Reading the Comics, September 28, 2019: Modeling Edition


The second half of last week’s mathematically-themed comic strips had an interesting range of topics. Two of them seemed to circle around the making of models. So that’s my name for this installment.

Ryan North’s Dinosaur Comics for the 26th has T-Rex trying to build a model. In this case, it’s to project how often we should expect to see a real-life Batman. T-Rex is building a simple model, which is fine. Simple models, first, are usually easier to calculate with. How they differ from reality can give a guide to how to make a more complex model. Or they can indicate the things that have to be learned in order to make a more complex model. The difference between a model’s representation and the observed reality (or plausibly expected reality) can point out problems in one’s assumptions, too.

T-Rex: 'Start with the number of children born to billionaires each year! Multiply by the chance of someone becoming an Olympic athlete! And multiply that by the unfortunate chance someone will witness their parents become victims of a violent crime as a child!' Dromiceiomimus: 'Good god! You're calculating---' T-Rex: 'YES. The expected real-life Batman generation rate.' Utahraptor: 'What do you get?' T-Rex: 'There's only about 1000 billionaires worldwide.' Utahraptor: 'And there were 2600 athletes last Olympics, so your odds are 1 in 2,307,692 of such peak physicality.' T-Rex: 'And if we estimate a 0.0001 chance of parent murder then ... that's one Batman every 25 million years, assuming every billionaire has a child each year. And is murdered each year. And I didn't even work the odds of becoming friends with Superman. I hate to say it, but reality SUCKS sometimes.'
Ryan North’s Dinosaur Comics for the 26th of September, 2019. Essays featuring discussion of some topic raised by Dinosaur Comics should appear at this link.

For example, T-Rex supposes that a Batman needs to have billionaire parents. This makes for a tiny number of available parents. But surely what’s important is that a Batman be wealthy enough he doesn’t have to show up to any appointments he doesn’t want to make. Having a half-billion dollars, or a “mere” hundred million, would allow that. Even a Batman who had “only” ten million dollars would be about as free to be a superhero. Similarly, consider the restriction to Olympic athletes. Astronaut Ed White, who on Gemini IV became the first American to walk in space, was not an Olympic athlete; but he certainly could have been. He missed by a split-second in the 400 meter hurdles race. Surely someone as physically fit as Ed White would be fit enough for a Batman. Not to say that “Olympic athletes or NASA astronauts” is a much bigger population than “Olympic athletes”. (And White was unusually fit even for NASA astronauts.) But it does suggest that merely counting Olympic athletes is too restrictive.

But that’s quibbling over the exact numbers. The process is a good rough model. List all the factors, suppose that all the factors are independent of one another, and multiply how likely it is each step happens by the population it could happen to. It’s hard to imagine a simpler model, but it’s a place to start.

'When Juanita entered the picture, the love triangle between Ken, Debra, and Bill became a love rhombus. But only when they convened at opposite, equal acute angles and opposite, equal obtuse angles. Otherwise, they were just a parallelogram looking for a good time.'
Greg Wallace’s Nothing Is Not Something for the 26th of September, 2019. I don’t seem to have tagged this strip before! Well, this essay and any future ones based on Nothing Is Not Something should appear at this link.

Greg Wallace’s Nothing Is Not Something for the 26th is a bit of a geometry joke. It’s built on the idiom of the love triangle, expanding it into more-sided shapes. Relationships between groups of people like this can be well-represented in graph theory, with each person a vertex, and each pair of involved people an edge. There are even “directed graphs”, where each edge contains a direction. This lets one represent the difference between requited and unrequited interests.

Sophie, dog, to Conspiracy Squirrels who have a drill digging up ground: 'What're you doing?' Left Squirrel: 'Digging all through the Earth.' Right Squirrel: 'To prove it's not flat.' Sophie: 'Ambitious. You know there's easier ways to prove Earth's round?' Right: 'ROUND?' Left: 'The Earth is a smushed rhombus. Everyone knows that!' Right: 'Where'd you go to school, Eddie Bravo University?' Left: 'If Earth is round what keeps it from rolling into the sun?' Sophie: 'OK, then, careful not to fall out the other side. Gravity's a conspiracy created by Canada geese to keep us out of the sky.' Left: 'Really?' Right, dashing off: 'I'll get the magnetic boots!'
Brian Anderson’s Dog Eat Doug for the 27th of September, 2019. The essays exploring some topic raised by Dog Eat Doug should appear at this link.

Brian Anderson’s Dog Eat Doug for the 27th has Sophie the dog encounter some squirrels trying to disprove a flat Earth. They’re not proposing a round Earth either; they’ve gone in for a rhomboid. Sophie’s right to point out that drilling is a really hard way to get through the Earth. That’s a practical matter, though.

Is it possible to tell something about the shape of a whole thing from a small spot? In the terminology, what kind of global knowledge can we get from local information? We can do some things. For example, we can draw a triangle on the surface of the Earth and measure the interior angles to see what they sum to. If this could be done perfectly, finding that the interior angles add up to more than 180 degrees would show the triangle’s on a spherical surface. But that also has practical limitations. Like, if we find that locally the planet is curved then we can rule out it being entirely flat. But it’s imaginable that we’d be on the one dome of an otherwise flat planet. At some point you have to either assume you’re in a typical spot, or work out ways to find what’s atypical. In the Conspiracy Squirrels’ case, that would be the edge between two faces of the rhomboid Earth. Then it becomes something susceptible to reason.

Mathematician at chalkboard full of symbols: 'Thus we arrive at the conclusion that one could go to a pay-by-weight salad bar and earn money by eating cheese, which is clearly impossible.' Caption: 'Disproving the idea of negative mass was remarkably easy.'
Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 27th of September, 2019. It’s not literally true that every Reading the Comics essay includes this strip. The essays with Saturday Morning Breakfast Cereal in them are at this link.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 27th has the mathematician making another model. And this is one of the other uses of a model: to show a thing can’t happen, show that it would have results contrary to reason. But then you have to validate the model, showing that its premises do represent reality so well that its conclusion should be believed. This can be hard. There’s some nice symbol-writing on the chalkboard here, although I don’t see that they parse. Particularly, the bit on the right edge of the panel, where the writing has a rotated-by-180-degrees ‘E’ followed by an ‘x’, a rotated-by-180-degrees ‘A’, and then a ‘z’, is hard to fit inside an equation like this. The string of symbols mean “there exists some x for which, for all z, (something) is true”. This fits at the start of a proof, or before an equation starts. It doesn’t make grammatical sense in the middle of an equation. But, in the heat of writing out an idea, mathematicians will write out ungrammatical things. As with plain-text writing, it’s valuable to get an idea down, and edit it into good form later.

Computer, talking to itself in a MICR-inspired font: 'Many people are amazed at the complex mathematical ability of a computer. Actually though, the concept is quite simple! Inside we're just filled with thousands of toes that we can count on!'
Tom Batiuk’s Funky Winkerbean Vintage for the 28th of September, 2019. This strip originally ran the 15th of November, 1973. Both 1970s-era vintage and such 2010s-era modern Funky Winkerbean strips which inspire discussion should be at this link.

Tom Batiuk’s Funky Winkerbean Vintage for the 28th sees the school’s Computer explaining the nature of its existence, and how it works. Here the Computer claims to just be filled with thousands of toes to count on. It’s silly, but it is the case that there’s no operation a computer does that isn’t something a human can do, manually. If you had the paper and the time you could do all the steps of a Facebook group chat, a game of SimCity, or a rocket guidance computer’s calculations. The results might just be impractically slow.


And that’s finished the comic strips of last week! Sunday I should have a new Reading the Comics post. And then tomorrow I hope to resume the Fall 2019 A to Z series with ‘J’. Thanks for reading.

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

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