Reading the Comics, November 18, 2015: All Caught Up Edition


Yes, I feel a bit bad that I didn’t have anything posted yesterday. I’d had a nice every-other-day streak going for a couple weeks there. But I had honestly expected more mathematically themed comic strips, and there just weren’t enough in my box by the end of the 17th. So I didn’t have anything to schedule for a post the 18th. The 18th came through, though, and now I’ve got enough to talk about. And that before I get to reading today’s comics. So, please, enjoy.

Scott Adams’s Dilbert Classics for the 16th of November (originally published the 21st of September, 1992) features Dilbert discovering Bell’s Theorem. Bell’s Theorem is an important piece of our understanding of quantum mechanics. It’s a theorem that excites people who first hear about it. It implies quantum mechanics can’t explain reality unless it can allow information to be transmitted between interacting particles faster than light. And quantum mechanics does explain reality. The thing is, and the thing that casual readers don’t understand, is that there’s no way to use this to send a signal. Imagine that I took two cards, one an ace and one an eight, seal them in envelopes, and gave them to astronauts. The astronauts each travel to ten light-years away from me in opposite directions. (They took extreme offense at something I said and didn’t like one another anyway.) Then one of them opens her envelope, finding that she’s got the eight. Then instantly, even though they’re twenty light-years apart, she knows the other astronaut has an ace in her envelope. But there is no way the astronauts can use this to send information to one another, which is what people want Bell’s Theorem to tell us. (My example is not legitimate quantum mechanics and do not try to use it to pass your thesis defense. It just shows why Bell’s Theorem does not give us a way to send information we care about faster than light.) The next day Dilbert’s Garbageman, the Smartest Man in the World, mentions Dilbert’s added something to Bell’s Theorem. It’s the same thing everybody figuring they can use quantum entanglement to communicate adds to the idea.

Tom Thaves’ Frank and Ernest for the 16th of November riffs on the idea of a lottery as a “tax on people who are bad at math”. Longtime readers here know that I have mixed feelings about that, and not just because I’m wary of cliché. If the jackpot is high enough, you can reach the point where the expectation value of the prize is positive. That is, you would expect to make money if you played the game under the same conditions often enough. But that chance is still vanishingly small. Even playing a million times would not make it likely you would more earn money than you spent. I’m not dogmatic enough to say what your decision should be, at least if the prize is big enough. (And that’s not considering the value placed on the fun of playing. One may complain that it shouldn’t be any fun to buy a soon-to-be-worthless ticket. But many people do enjoy it and I can’t bring myself to say they’re all wrong about feeling enjoyment.)

And it happens that on the 18th Brant Parker and Johnny Hart’s Wizard of Id Classics (originally run the 20th of November, 1965) did a lottery joke. That one is about a lottery one shouldn’t play, except that the King keeps track of who refuses to buy a ticket. I know when we’re in a genre.

Peter Mann’s The Quixote Syndrome for the 16th of November explores something I had never known but that at least the web seems to think is true. Apparently in 1958 Samuel Beckett knew the 12-year-old André Roussimoff. People of my age cohort have any idea who that is when they hear Roussimoff became pro wrestling star André the Giant. And Beckett drove the kid to school. Mann — taking, I think, a break from his usual adaptations of classic literature — speculates on what they might have talked about. His guess: Beckett attempting to ease one of his fears through careful study and mathematical treatment. The problem is goofily funny. But the treatment is the sort of mathematics everyone understands needing and understands using.

John Deering’s Strange Brew for the 17th of November tells a rounding up joke. Scott Hilburn’s The Argyle Sweater told it back in August. I suspect the joke is just in the air. Most jokes were formed between 1922 and 1978 anyway, and we’re just shuffling around the remains of that fruitful era.

Tony Cochrane’s Agnes for the 18th of November tells a resisting-the-word-problem joke. I admit expecting better from Cochrane. But casting arithmetic problems into word problems is fraught with peril. It isn’t enough to avoid obsolete references. (If we accept trains as obsolete. I’m from the United States Northeast, where subways and even commuter trains are viable things.) The problem also has to ask something the problem-solver can imagine wanting to know. It may not matter whether the question asks how far apart two trains, two cars, or two airplanes are, if the student can’t see their distance as anything but trivia. We may need better practice in writing stories if we’re to write story problems.

Reblog: Solitons and trains


Over at the Complex Projective 4-Space blog is a neat little problem: suppose you have a circular train track, and a couple trains of different length which roll at different speeds on the track, and interact by bouncing off one another and going the other way. Are their positions ever-changing, or do they, in time, come back to the way they were arranged when you first set them down, which is a kind of the recurrence problem mentioned in my bits about Arthur Christmas. The author, apgoucher, goes on to talk about vortex rings and solitons, and the ways they can interact. I think it’s worth some attention.

Complex Projective 4-Space

Suppose we have a circular track occupied by finitely many trains of various lengths travelling at the same speed. The trains collide elastically with each other. If the sum of the lengths of the trains is a rational multiple of the track length, then it can be proved that the trains will eventually return to their original configuration. Here’s an animated GIF I prepared earlier:

trains

It’s actually quite fun to prove that the system is periodic (there is a very short elementary proof, but you have to think outside the box). I’ll leave this as an exercise to the reader, and possibly give a solution in about a week or so, when you’ve had sufficient time to think about it. If you find a proof, include it in the ‘comments’ section at the foot of this page.

Now for something completely different and not at all related: solitons. Solitons…

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Just Answer 1/e Whenever Anyone Asks This Kind Of Question


I recently had the chance to ride the Leap-the-Dips at Lakemont Park (Altoona, Pennsylvania), the world’s oldest operating roller coaster. The statistics of this 1902-vintage roller coaster might not sound impressive, as it has a maximum height of about forty feet and a greatest drop of about nine feet, but it gets rather more exciting when you consider that the roller coaster car hasn’t got any seat belts or lap bar or other restraints (just a bar you can grab onto if you so choose), and that the ride was built before the invention of upstop wheels, the wheels that actually go underneath the track and keep roller coaster cars from jumping off. At each of the dips, yes, the car does jump up and off the track, and the car just keeps accelerating the whole ride. (Side boards ensure that once the car jumps off the tracks it falls back into place.) It’s worth the visit.

Looking at the wonderful mesh of wood that makes up a classic roller coaster like this inspired the question: could any of it be original? What’s the chance that any board in it has lasted the hundred-plus years of the roller coaster’s life (including a twelve-year stretch when the ride was not running, a state which usually means routine maintenance is being skipped and which just destroys amusement park rides)? Taking some reasonable guesses about the replacement rate per year, and a quite unreasonable guess about replacement procedure, I worked out my guess, given in the subject line above, and I figure to come back and explain where that all came from.