Category Archives: Uncategorized

So… yeah

Lately CJ has a habit of ending every story he tells by saying

“So… yeah.”

I first noticed it this summer, so I think he picked it up from his camp counselors. What does it mean? I tend to read it as something like

“I have told my story — what conclusions can we draw from it? Who can say? It is what it is.”

Is that roughly right? Per the always useful Urban Dictionary the phrase is

“used when relating a past event and teller is unsure or too lazy to think of a good way to conclude it”

but I feel like it has more semantic content than that. Though I just asked CJ and he says it’s just his way of saying “That’s all.” Like “Over and out.”

So yeah.

Benson Farb’s ICM talk

One of the things I’ve been spending a lot of time on mathematically is problems around representation stability and “FI-modules,” joint with Tom Church, Benson Farb, and Rohit Nagpal.  Benson just talked about this stuff at the ICM, and here it is:

In the latest stable representation theory news, Andy Putman and (new Wisconsin assistant professor!) Steven Sam have just posted an exciting new preprint about the theory of representations of GL_n(F_p) as n goes to infinity; this is kind of like the linear group version of what FI-modules does for symmetric groups.  (Or, if you like, our thing is their thing over the field with one element….!)  This is something we had hoped to understand but got very confused about, so I’m looking forward to delving into what Andy and Steven did here — expect more blogging!  In particular, they prove the Artinian conjecture of Lionel Schwartz.  Like I said, more on this later.

Hey, what’s that book you’re not reading?

bookfreshpressIn the Wall Street Journal this weekend I define a new metric aimed at identifying books people are buying but not reading.

How can we find today’s greatest non-reads? Amazon’s “Popular Highlights” feature provides one quick and dirty measure. Every book’s Kindle page lists the five passages most highlighted by readers. If every reader is getting to the end, those highlights could be scattered throughout the length of the book. If nobody has made it past the introduction, the popular highlights will be clustered at the beginning.

Thus, the Hawking Index (HI): Take the page numbers of a book’s five top highlights, average them, and divide by the number of pages in the whole book. The higher the number, the more of the book we’re guessing most people are likely to have read. (Disclaimer: This is not remotely scientific and is for entertainment purposes only!)

At the end I suggest we call this number the Piketty Index instead, because Piketty’s unlikely megahit Capital in the Twenty-First Century comes in with an index of 2.4%, the lowest in my sample.

But it’s not the winner anymore!  Hillary Clinton’s Hard Choices scores an amazing 1.9%.  But somehow I feel like HRC’s book is in a different category entirely; unlike Piketty, I’m not sure I believe it’s a book people even pretend to intend to read.

The piece got lots of press, including a nice writeup at Gizmodo today.  So I thought I’d add a few more comments here, to go past what I could do in an 800-word story.

  • Lots of people asked:  what about Infinite Jest?  In fact, that book was in the original piece but got cut for length.  Here’s the paragraph:

    Infinite Jest, by David Foster Wallace.  HI 6.4%.  There was a time, children, when you couldn’t ride the 1/9 without seeing a dozen recent graduates straining under the weight of Wallace’s big shambling masterpiece.  Apparently it was too heavy for most.  Yes, I included the endnotes in the page count.  This is another one whose most famous line – “I am in here” – doesn’t crack the Kindle top five.

  • Other books I computed that didn’t make it into the WSJ:  Stephen King’s new novel Mr. Mercedes scores 22.5%.  How To Win Friends and Influence People gets 8.8%.  And How Not To Be Wrong comes in at 7.7%.  In fact, the original idea for the piece came from my dismay that all the popular highlights in my book were from the first three chapters.  But actually that puts How Not To Be Wrong in the middle of the nonfiction pack!
  • Important:  I highly doubt the Piketty Index of the book is actually a good estimate for the median proportion completed.  And I think different categories of books can’t be directly compared.  All nonfiction books scored lower than all novels (except Infinite Jest!)  I don’t think that’s because nobody finishes nonfiction; I think it’s because nonfiction books usually have introductions, which contain lots of direct assertions and thesis statements, exactly the kind of thing Kindle readers seem to like highlighting.
  • Challenges:  can you find a book other than The Goldfinch whose index is greater than 50%?  Can you find a nonfiction book which beats 20%?  Can you find a book of any kind that scores lower than Hillary Clinton’s Hard Choices?

 

Sympathy for Scott Walker

The Milwaukee Journal-Sentinel suggests that the slow pace of job creation in Wisconsin, not recall campaign shenanigans, may be Scott Walker’s real enemy in his upcoming re-election campaign:

In each of Walker’s first three years, Wisconsin has added private-sector jobs more slowly than the nation as whole, and the gap is sizable. Wisconsin has averaged 1.3% in annual private-sector job growth since 2010; the national average has been 2.1%. Wisconsin’s ranking in private-sector job growth was 35 among the 50 states in 2011, 36 in 2012 and 37 in 2013.

Combining the first three years of Walker’s term, the state ranks behind all its closest and most comparable Midwest neighbors: Michigan (6 of 50), Indiana (15), Minnesota (20), Ohio (25), Iowa (28) and Illinois (33).

I think this is slightly unfair to Walker!  Part of the reason Michigan is doing so well in job growth since 2010 is that Michigan was hammered so very, very hard by the recession.  It had more room to grow.  Indiana’s unemployment rate was roughly similar to Wisconsin’s in the years leading up to the crash, but shot up to 10.8% as the economy bottomed out (WI never went over 9.2%.)  Now Indiana and Wisconsin are about even again.

But I do mean slightly unfair.  After all, Walker ran on a change platform, arguing that Jim Doyle’s administration had tanked the state’s economy.  In fact, Wisconsin weathered the recession much better than a lot of our neighbor states did.  (The last years Wisconsin was above the median for private-sector job growth?  2008 and 2010, both under Doyle.)   There’s some karmic fairness at play, should that fact come back to make Walker look like a weak job creator compared to his fellow governors.

 

 

Tagged , ,

Charles Franklin on “Data Visualization in Political Science,” Wednesday at Union South

Good talk:  my colleague Charles Franklin, currently on leave at Marquette running serious polling on Wisconsin’s weird political microclimate, is back in town this Wednesday to give a talk about data visualization in political science:

Polling Your Resources: Using Data Visualization in Political Science

  • DateWednesday, April 11, 2012
  • Time3 p.m.
  • LocationTITU, Union South
  • DescriptionUW-Madison faculty member Charles Franklin will share examples of data visualization and discuss helping students and the public make sense of political data. If you plan to use data visualization in your teaching, come and learn how Franklin has honed this topic for his course Understanding Political Numbers. Franklin’s academic research focuses on advanced statistical and graphical analysis of public opinion and election outcomes. Light refreshments will be served. Presented by Engage.

Bovine fraternal skin graft

Another thing I learned from the August 1951 issue of The Times Review of the Progress of Science is that cows can accept skin grafts from their fraternal twins, but humans can’t.  That’s because cow fetuses actually share some blood and tissue in the womb, and automatically get desensitized to those particular foreign entities when they’re young enough not to reject them.  This was totally new to me but apparently if I knew anything about immunology I would already be familiar with this, because Peter Medawar’s work on the phenomenon earned him the 1960 Nobel Prize and more or less launched the field of acquired transplantation tolerance.

There was also an anecdote about a baby switched at birth, who doctor proved to be the identical twin of another child in his birth family by grafting a patch of his skin onto the other kid!

Tagged , ,

Contest: worst math-related election metaphor

Just kidding: there’s not going to be a contest, because nobody’s beating Andrew Sullivan:

In one simple image, America’s soft power has been ratcheted up not a notch, but a logarithm.

What th-?

Googling reveals that I am not the first mathematician to read this sentence and say “What th-?”

Tagged , , ,

Turkelli on Hurwitz spaces and Malle’s conjecture

My Ph.D. student Seyfi Turkelli recently posted a really nice paper, “Connected components of Hurwitz schemes and Malle’s conjecture,” to the arXiv. It’s a beautiful example of the “hidden geometry” behind questions about arithmetic distributions, so I thought I’d say a little about it here.

The story begins with the old conjecture, sometimes attributed to Linnik, that the number of degree-n extensions of Q of discriminant at most X grows linearly with X, as X grows with n held constant. When n=2, this is easy; when n = 3, it is a theorem of Davenport and Heilbronn; when n=4 or 5, it is recent work of Bhargava; when n is at least 6, we have no idea.

Having no idea is, of course, no barrier to generalization. Here’s a more refined version of the conjecture, due to Gunter Malle. Let K be a number field, let G be a finite subgroup of S_n, and let N_{K,G}(X) be the number of extensions L/K of degree n whose discriminant has norm at most K, and whose Galois closure has Galois group G. Then there exists a constant c_{K,G} such that

Conjecture: N_{K,G}(X) ~ c_{K,G} X^a(G) (log X)^(b(K,G))

where a and b are constants explicitly described by Malle. (Malle doesn’t make a guess as to the value of c_{K,G} — that’s a more refined statement still, which I hope to blog about later…)

Akshay Venkatesh and I wrote a paper (“Counting extensions of function fields…”) in which we gave a heuristic argument for Malle’s conjecture over K = F_q(t). In that case, N_{K,G}(X) is the number of points on a certain Hurwitz space, a moduli space of finite covers of the projective line. We were able to control the dimensions and the number of irreducible components of these spaces, using in a crucial way an old theorem of Conway, Parker, Fried, and Volklein. The heuristic part arrives when you throw in the 100% shruggy guess that an irreducible variety of dimension d over F_q has about q^d points. When you apply this heuristic to the Hurwitz spaces, you get Malle’s conjecture on the nose.

So we were a little taken aback a couple of years later when Jurgen Kluners produced counterexamples to Malle’s theorem! We quickly figured out what was going on. There wasn’t anything wrong with our theorem; just our analogy. Our Hurwitz spaces were counting geometrically connected covers of the projective line. But a cover Y -> P^1/F_q which is connected, but not geometrically connected, provides a perfectly good field extension of F_q(t). If we’re trying to imitate the number field question, we’d better count those too. It had never occurred to us that they might outnumber the geometrically connected covers — but that’s just what happens in Kluners’ examples.

What Turkelli does in his new paper is to work out the dimensions and components for certain twisted Hurwitz spaces which parametrize the connected but not geometrically connected covers of P^1. This is a really subtle thing to get right — you can’t rely on your geometric intuition, because the phenomenon you’re trying to keep track of doesn’t exist over an algebraically closed field! But Turkelli nails it down — and as a consequence, he gets a new version of Malle’s conjecture, which is compatible with Kluners’ examples, and which I think is really the right statement. Which is not to say I know whether it’s true! But if it’s not, it’s at least the correct false guess given our present state of knowledge.

Tagged , , , , , , ,

Is there life after Potty Power?

We watched Potty Power a lot this summer. I mean, a lot. Like, John-Hinckley-watching-Taxi Driver a lot. After a while, I started wondering: who are the actors in Potty Power? Is this the kind of gig you take on your way to stardom? Or are there actors whose whole career is in toilet-training videos?

Jessica Cannon, the peppy MC and vocalist who manages to deliver lyrics like “Wash your hands / wash ‘em real good / wash your hands like you know you should” with a winning supper-club flair, appears in the New York Daily News in August 2006 as a struggling actor, working kids’ birthday parties and cocktail-waitressing between auditions to keep afloat. She’s now giving piano lessons in New York City. Matt Dyer, who plays the King to Cannon’s Queen in the play-within-a-play, “The Princess and the Potty,” got good reviews this year in a Norwich, CT production of “The Last Session,” a musical about AIDS and the music industry. Also appearing in “The Princess and the Potty” is the biggest success story of all, the scene-stealing jester Todd Alan Crain. He’s continued to appear in kids’ videos, but also seems to get consistent Off-Off-Broadway work, has some appearances on Comedy Central and the Onion News Network, and, best of all, toured the U.S. as Slim Goodbody. It sounds like what pays the bills is a steady series of jobs in the pharmaceutical industry, being the guy in the suit behind the desk who looks a little like a news anchor and introduces the in-house promotional film. I never wondered about who did jobs like that, but now I know — graduates of Potty Power.

Tagged , ,

My friend the delegate


Friend-of-the-blog Monica Youn was a delegate at the Democratic convention. In Slate, she reports on her four days in Denver:

“The yellow-vests have been overwhelmed by sheer numbers, and the convention floor has devolved to a state of nature in which only brute force prevails. Transverse movement has slowed to the point that it’s only by referring to external landmarks that you can tell, for instance, that the guy in the Uncle Sam hat has progressed eight feet in the last 20 minutes. From my vantage point, a few rows back from the floor, it’s like watching a slow-motion feed of the LaBrea, Calif., tar pits, observing once mighty creatures—Secret Service agents, EMTs, cameramen, Chuck Schumer—struggling with increasingly feeble gestures, then succumbing, brought down by the sheer weight of inertia.”

Based on the photo, Monica is in no position to be making fun of other people’s hats.

Here’s a poem of Monica’s, recently published in Guernica:

Ignatz Oasis

When you have left me
the sky drains of color

like the skin of a tightening fist.

The sun begins
its gold prowl

swatting at tinsel streamers
on the electric fan.

Crouching I hide
in the coolness I had stolen

from the brass rods of your bed.

Tagged , , ,
Follow

Get every new post delivered to your Inbox.

Join 553 other followers

%d bloggers like this: