For all the other parameters, 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.)
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.
As always, I adore any piece of tree-related reporting in the Times. The latest is about the American chestnut. I have read a bunch of tree books that talk about the destruction of the blight, but I thought this article did a really nice job explaining the cultural significance of what was lost. The newsy aspect is that the decades-long effort to breed a blight-resistant chestnut (first through cross-breeding with Asian chestnuts, subsequently via genetic engineering) is essentially complete: what is needed now is the approval of three federal agencies to allow the resistant trees to be released.
This has been on my shelf for a while — I certainly read some of it in 2011 (the bookmark I was using was an ATM receipt from FPSAC Iceland) but then set it aside until recently. Overall, I thought it did a good job of presenting a reasonably scientifically accurate account of our knowledge of natural history, from the big bang through the evolution and dispersal of modern humans, with an emphasis on telling an engaging narrative about who the people were who figured this all out and how they did so, appropriate for a lay audience. Some things are to be expected from reading an older pop-science book: for example, at the time of writing, New Horizons lay in the future rather than in the past, and what we can learn from genetics has expanded to an almost unimaginable degree. The most glaring oversight is how little attention human-induced climate change receives: it is mentioned in a couple of places, but with no sense that it represents an urgent threat.
Am in the middle of watching the second season of The Crown with D. We basically find it enjoyable. My only complaint is that I sometimes find it very hard to suspend my sense of disbelief that the characters all proceed as if “the monarchy” is an important or valuable institution, rather than an absurd historical artifact. (The hero of the first part of season 2 is clearly the Australian reporter “Helen King” in the second episode.) Oh, well.
This article about a 1969 episode in Potomac, MD, in which a school implemented anti-blonde apartheid during National Brotherhood Week, is deeply fascinating.
The blond students were forced to use separate restrooms, doors and drinking fountains, relegated to separate tables in the lunchroom and library and shunned by teachers and brunettes, even their friends, as Brown and others in the junior high at the time described it.
It is a shame that they were not able to interview more of the former students about it.
Mark Walston, another ninth-grader, also remembers that “the hall monitors became like neo-Nazis, they took their job just way too far and got physical with the kids.” He says as a result, some blond girls cried and went home early during the first two days of the exercise.
Most of the former students interviewed identified students who went overboard. However, when contacted, none of those enforcers responded to repeated requests for interviews.
The subtitle of this book is “a natural history of trees and people in the American cityscape”, but it is really a social history, not a natural history. Much of the book concerns the question of how the ornamental trees planted in American cities (like ginkoes, dawn redwoods, and flowering cherries) came to be discovered, imported, and popularized. Some chapters concern the central institutions of American tree culture (arboreta, Arbor Day, tree-care companies), the great American tree disasters (American elm and chestnut; ash borers and Asian longhorned beetles), or individual trees of note. Of many fascinating stories, I was particularly taken with the first attempt to bring Japanese flowering cherries to Washington, DC: in one of the first acts of quarantine taken by the USDA, all two thousand trees were destroyed because of the insects and fungi they carried. (A second shipment of trees, raised specifically to prevent infestations, was substituted a couple years later.) Overall a pleasant and informative book.
Over at JD2718, Jonathan asks the following question:
[A conference] presenter posed a problem that required finding three numbers that multiplied to make 72. The list included 1, 8, 9 and 2, 2, 18 and 3, 4, 6 and several other triples (groups of three numbers).
So I wondered, could we look at 72 and see how many factor triples it has? In general, how many factor triples does a number have?
Answering this question involves a lot of nice mathematics!