### Who knew he had it in him?

Feb. 8th, 2017 07:43 amPresident Trump seems to be on his way after only two weeks, with an illuminating example of the Alternative Facts approach to mathematical proof.

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President Trump seems to be on his way after only two weeks, with an illuminating example of the Alternative Facts approach to mathematical proof.

Why I'm having dreams about a math colloquium in the first place, much less one about this particular class of matrices, I don't know....

I find this last argument peculiar because it's the

Related to this is another feature of IRV: it tends to favor divisive, polarizing candidates over broadly-acceptable, unifying candidates. Suppose, for example, in the above election Peter Prettygood was the second choice of

None of the readers seemed to question the equation of "ranked voting" with "instant runoff voting". In fact, "ranked voting" is about how you

Of course, both Borda and Condorcet have better mathematical properties, e.g. "if your preferences are the exact opposite of mine, then your vote and mine exactly cancel one another out", which isn't true of IRV or single-vote plurality. But that's perhaps of more interest to mathematicians than the general public.

Which is almost certainly true. I've actually had occasion to use a little bit of calculus on the job (in doing analysis of algorithms), and in answering idle-curiosity physics problems, and I've used trigonometry to design tents, and I've used both trigonometry and linear algebra to write graphics programs, but 99.99% of the U.S. population will never need to do any of those things, either on the job or in private life. Most people need to be able to do arithmetic (with the aid of a calculator, but they need enough of a feel for numbers that they can tell whether the answers are at all plausible), and read a graph, and it would be nice if they knew that correlation isn't causation, and what statistical significance means. As a logician, I'd like it if ordinary citizens knew that "not all cats are grey" is equivalent to "at least one cat is not grey", and that "if that's a duck, then I'm Henry Ford" is

Anyway, the author documents vast numbers of students whose only academic problem is an inability to pass such irrelevant math classes (middle school, high school, or college), but who are denied the opportunity to study Shakespeare or Swahili or spot-welding. He points out that most of the doomsaying about an imminent shortage of STEM-qualified workers comes from employers who have a strong vested interest in creating an overabundance of such workers. And he likes to illustrate things with sample test questions.

Here's a question he likes:

A rectangular-shaped fuel tank measures 27-1/2 inches in length, 3/4 of a foot in width, and 8-1/4 inches in depth. How many gallons will the tank contain? (231 cubic inches = 1 gallon)

(a) 7.366 gallons

(b) 8.839 gallons

(c) 170,156 gallons

He likes this because it tests "did you read the question carefully?" -- specifically, did you convert 3/4 of a foot into 9 inches -- and do you know what needs to be multiplied and what divided? He says if you failed to notice the "feet", you would get the incorrect answer (a) (in fact, he's misplaced a decimal point: you would get .7366 gallons, which you should also be able to rule out through common sense because a tank that big has

Here's a question he doesn't like:

Two charges (+q and -q) each with mass 9.11 x 10^{31}kg, are place 0.5 m apart and the gravitational force (F_{g}) and electric force (F_{e}) are measured. If the ratio F_{g}/F_{e}is 1.12 x 10^{-77}, what is the new ratio if the distance between the charges is halved?

(a) 2.24 x 10^{-77}

(b) 1.12 x 10^{-77}

(c) 5.6 x 10^{-78}

(d) 2.8 x 10^{-78}

I have to confess I

However, I don't see a lot of benefit in asking this question on an MCAT (which is where it allegedly came from). Yes, identifying the relevant and irrelevant features of a problem is important to a doctor, but physics isn't.

For a certain board game, two dice are thrown to determine the number of spaces to move. One player throws the two dice and the same number comes up on each of the dice. What is the probability that the sum of the two numbers is 9?

(a) 0

(b) 1/6

(c) 2/9

(d) 1/2

(e) 1/3

Again, he doesn't like this question, and I do: it requires no arithmetic, no probability, no combinatorics, only the ability to see past the irrelevant stuff to what matters.

Is this what they call a "trick" question? One that requires common-sense reasoning, not just the application of a memorized procedure? If so, I'm all for them.

Anyway, I've only read a quarter of the book; we'll see what else he has to say.

Decades later, I read in Isidore's

Numbers are divided into even and odd numbers. Even numbers are subdivided into these categories: evenly even, evenly odd, and oddly even....An evenly even number is one that is divided equally into even numbers until it reaches the indivisible unity, as, for example, 64 has 32 at its midpoint; 32 has 16, 16 has 8, 8 has 4, 4 has 2, 2, has 1, which is an indivisible singularity.An evenly odd number is one that can undergo a division into equal parts, but then its parts cannot immediately be evenly dissected, like 6, 10, 38, 50. As soon as you divide this kind of number, you run into a number that you cannot cut evenly. An oddly even number is one whose parts can be divided equally, but the division does not go to the point of one, like 24.

(From

OK, so Isidore beat me out by 1350 years....

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