Obscure novels that are great

I was thinking about the amazing and barely read here TRIOMF, by Marlene van Niekerk, and asked on Twitter:  what are novels you think are truly great and which nobody knows about?  Like, say, less than 10 Amazon reviews, to use an imperfect measure?

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Imagine 33 percent

This, from the New York Times Book Review, bugged me:

There are 33 percent more such women in their 20s than men. To help us see what a big difference 33 percent is, Birger invites us to imagine a late-night dorm room hangout that’s drawing to an end, and everyone wants to hook up. “Now imagine,” he writes, that in this dorm room, “there are three women and two men.”

It’s not so bad that the reviewer was confused about percentages; it’s that she went out of her way to explain what the percentage meant, and said something totally wrong.

I figured the mistake was probably inherited from the book under review, so I checked on Google Books, and nope; the book uses the example, but correctly, as an example of how to visualize a population with 50% more women than men!

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Lipnowski-Tsimerman: How large is A_g(F_p)?

Mike Lipnowski and Jacob Tsimerman have an awesome new preprint up, which dares to ask:  how many principally polarized abelian varieties are there over a finite field?

Well, you say, those are just the rational points of A_g, which has dimension g choose 2, so there should be about p^{(1/2)g^2} points, right?  But if you think a bit more about why you think that, you realize you’re implicitly imagining the cohomology groups in the middle making a negligible contribution to the Grothendieck-Lefchetz trace formula.  But why do you imagine that?  Those Betti numbers in the middle are huge, or at least have a right to be. (The Euler characteristic of A_g is known, and grows superexponentially in dim A_g, so you know at least one Betti number is big, at any rate.)

Well, so I always thought the size of A_g(F_q) really would be around p^{(1/2) g^2}, but that maybe humans couldn’t prove this yet.  But no!  Lipnowski and Tsimerman show there are massively many principally polarized abelian varieties; at least exp(g^2 log g).  This suggests (but doesn’t prove) that there is not a ton of cancellation in the Frobenius eigenvalues.  Which puts a little pressure, I think, on the heuristics about M_g in Achter-Erman-Kedlaya-Wood-Zureick-Brown.

What’s even more interesting is why there are so many principally polarized abelian varieties.  It’s because there are so many principal polarizations!  The number of isomorphism classes of abelian varieties, full stop, they show, is on order exp(g^2).  It’s only once you take the polarizations into account that you get the faster-than-expected-by-me growth.

What’s more, some abelian varieties have more principal polarizations than others.  The reducible ones have a lot.  And that means they dominate the count, especially the ones with a lot of multiplicity in the isogeny factors.  Now get this:  for 99% of all primes, it is the case that, for sufficiently large g:  99% of all points on A_g(F_p) correspond to abelian varieties which are 99% made up of copies of a single elliptic curve!

That is messed up.


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Leibniz on music

Leibniz wrote:

Even the pleasures of sense are reducible to intellectual pleasures, known confusedly.  Music charms us, although its beauty consists only in the agreement of numbers and in the counting, which we do not perceive but which the soul nevertheless continues to carry out, of the beats or vibrations of sounding bodies which coincide at certain intervals.

Boy, do I disagree.  Different pleasures are different.

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Bobrowski-Kahle-Skraba on the null hypothesis in persistent homology

I really like persistent homology; it’s a very beautiful idea, a way to look for structure in data when you really don’t have any principled way to embed it in Euclidean space (or, even when it does come embedded in Euclidean space, to find the kind of structure that doesn’t depend too much on the embedding.)

But because I like it, I want to see it done well, so I have some minor complaints!

Complaint one:  Persistent homology, applied to H_0 only, is clustering, and we know a lot about clustering already.  (Update:  As commenters point out, this is really only so for persistent homology computed on the Vietoris-Rips complex of a point cloud, the “classical case…”!)  Not to say that the ideas of persistence can’t be useful here at all (I have some ideas about directed graphs I want to eventually work out) but my sense is that people are not craving new clustering algorithms.  I really like the work that tries to grapple with the topology of the data in its fullness; I was really charmed, for instance, by Ezra Miller’s piece about the persistent homology of fruit fly wings.  (There’s a lot of nice stuff about geometric probability theory, too — e.g., how do you take the “average” of a bunch of graded modules for k[x,y], which you may think of as noisy measurements of some true module you want to estimate?)

My second complaint is the lack of understanding of the null hypothesis.  You have some point cloud, you make a barcode, you see some bars that look long, you say they’re features — but why are you so sure?  How long would bars be under the null hypothesis that the data has no topological structure at all?  You kind of have to know this in order to do good inference.  Laura Balzano and I did a little numerical investigation of this years ago but now Omer Bobrowski, Matthew Kahle, and Primoz Skraba have proved a theorem!  (Kahle’s cool work in probabilistic topology has appeared several times before on Quomodocumque…)

They show that if you sample points from a uniform Poisson process on the unit cube of intensity n (i.e. you expect n points) the longest bar in the H_k barcode has

(death radius / birth radius) ~ [(log n)/(log log n)]^(1/k).

That is really short!  And it makes me feel like there actually is something going on, when you see a long barcode in practice.

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Going Out of Business

There’s a certain strain of 1960s-70s visual art that’s so sunny, so optimistic, so earnest in its belief that a better world is possible and that world would be really colorful, that it makes me cheerful whenever I see it.  (Relevant:  Mexico 68 Olympics poster.)  So I was happy to go by this in the Chazen today:

But it turns out that, while Mel Bochner is actually a painter active in that era, he made this in 2013!  Thanks for keeping it going, Mel Bochner, whoever you are.  I like this a lot and I like the Chazen for putting it up.

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Farting princess

Not gonna lie, AB is into talking about farts.  She’s 5, she likes farts, that’s how it is.  We have a new thing where she is the “farting princess” and whenever she farts I say

Well done, your farting majesty!”

and if she farts again,

“All the farting kingdom is enjoying your royal fart!”

She also likes “The Monster Mash” so I wrote a fart-centered take on this song which she really enjoys.  Lyrics follow.

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Patience and maturity

Wimpie de Klerk — older brother of F.W. de Klerk, who would later become the last apartheid ZA prime minister — was by the standards of mainstream Afrikaner politics a racial liberal.  Here’s how that sounds in December 1981:

Experience throughout the world shows that black groups have a thin skin in their attitude to whites, and the reverse is apparently often the case.  We simply have to accept this element of mutual hatred…

We, the whites, will have to take a lead, and forget about demanding an eye for an eye on the score of hatred.  We must exercise patience and maturity.

“Apparently” is my favorite part.

By the late 1980s, by the way, de Klerk, against his brother’s wishes, was participating in secret meetings with the ANC.

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The greatest Royal/Met

A while ago I wrote a little Python code that used career data from Baseball-Reference Play Index (the best $36/year a number-loving baseball fan can spend) to answer the question:  given a pair of teams, which player contributed the most to both teams?  My metric for this is

(WAR for team 1 * WAR for team 2)

in order to privilege players who balanced their contributions to both teams.

So who was the greatest Royal/Met?  In retrospect, this should have been obvious.  How many of the top 5 can you guess?

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A free writing tip, or: the extraordinary m*****f*****s who founded this country

It gets under my shirt when writers use “individuals” as a synonym for “people.”  It sounds bureaucratic, like a police report:  “Several individuals were observed entering the vehicle in the vicinity of the establishment…”

But people do this all the time, especially when they’re trying to sound a little formal.  I have a writing tip:  every sentence in which “individual” is used in this way is improved by replacing the word “individual” with “motherfucker.”

For example, the New York Times business bestseller list describes the book Succeed On Your Own Terms as an account of “The defining qualities shared by highly accomplished individuals.”

Now try:

“The defining qualities shared by highly accomplished motherfuckers.”

Doesn’t that sound like a better book?

Or consider the remarks by Republican National Committee chief of staff Katy Walsh, about the Koch brothers:

“I think it’s very dangerous and wrong to allow a group of very strong, well-financed individuals who have no accountability to anyone to have control over who gets access to the data when, why and how.”

Strong words, but

“I think it’s very dangerous and wrong to allow a group of very strong, well-financed motherfuckers who have no accountability to anyone to have control over who gets access to the data when, why and how,”

would have been stronger.

A great source of “individuals” is the amazing database of Presidential speeches and proclamations at UCSB.  Here’s Ronald Reagan, on October 24, 1986:

And when it happens and we’re able, for the first time, to reduce the number of nuclear weapons threatening mankind, it will be a result of the realism and commitment of solid motherfuckers like Don Nickles, motherfuckers who understand that peace through strength is not just a slogan, it’s a fact of life.

That’s what Reagan should have said, at any rate.

Bill Clinton on Flag Day 1997:

Adopted by the Continental Congress on June 14, 1777, the Stars and Stripes became the official flag of the young United States and a compelling symbol of our new independence. Woven into its folds were the hopes, dreams, and determination of the extraordinary motherfuckers who founded this country.

And Barack Obama, proclaiming National Maritime Day this May:

Our Nation is forever indebted to the brave privateers who helped secure our independence, fearlessly supplying our Revolutionary forces with muskets and ammunition. Throughout history, their legacy has been carried forward by courageous seafarers who have faithfully served our Nation as part of the United States Merchant Marine—bold motherfuckers who emerged triumphant in the face of attacks from the British fleet in the War of 1812, and who empowered the Allied forces as they navigated perilous waters during World War II.

But perhaps nobody did it better than John Quincy Adams, in his inaugural address of 1825, pleading for Americans to put aside their political differences and work together:

There still remains one effort of magnanimity, one sacrifice of prejudice and passion, to be made by the motherfuckers throughout the nation who have heretofore followed the standards of political party. It is that of discarding every remnant of rancor against each other, of embracing as countrymen and friends, and of yielding to talents and virtue alone that confidence which in times of contention for principle was bestowed only upon those who bore the badge of party communion.

John Quincy Adams was one bipartisan motherfucker.

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