is itself a morally problematic, even questionable, act.
Are there no editors anymore? What work is “even questionable” doing? Is it possible to imagine an act that was morally problematic but not morally questionable? And even if it is, is that thin distinction really what the writer of this piece about an HBO miniseries is going for? Or did they just think “is itself a morally problematic act” didn’t have enough heft, stuff another couple of non-nutritive words in there, admire the sentence’s new bulk, move on?
Start at a lattice point inside the quarter-circle in the positive quadrant. You and your opponent take turns: the allowable moves are to go up, right, or both at once (i.e. add (0,1), add (1,0), or add (1,1).) First person to leave the quarter-circle wins. What does it look like if you color a starting point black for “first-player loss” and yellow for “first-player win”? It looks like this:
I like the weird zones of apparent order here. Of course you can do this for any planar domain, any finite set of moves, etc. Are games like this analyzable at all?
I guess you could go a little further and compute the nimber or Grundy value associated to each starting position. You get:
What to make of this?
Here’s some hacky code, it’s simple.
M = 1000
return (a**2 + b**2 >= M*M)
return min([i for i in range(5) if not (i in L)])
L = np.zeros((M+2,M+2))
for a in reversed(range(M+2)):
for b in reversed(range(M+2)):
L[a,b] = 0
L[a,b] = Mex([L[a+1,b],L[a,b+1],L[a+1,b+1]])
One natural question: what proportion of positions inside the quarter-circle are first-player wins? Heuristically: if you imagine the value of positions as Bernoulli variables with parameter p, the value at my current position is 0 if and only if all three of the moves available to me have value 1. So you might expect (1-p) = p^3. This has a root at about 0.68. It does look to me like the proportion of winning positions is converging, but it seems to be converging to something closer to 0.71. Why?
By the way, the game is still interesting (but I’ll bet more directly analyzable) even if the only moves are “go up one” and “go right one”! Here’s the plot of winning and losing values in that case:
All of us living at a certain time on this planet together, and together experiencing all its earthly joys and sorrows, seeing the same sky, loving and hating what are, after all, the same things, each and every one of us condemned to suffer the same sentence, the same disappearance off the face of the earth, should really nurture the greatest tenderness towards each other, a feeling of the most heart-rending closeness, and should be literally screaming with terror and pain whenever we are parted by a fate which at any moment is fully capable of transforming every one of our separations, even if only meant to last ten minutes, into an eternal one. But, as you know, for most of the time, we are a long way from such sentiments, and often take leave of even those closest to us in the most thoughtless manner imaginable.
Ivan Bunin, “Long Ago,” 1921 (Sophie Lund, trans.)
AB has curly hair, really curly hair, and strangers comment on it all the time. My stance on this is to tell her “it’s not really polite for people to randomly comment on your appearance, but it’s not impolite enough for you to be impolite back — just say thanks and move on.” Is that the right stance?
Anyway, though, today someone at the farmer’s market said “I would die to have hair like yours” and AB said, in a non-combative, sunny way, “How would that help you if you were dead?” and I was super proud.
I gave a talk at Williams College last year and took a little while to visit one of my favorite museums, Mass MoCA. There’s a new installation there, by Taryn Simon, called Assembled Audience. You walk in through a curtained opening and you’re in a pitch-black space. It’s very quiet. And then, slowly, applause starts to build. Bigger and bigger. About a minute of swell until the invisible crowd out there in the dark is going absolutely fucking nuts.
And I have to be honest, whatever this may say about me: I felt an incredible warmth and safety and satisfaction, standing there, being clapped for and adored by a recording of a crowd. Reader, I stayed for a second cycle.
As an eternal 1990s indie-pop nerd I could not but be thrilled this week when I realized I was going to Bristol
on the National Express.
Bristol, besides having lots of great mathematicians to talk to, is much lovelier than I knew. There’s lots of terrain! It seems every time you turn a corner there’s another fine vista of pastel-painted row houses and the green English hills far away. There’s a famous bridge. I walked across it, then sat on a bench at the other side doing some math, in the hopes I’d think of something really good, because I’ve always wanted to scratch some math on a British bridge, William Rowan Hamilton-style. Didn’t happen. There was a bus strike in Bristol for civil rights because the bus companies didn’t allow black or Indian drivers; the bus lines gave in to the strikers and integrated on the same day Martin Luther King, Jr. was saying “I have a dream” in Washington, DC. There’s a chain of tea shops in Bristol called Boston Tea Party. I think it’s slightly weird to have a commercial operation named after an anti-colonial uprising against your own country, but my colleagues said no one there really thinks of it that way. The University of Bristol, by the way, is sort of the Duke of the UK, in that it was founded by a limitless bequest from the biggest tobacco family in the country, the Willses. Bristol also has this clock:
Instructive anecdote. I needed a somewhat expensive book and the UW library didn’t have it. So I decided to buy it. Had the Amazon order queued up and ready to go, $45 with free shipping, then had a pang of guilt about the destruction of the publishing industry and decided it was worth paying a little extra to order it directly from the publisher (Routledge.)
From the publisher it was $41, with free shipping.
I think it really did used to be true that the Amazon price was basically certain to be the best price. Not anymore. Shop around!
David Brooks writes in the New York Times that we should figure out how to bottle the civic health southwest Nebraska enjoys:
Everybody says rural America is collapsing. But I keep going to places with more moral coherence and social commitment than we have in booming urban areas. These visits prompt the same question: How can we spread the civic mind-set they have in abundance?
For example, I spent this week in Nebraska, in towns like McCook and Grand Island. These places are not rich. At many of the schools, 50 percent of the students receive free or reduced-cost lunch. But they don’t have the pathologies we associate with poverty.
Crime is low. Many people leave their homes and cars unlocked.
Is it? And do they? I didn’t immediately find city-level crime data that looked rock solid to me, but if you trust city-data.com, crime in Grand Island roughly tracks national levels while crime in McCook is a little lower. And long-time Grand Island resident Gary Christensen has a different take than Brooks does:
Gary Christensen, a Grand Island resident for over 68 years says times are changing. “It was a community that you could leave you doors open leave the keys in your car and that kind of thing, and nobody ever bothered it. But those days are long gone,” said Gary Christensen, resident.
One way you can respond to this is to say I’m missing the point of Brooks’s article. Isn’t he just saying civic involvement is important and it’s healthy when people feel a sense of community with their neighbors? Are the statistics really that important?
Yes. They’re important. Because what Brooks is really doing here is inviting us to lower ourselves into a warm comfortable stereotype; that where the civic virtues are to be found in full bloom, where people are “just folks,” are in the rural parts of Nebraska, not in New Orleans, or Seattle, or Laredo, or Madison, and most definitely not in Brooklyn or Brookline or Bethesda. But he can’t just say “you know how those people are.” There needs to be some vaguely evidentiary throat-clearing before you launch into what you were going to say anyway.
Which is that Nebraska people are simple dewy real Americans, not like you, urbanized coastal reader of the New York Times. I don’t buy it. McCook, Nebraska sounds nice; but it sounds nice in the same way that urbanized coastal communities are nice. You go someplace and talk to a guy who’s on the city council, you’re gonna be talking to a guy who cares about his community and thinks a lot about how to improve it. Even in Bethesda.
Constantly they are thinking: Does this help my town or hurt it? And when you tell them that this pervasive civic mind-set is an unusual way to be, they look at you blankly because they can’t fathom any other.
There’s Brooks in a nutshell. The only good people are the people who don’t know any better than to be good. By saying so, he condescends to his subjects, his readers, and himself all at once. I don’t buy it. I’ll bet people in southwest Nebraska can fathom a lot more than Brooks thinks they can. I think they probably fathom David Brooks better than he fathoms them.
Madison had a primary election last night for mayor and for several seats on the City Council and School Board. Turnout was high, as it seems to always be in Dane County lately. The Dane County Clerk has all the results in handy csv form, so you can just download things and start having some fun! There were four major candidates for mayor, so each ward in the city can be mapped to a point in R^4 by the vote share it gave to each of those; except of course this is really R^3 because the vote shares sum to 1. It’s easier to see R^2 than R^3 so you can use PCA to project yourself down to a nice map of wards:
This works pretty well! The main axis of variation (horizontal here) is Soglin vote, which is higher on the left and lower on the right; this vector is negatively weighted on Rhodes-Conway and Shukla but doesn’t pay much attention to Cheeks. The vertical axis mostly ignores Shukla and represents Cheeks taking votes from Rhodes-Conway at the top, and losing votes to Rhodes-Conway at the bottom. You can see a nice cluster of Isthmus and Near West wards in the lower right; Rhodes-Conway did really well there. 57 and 48 are off by themselves in the upper right corner; those are student wards, distinguished in the vote count by Grumpy Old Incumbent Paul Soglin getting next to no votes. And I mean “next to no” in the literal sense; he got one vote in each of those wards!
You can also do some off-the-shelf k-means clustering of those vectors in R^4 and you get meaningful results there. Essentially arbitrarily I broke the wards into 5 clusters and got:
Now what would be interesting is to go back and compare this with the ward-by-ward results of the gubernatorial primary last August! But I have other stuff to do today. Here’s some code so I remember it; this stuff is all simple and I have made no attempt to make the analysis robust.
Update: I did the comparison with the August primary; interestingly, I didn’t see very many strong relationships. Soglin-for-mayor wards were typically also Soglin-for-governor wards. Wards that were strong for Kelda Helen Roys were also strong for Raj Shukla and weak for Soglin, but there wasn’t a strong relationship between Roys vote and Rhodes-Conway vote. On the other hand, Rhodes-Conway’s good wards also tended to be good ones for… Mike McCabe??