## Reading the Comics, November 2, 2019: Eugene the Jeep Edition

I knew by Thursday this would be a brief week. The number of mathematically-themed comic strips has been tiny. I’m not upset, as the days turned surprisingly full on me once again. At some point I would have to stop being surprised that every week is busier than I expect, right?

Anyway, the week gives me plenty of chances to look back to 1936, which is great fun for people who didn’t have to live through 1936.

Elzie Segar’s Thimble Theatre rerun for the 28th of October is part of the story introducing Eugene the Jeep. The Jeep has astounding powers which, here, are finally explained as being due to it being a fourth-dimensional creature. Or at least able to move into the fourth dimension. This is amazing for how it shows off the fourth dimension being something you could hang a comic strip plot on, back in the day. (Also back in the day, humor strips with ongoing plots that might run for months were very common. The only syndicated strips like it today are Gasoline Alley, Alley Oop, the current storyline in Safe Havens where they’ve just gone and terraformed Mars, and Popeye, rerunning old daily stories.) The Jeep has many astounding powers, including that he can’t be kept inside — or outside — anywhere against his will, and he’s able to forecast the future.

Could there be a fourth-dimensional animal? I dunno, I’m not a dimensional biologist. It seems like we need a rich chemistry for life to exist. Lots of compounds, many of them long and complicated ones. Can those exist in four dimensions? I don’t know the quantum mechanics of chemical formation well enough to say. I think there’s obvious problems. Electrical attraction and repulsion would fall off much more rapidly with distance than they do in three-dimensional space. This seems like it argues chemical bonds would be weaker things, which generically makes for weaker chemical compounds. So probably a simpler chemistry. On the other hand, what’s interesting in organic chemistry is shapes of molecules, and four dimensions of space offer plenty of room for neat shapes to form. So maybe that compensates for the chemical bonds. I don’t know.

But if we take the premise as given, that there is a four-dimensional animal? With some minor extra assumptions then yeah, the Jeep’s powers fit well enough. Not being able to be enclosed follows almost naturally. You, a three-dimensional being, can’t be held against your will by someone tracing a line on the floor around you. The Jeep — if the fourth dimension is as easy to move through as the third — has the same ability.

Forecasting the future, though? We have a long history of treating time as “the” fourth dimension. There’s ways that this makes good organizational sense. But we do have to treat time as somehow different from space, even to make, for example, general relativity work out. If the Jeep can see and move through time? Well, yeah, then if he wants he can check on something for you, at least if it’s something whose outcome he can witness. If it’s not, though? Well, maybe the flow of events from the fourth dimension is more obvious than it is from a mere three, in the way that maybe you can spot something coming down the creek easily, from above, in a way that people on the water can’t tell.

Olive Oyl and Popeye use the Jeep to tease one another, asking for definite answers about whether the other is cute or not. This seems outside the realm of things that the fourth dimension could explain. In the 1960s cartoons he even picks up the power to electrically shock offenders; I don’t remember if this was in the comic strips at all.

Elzie Segar’s Thimble Theatre rerun for the 29th of October has Wimpy doing his best to explain the fourth dimension. I think there’s a warning here for mathematician popularizers here. He gets off to a fair start and then it all turns into a muddle. Explaining the fourth dimension in terms of the three dimensions we’re familiar with seems like a good start. Appealing to our intuition to understand something we have to reason about has a long and usually successful history. But then Wimpy goes into a lot of talk about the mystery of things, and it feels like it’s all an appeal to the strangeness of the fourth dimension. I don’t blame Popeye for not feeling it’s cleared anything up. Segar would come back, in this storyline, to several other attempted explanations of the Jeep’s powers, although they do come back around to, y’know, it’s a magical animal. They’re all over the place in the Popeye comic universe.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 28th of October is a riff on predictability and encryption. Good encryption schemes rely on randomness. Concealing the content of a message means matching it to an alternate message. Each of the alternate messages should be equally likely to be transmitted. This way, someone who hasn’t got the key would not be able to tell what’s being sent. The catch is that computers do not truly do randomness. They mostly rely on quasirandom schemes that could, in principle, be detected and spoiled. There are ways to get randomness, mostly involving putting in something from the real world. Sensors that detect tiny fluctuations in temperature, for example, or radio detectors. I recall one company going for style and using a wall of lava lamps, so that the rise and fall of lumps were in some way encoded into unpredictable numbers.

Robb Armstrong’s JumpStart for the 2nd of November is a riff on the Birthday “Paradox”, the thing where you’re surprised to find someone shares a birthday with you. (I have one small circle of friends featuring two people who share my birthday, neatly enough.) Paradox is in quotes because it defies only intuition, not logic. The logic is clear that you need only a couple dozen people before some pair will probably share a birthday. Marcie goes overboard in trying to guess how many people at her workplace would share their birthday on top of that. Birthdays are nearly uniformly spread across all days of the year. There are slight variations; September birthdays are a little more likely than, say, April ones; the 13th of any month is a less likely birthday than the 12th or the 24th are. But this is a minor correction, aptly ignored when you’re doing a rough calculation. With 615 birthdays spread out over the year you’d expect the average day to be the birthday of about 1.7 people. (To be not silly about this, a ten-day span should see about 17 birthdays.) However, there are going to be “clumps”, days where three or even four people have birthdays. There will be gaps, days nobody has a birthday, or even streaks of days where nobody has a birthday. If there weren’t a fair number of days with a lot of birthdays, and days with none, we’d have to suspect birthdays weren’t random here.

There were also a handful of comic strips just mentioning mathematics, that I can’t make anything in depth about. Here’s two.

T Shepherd’s Snow Sez for the 1st of November nominally talks about how counting can be a good way to meditate. It can also become a compulsion, with hazards, though.

Terri Libenson’s The Pajama Diaries for the 2nd of November uses mathematics as the sort of indisputably safe topic that someone can discuss in place of something awkward.

And that is all I have to say for last week’s comics. Tuesday I should publish the next Fall 2019 A to Z essay. I also figure to open the end of the alphabet up to nominations this week. My next planned Reading the Comic post should be Sunday. Thanks for reading.

## Reading the Comics, September 14, 2019: Friday the 13th Edition

The past week included another Friday the 13th. Several comic strips found that worth mention. So that gives me a theme by which to name this look over the comic strips.

Charles Schulz’s Peanuts rerun for the 12th presents a pretty wordy algebra problem. And Peppermint Patty, in the grips of a math anxiety, freezing up and shutting down. One feels for her. Great long strings of words frighten anyone. The problem seems a bit complicated for kids Peppermint Patty’s and Franklin’s age. But the problem isn’t helping. One might notice, say, that a parent’s age will be some nice multiple of a child’s in a year or two. That in ten years a man’s age will be 14 greater than the combined age of their ages then? What imagination does that inspire?

Grant Peppermint Patty her fears. The situation isn’t hopeless. It helps to write out just what know, and what we would like to know. At least what we would like to know if we’ve granted the problem worth solving. What we would like is to know the man’s age. That’s some number; let’s call it M. What we know are things about how M relates to his daughter’s and his son’s age, and how those relate to one another. Since we know several things about the daughter’s age and the son’s age it’s worth giving those names too. Let’s say D for the daughter’s age and S for the son’s.

So. We know the son is three years older than the daughter. This we can write as $S = D + 3$. We know that in one year, the man will be six times as old as the daughter is now. In one year the man will be M + 1 years old. The daughter’s age now is D; six times that is 6D. So we know that $M + 1 = 6D$. In ten years the man’s age will be M + 10; the daughter’s age, D + 10; the son’s age, S + 10. In ten years, M + 10 will be 14 plus D + 10 plus S + 10. That is, $M + 10 = 14 + D + 10 + S + 10$. Or if you prefer, $M + 10 = D + S + 34$. Or even, $M = D + S + 24$.

So this is a system of three equation, all linear, in three variables. This is hopeful. We can hope there will be a solution. And there is. There are different ways to find an answer. Since I’m grading this, you can use the one that feels most comfortable to you. The problem still seems a bit advanced for Peppermint Patty and Franklin.

Julie Larson’s The Dinette Set rerun for the 13th has a bit of talk about a mathematical discovery. The comic is accurate enough for its publication. In 2008 a number known as M43112609 was proven to be prime. The number, 243,112,609 – 1, is some 12,978,189 digits long. It’s still the fifth-largest known prime number (as I write this).

Prime numbers of the form 2N – 1 for some whole number N are known as Mersenne primes. These are named for Marin Mersenne, a 16th century French friar and mathematician. They’re a neat set of numbers. Each Mersenne prime matches some perfect number. Nobody knows whether there are finite or infinitely many Mersenne primes. Every even perfect number has a form that matches to some Mersenne prime. It’s unknown whether there are any odd perfect numbers. As often happens with number theory, the questions are easy to ask but hard to answer. But all the largest known prime numbers are Mersenne primes; they’re of a structure we can test pretty well. At least that electronic computers can test well; the last time the largest known prime was found by mere mechanical computer was 1951. The last time a non-Mersenne was the largest known prime was from 1989 to 1992, and before that, 1951.

Mark Parisi’s Off The Mark for the 13th starts off the jokes about 13 for this edition. It’s also the anthropomorphic-numerals joke for the week.

Doug Savage’s Savage Chickens for the 13th is a joke about the connotations of numbers, with (in the western tradition) 7 lucky and 13 unlucky. And many numbers just lack any particular connotation.

T Shepherd’s Snow Sez for the 13th finishes off the unlucky-13 jokes. It observes that whatever a symbol might connote generally, your individual circumstances are more important. There are people for whom 13 is a good omen, or for whom Mondays are magnificent days, or for whom black cats are lucky.

These are all the comics I can write paragraphs about. There were more comics mentioning mathematics last week. Here were some of them:

Brian Walker, Greg Walker, and Chance Browne’s Hi and Lois for the 14th supposes that a “math nerd” can improve Thirsty’s golf game.

Bill Amend’s FoxTrot Classics for the 14th, rerunning a strip from 1997, is a word problem joke. I needed to re-read the panels to see what Paige’s complaint was about.

Greg Evans’s Luann Againn for the 14th, repeating a strip from 1991, is about prioritizing mathematics homework. I can’t disagree with putting off the harder problems. It’s good to have experience, and doing similar but easier problems can help one crack the harder ones.

Jonathan Lemon’s Rabbits Against Magic for the 14th is the Rubik’s Cube joke for the week.

And that’s my comic strips for the week. I plan to have the next Reading the Comics post here on Sunday. The A to Z series resumes tomorrow, all going well. I am seeking topics for the letters I through N, at this post. Thank you for reading, and for offering your thoughts.

## Reading the Comics, March 26, 2019: March 26, 2019 Edition

And we had another of those peculiar days where a lot of strips are on-topic enough for me to talk about.

Eric the Circle, this one by Kyle, for the 26th has a bit of mathematical physics in it. This is the kind of diagram you’ll see all the time, at least if you do the mathematics that tells you where things will be and when. The particular example is an easy problem, a thing rolling down an inclined plane. But the work done for it applies to more complicated problems. The question it’s for is, “what happens when this thing slides down the plane?” And that depends on the forces at work. There’s gravity, certainly . If there were something else it’d be labelled. Gravity’s represented with that arrow pointing straight down. That gives us the direction. The label (Eric)(g) gives us how strong this force is.

Where the diagram gets interesting, and useful, are those dashed lines ending in arrows. One of those lines is, or at least means to be, parallel to the incline. The other is perpendicular to it. These both reflect gravity. We can represent the force of gravity as a vector. That means, we can represent the force of gravity as the sum of vectors. This is like how we can can write “8” or we can write “3 + 5”, depending on what’s more useful for what we’re doing. (For example, if you wanted to work out “67 + 8”, you might be better off doing “67 + 3 + 5”.) The vector parallel to the plane and the one perpendicular to the plane add up to the original gravity vector.

The force that’s parallel to the plane is the only force that’ll actually accelerate Eric. The force perpendicular to the plane just … keeps it snug against the plane. (Well, it can produce friction. We try not to deal with that in introductory physics because it is so hard. At most we might look at whether there’s enough friction to keep Eric from starting to slide downhill.) The magnitude of the force parallel to the plane, and perpendicular to the plane, are easy enough to work out. These two forces and the original gravity can be put together into a little right triangle. It’s the same shape but different size to the right triangle made by the inclined plane plus a horizontal and a vertical axis. So that’s how the diagram knows the parallel force is the original gravity times the sine of x. And that the perpendicular force is the original gravity times the cosine of x.

The perpendicular force is often called the “normal” force. This because mathematical physicists noticed we had only 2,038 other, unrelated, things called “normal”.

Rick Detorie’s One Big Happy for the 26th sees Ruthie demand to know who this Venn person was. Fair question. Mathematics often gets presented as these things that just are. That someone first thought about these things gets forgotten.

John Venn, who lived from 1834 to 1923 — he died the 4th of April, it happens — was an English mathematician and philosopher and logician and (Anglican) priest. This is not a rare combination of professions. From 1862 he was a lecturer in Moral Science at Cambridge. This included work in logic, yes. But he also worked on probability questions. Wikipedia credits his 1866 Logic Of Chance with advancing the frequentist interpretation of probability. This is one of the major schools of thought about what the “probability of an event” is. It’s the one where you list all the things that could possibly happen, and consider how many of those are the thing you’re interested in. So, when you do a problem like “what’s the probability of rolling two six-sided dice and getting a total of four”? You’re doing a frequentist probability problem.

Venn Diagrams he presented to the world around 1880. These show the relationships between different sets. And the relationships of mathematical logic problems they represent. Venn, if my sources aren’t fibbing, didn’t take these diagrams to be a new invention of his own. He wrote of them as “Euler diagrams”. Venn diagrams, properly, need to show all the possible intersections of all the sets in play. You just mark in some way the intersections that happen to have nothing in them. Euler diagrams don’t require this overlapping. The name “Venn diagram” got attached to these pictures in the early 20th century. Euler here is Leonhard Euler, who created every symbol and notation mathematicians use for everything, and who has a different “Euler’s Theorem” that’s foundational to every field of mathematics, including the ones we don’t yet know exist. I exaggerate by 0.04 percent here.

Although we always start Venn diagrams off with circles, they don’t have to be. Circles are good shapes if you have two or three sets. It gets hard to represent all the possible intersections with four circles, though. This is when you start seeing weirder shapes. Wikipedia offers some pictures of Venn diagrams for four, five, and six sets. Meanwhile Mathworld has illustrations for seven- and eleven-set Venn diagrams. At this point, the diagrams are more for aesthetic value than to clarify anything, though. You could draw them with squares. Some people already do. Euler diagrams, particularly, are often squares, sometimes with rounded corners.

Venn had his other projects, too. His biography at St Andrews writes of his composing The Biographical History of Gonville and Caius College (Cambridge). And then he had another history of the whole Cambridge University. It also mentions his skills in building machines, though only cites one, a device for bowling cricket balls. The St Andrews biography says that in 1909 “Venn’s machine clean bowled one of [the Australian Cricket Team’s] top stars four times”. I do not know precisely what it means but I infer it to be a pretty good showing for the machine. His Wikipedia biography calls him a “passionate gardener”. Apparently the Cambridgeshire Horticultural Society awarded him prizes for his roses in July 1885 and for white carrots in September that year. And that he was a supporter of votes for women.

Ashleigh Brilliant’s Pot-Shots for the 26th makes a cute and true claim about percentiles. That a person will usually be in the upper 99% of whatever’s being measured? Hard to dispute. But, measure enough things and eventually you’ll fall out of at least one of them. How many things? This is easy to calculate if we look at different things that are independent of each other. In that case we could look at 69 things before there we’d expect a 50% chance of at least one not being in the upper 99%.

It’s getting that independence that’s hard. There’s often links between things. For example, a person’s height does not tell us much about their weight. But it does tell us something. A person six foot, ten inches tall is almost certainly not also 35 pounds, even though a person could be that size or could be that weight. A person’s scores on a reading comprehension test and their income? But test-taking results and wealth are certainly tied together. Age and income? Most of us have a bigger income at 46 than at 6. This is part of what makes studying populations so hard.

T Shepherd’s Snow Sez for the 26th is finally a strip I can talk about briefly, for a change. Snow does a bit of arithmetic wordplay, toying with what an expression like “1 + 1” might represent.

There were a lot of mathematically-themed comic strips last week. There’ll be another essay soon, and it should appear at this link. And then there’s always Sunday, as long as I stay ahead of deadline. I am never ahead of deadline.