P.G. Wodehouse

So I started reading a few of his novels, including the collection “What Ho!” What to say? He’s generally good for a laugh; much of the humor has a timeless aspect that stands up pretty well after decades. I would expect his work to be less appealing to female readers. The use of language for comedic effect in individual sentences is often wonderful, e.g.,

I do not know if you have had any experience of suburban literary societies, but the one that flourished under the eye of Mrs Willoughby Smethurst at Wood Hills was rather more so than the average.

P.G. Wodehouse, “The Clicking of Cuthbert”

He’s a good author to have on the bedside table to read while drifting off. The amount of recycling that goes on is extreme: for example, “The Code of the Woosters” and “Stiff Upper Lip, Jeeves” have precisely the same characters playing out precisely the same story (the first is probably funnier and also has fewer blatantly racist bits). Perhaps when you write 90 books + hundreds of other pieces that’s going to happen, but in his case it seems like overkill.

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I wrote the post below in 2016, but for some reason I never published it; better late than never, I guess.  I referenced the Four and Twenty Blackbirds Pie Book more recently, too.

I received several pieces of pie-making  equipment/guidance for my birthday, and am starting to put them to use.  First, a simple apple tart:
Second, a pear and anise pie with a lattice crust:

 The recipe for the latter came from The Four and Twenty Blackbirds Pie Book by Emily and Melissa Elsen, which is a collection of “uncommon” recipes.  They were both tasty.

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Trapezoids, and blogs

Atrios remarked on the (slow, in-progress) death of the open internet, as in blogs etc. And Jonathan’s offhand remark about his blog’s heyday is another anecdatum pointing in the same direction. Anyhow, that’s not what this post is about; it’s about the second of two geometry puzzles from JD2718:

Are there four segments from which it is possible to construct a quadrilateral, but from which it is not possible to construct a trapezoid?

The answer, I suppose, is “it depends whether you think a parallelogram is a trapezoid”: if the opposite pairs of edges are equal in length, you’ll always have a parallelogram. But if there are a pair of opposite unequal sides, you can always do something: if we have edges a, b, c, d with a > c, then we can draw the figure thusly

with x = \dfrac{a - c + \frac{b^2 - d^2}{a - c}}{2} and y =  \dfrac{a - c - \frac{b^2 - d^2}{a - c}}{2}. (These formulas allow x and y to be negative, in case b and d differ quite a lot, pushing the top edge off to one side or the other. Hopefully I have not missed any subtleties about different drawings!)

When the edge lengths are obliging, one can think in terms of hinges:

Since the right vertex of the blue edge begins below the left vertex but ends above it, at some point they must be level, i.e., the blue edge must be parallel to the black edge.

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Medals per capita

So I made a joke to a friend about how, after Slovenia got their first medal, they were doing really well on a medals per capita basis.  And then, being me, I took this joke too far and actually started tracking the performance of this metric, and posting updates on FB.  Trust me, it was hilarious, you really missed out.  For posterity, here are the final top 10 (which incidentally are also the countries that had at least 2 medals per million population; population data from the CIA World Factbook).

CountryGSBPopulation (thousands)Medals per 1 M people
San Marino0123487.04
New Zealand7674,9914.01

Because I’m friends with a lot of people with PhDs in the sciences, this led to some methodological nit-picking.  One possible alternative measure is medals / GDP, where there is a much higher correlation coefficient (0.79 versus 0.42); here are the top ten in that measure.

CountryGSBGDP (B $ PPP)Medals/GDP
San Marino0122.008149

Obviously someone at the Washington Post was following me avidly, because Chuck Culpepper wrote a whole article about the last-place finisher among nations that won a medal: With 1.3 billion people and 35 medals ever, India remains an Olympic mystery. But I feel like the WaPo article really missed a crucial angle, namely, that all the large South Asian nations are chronic under-performers at the Olympics: Pakistan has only ever won 10 Olympic medals, and the most recent was in 1992; Sri Lanka has only ever won 2, and Bangladesh and Nepal have never won any.  (India was not quite last among medal-winning nations on a medals / GDP basis this year: they just squeaked past Saudi Arabia.)

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“Ever since Darwin” by Stephen Jay Gould

I picked this collection of essays (selected from Gould’s mid-1970s contributions to Natural History) up during a recent visit to Rodgers Book Barn (along with “The Panda’s Thumb”, and another book I’ll write about later). Pop-science writing always runs the risk of becoming out-dated, but this collection holds up remarkably well after 45 years. I particularly appreciated the discussion of the history of ideas – for example, why the acceptance of continental drift was contingent on the theory of plate tectonics (and therefore on the discovery of the Mid-Atlantic Ridge). Gould’s discussion of race science could practically be contemporary (e.g., these recent debates on how Wikipedia should treat the question of race and intelligence: 1 2). I am looking forward to moving on to “The Panda’s Thumb”. Also, this made me laugh out loud:

One day, at the New York World’s Fair in 1964, I entered the Hall of Free Enterprise to escape the rain. Inside, prominently displayed, was an ant colony bearing the sign: “Twenty million years of evolutionary stagnation. Why? Because the ant colony is a socialist, totalitarian system.”

Gould, “Sizing up human intelligence”

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“Jackson, 1964” by Calvin Trillin

Trillin is wonderful and I would read pretty much anything he writes (though Tepper isn’t going out wasn’t my favorite). This collection (published in 2015) is of his reporting on race over 40 years, beginning in 1964. (There is another collection of his slightly earlier reporting on the desegregation of the University of Georgia.) Some pieces are personal-interest stories that are enjoyable but don’t feel terribly consequential; a couple have lost some of their urgency (like the brutal piece on the Senate hearings for Griffin Bell, Carter’s first Attorney General); but most feel exceptionally contemporary. For example, here’s Trillin writing in 1975 about the killing of Joseph Herbert, a black man, by the white police officer Allen Earlywine, following a traffic stop:

In response to Bayley’s remarks that the [inquest] jury’s findings had been contradictory, the foreman said that he took the votes of those who believed Earlywine to have been in fear for his life to mean that any white man would be afraid in a black neighborhood at night. … Bayley and Hanson became illustrations for those who argue that in the final issue between the races–the issue of whether a black life has the value of a white life–openly repressive white authority and seemingly sympathetic white authority are, in Tyree Scott’s words, “functionally the same.”

Calvin Trillin, in “Causes and Circumstances”, The New Yorker, 1975.

(Christopher Bayley was the reformist prosecutor who declined to prosecute Earlywine, Robert Hanson was the police chief of Seattle at the time, and Tyree Scott was a local activist.)

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Finding the magic coins

I’ve been reading through Daniel Velleman and Stan Wagon’s puzzle book Bicycle or Unicycle? and generally enjoying it – the puzzles include simple variations on classics, clever things I haven’t seen before, and some nontrivial uses of real mathematical thinking (as in the title puzzle, which asks whether it is possible for a bicycle to move in such a way that its rear wheel follows exactly along the path of its front wheel). Of course, Tanya’s blog appears several times. The solutions often go beyond the puzzle posed. As is to be expected, they have some coin-weighing puzzles. Here is a generalization of one of them:

You are presented with a set of N coins, among which S are special. You cannot tell which ones are special and which ones are not. Your goal is to choose a subset of coins that contains exactly k special coins. After each choice, an oracle tells you whether or not you have succeeded. What is the value f(N, S, k) of the smallest number of guesses you need to make to succeed?

Velleman–Wagon ask for the value of f(8, 4, 2); their source for the problem is the puzzle column from the MSRI newsletter, which asks to show that f(100, 50, 25) ≤ 50. Here are some some additional facts one might like to show (assuming, as is natural, that 0 ≤ kSN):

  • f(N, N, k) = f(N, S, S) = f(N, S, 0) = 1 for all choices of N, S, k
  • f(N, S, k) = f(N, S, S - k)
  • f(N, 2, 1) \leq \lceil \log_2(N)\rceil
  • f(N, 3, 1) \leq 2 \lceil \log_2(N) \rceil

Can one say anything interesting in general? For example, what is the asymptotic growth of f(N, 2k, k) for fixed k?

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American woman math PhDs of the 1940s

Apparently I’ve had this blog for a really long time: just over nine years ago, I wrote about Margaret A. M. Murray’s book “Women Becoming Mathematicians”. This post is just to note that the latest AMS Notices contains an article by Murray that provides an update on her work, which is documented in more detail on her webpage womenbecomingmathematicians.net.

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This tickled my fancy:

For all the other parameters, G(de, e, r) has no real structure.

[R. Corran, E.-K. Lee, S.-J. Lee, Braid groups of imprimitive complex reflection groups, J. Algebra, 2015]

(No, it’s not floppy — it’s a complex reflection group. Here “real” means the real numbers, and “complex” means the complex numbers; some complex reflection groups can be described using only the real numbers, but not this one.)

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Mac and cheese with broccoli

For a long time, D has been trying to convince me to make a version of mac and cheese with broccoli in it. I have objected because I am a mac and cheese traditionalist, but finally she prevailed upon me this weekend. The recipe is: make mac and cheese, cut up broccoli, throw the broccoli in when you mix the sauce and pasta. The result was completely fine:

We ate it with Brussels sprouts, because I guess you can’t have too much Brassica in one meal.

Ultimately, I think I would have been slightly happier with plain mac and cheese and a side of steamed broccoli; D says something was gained by getting the broccoli cheesy.

Visible in both photos is the latest New Yorker cover, which I liked.

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