## Terrible notation Hall of Fame

This one is a little harder to explain than my earlier post. Your attention should be focused on the line in the middle that begins “N(T) = …” and ends with a diamond. That line contains three copies of the letter R: the first is in italics, while the latter two are in a sans serif font. What is astonishing is that the first and third copies of the letter R mean the same thing (they both denote the set of real numbers), while the middle one (in the same font as the third) denotes a completely separate thing, the image of a linear transformation. (In case you are wondering, these notations are consistent throughout the book (Linear Algebra by Friedberg, Insel, and Spence), it’s not like there’s just a typo here.) There are at least four major problems with this notation; yet somehow, this book is in its 5th edition and still using it.

(In other respects it’s a very good book! But the conscious notational choices of the authors are just amazingly awful.)

Posted in Books, Education, Math | Tagged | 1 Comment

## How not to do voting theory

This WaPo op-ed (by Edward Foley and Eric Maskin) is so, so bad that I’m still upset about it two days later. They criticize Alaska’s instant runoff election system because it doesn’t meet the Condorcet criterion: Pelota won, even though she wouldn’t have won in a head-to-head match with Begich. Then they propose a different system (basically a mishmash of IRV and Borda count), re-analyze the ballots from the election that was held, and argue that their system is better because Begich would have won. This argument is so incredibly dumb that, two days after reading it, I still want to write down a rant:

• Every voting system has flaws (there’s even a theorem about it) so given any voting system one can construct an argument of the form, “this system has flaw X, but this other system doesn’t, so we should use the other system,” and such arguments are always totally worthless. For any argument about two voting systems to have value, it must compare the weaknesses of both systems and argue about their relative importance.
• The problems with the system they propose are incredibly transparent and much worse than the problems with IRV: it’s obvious how to vote strategically in their system, and any marginally informed partisan voter will not rank members of the opposing party (or, in some situations, rank weak candidates from the opposing party above strong candidates). IRV is susceptible in theory to this kind of strategic voting, but in practice it’s not actually possible to figure out how to do it — whereas in their system both parties and their candidates would explain to their supporters not to rank candidates from the opposing party.
• Because of the preceding point, you cannot possibly assume that voters would vote the same way in the two systems! So the entire exercise of re-analyzing the ballots from an IRV election as if it were held under a different system is meaningless: if the election had been held under their system, voters wouldn’t have voted the same way.
• Finally, their system also doesn’t satisfy the Condorcet criterion! So there’s not even a theory here about this begin better, it’s literally just “look in this one election it would have changed the outcome, so it’s better”! I don’t have the words to express how stupid this is!

Professor of constitutional law at Ohio State! Nobel-prize winning professor of economics at Harvard!! I mean give me a frigging break.

Posted in Math, What's the news? | | 2 Comments

## Terrible calculus answers Hall of Fame

What is so beautiful about this is that even if you don’t have any idea what a derivative is, how to compute one, or what the pictures mean, it is still completely clear how bad this answer is.

## “Travels with Alice” by Calvin Trillin

Like his fiction, Trillin’s nonfiction humor occupies a place in my life similar to Wodehouse: something you can pick up when you need a guaranteed laugh, good for the level of commitment of just-before-bed reading. The opening piece contains some unforgettable lines: several days later I am still chuckling about “I’m fixin’ to show y’all some real nice liederhosen” (offered by a clerk at an imaginary ersatz Alpine village in Georgia). The best pieces might be the three that touch on taureaux piscene and babyfoot (and perhaps not coincidentally have the most plot). Anyhow, goes up on my shelf along with the Tummy Trilogy, in the expectation that it will come down from time to time for rereading.

## “Oranges” by John McPhee

So I love reading pretty much anything by McPhee — the man knows how to craft a sentence — and this book is full of interesting information (even when you discount for the fact that presumably most of it is long out-of-date), but it lacked any global narrative structure and I found that somewhat frustrating. Also, my sense of understanding what I was reading would have been enhanced by including one (1) map of the state of Florida and one (1) diagram of an orange.

Posted in Book reviews, Books, Trees | 2 Comments

## The big point theorem

The solution Tanya attributes to Jason Rosenhouse here reminds me of my favorite theorem of applied mathematics education:

Theorem (Big Point Theorem). Any three lines are concurrent, provided you draw the point big enough.

Edit 8/18: And now Tanya has written about it as well.

## I also wonder how many people have PET LOBSTERs.

So sayeth a crossword puzzle constructor. Which led me to: pet rock lobster roll tide pool noodle soup dumpling house pet …. (Presumably this sort of theme has been done before.)