never reflect differences of intellect.  I disagree.  Some opinions are so stupid their owners, if not merely ignorant, must be stupid.

Yet, it is simply true that -- often enough -- the same one of us who is so stupid as to believe the Theory of Evolution is a conspiracy of the world's 500,000 biologists, is nevertheless a brilliant (or at least competent) engineer.  How can we account for that?

Mr. B once said something that I think is about half true: “No matter how good you get at math, you will never cease to make mistakes. But if you practice, you will catch your mistakes as you make them, and then correct them yourself, instead of needing someone else to correct them for you.”

I think it sometimes happens that way.  But I also think very few -- if any -- of us ever get so good that we catch and correct every one of our own mistakes, whether in math or in any other field.  We will always need the help of others.  Indeed, it seems one reason the sciences have been so successful at establishing reliable facts and producing predictive theories is because they employ methods of inquiry that encourage people to correct each other's mistakes.  That is, science is a profoundly cooperative endeavor.

Buckley once described some of the notions of the John Birch society as "paranoid and idiotic".  To some extent, those two things go together.  A "paranoid" person is typically unwilling to accept anyone correcting his ideas.  Quite often, the result is his ideas drift into idiocy.  That's to say, it seems one of the best ways to become stupid is to systematically reject or ignore the efforts of others to correct us when we are wrong.

But why are we humans so often wrong in the first place?

Hugo Mercier and Dan Sperber have come up with a rather interesting theory that could go far to explain why our species of great ape seems prone to cognitive errors.  It's called "The Argumentative Theory", and it is well worth reading up on.

The gist of it is that our ability to reason evolved -- not to figure out what is true or false -- but to win arguments, or to persuade others to do what we want them to do.  Consequently, our ability to think logically and evidentially is imperfect -- one might even say, "somewhat remedial".

Part of the evidence for the Argumentative Theory is our species built in cognitive biases.  By "built in", I mean that the biases seem hereditary.  The fact our thinking is inherently biased is strong evidence our thinking evolved for some other function than to merely figure out what is true or false.  Mercier and Sperber would say that function was to persuade people.

Regardless of whether the function of reason is to discern reality or to win arguments, the fact our species is so prone to cognitive error might go far in explaining how it happens that the same person can be smart in some ways and stupid in others.  That is, perhaps we are smartest -- or at least, we tend to act smartest -- when we have some corrective feedback.

That feedback might come in the form of ourselves "checking our work" -- as when we check a mathematical solution.  It might come in the form of  whether we achieve our intended outcome -- as when we fix a car so that it runs again.  Or the corrective feedback might come in the form of constructive criticism from others.

Perhaps the less corrective feedback we have, the more likely we are to adopt stupid opinions.  Or, in other words, we should not expect our own reason alone to take us where we want to go.  Rather, we should expect our reason plus some form of corrective feedback to take us there.

I think my high school math teacher, if he were alive to read this essay, would be appalled by my suggestion that -- no matter how good we get -- we are still wise to listen to the critiques of others.  It seems to me Mr. B cared so little to hear the opinions of others that he might as well have been a space alien orbiting his own little planet and all but totally out of touch with earth.  He seemed to think he was his own sufficient critic.  And perhaps his lack of concern for the input of others explains why he found it so easy to harbor so many "paranoid and idiotic" notions.  Notions that, in a sense, were more stupid than he was.


  1. I've been thinking about this same issue - recently I've been reading a book on the history of Philosophy - and was surprised to find that brilliant thinkers like Descartes and Leibniz who developed branches of mathematics, also developed arguments like this one (variations on it) for the existence of God:

    If you can IMAGINE God, you are imagining a perfect being. If God were NOT to exist, he would be lacking a property of a perfect being, since EXISTENCE itself is an attribute of perfection. So, if you're imagining a God that does not exist, you're not imagining God. Therefore God must exist. ??

  2. When you look at what Paul Krugman wrote about Olivier Blanchard today, or what I wrote about Christopher Hitchens, one theme emerges - people who are smart sometimes forget that they can still be spectacularly wrong. Or, perhaps to be more accurate, they assume that they're so smart that others must be wrong.

    People who are experts in a field have spent a lot of time learning about that field. They haven't learned as much about other fields, and so their opinions aren't nearly as likely to be right. Experts who don't know that are all too plentiful.

  3. The thing is that 'the function of reason' can lead one in so many directions... For instance, those that have firmly believed that women are 'the weaker sex,' or that slavery is a right and natural thing, or that the earth is flat, or that global warming is, in fact, not taking place, could no doubt have given you a very 'reasonable and logical' explanation for their beliefs. They could, no doubt, present that their views were 'forged of sound logic and a weight of evidence.' Anyone who believed otherwise, they might tell you, is 'stupid' and 'in need of correction.' Most insidious, this function of reason is...

  4. One of my lifetime's frustrations is this prostitution of reason in the cause of winning arguments, rather than in a genuine effort to find out what is going on. As if the most important thing on earth were to prove that you could make another person wrong. (I have been deeply hurt by a few people in the blogging world who seemed focused on this rather than on making connections between people interested in the same ideas.)

  5. I think religious beliefs, faith, precede all other values, even, perhaps especially, logical conclusions.

    If you begin life as an Intel Chip you will always be an Intel Chip. On the other hand, if you begin life as a Motorola Chip (I know I'm showing my age here), you will always be a Motorola Chip.

    It's almost as if people are hard wired once they reach a certain (very young) age.

  6. Jon, I recall the ontological argument for the existence of god is an interesting one with about a thousand subtle variations. I've never been quite able to accept it, though. What about you?

  7. I agree, Cujo. It seems all too easy to think that someone who is, say, a good physicist might know something about biology too. In reality, though, that doesn't happen often enough to count on it.

  8. Garnet, you raise a number of issues that I wish to address. Unfortunately, I'll need more space for that than I have here. So, I'm going to address what you have said in a separate blog post. Thanks for the inspiration!

  9. Spot on, Sledpress! Even if reason evolved to win arguments -- as the two scientists suggest -- it's entirely annoying to see someone employ it for that purpose.

  10. That's quite an interesting perspective, Loren. I'm honestly not sure yet what I think of that. But I'm enjoying the pondering of it!


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