Tuesday, December 20, 2011

About That Harvard Exam (Sidis Part 3A)

An anonymous commenter linked to the 1869 Harvard entrance exam that was dug up by a NYTimes writer and made the rounds last year.  It looks pretty intimidating at first glance, and the commenter used it as evidence that Billy Sidis's entrance into Harvard in 1909 was a pretty solid accomplishment in itself.  Interestingly, the boy's getting in was probably even better than the exam would indicate.  Harvard was no great shakes in 1869, but had improved considerably by 1909, and was one of the world's best by then.  I will note that it was still not what we think of today.  Competitive university admission is mostly a post WWII, or even post 1960 phenomenon.  Many of the brightest did indeed go to the Ivies, the Little Ivies, or the Seven Sisters,* but you simply couldn't count on it.  The rich and the alums got their kids in, and nationally, people stayed closer to home and many of the brightest went to other schools, far more than, say, in 1990.

The gap exactly covers the period of Charles William Eliot's presidency of Harvard, if you want more background than I will give here.

But the test.  That Latin and Greek looks awfully impressive right out of the gate. If you are older, and/or a reader of history, and/or a traditionalist, you may still have Latin Envy, believing that a "proper" education must include it, and Greek!  Why, that just seals it.  A different alphabet and everything.  Weren't they smart, then?

No, not especially. They had had six years of Latin and four of Greek by then, whether by tutor or at academy.  If you took any languages at all in late 20th C, and make the mental comparison of what, exactly, they were being asked to do, it looks much less impressive.  Note also, there was a standard set of works studied in those languages, which these questions are drawn from, plus frequent drill in grammar. Even if you had Latin yourself, you should note that the primary authors studied now are not quite the same as studied then, nor in quite the same way. These exam questions are essentially "Did you have proper teachers, are you reasonably bright, and did you make a moderate effort these last few years?"

Before I get into the math, let me note the major difference, then and now.  Look at what is missing in this exam.  There is no biology, no chemistry, no physics, and certainly no other sciences such as geology or economics.  There are no questions on English Literature - no Shakespeare, Chaucer, Milton - and certainly no American literature (horrors!  To even imagine such a thing!).  No modern languages, no history other than ancient, no world events, no weather, no basic medicine.  Even deeper, no methods of research, and no use of reference materials.  Because these were not taught to young men.  They were taught English Composition and Grammar, Latin and Greek, Ancient History, and the mathematics you see here.  That's it.

Thus, their facility with L&G is dropping even farther down the list of impressiveness.  Most of what 7th-12th graders have to learn today they did not have to even pretend to know.  They were being trained to be gentlemen.  The push for more useful arts was just beginning in this country.

The mathematics would look worrisome at first, but on closer examination, not so.  The arithmetic is mostly just big numbers, and irritating, tedious working by hand.  We forget mathematics that we don't use very quickly, but these students were still immersed.

Two stories:  I was a math wizard, but I had to relearn a lot of it each time a son got beyond the first few weeks of algebra in HS.  The terms and symbols were familiar, but I couldn't remember where they went.  I could get it back, but I had to sit and stare, consult the index, and trial-and-error a bit.  All year, for both algebra and geometry. (And as the first two seldom needed help, I was even less prepared for the others.) Story 2: There was a math magazine when I was in school, which posed problems each month.  It printed the names of those who solved them the next month. I did a few months of that in 12th grade.  Because of going to St Paul's for summer studies, I recognised the names of many of the other NH students who got problems right.  One month, there was a problem where I was the only kid in the country to submit a right answer - something about rotating one parabola along another and describing where the focus went.  Very cool.  I pretended, in my conceit , that I was the only one able to get it, which was insane.  How many students, even the nerdy math ones, read magazines and submitted problems?  Fast forward one year.  I was in a different type of math at college, but for some reason wanted to review my accomplishment from the year before.  Narcissism, likely.  I could not follow the solution I had myself written, only one year later.

We lose new abstract thoughts quickly, unless they are used.  Look at the logarithms, trig, and plane geometry in the exam.  Even if you can't even remember how to begin to solve it now, do you recognise the words and ideas? Do you have some recollection of solving problems sort of like that?  Then in all likelihood, you could have done those problems when you were in 11th-12th grade.  And especially, if you didn't have to study any Biochem, Shakespeare, or Intro to Psychology as well.  If you had the same five subjects pretty much year after year, you'd know 'em quite well.

Also - there was some different emphasis in what maths were taught then.  Trig was the top shelf, and you got two years of drill in it.  No sets, calculus, or statistics for you.

Also - read the directions. See how few questions were required.

Also - it doesn't say what a passing score was, does it?

185 out of 215 applicants got into Harvard that year.

*Fun trivia test for you:  name 'em.  I got five on my first try, then a sixth popped into my head a year or so later (this was before internet).  I never did get the seventh until I looked it up.


james said...

Small Latin and less Greek here; recalling my own high school days and looking at this exam. (BTW, the link is bad. I went to the comment to find the right one.) If the language were French I could have made a stab at it back when that was fresher in my mind, so you're probably right about the skill levels required. The arithmetic is tedious but trivial (if you remember how many shillings are in a pound), ditto the algebra and trig, and the geometry wouldn't pose much of a problem if you knew the jargon ("are to each other" I gather refers to area).

So they looked for grammar, geometry, and arithmetic, but not logic, rhetoric, astronomy or music. Did they assume you'd taken the Grand Tour?

Texan99 said...

Of course I'd have bombed the Latin and Greek, but I could do the math even today, or at least the little that I've forgotten I'd have handled easily when I was 18 and it was fresher. On the other hand, I couldn't have done it when I was 11.

On the third hand, my dad was exposing me to fun things about 4D geometry when I was quite young, in part because it was a staple of some of our favorite science fiction (". . . And He Built a Crooked House"). You don't have to be a genius to grasp that stuff, just interested. I'm not saying I'd have come up with it on my own age 11, but as we were discussing below, it's not so clear that Sidis did, either.

Now I guess I'm going to have to go try to figure out the function that describes the focus of one parabola that's rotated along another, see if I have any brain cells left.

My father attended a podunk local college, all he and his family could afford, where he was mostly self-taught. When he was a senior, he caught the attention of a professor by casually expounding a theory about cyclical expanding and contracting universes. The professor thought it suggested such original brilliance that he got him into Phi Beta Kappa largely on the strength of it. In fact, however, the idea was commonplace among the science fiction writers that my father loved at the time (1940s). It's easy to draw starstruck conclusions from too little data, especially when the judges have lacked exposure to really out-of-the-ballpark genius.

Anonymous said...

So your criticisms of the math section as a measure of intelligence are that:

Math in general is abstract. After you learn it, not practicing it can reduce your ability to do it. After your ability has declined, you may be able to remember terms and symbols, but not how to apply them. Even if you're brilliant at it, you may have great difficulty following your own derivations from a year earlier.

On this particular test, the difficulty or complexity of a problem is sometimes increased by forcing the test taker to manipulate large numbers rather than forcing them to use novel methods. The test only covers half a dozen areas of math that the test taker may have been exposed to, and is not a survey of all the math known to humanity.

In conclusion, the math section looks harder than it *REALLY* is, and just because the questions look like ones from the GRE (only harder), and nearly all college educated people we know could solve less than half of them, we shouldn't assume that passing it is an indication of high intelligence

Texan99 said...
This comment has been removed by the author.
Texan99 said...

Anonymous, do you really think nearly all college-educated people we know could solve less than half of the math problems? That's certainly not true of the college-educated people I know. These problems are fairly basic math. The other kids in my 11th grade high school math classes could have taken them in stride. (These were special-track classes for college-bound kids, but not some kind of super-duper genius classes, just public school in the late 1970s.)

The really clever folks I sometimes ran into in college, who could solve problems at a glance that I had to labor over, could have done these standing on their heads. Again, these were very bright students, but not ones who were on their way to winning Nobel Prizes or Fields Medals, let alone becoming household names as "the smartest guy ever."

The 1869 entrance exam math problems would be really difficult for people who never studied much math, which is quite common nowadays. But you'll get a distorted picture of how smart someone is if you compare his performance in a field he's actually studied to that of people who no longer find it important to study that same field at all.

Anonymous said...

The 50th percentile for math SAT scores falls at about 500 on a scale of 200-800, and corresponds to getting about half the questions right. Considering that some students who take the SAT don't go to college, and still others drop out, the average score of college graduates is a bit higher, but that puts us in the ballpark.

Now which is harder, the average SAT math question when you have a calculator and multiple choice bubbles, or the average math question on the old Harvard entrance exam? It’s not even close. I stand by my previous statements. When subjected to rigorous scrutiny, they hold up.

Texan99 said...

Oh, I don't disagree that it's quite a respectable test. I'd love to see high school students take it today. I thought you were arguing that Sidis's ability to do well on it argued for his being the smartest fella evah. Pardon if I misunderstood.

Assistant Village Idiot said...

The math is not harder than the GRE. #4 - at a glance, the answer is going to be about 0.21, further decimal places to be worked out tediously by hand. I worked problems like that in 7th grade for fun all the time. I am nothing near the smartest person in town, never mind the world.

It is not true that this is only a sample of the types of math they would have studied. These are exactly what they studied. Read the link on Eliot yourself, if you like, or read up on the history of education in the 19th C.

Or you can just hold your assumptions about how much harder schools were then.

I will also add that we do not know whether Sidis did take any entrance exam. His father claimed he took one for MIT, but no record exists. He was admitted as a "Special Student." We don't know what it means.

Anonymous said...

“He was admitted as a "Special student." We don't know what it means.”

It means he did went through the exact same courses, but didn't matriculate until his senior year due to Harvard's admissions policies. The math in his courses would have been harder than the math on the entrance exam. So whether he actually took it is a moot point.

“I worked problems like that in 7th grade for fun all the time. I am nothing near the smartest person in town, never mind the world.”

In other words, you were in Prometheus, and a self professed math-whiz, but still several years behind Sidis in math at the same age. (though it's notable that you were held back by the educational system, whereas he was not) By the way, what *is* the IQ of the smartest person in your town?

Texan99 said...

I have a hard time understanding how anyone could come to such extravagant opinions about a guy like Sidis on the basis of such spotty evidence, and continue gripping them so fiercely. Is he a relative or something? Do you feel the world has neglected him unfairly? To me it seems mostly a sad story of wasted potential.

Assistant Village Idiot said...

It has become merely silly to argue with anonymous. He picks and chooses what he will respond to, then misunderstands what is said.

I am content with my statements. You may have the last word.

Sam L. said...

Texan99, that third hand is The Gripping Hand.

Texan99 said...

Sam -- don't I know it! One of my favorite novels. I'll bet I've read it seven times.

Texan99 said...

PS, not "The Gripping Hand" itself (the sequel), but the original "Mote in God's Eye." The sequel was OK.