My High School Math Teacher was a Space Alien!

(About a 7 minute read)

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 nonsense.  Many people believe that differences of opinion never reflect differences of intellect.  I’m not so sure.  It seems to me some opinions are so stupid their owners, if not merely ignorant, must be stupid.  But then I’m no psychologist, so maybe I’m wrong about that.

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 (1) evaluate arguments intended to persuade us to do something, and (2) 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 by arguments and to evaluate their efforts to persuade us by arguments.

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  well trusted 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.

5 thoughts on “My High School Math Teacher was a Space Alien!

  1. I skimmed Hugo Mercier and Dan Sperber’s article. It makes sense. The Arugmentative Theory may be a way to distinguish an unconscious AI machine’s processing from what humans (and perhaps other species) do when we “reason” or rationalize our positions.

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    • That’s a fascinating speculation, Frank! Thank you so much for that!

      I sometimes think that another way we might be able to distinguish would be to notice perhaps subtle differences in how machines and humans prioritized things — since it appears prioritization in humans depends on emotions. At least that’s the current science on the subject, I think.

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  2. A real hearty shame that republicans have lost their sanity. I did not know who William F Buckley was, and am glad to see that once upon a time in America there was a balance, or at least a balance comparable to today’s politicians. I hope this changes, for the good of the world.

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