This feels unsatisfying to me and I’m not fully sure why.
If we want to know why Johnny English does things with his left hand, we could say “because he’s left-handed”. But we know he’s left-handed because he does things with his left hand. That seems just as circular, but still basically fine as an answer? More broadly we’d say “look, some people just favor their left hand. We don’t know exactly why, but there’s a fraction of the population who tends to do things with their left hand, even when it causes them to smear ink or makes scissors less efficient. We call these people left-handed.”
So when we say “Johnny English does things with his left hand because he’s left-handed”… it’s arguably more definition than explanation, but it does also have predictive power. It points at a pattern that lets us say “okay, Johnny English will probably use his left hand in this situation too, and if we try to make him use his right instead he probably won’t do a very good job”.
Handedness is a discrete phenomenon with two peaks. 90% of people are right-handed, 10% are left-handed and the cross-dominant population is small. “Right-handed verses left-handed” is a natural bucket because there is a trough between them on the handedness histogram.
Intelligence, on the other hand, exhibits a bell curve with a single peak. There is no trough on which to draw a dividing line between “smart” and “stupid”. The bucket is arbitrary instead of natural.
The English words “smart” and “stupid” are vague. They do not point to a numerical location on the bell curve. We could draw the line between smart and stupid at an IQ of 70, 100 or 145. If we draw the line at x then the theory has almost no explanatory power. You cannot say “Johnny English does stupid things because he is stupid” when you draw the dividing line at x because a person with an IQ of x−1 does almost exactly as many stupid things as a person with an IQ of x+1. (The observed difference in stupidity between individuals of IQ x−1 and x+1 is swamped by noise.)
Could we rephrase HumaneAutomaton’s question in terms of a continuous distribution instead of a binary distinction?
Yes, but it would cost a lot of entropy.
Suppose Johnny English did things with a stupidity level such that his posterior expected IQ is 85. It could be that Johnny English has an IQ of 85. It could be that Johnny English has an IQ of 65 and got lucky. It could be that Johnny English has ah IQ of 105 and got unlucky.
Under the best of circumstances it takes much more information to nail down Johnny English’s precise intelligence level than to deduce his handedness. History is not the best of circumstances. We have scarce data, deal with confounding unknowns and must counteract historiographic bias.
Handedness is different from IQ in two ways, both related to the continuous-discrete distinction.
It takes more information to deduce precise IQ than precise handedness and we usually don’t have that information for historical figures.
IQ predicts specific behavior with less precision than how well handedness predicts behavior. Context is more important for judging intelligence than for judging handedness.
To put it in terms of Occam’s razor, continuous distributions have many buckets. Hypotheses with many are more complex than theories with few buckets. IQ has more buckets than handedness.
Did the intelligence of individuals influence historical events? Yes. Can we isolate the signal? Generally, no.
This feels unsatisfying to me and I’m not fully sure why.
If we want to know why Johnny English does things with his left hand, we could say “because he’s left-handed”. But we know he’s left-handed because he does things with his left hand. That seems just as circular, but still basically fine as an answer? More broadly we’d say “look, some people just favor their left hand. We don’t know exactly why, but there’s a fraction of the population who tends to do things with their left hand, even when it causes them to smear ink or makes scissors less efficient. We call these people left-handed.”
So when we say “Johnny English does things with his left hand because he’s left-handed”… it’s arguably more definition than explanation, but it does also have predictive power. It points at a pattern that lets us say “okay, Johnny English will probably use his left hand in this situation too, and if we try to make him use his right instead he probably won’t do a very good job”.
Handedness is a discrete phenomenon with two peaks. 90% of people are right-handed, 10% are left-handed and the cross-dominant population is small. “Right-handed verses left-handed” is a natural bucket because there is a trough between them on the handedness histogram.
Intelligence, on the other hand, exhibits a bell curve with a single peak. There is no trough on which to draw a dividing line between “smart” and “stupid”. The bucket is arbitrary instead of natural.
The English words “smart” and “stupid” are vague. They do not point to a numerical location on the bell curve. We could draw the line between smart and stupid at an IQ of 70, 100 or 145. If we draw the line at x then the theory has almost no explanatory power. You cannot say “Johnny English does stupid things because he is stupid” when you draw the dividing line at x because a person with an IQ of x−1 does almost exactly as many stupid things as a person with an IQ of x+1. (The observed difference in stupidity between individuals of IQ x−1 and x+1 is swamped by noise.)
Could we rephrase HumaneAutomaton’s question in terms of a continuous distribution instead of a binary distinction?
Yes, but it would cost a lot of entropy.
Suppose Johnny English did things with a stupidity level such that his posterior expected IQ is 85. It could be that Johnny English has an IQ of 85. It could be that Johnny English has an IQ of 65 and got lucky. It could be that Johnny English has ah IQ of 105 and got unlucky.
Under the best of circumstances it takes much more information to nail down Johnny English’s precise intelligence level than to deduce his handedness. History is not the best of circumstances. We have scarce data, deal with confounding unknowns and must counteract historiographic bias.
Handedness is different from IQ in two ways, both related to the continuous-discrete distinction.
It takes more information to deduce precise IQ than precise handedness and we usually don’t have that information for historical figures.
IQ predicts specific behavior with less precision than how well handedness predicts behavior. Context is more important for judging intelligence than for judging handedness.
To put it in terms of Occam’s razor, continuous distributions have many buckets. Hypotheses with many are more complex than theories with few buckets. IQ has more buckets than handedness.
Did the intelligence of individuals influence historical events? Yes. Can we isolate the signal? Generally, no.
Thou shall not speak of scissors! Apparatus of the devil that be!
.. yes, I am left-handed :P