Today we attended a local event put on by one of the schools our daughter is considering--hosted by local alumni, organized, apparently, by someone from the school's admission department, attended by potential students, their parents, and school alumni.

It was a pleasant event, but not, I think, very informative. The problem, which I discussed in an earlier entry, is that all schools, at least all of the liberal arts colleges we are looking at, make essentially the same claims. They are all warm, friendly, non-competitive places, with easily accessible faculty doing cutting edge research, populated by creative, intelligent, tolerant, diverse students.

For the most part the claims are hard to test. Listening to alumni, it's clear that they think well of the school. But the alumni who come to such events are not a random sample and, perhaps more important, most of them have no good basis of comparison. They know what their experience was at that school but not what their experience would have been at one of its competitors.

The event included a movie, produced by students, lauding the school. Two things struck me. One was the effort to show what happy non-conformists the students were. The problem, of course, is that the more the school emphasizes the importance of that, the more one suspects that their sort of nonconformity is what students are conforming to. Judging at least by the schools we saw and, more, by what they said about themselves, the real nonconformist would have been wearing suit and tie and getting his exercise playing tennis instead of ultimate frisbee.

The other thing that struck me in the movie was not, I think, intended by its producers. One of the students, explaining how wonderful the school was, described it as undefinable--"like the square root of two."

The square root of two is quite easily defined--it is that number that, multiplied by itself, equals two. The correct term is "irrational," but I don't think that's how he wanted to describe his college. The actual information conveyed by that segment was that at least one student at that college was both mathematically illiterate and mathematically pretentious, and that nobody making the movie knew enough elementary mathematics, or was paying enough attention, to do a retake with the error corrected. I don't think that was the message that the school intended to give to potential students and their parents.

It was a pleasant event, but not, I think, very informative. The problem, which I discussed in an earlier entry, is that all schools, at least all of the liberal arts colleges we are looking at, make essentially the same claims. They are all warm, friendly, non-competitive places, with easily accessible faculty doing cutting edge research, populated by creative, intelligent, tolerant, diverse students.

For the most part the claims are hard to test. Listening to alumni, it's clear that they think well of the school. But the alumni who come to such events are not a random sample and, perhaps more important, most of them have no good basis of comparison. They know what their experience was at that school but not what their experience would have been at one of its competitors.

The event included a movie, produced by students, lauding the school. Two things struck me. One was the effort to show what happy non-conformists the students were. The problem, of course, is that the more the school emphasizes the importance of that, the more one suspects that their sort of nonconformity is what students are conforming to. Judging at least by the schools we saw and, more, by what they said about themselves, the real nonconformist would have been wearing suit and tie and getting his exercise playing tennis instead of ultimate frisbee.

The other thing that struck me in the movie was not, I think, intended by its producers. One of the students, explaining how wonderful the school was, described it as undefinable--"like the square root of two."

The square root of two is quite easily defined--it is that number that, multiplied by itself, equals two. The correct term is "irrational," but I don't think that's how he wanted to describe his college. The actual information conveyed by that segment was that at least one student at that college was both mathematically illiterate and mathematically pretentious, and that nobody making the movie knew enough elementary mathematics, or was paying enough attention, to do a retake with the error corrected. I don't think that was the message that the school intended to give to potential students and their parents.

## 18 comments:

Once again, David, you're uncharitably attempting to tell people what they mean is incorrect.

undefined: not capable of being precisely or readily described

If the student is talking about the sequence of digits, they are not readily described. Go ahead, show me how readily you recite the first thousand or so digits from your memory. "Like the square root of two" does not describe the digits explicitly: it refers to the need to calculate to determine the digits.

"Irrational" is mathematically correct, but it's obvious to anyone that the student wouldn't have wanted to describe his college experience as irrational. Indeed, the idea that the student needed to be pedantically correct to communicate accurately with a casual mathematical analogy is ludicrous. I wish you took such pains to criticize your fellow libertarians for their crimes of that sort. (I'll save my complaints for the grosser errors.)

What he was probably referring to was that there is no apparent pattern to the sequence of digits of an irrational number such as the square root of two, something that is routinely taught in math classes.

A better substitute than irrational would have been to describe it as transcendental like pi.

David Friedman to unnammed pretentious, math illiterate college: "Owned."

Pi might have been a better choice, a transcendental college would probably rock.

That college is great for preparing a student for the Presidency, the Supreme Court, or Congress, where, almost without exception, the officeholders are, and, in the modern era, have always been, just as innumerate.

Of the Supremes, for example, only Breyer has shown any competence in math, and that was in high school.

"More on Colleges"

No pun intended?

Mike: according to the American Heritage Dictionary (for instance), 'define' means 'To state the precise meaning of'.

As David defined the term in question by stating its precise meaning, it is evidently not undefinable.

A mathematical term can be precisely defined without listing all of its digits.

Once again, David, you're uncharitably attempting to tell people what they mean is incorrect.Like your grammar? Im sorry, but youre kindof asking for that with your tone.

If the guy chooses to use a mathematical example, it seem reasonable to judge its mathematical content. Which simply is blatantly incorrect. Perhaps by your (in my opinion lacking) definition of undefined it is not: in a mathematical context it most definitely is. Implicit definitions are perfectly fine definitions: whether or not a number can be explicitly evaluated is a completely orthogonal matter with its own terminology.

And i wouldnt have thought much about it when the guy used it in a live presentation, but considering it made it into a promotional video makes it something worthy of a blogpost id say. Ok, so there arnt many people around there with a clue about mathematics: thats not very shocking for a liberal arts school ofcource. But what you can hold against them is their appearent unawareness of their own limitations. If none of the people overseeing production could verifiy the validity of their actors' text, they should have left it out or consulted someone who did.

You could say his answer reminded you of the ratio of the hypotenuse of a right triangle with sides of equal length to one of its sides. The sky never reminds a math major of the ratio of the circumference of a circle to its diameter, but it beats philosophy.

I'd be careful of that school: they might brainwash your daughter into being a Pythagorean. And we all know how they treated nonconformists.

David wrote:

"The square root of two is quite easily defined--it is that number that, multiplied by itself, equals two."

Almost,

-sqrt(2)*(-sqrt(2))=2

Better yet:

Length of diagonal of a unit square [easiest]; positive x intercept of y=x^2-2; sqrt(i)/i+sqrt(i) where i^2=-1 [neat but less primitive]; various infinite products and sums.

There are many, many identities that could be used as a definition.

sqrt(2) is easier to define than non-conformity(!)

Most of you still don't get it. You're focusing on a mathematical meaning of defined, when the student was using the word undefinable in a non-mathematical sense; in a simile. (If that's really the word the student used: David didn't include it in the quote.)

So David's first error was in focusing on the wrong word. Undefined, which is what the student actually used, refers to expressions such as 1/0. Not to irrational numbers. That would be the students error if you pedantically presume he meant it in a literal, mathematical sense.

As Vadim pointed out, "the square root of two" is also ambiguous: that not the same as defined or undefined. That error is shared between Friedman and the student. (And I didn't notice it either.)

And Friedman's other error is not considering which aspect of "the square root of two" the student meant in his simile. As I pointed out before, the student could have been referring to the value or (much more likely) the sequence of digits.

Oh, and Taylor wrote: 'David Friedman to unnammed pretentious, math illiterate college: "Owned."' If we look at your statement, we can point out that at no time did David take posession of the college. Your pretension of coolness using an illiterate colloquial term is exactly the same non-problem.

If we want to see much worse problems at colleges, we can look to Harvard (David's undergraduate college), where tenured faculty such as Timothy Leary and Richard Herrnstein have published atrocities.

Obviously it's not such an easy issue after all, given all the discussion.

By the way, who else has seen the intro to "A Private Universe"? They interview Harvard graduates at commencement, and most of them give an incorrect explanation of why there are seasons.

Common knowledge is not so common, even for people getting the best formal education around.

-Daublin

1. I believe the word the student used--and that I used in my original post here--was "undefinable" not "undefined." The square root of two is definable.

2. I considered, in writing the original post, the fact that the negative square root of two also fits the definition. It struck me as an unnecessary complication. Strictly speaking, the negative square root of two is indeed a square root of two, although one usually applies the term to the positive root.

3. My interpretation of the student's statement was that he remembered there was something special about the square root of two but not exactly what, and was bringing it in in order to demonstrate his mathematical erudition. Mike's, I think, is that he meant that his college, like the square root of two, couldn't be precisely described. The point of the film, however, was to boost the college, and to say "one could give a good description in a hundred words, a very good description in two hundred, but there is no way of giving an absolutely perfect description" doesn't qualify.

Mike writes:

"Oh, and Taylor wrote: 'David Friedman to unnammed pretentious, math illiterate college: "Owned."' If we look at your statement, we can point out that at no time did David take posession of the college. Your pretension of coolness using an illiterate colloquial term is exactly the same non-problem."

On the contrary.

The student was attempting to use the jargon of mathematics and getting it wrong, thus demonstrating his ignorance of what he pretended to know. Taylor is attempting to use a different jargon and, so far as I know, getting it right.

To make the cases comparable you need a further step--a demonstration that he is misusing "owned."

I didn't, after all, object that two isn't a tree, doesn't have roots, and that roots aren't square, which would be equivalent to your objection that Taylor's use of one meaning of "owned" doesn't correspond to the literal meaning of the word.

All of which is an interesting observation of some non-trivial degree of importance, but not precisely relevant to any larger question.

("Non-trivial" is the term I use when I'm trying to be pretentious.)

;-)

And it's not "owned" it's "Pwnd" I think... I may have to ask one of my children.

The larger question of chosing a College or University? Might as well chose on the intangibles, which campus is prettiest or has the nicest book store or patio for sipping soy latte, or which one is closest to home and would require the least traveling expense and issues, which one has the coolest name for the car window sticker to send home to mom and dad... those sorts of things.

Which would be the coolest for your daughter to say she graduated from?

As entertaining as this is the actual decision making process is likely not significantly enhanced by trying to get all the facts in order to divinate the events of four years that haven't happened yet.

Or alternately, try to decide which school is in most need of a troublemaker rather than a conformist. :-)

David wrote 'To make the cases comparable you need a further step--a demonstration that he is misusing "owned."'

"Owned is a slang word that originated among 1990s hackers, where it referred to "rooting" or gaining administrative control over someone else's computer... Owned has now spread beyond computer and gaming contexts and become part of standard slang, where it usually entails defeat or humiliation..."

Obviously you didn't use the early meaning. I'm presuming you didn't intend "defeat or humiliation". Does that fulfill your suggested requirement?

Mike writes:

"I'm presuming you didn't intend "defeat or humiliation".

I didn't, but I think Taylor did.

David Friedman to Mike Huben : "Owned."

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