Mathematical Flimflam

[Audio version available at http://mathenchant.org/050.mp3.]

I’m a pure mathematician with no background in applied mathematics. But lately I’ve been striving to make a name for myself in the less-crowded field of mis-applied mathematics, and bogus science more broadly.

Now you may be asking yourself, is bogus science really less crowded a field than good science? After all, if Sturgeon’s law (“Ninety percent of everything is crap”) applies to science, then we can expect crappy science to predominate over the good kind. But bogosity transcends mere crappiness. For something to be bogus, I think there must be an attempt to deceive. Or at least, there must be the appearance of an attempt to deceive. Sometimes the appearance is itself a sham, and that’s the kind of second-order bogosity I enjoy practicing, when I try my hardest to act like someone who genuinely believes (and wants others to believe) a nonsensical theory.

My forum is the Festival of Bad Ad Hoc Hypotheses (BAHFest), held periodically in various locations around the world (San Francisco, Seattle, Cambridge, Sydney, and London). It’s a celebration of well-argued and thoroughly researched but completely incorrect scientific theories. BAHFest is dedicated to the proposition that no matter how absurd a premise is, you can find a way to abuse the tools of science to support your cause and make people laugh in the process. (Or make nerds laugh, anyway.)

BAHFest was the brainchild of Zach Weinersmith whose Infantapulting Hypothesis got the game going.

Carnival of Mathematics #170

I’m hosting issue number 170 because I have a thing for the number’s largest prime factor, but it turns out there’s a reason for a Martin Gardner fan like me to appreciate the number itself: 170 is the number of steps¹ needed to solve a classic mechanical puzzle called The Brain invented by computer scientist Marvin H. Allison, Jr., described by Martin Gardner in his Scientific American essay “The Binary Gray Code”, and still available from Amazon.

The Brain, aka The Brain Puzzle, aka The Brain Puzzler.

Here’s what Gardner says about The Brain:

It consists of a tower of eight transparent plastic disks that rotate horizontally around their centers. The disks are slotted, with eight upright rods going through the slots. The rods can be moved to two positions, in or out, and the task is to rotate the disks to positions that permit all the rods to be moved out. The Gray code supplies a solution in 170 moves.

A Mathematician in the Jury Box, or, “But how should we define ‘intoxicated’?”

Back in the 1990s, when I was serving on a jury in a one-day trial, my mathematical temperament got me in hot water with my fellow jurors; fortunately, my outside-the-classroom mathematical training got me out of it. But that doesn’t come in until the end of the story.

The case featured a couple of surprising twists — which is in itself surprising, since even a single twist is unusual in a one-day trial. It had seemed at first like a very straightforward drunk-driving charge. The defendant went to a party, drank some alcohol, left the party feeling unwell, got into his car, drove off, and blacked out, though with enough advance warning of his impending unconsciousness that he was able to pull over to the side of the road and turn on his hazard lights before passing out. A police officer found him slumped over the wheel of his car. The officer smelled his breath and it smelled of alcohol. The District Attorney presented these facts confidently, as if this was going to be an open-and-shut case. But then, in the kind of surprise you see only on television, the defense attorney asserted (with medical records to support his assertion) that in fact the defendant was diabetic, that someone with diabetes can go into hypoglycemic shock if they ingest a little bit of alcohol on an empty stomach, that the breath of someone in hypoglycemic shock is often nearly indistinguishable from the breath of someone who is drunk, and that the amount of alcohol that the defendant had drunk at the party was, according to witnesses, well under the amount that would cause blood alcohol concentration to reach .08% (the legal definition of “too much”).

Mazes, Puzzles, and Proofs

Many family restaurants offer paper placemats that entice children into solving puzzles as an alternative to kicking each other under the table, blowing bubbles in their beverages, and so on. I remember those placemats from my own childhood and I recall mazes in particular. The mazes weren’t large, but the designers, in their quest to keep us kids occupied as long as possible, would put long dead-ends near the start of the maze. I quickly hit on a strategy that the emphatically named Thomas T. Thomas also found, as he later recounted in his charming essay “Working Backward“: 

One of the most valuable techniques in problem solving I learned in the third grade. But it certainly wasn’t a lesson my teacher intended.

Flip Your Students, Flip Yourself

Collect content-summaries; return them at exams.

I’ll explain that prescription shortly. But first, a confession:

The title of this essay, in which the word “flip” refers to the pedagogical innovation called the “flipped classroom”, is misleading because I’m not going to tell you how to run a flipped classroom. For those of you who haven’t heard, the flipped classroom approach to education is based on moving lecture-delivery out of the classroom and into the dorm room. No, not by having the professor show up in everyone’s dorm room to deliver content on an individual basis; that would be both impractical and improper. Instead, the professor prepares a video, and the students watch it on their laptops. That way, when the students show up in the classroom, they can focus on teacher-supervised activities that take their knowledge to the next level.

Who Mourns the Tenth Heegner Number?

I’m the urban spaceman, baby; I’ve got speed.
I’ve got everything I need.

− Neil Innes, “I’m the Urban Spaceman” (Bonzo Dog Doo-Dah Band)

There’s an episode¹ of a science-fiction television series in which space travelers land on a planet peopled by their own descendants. The descendants explain that the travelers will try to leave the planet and fail, accidentally stranding themselves several centuries in the past. Armed with this knowledge, the travelers can try to thwart their destiny; but are they willing to do so, if their successful escape would doom their descendants, leaving the travelers with the memory of descendants who, thanks to their escape, never were?

This is science fiction, but it’s also math. More specifically, it’s proof by contradiction. As Ben Blum-Smith recently wrote on Twitter: “Sufficiently long contradiction proofs *make me sad*! When you stick with the mathematical characters long enough, you start to get attached, and then they disappear, never to have existed in the first place.”

Cartoon by Ben Orlin. You can buy his book “Math With Bad Drawings”.

This will be an essay about things that seem as if they exist but which, when you study them deeply enough, turn out not to exist after all.

The Magic of Nine

The kind of magic that grabs (and enchants) me is fantasy-literature magic, not stage-magic, but this month I’ll make an exception to talk about a new math trick inspired by Art Benjamin’s fun-packed book “The Magic of Math: Solving for x and Figuring Out Why”.

After you read this essay, you’ll be able to compute the answer to questions like “What’s the remainder when you divide 123456789 by 9?” or “What’s the sum of the digits when you multiply 123456789 by 9?” without setting pencil to paper, purely through the power of your mind. But before I explain that, I’d better address the question many of you are asking: why would anyone want to learn how to do this sort of thing? (Short answers: to stay sane, to balance their checkbook, and/or to become fame-ish.)

But first, a few words about numbers, rapidity, and mental math.

I HATE NUMBERS¹