Pandemic social life as villanelle

When I took creative writing in high school my idea of writing a poem was writing down some thoughts that felt expressive to me and organizing those thoughts into lines of various lengths. Our teacher gave us assignments to write poems in form: sonnets, pantoums, villanelles. This seemed artificial and out-of-date and absurdly restrictive. Why should line 2 have to rhyme with line 5?

What our teacher said was that the absurd restrictions are there to be restrictions. If you sit down with the goal of expressing yourself you only say what you intend to say and this is rarely interesting. The restrictions of form force you into a channel you’re not used to and then you might find yourself saying something you didn’t know you wanted to say.

So maybe pandemic social life was like that? It sort of was, for me. I wasn’t in the office so I didn’t see math people and chat with them there as usual. I wasn’t running into people at the coffeeshop. So I did some things I didn’t usually do. I was on Zoom calls with groups of people from my class in high school. I impulsively accepted Misha Glouberman’s invitations to be on Zoom calls with groups of Canadians I barely knew. I called old friends on the phone without warning them I was going to call, and talked to them. People I usually talk to about every five years I talked to every three months.

Writing a sonnet in class doesn’t mean you go around talking in sonnets afterwards. Maybe you never write a sonnet again. But the things I did when my social life ran through this weird channel are things I’m glad I did.

Pandemic blog 41: dream

I’m in New York City. An app on my phone shows me when anyone in my contact list comes nearby, and I see that my friend Mark Poirier is just a block away — I haven’t seen him in years, what a treat! So I go meet up with him. We’re hungry so we go to an underground food court to get doner kebab. But suddenly I realize, I’m not wearing a mask, nobody‘s wearing a mask, what am I doing inside in a crowded place unmasked? Fortunately I have one with me, so I put it on; but a woman in a block-print T-shirt first glares at me, then gets into it with me, insisting that I shouldn’t wear one. I don’t know how to respond; I feel chastened, even though I know I’m in the right.

Edits

New Year’s Eve is a time to think about what we’ll remember from the year about to expire, so this is a post about memory.

A few years back, Christina Nunez, who went to high school with me, wrote a blog post which included this recollection of the history class we both took:

This class was supposed to be an “honors” class, but it slowly became apparent that we were learning nothing at all outside of the reading and research we were required to do on our own. The classes were taken up mostly by two things, in my memory: watching videos about cathedrals, and listening to our teacher talk unrestrained about stuff that had nothing to do with history. Mr. C was a relatively tall, big man with a belly, a mustache somewhere between horseshoe and walrus, and a very sharp, incisive way of speaking. His way of holding forth made you feel—in the beginning—that it might be important to listen, because something was going to be revealed. He would punctuate his lectures, which often had nothing at all to do with history, with questions to the group. “Who here has ever had a dream?” he would ask, and we raised our hands, and then waited for the point.

Later, we learned not to bother raising our hands or waiting for the point.

…

Toward the end of the semester, a kid named Jordan had taken to sitting in the back of the class on the floor, backpack in front of him, and sleeping either slumped over or with his head lolled back against the wall. This was typical teen behavior made slightly untypical by the fact that Jordan was an academic prodigy. He was the kid who got a perfect score on his SATs before we were even supposed to take the SATs…

So when a kid like Jordan sat at the back of class sleeping, it was amusingly refreshing, because kids like us who got placed in those classes tended not to be the ones sleeping at the back of class. But it was also a little unnerving, because he was signaling a truth that was sort of scandalous for this particular track at this particular school at this particular time: this class and this teacher were an absolute fucking joke.

Mr. C tolerated this open act of defiance from Jordan for I don’t know how long before he finally got sick of it. One day, he began yelling. Jordan ignored it at first, but then he was roused to perform a sleepy, casual and yet brutal takedown of Mr. C as a teacher. It was something along the lines of I don’t need to take this class, you have nothing to teach me, I am learning nothing here that I can’t learn from a book. Et cetera. Mr. C lost it. I think spittle formed as he ordered Jordan out of the classroom. The kid picked up his backpack and walked out. I had never seen Jordan act remotely disrespectful, and had never seen a teacher so boldly—no, deservedly—challenged, and it was kind of thrilling but also a little sad. All of us, including Mr. C, were wasting our time in that room, and there was really nothing to be done about it.

That’s a pretty great story!  It obviously made a big impression on Christina, and why not?  I did something memorably crazy and out of the ordinary.

But I don’t remember it.  Not at all.  Not even with this reminder.

It happened, though.  Here’s how I know.  Because what I do remember is that I wasn’t allowed in Mr. C’s classroom.  I remember sitting outside in the hall day after day while all the other kids were in class.  Who knows how long?  I remember I was reading a Beckett play I got out of the school library.  I think it was Krapp’s Last Tape.  It never occurred to me, in the thirty years between then and now, to wonder what I did to get kicked out of class to read Beckett by myself while my friends were open quote learning close quote history.

I opened up a Facebook thread and asked my classmates about Christina’s story.  It happened; they remembered it.  I still didn’t.  And I still don’t.

It doesn’t seem like the sort of thing I would do, does it?  It doesn’t seem to me like the sort of thing I would do.  My memory of high school is that I followed all the rules.  I went to football games.  I went to pep rallies.  I liked high school.  Or did I?  Maybe, because I think of myself as somebody who liked high school, I’ve just edited out the moments when I didn’t like it.  Who knows what else I don’t remember?  Who knows who else I was angry at, who else I defied or denounced, what else got edited out because it didn’t fit the theme of the story?

And who knows what’s happening now that I’ll later edit out of my 2018?  Maybe a lot.  Most things don’t get blogged.  They just get lost.  You can’t have a new year unless you get rid of the old year.  You keep some things, you lose more.  And what you lose isn’t random.  You decide what to remove from yourself, and, having decided, you lose the decision, too.

Mathematicians becoming data scientists: Should you? How to?

I was talking the other day with a former student at UW, Sarah Rich, who’s done degrees in both math and CS and then went off to Twitter.  I asked her:  so what would you say to a math Ph.D. student who was wondering whether they would like being a data scientist in the tech industry?  How would you know whether you might find that kind of work enjoyable?  And if you did decide to pursue it, what’s the strategy for making yourself a good job candidate?

Sarah exceeded my expectations by miles and wrote the following extremely informative and thorough tip sheet, which she’s given me permission to share.  Take it away, Sarah!

 

 

People I saw

Another post for my own records, just to keep track of all the old friends and new acquaintances I was happy to see while traveling for How Not To Be Wrong.  Ordered roughly chronologically and from memory:

Paula and Jay Gitles, Aleeza Strubel, Daniel Biss, Stephen Burt, Jessie Bennett, Jay Pottharst, Bob and Donna Friedman, Vineeta Vijayaraghavan, Larry Hardesty, Moon Duchin, Mira Bernstein, Jerry and Cynthia and Rachel Frenkil, Audrey and Scott Zunick, Joe Schlam, Dick Gross, Noam Elkies, Ben and Elishe Wittes, Eric Walstein, Larry Washington, Manil Suri, Ivars Peterson, Tina Hsu, David Plotz, Josh Levin, Amy Eisner, Deane Yang, Michelle Shih, Warren Bass, Meredith Broussard, Jon Hanke, Tom Scocca, Cathy O’Neil, John Swansburg, Mike Pesca, Kardyhm Kelly, Charlie Jane Anders, Mimi Lipson, Annalee Newitz, Ken Katz, Jill Himmelfarb, The Invisible Cities, Patrick LaVictoire, Akshay Venkatesh, Ravi Vakil, Gary Antonick, David Carlton, Liesl Bross, Miranda Bross, Mark Lucianovic, Tom Church, Yuran Lu, Daniel Kane, Leslie Rappoport, Douglas Wolk, Derek Garton, Matt Haughey, Josh Millard, Brian LaMacchia, Lionel Levine, Ana Crossman (and her mom), Heather Evans (and her mom), Bianca Viray.

 

It was very social!  And sorry to the people I’ve inevitably skipped.

 

Ought there be a school just for math kids?

Proof School is a proposed San Francisco middle/high school (grades 7-12) which proposes to do three hours of higher math a day.

“THERE OUGHT TO BE A SCHOOL JUST FOR MATH KIDS,” WE SAID. “BUT THERE ISN’T ONE.”

THEN WE ASKED, “WHY DON’T WE BUILD ONE?”

It seems certain this will be a great school, given that people like Ravi Vakil, Mira Bernstein and Richard Rusczyk are involved.

But I can’t help but be slightly put off by the presentation.  “We get math kids” is used as a kind of unifying slogan — in fact, it’s even trademarked!  (I hope my quoting it here does not require some form of license.)

I think it’s bad for us to carve out “math kid” as a kind of kid, separate from all others.  I think there ought to be an amazing school like the one Ravi and friends are building, but I don’t think it ought to be “just for math kids.”

 

 

How much is the stacks project graph like a random graph?

Cathy posted some cool data yesterday coming from the new visualization features of the magnificent Stacks Project.  Summary:  you can make a directed graph whose vertices are the 10,445 tagged assertions in the Stacks Project, and whose edges are logical dependency.  So this graph (hopefully!) doesn’t have any directed cycles.  (Actually, Cathy tells me that the Stacks Project autovomits out any contribution that would create a logical cycle!  I wish LaTeX could do that.)

Given any assertion v, you can construct the subgraph G_v of vertices which are the terminus of a directed path starting at v.  And Cathy finds that if you plot the number of vertices and number of edges of each of these graphs, you get something that looks really, really close to a line.

Why is this so?  Does it suggest some underlying structure?  I tend to say no, or at least not much — my guess is that in some sense it is “expected” for graphs like this to have this sort of property.

Because I am trying to get strong at sage I coded some of this up this morning. One way to make a random directed graph with no cycles is as follows:  start with N edges, and a function f on natural numbers k that decays with k, and then connect vertex N to vertex N-k (if there is such a vertex) with probability f(k).  The decaying function f is supposed to mimic the fact that an assertion is presumably more likely to refer to something just before it than something “far away” (though of course the stack project is not a strictly linear thing like a book.)

Here’s how Cathy’s plot looks for a graph generated by N= 1000 and f(k) = (2/3)^k, which makes the mean out-degree 2 as suggested in Cathy’s post.

Pretty linear — though if you look closely you can see that there are really (at least) a couple of close-to-linear “strands” superimposed! At first I thought this was because I forgot to clear the plot before running the program, but no, this is the kind of thing that happens.

Is this because the distribution decays so fast, so that there are very few long-range edges? Here’s how the plot looks with f(k) = 1/k^2, a nice fat tail yielding many more long edges:

My guess: a random graph aficionado could prove that the plot stays very close to a line with high probability under a broad range of random graph models. But I don’t really know!

Update:  Although you know what must be happening here?  It’s not hard to check that in the models I’ve presented here, there’s a huge amount of overlap between the descendant graphs; in fact, a vertex is very likely to be connected all but c of the vertices below it for a suitable constant c.

I would guess the Stacks Project graph doesn’t have this property (though it would be interesting to hear from Cathy to what extent this is the case) and that in her scatterplot we are not measuring the same graph again and again.

It might be fun to consider a model where vertices are pairs of natural numbers and (m,n) is connected to (m-k,n-l) with probability f(k,l) for some suitable decay.  Under those circumstances, you’d have substantially less overlap between the descendant trees; do you still get the approximately linear relationship between edges and nodes?

Interview with DeMarco and Wilkinson

Nice joint interview with Laura DeMarco and Amie Wilkerson at Scientific American.

I didn’t know this about Amie:

 I went to college, and I was feeling very insecure about my abilities in mathematics, and I hadn’t gotten a lot of encouragement, and I wasn’t really sure this was what I wanted to do, so I didn’t apply to grad school. I came back home to Chicago, and I got a job as an actuary. I enjoyed my work, but I started to feel like there was a hole in my existence. There was something missing. I realized that suddenly my universe had become finite. Anything I had to learn for this job, I could learn eventually. I could easily see the limits of this job, and I realized that with math there were so many things I could imagine that I would never know. That’s why I wanted to go back and do math.

This was basically me, too.  After college I got into the fiction writing program at Johns Hopkins, which made me think maybe I could really make it as a writer, and I deferred grad school and moved to Baltimore and wrote fiction all day every day for a year, and while I valued that experience a lot, there was not a single day of it where I didn’t kind of wish I were doing math.  Having had that experience — not just suspecting but knowing how annoying it is not to be doing math — took the edge off the pain of the painful parts of grad school.

In which I have a quarter-million friends of friends on Facebook

One of the privacy options Facebook allows is “restrict to friends of friends.”  I was discussing with Tom Scocca the question of how many people this actually amounts to.  FB doesn’t seem to offer an easy way to get a definitive accounting, so I decided to use the new Facebook Graph Search to make a quick and dirty estimate.  If you ask it to show you all the friends of your friends, it just tells you that there are more than 1000, but doesn’t supply an exact number.  If you want a count, you have to ask it something more specific, like “How many friends of my friends are named Constance?”

In my case, the answer is 25.

So what does that mean?  Well, according to the amazing NameVoyager, between 100 and 300 babies per million are named Constance, at least in the birthdate range that contains most of Facebook’s user base and, I expect, most of my friends-of-friends (herafter, FoFs) as well.  So under the assumption that my FoFs are as likely as the average American to be named Constance, there should be between 85,000 and 250,000 FoFs.

That assumption is massively unlikely, of course; name choices have strong correlations with geography, ethnicity, and socioeconomic thingamabobs.  But you can just do this redundantly to get a sense of what’s going on.  59 of my FoFs are named Marianne, a name whose frequency ranges from 150-300 parts per million; that suggests a FoF range of about 200-400K.

I did this for a few names (50 Geralds, 18 Charitys (Charities??)) and the overlaps of the ranges seemed to hump at around 250,000, so that’s my vague estimate for the number.

Bu then I remembered that there was actually a paper about this on the arXiv, “The Anatomy of the Facebook Graph,” by Ugander, Karrer, Backstrom, and Marlow, which studies exactly this question.  They found something which is, to me, rather surprising; that the number of FoFs grows approximately linearly in the number of friends.  The appropriate coefficients have surely changed since 2011, but they get a good fit with

#FoF = 355(#friends) – 15057.

For me, with 680 friends, that’s 226,343.  Good fit!

This 2012 study from Pew (on which Marlow is also an author) studies a sample in which the respondents had a mean 245 Facebook friends, and finds that the mean number of FoFs was 156,569.  Interestingly, the linear model from the earlier paper gives only 72,000, though to my eye it looks like 245 is well within the range where the fit to the line is very good.

The math question this suggests:  in the various random-graph models that people like to use to study social networks, what is the mean size of the 2-neighborhood of x (i.e. the number of FoFs) conditional on x having degree k?  Is it ever linear in k, or approximately linear over some large range of k?

Dan Sharfstein wins Guggenheim

Congratulations to Dan Sharfstein, who is one of this year’s Guggenheim Fellows!  I have written before about my admiration for Dan’s book The Invisible Line, and this seems a good occasion to say again — if you’re at all interested in the long, complicated history of race in America, buy the book and read it.  His new book will be about Oliver Otis Howard and the Freedmen’s Bureau.  This is the kind of project that requires long, deep research and painstaking thought.  I don’t know if we can Kickstarter things like this, and I’m glad we have the Guggenheim Foundation to help make them possible.