By the way, sometime yesterday this blog received its millionth visit.

By the way, sometime yesterday this blog received its millionth visit.

Lots of good stuff happening in math blogging!

- Matt Baker is blogging! Lately: an appreciation of Robert Coleman, and Riemann-Roch for graphs.
- Frank Calegari is blogging! Actually he’s been blogging for a while but there’s tons of good stuff on here lately. Two recent posts that tie in closely with my own interests: The congruence subgroup property for thin groups, and The thick diagonal, in which Frank’s student Vlad Serban solves a puzzle I asked about, and much more besides. Also, Cheeseboard still wins.
- Adriana Salerno is blogging! Mostly about the profession and specifically the situation of young researchers in math. I like this post about collaborator visits because my old friend Leila Schneps, who taught me about the fundamental group, guest-stars in it!
- And just so it’s not all number theorists: Afonso Bandeira is blogging! I don’t even know this guy, but he’s writing tons of interesting stuff about problems in what I like to call “applied pure math,” questions about geometry of large sets and classification and convex relaxation and embeddings of metric spaces and etc. and etc.

This is the thousandth post.

I was going to use this space to give you some statistics, maybe make a Wordle, etc., but I couldn’t figure out how to get WordPress to give me the relevant statistics.

So let’s just say I’ve written a lot of stuff on this blog. No way is the mean post less than 200 words long, so let’s say close to a thousand print pages. And I’m really, really glad. I know lots of people think the blog is dead and we’re all to fling aphorisms at each other on Twitter and Facebook instead. I love aphorism-flinging, but, for me, blogging sits in a kind of perfect sweet spot; “published” enough that I feel someone’s out there reading, informal enough that I don’t mind making mistakes, short enough that I can bang out a post without compromising a workday, long enough that I can shape an argument that’s not just an aphorism. Writing this blog, and reading other people’s blogs, has enriched my published writing and my mathematics too. And I think in some small way it’s been useful to others — the blog has been cited at least 4 times on the arXiv! That’s more than plenty of my papers.

I don’t care if the blog is dead — if you’re on the fence about starting one, I say you should do it.

A few notes:

- My most popular post, by a mile, was my post alerting the community to Mochizuki’s claimed proof of ABC, which was linked to by several big sites like Hacker News. It’s been viewed over 50,000 times. The next most popular was a post about a hiring controversy in math that I won’t link to because the matter is long settled to everyone’s satisfaction. Next was a post sharing an anonymous account of treatment at a halfway house which is believed to be by David Foster Wallace. In fact, of the 10 most popular posts, 7 are about math, 2 are about David Foster Wallace, and the remaining one is Is There Life After
*Potty Power*? which, based on my search logs and the comments, gets a lot of views from people who, after hundreds of viewings, have developed a romantic attachment to the star of a toilet-training video. - From this you should get the basic idea — people like the math posts a lot and the literature posts a fair amount. And nobody cares about the Orioles at all.
- When I was considering starting this blog, I asked David Carlton, who’s been doing it much longer, what the secret was to keeping up a blog and not letting it die out. “Low standards,” he told me. What he meant: to blog you have to be willing to to write things that are inarticulate, or not fully-thought-through, or which still have pieces missing; otherwise blog entries (like some math papers!) end up languishing, invisible and unfinished, forever. I think it would be better for math if those messy and partial ideas were more public than they are, and I think one way for this to happen is for more mathematicians to blog. And to have low standards.

I’m told that one trick to the astonishing feats carried out by world-class competitive eaters is that your satiety sensor is on something like a twenty-minute delay; so you can really pack an immense amount of food into your body before your brain realizes you’re doing something your stomach doesn’t want you to do.

I was talking to a colleague who wants to start a blog and asked for some advice, and I realized that blogging is kind of like this, too. My math posts are very casual and full of mistakes, and the reason is that my practice is to write a post as soon as it occurs to me — I then have about a half hour before my brain says “Wait, you’re supposed to be working right now.” So in that half hour I have to write as fast as I can, like Kobayashi smashing hot dogs into his mouth.

Yes, this is me blogging:

Is this a good time to mention that I once drank a gallon of milk in four minutes? Here are my tips for success at this important task:

- Filling and chugging and refilling and rechugging a glass, rather than drinking straight from the jug; this makes it more like doing a normal thing ten times in very short succession, rather than the abnormal and stupid thing that you are actually doing;
- Not knowing it’s supposed to be impossible;
- Being 16.

I’ve been thinking about changing the theme of this blog. But I realize that I have very little knowledge about blog design. Some things I thought I might like:

- A serif text font instead of the sans serif I use now;
- A wider design that keeps the sidebar a little farther from the main text;
- Something whose quote format doesn’t involve a giganto quotation mark.

But you are the people reading this, so your opinions matter more than mine! Are serif fonts indeed more reasonable? Is wider better or worse? (I keep the browser window very wide, like a screen, but for all I know, maybe people use the aspect ratio of a piece of paper.) Am I right that it’s completely unacceptable for only excerpts from the post to appear on the front page?

Feel free to suggest specific themes or general design principles. I just want to be presentable!

Those of us outside Silicon Valley tend to think of it as a single entity — but venture capitalists and developers are not the same people and don’t have the same goals. I learned about this from David Carlton’s blog post. Cathy O’Neil reposted it this morning. It’s kind of cool that the three of us, who started grad school together and worked with Barry Mazur, are all actively blogging! We just need to get Matt Emerton in on it and then we’ll have the complete set. Maybe we could even launch a new blogging platform and call it **mazr**. You want startup culture, I’ll give you startup culture!

The comments on yesterday’s post turned into another boring “feminism sux / feminism roolz” thread. I get it — some people think it’s worth thinking about gender issues in math, some people don’t, people are going to have that discussion. Fine.

My request: if you are going to comment on a “women in math,” thread, or for that matter, any other thread that gets people’s political dander up, try to direct your comment at the material of the particular post. If your comment would apply equally well to any imaginable post about women in math, then maybe don’t post it.

This month’s *On Wisconsin *has a feature on UW faculty blogs, including this one. I had no idea there were so many! John Hawks, who writes bracingly about anthropology, is said to get 8,000 hits a day. (I get…. fewer than that.) Deborah Blum, who teaches our aspiring science journalists, stands up for science blogging at Speakeasy Science. Economics prof Menzie Chinn co-blogs at Econbrowser; lots of good material up there right now about the state of the Wisconsin budget. And our communications grad students have a group blog, Antenna: great news for people like me who have no idea what our communications grad students do. (It seems that among other things they think carefully about reality TV, an activity of which I approve.)

Use comments to promote any UW blogs the article missed!

Reader majordomo comments on my post about the Sat. Nite Duets/Fatty Acids:

What is with you and obscure bands, I don’t understand your obsession with nameless, obscure bands. You’re probably one of those guys who hate the Beatles because too many people like them, right ?

Actually, no. When I was 11 the only two albums I owned were Beatles best-ofs, the Blue Album and the Red Album. I thought the Beatles were the best band in the history of rock music. And I still think so!

But the Beatles have armies of people to write about their greatness. Who will blog about Sat. Nite Duets and Fatty Acids, or Yellow Ostrich, or Grammar, or Carsick Cars, or The Stevedores, if not me? These people work hard on their records, they give them away free or almost free — why shouldn’t they get some tiny signal from the world outside that somebody liked the songs they wrote?

By the way, I went to the show to see Sat. Nite Duets but Fatty Acids turned out to be great too. Here’s “Astrovan”:

I hope that was not annoying to majordomo. In case it was, here’s “I am the Walrus.” CJ watches this video a lot and I’ve fallen in love with the song all over again. How do they get so much stuff *in *there?

Good Lord, did you know Styx covered “I am the Walrus?” I did not. It is awful.

As it happens, I actually had a post about Styx in mind! I’ll put it up now. I hope it is mainstream enough for majordomo.

The following brain-teaser has been going around, identified as a question from a Google interview (though there’s some controversy about whether Google actually uses questions like this.)

There’s a certain country where everybody wants to have a son. Therefore each couple keeps having children until they have a boy; then they stop. What fraction of the population is female?

Steve Landsburg posted a version of this question on his blog. “The answer they expect,” he writes, “is simple, definitive, and wrong… Are you smarter than the folks at Google? What’s the answer?”

Things quickly went blooey. Google’s purported answer — fiercely argued for by lots of Landsburg’s readers — is 1/2. Landsburg said the right answer was less. A huge comment thread and many follow-up posts ensued. Lubos Motl took time out from his busy schedule of yelling at mathematicians about string theory to yell at Landsburg about probability theory. Landsburg offered to bet Motl, or anybody else, $15,000 that a computer simulation would demonstrate the correctness of his answer.

What’s going on here? How could a simple probability question have stirred up such a ruckus?

Here’s Landsburg’s explanation of the question:

What fraction of the population should we

expectto be female? That is, in a large number of similar countries, what would be the average proportion of females?

If G is the number of girls, and B the number of boys, Landsburg is asking for the expected value E(G/(G+B)). And let’s get one thing straight: Landsburg is absolutely right about this expected value. For any finite number of families, it is strictly less than 1/2. (See the related Math Overflow thread for a good explanation.) Landsburg has very patiently knocked down the many wrong arguments to the contrary in his comments section. Anybody who bets against him, on his terms, is going to lose.

Nonetheless, I’m about to explain why Landsburg is wrong.

You see, Google’s version of the question doesn’t specify anything about expectation. They might just as well have meant: “What is the proportion of the expected number of females in the expected population?” Which is to say, “What is E(G)/E(G) + E(B)”? And the answer to *that* question is 1/2. Just to emphasize the subtlety involved here:

On average, the number of boys and the number of girls are the same. Furthermore, the proportion of girls is, on average, less than 1/2.

Weird, right? E(G)/E(G) + E(B) isn’t what Landsburg was asking for — but, if Google’s answer was 1/2, it’s presumably the question they had in mind. To accuse them of getting their own question “wrong” is a bit rich.

But let me go all in — I actually think Landsburg’s interpretation of the question is not only different from Google’s, but in some ways inferior! Because averaging ratios with widely ranging denominators is kind of a weird thing to do. You can certainly compute the average population density of all the U.S. states — but *should you?* What meaning or use would the result have?

I had a really pungent example ready to deploy, which illustrates the perils of averaging ratios and explains why Landsburg’s version of the question was a little weird. Then I went to the Joint Meetings before getting around to writing this post. And when I got back, I discovered that Landsburg had posted the same example on his own blog — *in support* of his point of view! Awesome. Here it is:

There’s a certain country where everybody wants to have a son. Therefore each couple keeps having children until they have a boy; then they stop. In expectation, what is the ratio of boys to girls?

The answer to this question is, of course, infinity; in a finite population there *might* be no girls, so B/G is infinite with some positive probability, so E(B/G) is infinite as well.

But the correctness of that answer surely tells us this is a terrible question! Averaging is a terribly cruel thing to do to a bunch of ratios. One zero denominator and you’ve wiped out your entire dataset.

What if Landsburg had phrased his new question along the lines of Google’s original puzzle?

There’s a certain country where everybody wants to have a son. Therefore each couple keeps having children until they have a boy; then they stop. What is the ratio of boys to girls in this country?

Honest question: does Landsburg truly think that infinity is the only “right answer” to this question? Does he think infinity is a *good* answer? Would he hire a person who gave that answer? Would you?

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