“Dialogues on mathematics” by Alfred Renyi

For various reasons I have recently been reading a bunch of books broadly addressing the theme “what is mathematics?”  (Linderholm was accidentally a lead-in, and clearly belongs in the category.)  This one is a short (under 100 pages) and snappy read, and should be accessible to just about anyone.  I read it in an hour or two and enjoyed pretty much all of it (although Galileo is a windbag and drags on a little bit).  Manages to touch at least briefly on all the really important things (e.g., mathematical beauty, the connection between research and teaching, mathematical Platonism, the broad applicability of mathematics).

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“Mathematics Made Difficult” by Carl E. Linderholm

I have seen attributed to Halmos (Linderholm’s advisor) the description of this book as an in-joke to the mathematical community, and that’s about right: I don’t think it would be possible to explain why it’s funny to someone who doesn’t know at least a bit of category theory, among other things, and of course some parts are more amusing than others.  Probably any mathematician could find something that tickles them particularly; for me, it was that the section “What are brackets?” ends with an absurdist derivation of the Catalan numbers.  I also thought the exercises were particularly wonderful.  (On the other hand, the long-winded send-ups of word problems felt tedious.)  Overall, the thing it most reminds me of is 1066 and all that.

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“The Table Comes First” by Adam Gopnik

In the preface, Gopnik writes, “We shouldn’t intellectualize food,” and on that count I think the book is a failure; as a result, some chapters are something of a slog. But others are wonderful.  (They vary quite a lot in style and tone, and don’t make a very cohesive whole – presumably because they were written as a series of unconnected essays for the New Yorker.)  I loved the chapter on the history of recipes and recipe books, and the letters to Elizabeth Pennell, which even allow for a plot twist of sorts.  I found the philosophizing about (against, really) vegetarianism particularly unconvincing, but he does get a good burn in on Mark Bittman:

[Bittman] is cautious, and even skeptical; while Rosso and Lukins “love” and “crave” their filet of beef, to all of animal flesh Bittman allows no more than “Meat is filling and requires little work to prepare.  It’s relatively inexpensive and an excellent source of many nutrients.  And most people like it.”  Most people like it!  Rosso and Lukins would have tossed out any recipe, much less an entire food group, of which no more than that could be said.  Lamb is a thing they “fall in love with again every season of the year,” and of pork they know that it is “divinely succulent.”  Bittman thinks that most people like it.

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West Virginia teacher strike

So, West Virginia teachers (some of whom are unionized, but whose unions are not recognized by the state) have been on strike for a week, continuing even after their union leadership struck a deal with the governor.  (The strikers fear, quite reasonably, that the legislature and other parties will not carry through.)  It’s quite inspiring!  Here are some good articles about it:

Gov. Jim Justice announces 5-percent raise for all West Virginia educators

A Massive Strike Is Actually Working




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“Modular Origami Polyhedra” by Lewis Simon, Bennett Arnstein, and Rona Gurkewitz

Haven’t had an origami post in a while!  This book was as Christmas gift.  It consists of an assortment of instructions for modular origami: about ten different versions of the Sonobe unit, a variety of cube-based units they call the “decoration box” module, and an assortment of others.  The Sonobe variations aren’t so interesting to me (they don’t change the geometry of the polyhedra you can make), but there are a number of other models that seem very interesting.  Here are my first few excursions:

6-color “decoration box” cube

This module is annoying because it (or its relatives) can be used to make other polyhedra than cubes, but you have to change the module (unlike in the case of Sonobe).  On the other hand, because it makes polyhedral skeleta, you can do other cool things:

Interlocking three-color “decoration box” cubes

Another model that seems to have more flexibility is the “gyroscope”:

“Gyroscope” octahedron

Gurkewitz has a webpage with some beautiful photos and more information.  (Unfortunately the photos of assembled constructions in the book itself are dark, grainy, and monochrome.)

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“Being Mortal” by Atul Gawande

Gawande is a wonderful writer who does a good job moving back and forth between the clinical and personal/anecdotal parts of his story.  This could be a bit formulaic, but one of his case-studies is his own father and I found that rescues it from that fate.  A moving and thoughtful discussion of the role of the medical profession in the lives of people with terminal illness or who are nearing death.

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Coincidences among small groups

I like to study reflection groups of various kinds.  Let Sn denote the group of permutations of n points, let GL(n, q) denote the general linear group of invertible linear transformations of an n-dimensional vector space over the finite field with q elements, and let GA(n, q) denote the general affine group of invertible affine transformations of an n-dimensional affine space over the finite field with q elements.  Then:

  • S1 is isomorphic to GL(1, 2), which permutes the single non-origin point in a two-element vector space.
  • S2 is isomorphic to GA(1, 2), which permutes the two points in a two-element affine space.
  • S3 is isomorphic to GL(2, 2), which permutes the three non-origin points arbitrarily.
  • S4 is isomorphic to GA(2, 2), which permutes all four points arbitrarily.

Except for the second of these (where the non-identity transformation is a translation but not a reflection), these isomorphisms are actually isomorphisms as reflection groups, in the sense that the reflections in Sn (viewed as a matrix group acting on n-dimensional real space) are exactly the transpositions, and in the isomorphisms above they correspond exactly to the reflections (elements that fix a hyperplane pointwise).

I don’t have any meaning to draw from this, but it amuses me.

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