Reading the Comics, August 2, 2018: Non-Euclidean Geometry Edition

There’s really only the one strip that I talk about today that gets into non-Euclidean geometries. I was hoping to have the time to get into negative temperatures. That came up in the comics too, and it’s a subject close to my heart. But I didn’t have time to write that and so must go with what I did have. I’ve surely used “Non-Euclidean Geometry Edition” as a name before too, but that name and the date of August 2, 2018? Just as surely not.

Mark Anderson’s Andertoons for the 29th is the Mark Anderson’s Andertoons for the week, at last. Wavehead gets to be disappointed by what a numerator and denominator are. Common problem; there are many mathematics things with great, evocative names that all turn out to be mathematics things.

Both “numerator” and “denominator”, as words, trace to the mid-16th century. They come from Medieval Latin, as you might have guessed. “Denominator” parses out roughly as “to completely name”. As in, break something up into some number of equal-sized pieces. You’d need the denominator number of those pieces to have the whole again. “Numerator” parses out roughly as “count”, as in the count of how many denominator-sized pieces you have. So for all that numerator and denominator look like one another, with with the meat of the words being the letters “n-m–ator”, their centers don’t have anything to do with one another. (I would believe a claim that the way the words always crop up together encouraged them to harmonize their appearances.)

On the board, the fraction 3/4 with the numerator and denominator labelled. Wavehead: 'You know, for something that sounds like two killer robots, this is really disappointing.'
Mark Anderson’s Andertoons for the 29th of July, 2018. Poor Wavehead is never going to get over his disappointment when he learns about the Fredholm Alternative. I still insist it’s an underrated mid-70s paranoia-thriller.

Johnny Hart’s Back to BC for the 29th is a surprisingly sly joke about non-Euclidean geometries. You wouldn’t expect that given the reputation of the comic the last decade of Hart’s life. And I did misread it at first, thinking that after circumnavigating the globe Peter had come back to have what had been the right line touch the left. That the trouble was his stick wearing down I didn’t notice until I re-read.

But Peter’s problem would be there if his stick didn’t wear down. “Parallel” lines on a globe don’t exist. One can try to draw a straight line on the surface of a sphere. These are “great circles”, with famous map examples of those being the equator and the lines of longitude. They don’t keep a constant distance from one another, and they do meet. Peter’s experiment, as conducted, would be a piece of proof that they have to live on a curved surface.

Peter, holding up a Y-shaped stick: 'In proving to you rather dense individuals that parallel lines never meet I am about to embark on a heretofore unprecedented expedition which will encompass the globe. See you.' (He walks off, dragging both ends of the stick in the ground, creating parallel lines. He walks several panels; 'Fifty Thousand Miles Later' as the stick wears down and the parallel lines get less far apart ... he gets back where he started, with the stick worn down to a single ribbon, and the surviving line left.)
Johnny Hart’s Back to BC for the 29th of July, 2018. It originally ran it looks like, the 13th of August, 1961. Or I’m reading the second row, second panel wrong.

And this gets at one of those questions that bothers mathematicians, cosmologists, and philosophers. How do we know the geometry of the universe? If we could peek at it from outside we’d have some help, but that is a big if. So we have to rely on what we can learn from inside the universe. And we can do some experiments that tell us about the geometry we’re in. Peter’s line example would be one; he can use that to show the world’s curved in at least one direction. A couple more lines and he’d be confident the world was a sphere. If we could make precise enough measurements we could do better, with geometric experiments smaller than the circumference of the Earth. (Or universe.) Famously, the sum of the interior angles of a triangle tell us something about the space the triangle’s inscribed in. There are dangers in going from information about one point, or a small area, to information about the whole. But we can tell some things.

Dr Strange-y type doing mind stuff: 'Using my MENTALISTIC powers of the occult, I shall attempt to DOUBLE your brain power, Captain Victorious! Peruse the potency of ... PROFESSOR PECULIAR!' Captain Victorious: 'Mind ... reeling! So much ... information!! ... Two plus two equals ... four! Hey! It worked!' Professor Peculiar: 'I guess double was too relative a term.'
Phil Dunlap’s Ink Pen rerun for the 29th of July, 2018. This one originally ran the 21st of August, 2011.

Phil Dunlap’s Ink Pen for the 29th is another use of arithmetic as shorthand for intelligence. Might be fun to ponder how Captain Victorious would know that he was right about two plus two equalling four, if he didn’t know that already. But we all are in the same state, for mathematical truths. We know we’ve got it right because we believe we have a sound logical argument for the thing being true.

A 'Newton Enterprises' boat pulls up to a desert island. A skeleton's under the tree; beside it, a whiteboard that starts with 'Coconut' and proceeds through a few lines of text to, finally, 'F = GMm/R^2'. Caption: 'How Newton actually stumbled across his formula for the theory of gravity.'
Brian Boychuk and Ron Boychuk’s Chuckle Brothers for the 30th of July, 2018. All right, so the rubber boat is an obvious anachronism. But Newton’s pal Edmond Halley made some money building diving bells for people to excavate shipwrecks and if that doesn’t mess with your idea of what the 17th century was you’re a stronger one than I am.

Brian Boychuk and Ron Boychuk’s Chuckle Brothers for the 30th is a riff on the story of Isaac Newton and the apple. The story of Newton starting his serious thinking of gravity by pondering why apples should fall while the Moon did not is famous. And it seems to trace to Newton. We have a good account of it from William Stukeley, who in the mid-18th century wrote Memoirs of Sir Isaac Newton’s Life. Stukeley knew Newton, and claimed to get the story right from him. He also told it to his niece’s husband, John Conduitt. Whether this is what got Newton fired with the need to create such calculus and physics, or whether it was a story he composed to give his life narrative charm, is beyond my ability to say. It’s an important piece of mathematics history anyway.

If you’d like more Reading the Comics essays you can find them at this link. Some of the many essays to mention Andertoons are at this link. Other essays mentioning B.C. (vintage and current) are at this link. The comic strip Ink Pen gets its mentions at this link, although I’m surprised to learn it’s a new tag today. And the Chuckle Brothers I discuss at this link. Thank you.

Author: Joseph Nebus

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

3 thoughts on “Reading the Comics, August 2, 2018: Non-Euclidean Geometry Edition”

  1. Maybe I’ve misunderstood you, but what about the equator and the lines of latitude? They do keep a constant distance from each other, and they don’t meet. Isn’t the equator always the same distance from, say the parallel at 10 degrees north?


    1. You’re right about the lines of latitude being constant distances from each other (at least, I guess, if you ignore weird little anomalies in the Earth’s shape). But the role that ‘straight lines’ play in a Euclidean geometry is played, in spherical geometry, by Great Circles. The lines of latitude, other than the equator, are pretty good circles, but they’re not Great ones. They’re considered ‘Small Circles’.


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