Reading the Comics, February 3, 2020: Fake Venn Diagrams and Real Reruns Edition

Besides kids doing homework there were a good ten or so comic strips with enough mathematical content for me to discuss. So let me split that over a couple of days; I don’t have the time to do them all in one big essay.

Sandra Bell-Lundy’s Between Friends for the 2nd is declared to be a Venn Diagram joke. As longtime readers of these columns know, it’s actually an Euler Diagram: a Venn Diagram requires some area of overlap between all combinations of the various sets. Two circles that never touch, or as these two do touch at a point, don’t count. They do qualify as Euler Diagrams, which have looser construction requirements. But everything’s named for Euler, so that’s a less clear identifier.

Caption: 'The Venn Diagram of the Sandwich Generation.' Two tangent circles, one 'The Problem' and one 'The Solution'. Two friends sit pondering this over coffee 'It's what put the 'vent' in 'venti'.'
Sandra Bell-Lundy’s Between Friends for the 2nd of February, 2020. Essays mentioning Between Friends and its imperfectly formed Venn Diagrams are at this link.

John Kovaleski’s Daddy Daze for the 2nd talks about probability. Particularly about the probability of guessing someone’s birthday. This is going to be about one chance in 365, or 366 in leap years. Birthdays are not perfectly uniformly distributed through the year. The 13th is less likely than other days in the month for someone to be born; this surely reflects a reluctance to induce birth on an unlucky day. Births are marginally more likely in September than in other months of the year; this surely reflects something having people in a merry-making mood in December. These are tiny effects, though, and to guess any day has about one chance in 365 of being someone’s birthday will be close enough.

Toddler, pointing: 'Ba ba ba.' Dad: 'Her? ... Excuse me, my son would like to give you something.' Woman: 'Uh ... OK?' Dad: 'It's a birthday card he made.' Woman: 'But it's not my birthday. ... It's ... lovely.' Dad: 'He likes to give them out to random people. He figures the odds are 1 in 365 it'll be someone's birthday and it'll make them happy.' Woman: 'What are the odds it won't be someone's birthday and it'll still make them happy?'
John Kovaleski’s Daddy Daze for the 2nd of February, 2020. Essays which mention something from Daddy Daze should be at this link.

If the child does this long enough there’s almost sure to be a match of person and birthday. It’s not guaranteed in the first 365 cards given out, or even the first 730, or more. But, if the birthdays of passers-by are independent — one pedestrian’s birthday has nothing to do with the next’s — then, overall, about one-365th of all cards will go to someone whose birthday it is. (This also supposes that we won’t see things like the person picked saying that while it’s not their birthday, it is their friend’s, here.) This, the Law of Large Numbers, one of the cornerstones of probability, guarantees us.

Conference room. Projected on a wall is 'Diplopia', represented by two overlapping circles. Man at the table asks: 'Is everyone seeing a Venn diagram, or just me?'
Mark Anderson’s Andertoons for the 2nd of February, 2020. Some of the many essays mentioning Andertoons are at this link.

Mark Anderson’s Andertoons for the 2nd is the Mark Anderson’s Andertoons for the week. And it’s a Venn Diagram joke, at least if the two circles are “really” there. Diplopia is what most of us would call double vision, seeing multiple offset copies of a thing. So the Venn diagram might be an optical illusion on the part of the businessman and the reader.

Man in the Accounting department, to a person entering: 'Hey, c'mon in, Warren. We were just crunching a few numbers.' Another person is jumping up and down on a 2, a 3, and has broken several other numerals.
Brian Boychuk and Ron Boychuk’s Chuckle Brothers repeat for the 3rd of February, 2020. It originally ran the 22nd of February, 2011. Essays featuring some aspect of The Chuckle Brothers are at this link.

Brian Boychuk and Ron Boychuk’s Chuckle Brothers for the 3rd is not quite the anthropomorphic numerals joke of the week. At least, it’s built on manifesting numerals and doing things with them.

Letters 'x' and 'y' sit at a bar. The y says, 'I just knew that someday, our paths would intersect.'
Dave Blazek’s Loose Parts for the 3rd of February, 2020. Essays with some mention of topics raised by Loose Parts are at this link.

Dave Blazek’s Loose Parts for the 3rd is an anthropomorphic mathematical symbols joke. I suppose it’s algebraic symbols. We usually get to see the ‘x’ and ‘y’ axes in (high school) algebra, used to differentiate two orthogonal axes. The axes can be named anything. If ‘x’ and ‘y’ won’t do, we might move to using \hat{i} and \hat{j} . In linear algebra, when we might want to think about Euclidean spaces with possibly enormously many dimensions, we may change the names to \hat{e}_1 and \hat{e}_2 . (We could use subscripts of 0 and 1, although I do not remember ever seeing someone do that.)

Mikki: 'First our teacher says 6 and 4 make 10. Then she says 7 and 3 equals 10. Then 5 and 5 make 10. We need a teacher who can make up her mind.'
Morrie Turner’s Wee Pals repeat for the 3rd of February, 2020. Many, but not all, of the essays featuring Wee Pals are at this link.

Morrie Turner’s Wee Pals for the 3rd is a repeat, of course. Turner died several years ago and no one continued the strip. But it is also a repeat that I have discussed in these essays before, which likely makes this a good reason to drop Wee Pals from my regular reading here. There are 42 distinct ways to add (positive) whole numbers up to make ten, when you remember that you can add three or four or even six numbers together to do it. The study of how many different ways to make the same sum is a problem of partitioning. This might not seem very interesting, but if you try to guess how many ways there are to add up to 9 or 11 or 15, you’ll notice it’s a harder problem than it appears.

And for all that, there’s still some more comic strips to review. I will probably slot those in to Sunday, and start taking care of this current week’s comic strips on … probably Tuesday. Please check in at this link Sunday, and Tuesday, and we’ll see what I do.

Reading the Comics, September 29, 2019: September 29, 2019 Edition

Several of the mathematically-themed comic strips from last week featured the fine art of calculation. So that was set to be my title for this week. Then I realized that all the comics worth some detailed mention were published last Sunday, and I do like essays that are entirely one-day affairs. There are a couple of other comic strips that mentioned mathematics tangentially and I’ll list those later this week.

John Hambrock’s The Brilliant Mind of Edison lee for the 29th has Edison show off an organic computer. This is a person, naturally enough. Everyone can do some arithmetic in their heads, especially if we allow that sometimes approximate answers are often fine. People with good speed and precision have always been wonders, though. The setup may also riff on the ancient joke of mathematicians being ways to turn coffee into theorems. (I would imagine that Hambrock has heard that joke. But it is enough to suppose that he’s aware many adult humans drink coffee.)

Edison: 'Welcome to Edison's Science Sunday. I'm going to show you how to build a simple organic calculator. I'll use a bale of hay, a pot of coffee, and Bob the postman. First, I'll have Bob sit on the hay.' Joules, rat: 'OK, now what?' Edison: 'Bob, what is 46 times 19?' Bob :'874.' Joules: 'You have GOT to be kidding me!' Edison: 'He's a whiz with numbers.' Joules: 'Where does the coffee come in?' Edison: 'It extends Bob's battery life.' Bob: 'Cream and sugar, please.'
John Hambrock’s The Brilliant Mind of Edison lee for the 29th of September, 2019. Essays featuring something mentioned in Edison Lee appear at this link.

John Kovaleski’s Daddy Daze for the 29th sees Paul, the dad, working out the calculations his son (Angus) proposed. It’s a good bit of arithmetic that Paul’s doing in his head. The process of multiplying an insubstantial thing by many, many times until you get something of moderate size happens all the time. Much of integral calculus is based on the idea that we can add together infinitely many infinitesimal numbers, and from that get something understandable on the human scale. Saving nine seconds every other day is useless for actual activities, though. You need a certain fungibility in the thing conserved for the bother to be worth it.

Kid: 'Ba ba'. Dad: 'A brilliant math-related idea?' Kid: 'Ba ba ba ba'. Dad: 'We don't need to wash *all* your toes every time you take a bath since they're not *that* dirty?' 'Ba ba ba ba ba' 'OK, if I've got this. There's 8 space between your 10 toes, each space takes 1.25 seconds to wash. If we wash only one space per bath we save 8.75 seconds each time. Three baths a week, this saves 1365 seconds (22.75 minutes) every year. Gee, what'll we do with all that extra time?' 'Ba ba ba'. 'Play 'This Little Piggy' 107.4 times.'
John Kovaleski’s Daddy Daze for the 29th of September, 2019. This is a new tag. Well, the comic is barely a year old. But this and other essays featuring Daddy Daze should be at this link.

Dan Thompson’s Harley for the 29th gets us into some comic strips not drawn by people named John. The comic has some mathematics in it qualitatively. The observation that you could jump a motorcycle farther, or higher, with more energy, and that you can get energy from rolling downhill. It’s here mostly because of the good fortune that another comic strip did a joke on the same topic, and did it quantitatively. That comic?

Harley, racing on the motorcycle: 'Speeding down this mountain should launch us over Pointy Rock Canyon.' Cat, riding behind: 'How do you figure that?' Harley: 'Math, my friend. Harley + Speed + Ramp = Jump The Canyon. It's so simple, it's genius!' Cat: 'We're going faster than we've ever gone!' Harley: 'I think I heard a sonic boom!' Cat: 'I see the rap!' Harley: 'I see my brilliance!' (They race up the ramp. Final panel, they're floating in space.) Cat: 'Didn't you flunk math in school?' Harley: 'Not the third time.'
Dan Thompson’s Harley for the 29th of September, 2019. This just barely misses being a new tag. This essay and the other time I mentioned Harley are at this link. I’ll keep you up dated if there are more essays to add to this pile.

Bill Amend’s FoxTrot for the 29th. Young prodigies Jason and Marcus are putting serious calculation into their Hot Wheels track and working out the biggest loop-the-loop possible from a starting point. Their calculations are right, of course. Bill Amend, who’d been a physics major, likes putting authentic mathematics and mathematical physics in. The key is making sure the car moves fast enough in the loop that it stays on the track. This means the car experiencing a centrifugal force that’s larger than that of gravity. The centrifugal force on something moving in a circle is proportional to the square of the thing’s speed, and inversely proportional to the radius of the circle. This for a circle in any direction, by the way.

So they need to know, if the car starts at the height A, how fast will it go at the top of the loop, at height B? If the car’s going fast enough at height B to stay on the track, it’s certainly going fast enough to stay on for the rest of the loop.

Diagram on ruled paper showing a track dropping down and circling around, with the conservation-of-energy implications resulting on the conclusion the largest possible loop-the-loop is 4/5 the starting height. Peter: 'I don't think this will work. Your calculations assume no friction.' Jason: 'Peter, please. We're not stupid.' (Jason's friend Marcus is working on the track.) Mom: 'Kids, why is there a Hot Wheels car soaking in a bowl of olive oil?'
Bill Amend’s FoxTrot for the 29th of September, 2019. Essays featuring either the current-run Sunday FoxTrot or the vintage FoxTrot comics from the 90s should be at this link.

The hard part would be figuring the speed at height B. Or it would be hard if we tried calculating the forces, and thus acceleration, of the car along the track. This would be a tedious problem. It would depend on the exact path of the track, for example. And it would be a long integration problem, which is trouble. There aren’t many integrals we can actually calculate directly. Most of the interesting ones we have to do numerically or work on approximations of the actual thing. This is all right, though. We don’t have to do that integral. We can look at potential energy instead. This turns what would be a tedious problem into the first three lines of work. And one of those was “Kinetic Energy = Δ Potential Energy”.

But as Peter observes, this does depend on supposing the track is frictionless. We always do this in basic physics problems. Friction is hard. It does depend on the exact path one follows, for example. And it depends on speed in complicated ways. We can make approximations to allow for friction losses, often based in experiment. Or try to make the problem one that has less friction, as Jason and Marcus are trying to do.

Caption: 'ODDITIONS'. Several people with large numerals as head stand around, reading scripts; the one with a 3 head recites, 'To be or not to be? That is the question.' A 9 leans in, saying, 'Next!'
Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 29th of September, 2019. The occasional essay featuring Mustard and Boloney appears at this link. I feel a bit glad to see this doesn’t seem to be a rerun, or at least it’s not one I’ve discussed before.

Jeffrey Caulfield and Alexandre Rouillard’s Mustard and Boloney for the 29th is the anthropomorphic numerals joke for the week. This is a slight joke to include here. But there were many comic strips of slight mathematical content. I intend to list them in an essay on Wednesday.

Tuesday I plan to be a day for the Fall 2019 A-to-Z. Again, thank you for reading.