Reading the Comics, March 11, 2017: Accountants Edition

And now I can wrap up last week’s delivery from Comic Strip Master Command. It’s only five strips. One certainly stars an accountant. one stars a kid that I believe is being coded to read as an accountant. The rest, I don’t know. I pick Edition titles for flimsy reasons anyway. This’ll do.

Ryan North’s Dinosaur Comics for the 6th is about things that could go wrong. And every molecule of air zipping away from you at once is something which might possibly happen but which is indeed astronomically unlikely. This has been the stuff of nightmares since the late 19th century made probability an important part of physics. The chance all the air near you would zip away at once is impossibly unlikely. But such unlikely events challenge our intuitions about probability. An event that has zero chance of happening might still happen, given enough time and enough opportunities. But we’re not using our time well to worry about that. If nothing else, even if all the air around you did rush away at once, it would almost certainly rush back right away.

Steve Kelley and Jeff Parker’s Dustin for the 7th of March, 2017. It’s the title character doing the guessing there. Also, Kelley and Parker hate their title character with a thoroughness you rarely see outside Tom Batiuk and Funky Winkerbean. This is a mild case of it but, there we are.

Steve Kelley and Jeff Parker’s Dustin for the 7th of March talks about the SATs and the chance of picking right answers on a multiple-choice test. I haven’t heard about changes to the SAT but I’ll accept what the comic strip says about them for the purpose of discussion here. At least back when I took it the SAT awarded one point to the raw score for a correct answer, and subtracted one-quarter point for a wrong answer. (The raw scores were then converted into a 200-to-800 range.) I liked this. If you had no idea and guessed on answers you should expect to get one in five right and four in five wrong. On average then you would expect no net change to your raw score. If one or two wrong answers can be definitely ruled out then guessing from the remainder brings you a net positive. I suppose the change, if it is being done, is meant to be confident only right answers are rewarded. I’m not sure this is right; it seems to me there’s value in being able to identify certainly wrong answers even if the right one isn’t obvious. But it’s not my test and I don’t expect to need to take it again either. I can expression opinions without penalty.

Mark Anderson’s Andertoons for the 7th is the Mark Anderson’s Andertoons for last week. It’s another kid-at-the-chalkboard panel. What gets me is that if the kid did keep one for himself then shouldn’t he have written 38?

Brian Basset’s Red and Rover for the 8th mentions fractions. It’s just there as the sort of thing a kid doesn’t find all that naturally compelling. That’s all right I like the bug-eyed squirrel in the first panel.

Bill Holbrook’s On The Fastrack for the 9th of March, 2017. I confess I’m surprised Holbrook didn’t think to set the climax a couple of days later and tie it in to Pi Day.

Bill Holbrook’s On The Fastrack for the 9th concludes the wedding of accountant Fi. It uses the square root symbol so as to make the cake topper clearly mathematical as opposed to just an age.

Reading the Comics, June 26, 2015: June 23, 2016 Plus Golden Lizards Edition

And now for the huge pile of comic strips that had some mathematics-related content on the 23rd of June. I admit some of them are just using mathematics as a stand-in for “something really smart people do”. But first, another moment with the Magic Realism Bot:

A watchmaker realises that a golden lizard is controlling mathematics.

— Magic Realism Bot (@MagicRealismBot) June 25, 2016

So, you know, watch the lizards and all.

Tom Batiuk’s Funky Winkerbean name-drops E = mc² as the sort of thing people respect. If the strip seems a little baffling then you should know that Mason’s last name is Jarr. He was originally introduced as a minor player in a storyline that wasn’t about him, so the name just had to exist. But since then Tom Batiuk’s decided he likes the fellow and promoted him to major-player status. And maybe Batiuk regrets having a major character with a self-consciously Funny Name, which is an odd thing considering he named his long-running comic strip for original lead character Funky Winkerbean.

Tom Batiuk’s Funky Winkerbean for the 23rd of June, 2016. They’re in the middle of filming one or possibly two movies about the silver-age comic book hero Starbuck Jones. This is all the comic strip is about anymore, so if you go looking for its old standbys — people dying — or its older standbys — band practice being rained on — sorry, you’ll have to look somewhere else. That somewhere else would be the yellowed strips taped to the walls in the teachers lounge.

Charlie Podrebarac’s CowTown depicts the harsh realities of Math Camp. I assume they’re the realities. I never went to one myself. And while I was on the Physics Team in high school I didn’t make it over to the competitive mathematics squad. Yes, I noticed that the not-a-numbers-person Jim Smith can’t come up with anything other than the null symbol, representing nothing, not even zero. I like that touch.

Ryan North’s Dinosaur Comics rerun is about Richard Feynman, the great physicist whose classic memoir What Do You Care What Other People Think? is hundreds of pages of stories about how awesome he was. Anyway, the story goes that Feynman noticed one of the sequences of digits in π and thought of the joke which T-Rex shares here.

π is believed but not proved to be a “normal” number. This means several things. One is that any finite sequence of digits you like should appear in its representation, somewhere. Feynman and T-Rex look for the sequence ‘999999’, which sure enough happens less than eight hundred digits past the decimal point. Lucky stroke there. There’s no reason to suppose the sequence should be anywhere near the decimal point. There’s no reason to suppose the sequence has to be anywhere in the finite number of digits of π that humanity will ever know. (This is why Carl Sagan’s novel Contact, which has as a plot point the discovery of a message apparently encoded in the digits of π, is not building on a stupid idea. That any finite message exists somewhere is kind-of certain. That it’s findable is not.)

e, mentioned in the last panel, is similarly thought to be a normal number. It’s also not proved to be. We are able to say that nearly all numbers are normal. It’s in much the way we can say nearly all numbers are irrational. But it is hard to prove that any numbers are. I believe that the only numbers humans have proved to be normal are a handful of freaks created to show normal numbers exist. I don’t know of any number that’s interesting in its own right that’s also been shown to be normal. We just know that almost all numbers are.

But it is imaginable that π or e aren’t. They look like they’re normal, based on how their digits are arranged. It’s an open question and someone might make a name for herself by answering the question. It’s not an easy question, though.

Missy Meyer’s Holiday Doodles breaks the news to me the 23rd was SAT Math Day. I had no idea and I’m not sure what that even means. The doodle does use the classic “two trains leave Chicago” introduction, the “it was a dark and stormy night” of Boring High School Algebra word problems.

Stephan Pastis’s Pearls Before Swine is about everyone who does science and mathematics popularization, and what we worry someone’s going to reveal about us. Um. Except me, of course. I don’t do this at all.

Ashleigh Brilliant’s Pot-Shots rerun is a nice little averages joke. It does highlight something which looks paradoxical, though. Typically if you look at the distributions of values of something that can be measured you get a bell cure, like Brilliant drew here. The value most likely to turn up — the mode, mathematicians say — is also the arithmetic mean. “The average”, is what everybody except mathematicians say. And even they say that most of the time. But almost nobody is at the average.

Looking at a drawing, Brilliant’s included, explains why. The exact average is a tiny slice of all the data, the “population”. Look at the area in Brilliant’s drawing underneath the curve that’s just the blocks underneath the upside-down fellow. Most of the area underneath the curve is away from that.

There’s a lot of results that are close to but not exactly at the arithmetic mean. Most of the results are going to be close to the arithmetic mean. Look at how many area there is under the curve and within four vertical lines of the upside-down fellow. That’s nearly everything. So we have this apparent contradiction: the most likely result is the average. But almost nothing is average. And yet almost everything is nearly average. This is why statisticians have their own departments, or get to make the mathematics department brand itself the Department of Mathematics and Statistics.

What is .19 of a bathroom?

I’ve had a little more time attempting to teach probability to my students and realized I had been overlooking something obvious in the communication of ideas such as the probability of events or the expectation value of a random variable. Students have a much easier time getting the abstract idea if the examples used for it are already ones they find interesting, and if the examples can avoid confusing interpretations. This is probably about 3,500 years behind the curve in educational discoveries, but at least I got there eventually.

A “random variable”, here, sounds a bit scary, but shouldn’t. It means that the variable, for which x is a popular name, is some quantity which might be any of a collection of possible values. We don’t know for any particular experiment what value it has, at least before the experiment is done, but we know how likely it is to be any of those. For example, the number of bathrooms in a house is going to be one of 1, 1.5, 2, 2.5, 3, 3.5, up to the limits of tolerance of the zoning committee.

The expectation value of a random variable is kind of the average value of that variable. You find it by taking the sum of each of the possible values of the random variable times the probability of the random variable having that value. This is at least for a discrete random variable, where the imaginable values are, er, discrete: there’s no continuous ranges of possible values. Number of bathrooms is clearly discrete; the number of seconds one spends in the bathroom is, at least in principle, continuous. For a continuous random variable you don’t take the sum, but instead take an integral, which is just a sum that handles the idea of infinitely many possible values quite well.