Oh, what a tangled web we weave 

You can't fire a tenured professor for voicing approval of the 9/11 attacks. But surely you can fire him for lying about his identity and plagiarism, right?


Anybody need a free copy of Hartshorne's "Algebraic Geometry"? 

All you have to do is click on here and complete a couple of promotional offers (applying for a credit card, sign up for a Blockbuster or Netflix membership, or other stuff).

I'm going to guess that this isn't one of their bigger draws.


Just got through my first grown-up seminar talk ever.


Issues of intrinsic aptitude hamper Larry Summers's critics 

Here's (part of) what Larry Summers actually said:

The second thing that I think one has to recognize is present is what I would call the combination of, and here, I'm focusing on something that would seek to answer the question of why is the pattern different in science and engineering, and why is the representation even lower and more problematic in science and engineering than it is in other fields. And here, you can get a fair distance, it seems to me, looking at a relatively simple hypothesis. It does appear that on many, many different human attributes-height, weight, propensity for criminality, overall IQ, mathematical ability, scientific ability-there is relatively clear evidence that whatever the difference in means-which can be debated-there is a difference in the standard deviation, and variability of a male and a female population. And that is true with respect to attributes that are and are not plausibly, culturally determined. If one supposes, as I think is reasonable, that if one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean. And perhaps it's not even talking about somebody who is three standard deviations above the mean. But it's talking about people who are three and a half, four standard deviations above the mean in the one in 5,000, one in 10,000 class. Even small differences in the standard deviation will translate into very large differences in the available pool substantially out. I did a very crude calculation, which I'm sure was wrong and certainly was unsubtle, twenty different ways. I looked at the Xie and Shauman paper-looked at the book, rather-looked at the evidence on the sex ratios in the top 5% of twelfth graders. If you look at those-they're all over the map, depends on which test, whether it's math, or science, and so forth-but 50% women, one woman for every two men, would be a high-end estimate from their estimates. From that, you can back out a difference in the implied standard deviations that works out to be about 20%. And from that, you can work out the difference out several standard deviations. If you do that calculation-and I have no reason to think that it couldn't be refined in a hundred ways-you get five to one, at the high end. Now, it's pointed out by one of the papers at this conference that these tests are not a very good measure and are not highly predictive with respect to people's ability to do that. And that's absolutely right. But I don't think that resolves the issue at all. Because if my reading of the data is right-it's something people can argue about-that there are some systematic differences in variability in different populations, then whatever the set of attributes are that are precisely defined to correlate with being an aeronautical engineer at MIT or being a chemist at Berkeley, those are probably different in their standard deviations as well. So my sense is that the unfortunate truth-I would far prefer to believe something else, because it would be easier to address what is surely a serious social problem if something else were true-is that the combination of the high-powered job hypothesis and the differing variances probably explains a fair amount of this problem.

Naturally, in this New York Times piece the authors get from "there's a bigger spread in the mathematical abilities of men than there is in women" to "women aren't as good as men".

Granted, Larry Summers's evidence for his proposition consist of one study of twelfth-graders and a bunch of back-of-the-envelope calculations, but it's clear that he's put some amount of thought into his theory. Just looking at a table of values for the cumulative distribution function N, N(-2) = 0.0228 and N(-1.6) = 0.0548. So a 20% difference in the standard deviations for men and women would lead to approximately a 2-1 ratio in the number of men to women within the top 4% of the population or so. If we hypothesize that a man needs to be 2.5 standard deviations above the norm to be a successful scientist, we have N(-2.5) = 0.0062. But since 2.5 male standard deviations would equal 3 female standard deviations, we have N(-3) = 0.0013. Voila, a 5-1 ratio in the number of men to women.

My own limited evidence might undercut the differences-in-variability theory; I looked at my most recent multivariable class and calculated about the same average and standard deviation in grades for men and women. However, that's for a preselected class of students whose abilities lie in a specific range, so that isn't completely compelling evidence either. The point is that (1) Summers's theory (which surely is not original) deserves serious, dispassionate inquiry, and that (2) a fair number of Summers's critics either suffer from innumeracy or are willfully misinterpreting his thesis. But I guess nowadays it's not possible to make comments about an aggregate of people without people thinking that it applies to them as individuals.

One final (facetious) thought: the flip side of Summers's theory is that men are also five times as likely as women to be dumb as rocks (at least mathematically). Why is there not a humongous kerfluffle about this insinuation?


The dotcom bubble bursts, again 

Exaggerated enthusiasm, overagressive growth, inflated salaries...and then the crash.

The NHL has cancelled the 2004-05 season.

Steve Yzerman may well have to retire, his last game ending when he got drilled in the eye with a puck.


Blogging is an occupational hazard 

Whoops, that probably should say "blogging can be hazardous to your occupation."

Anyway, Google axed some guy for complaining about the company on his blog.

I think it's pretty lousy for a company to fire an employee for this sort of thing. It's not like he was giving away proprietary trade secrets or anything. But at the same time, bloggers should consider that literally the entire universe can read what they write, so it makes sense not to blog about work.

And no, I'm not going to boycott Blogger on account of Google. I might boycott Blogger if and when I get my own domain and install MoveableType or similar software on it.

(HT: Ben Wang)


Odds on Paul McCartney' first song 

From SportsInteraction, as of 1:13 PM EST:

Ticket To Ride 3.5-1
The Long And Winding Road 4.5-1
Come Together 6-1
Get Back 7-1
Cant Buy Me Love 9-1
Help! 11-1
Love Me Do 11-1
Something 11-1
With A Little Help From My Friends 11-1
Helter Skelter 11-1
Twist And Shout 13-1
Band On The Run 13-1
Please Please Me 13-1
She Loves You 13-1
Hello Goodbye 15-1
Dont Let Me Down 15-1
Maybe I'm Amazed 17-1
Sgt. Peppers Lonely Hearts Club Band 17-1
Here Comes The Sun 17-1
A Hard Days Night 17-1
I Want To Hold You Hand 17-1
From Me To You 17-1
We Can Work It Out 19-1
Silly Love Songs 19-1
Ebony And Ivory 19-1
Say Say Say 19-1
Listen To What The Man Said 21-1
Let It Be 21-1
I Feel Fine 21-1
All You Need Is Love 21-1
Paperback Writer 26-1
Thank You Girl 26-1
Yesterday 26-1
Blackbird 26-1
Baby You're A Rich Man 29-1
Penny Lane 34-1
Day Tripper 34-1
Pipes Of Peace 34-1
No More Lonely Nights 34-1
In My Life 34-1
Hey Jude 34-1
Magical Mystery Tour 41-1
We All Stand Together 41-1
Till There Was You 51-1
A Day In The Life 51-1
My Love 51-1
Eleanor Rigby 51-1
Strawberry Fields Forever 51-1
Mull Of Kintyre 67-1
Something 67-1
Martha My Dear 81-1
Back In The U.S.S.R. 101-1
Lady Madonna 101-1
Yellow Submarine 101-1
I Am The Walrus 151-1
Why Dont We Do It In The Road 201-1

UPDATE: The winner is "Drive My Car", which isn't even on the books.



Insurgents capture a toy soldier and hold it hostage, leading to hilarious consequences.

I don't know if it was actually a group of insurgents who staged the hoax, or just a bunch of random guys. Though it doesn't seem too likely to me, I'm hoping it's the former, as that'd be a sign that the insurgents are getting desperate

This page is powered by Blogger. Isn't yours?