## Reading the Comics, 1 September 2018: Retirement Of A Tag Edition

I figure to do something rare, and retire one of my comic strip tags after today. Which strip am I going to do my best to drop from Reading the Comics posts? Given how many of the ones I read are short-lived comics that have been rerun three or four times since I started tracking them? Read on and see!

Bill Holbrook’s On The Fastrack for the 29th of August continues the sequence of Fi talking with kids about mathematics. My understanding was that she tried to give talks about why mathematics could be fun. That there are different ways to express the same number seems like a pretty fine-grain detail to get into. But this might lead into some bigger point. That there are several ways to describe the same thing can be surprising and unsettling to discover. That you have, when calculating, the option to switch between these ways freely can be liberating. But you have to know the option is there, and where to look for it. And how to see it’ll make something simpler.

Bill Holbrook’s On The Fastrack for the 30th of August gets onto a thread about statistics. The point of statistics is to describe something complicated with something simple. So detail must be lost. That said, there are something like 2,038 different things called “average”. Each of them has a fair claim to the term, too. In Fi’s example here, 73 degrees (Fahrenheit) could be called the average as in the arithmetic mean, or average as in the median. The distribution reflects how far and how often the temperature is from 73. This would also be reflected in a quantity called the variance, or the standard deviation. Variance and standard deviation are different things, but they’re tied together; if you know one you know the other. It’s just sometimes one quantity is more convenient than the other to work with.

Bill Holbrook’s On The Fastrack for the 1st of September has Fi argue that apparent irrelevance makes mathematics boring. It’s a common diagnosis. I think I’ve advanced the claim myself. I remember a 1980s probability textbook asking the chance that two transistors out of five had broken simultaneously. Surely in the earlier edition of the textbook, it was two vacuum tubes out of five. Five would be a reasonable (indeed, common) number of vacuum tubes to have in a radio. And it would be plausible that two might be broken at the same time.

It seems obvious that wanting to know an answer makes it easier to do the work needed to find it. I’m curious whether that’s been demonstrated true. Like, it seems obvious that a reference to a thing someone doesn’t know anything about would make it harder to work on. But does it? Does it distract someone trying to work out the height of a ziggurat based on its distance and apparent angle, if all they know about a ziggurat is their surmise that it’s a thing whose height we might wish to know?

Tom Toles’s Randolph Itch, 2 am rerun for the 30th of August is an old friend that’s been here a couple times. I suppose I do have to retire the strip from my Reading the Comics posts, at least, although I’m still amused enough by it to keep reading it daily. Simon Garfield’s On The Map, a book about the history of maps, notes that the X-marks-the-spot thing is an invention of the media. Robert Louis Stevenson’s Treasure Island particularly. Stevenson’s treasure map, Garfield notes, had to be redrawn from the manuscript and the author’s notes. The original went missing in the mail to the publishers. I just mention because I think that adds a bit of wonder to the treasure map. And since, I guess, I won’t have the chance to mention this again.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 30th of August satisfies the need for a Venn Diagram joke this time around. It’s also the strange-geometry joke for the week. Klein bottles were originally described by Felix Klein. They exist in four (or more) dimensions, in much the way that M&oum;bius strips exist in three. And like the M&oum;bius strip the surface defies common sense. You can try to claim some spot on the surface is inside and some other spot outside. But you can get from your inside to your outside spot in a continuous path, one you might trace out on the surface without lifting your stylus.

If you were four-dimensional. Or more. If we were to see one in three dimensions we’d see a shape that intersects itself. As beings of only three spatial dimensions we have to pretend that doesn’t happen. It’s the same we we pretend a drawing of a cube shows six squares all of equal size and connected at right angles to one another, even though the drawing is nothing like that. The bottle-like shape Weinersmith draws is, I think, the most common representation of the Klein bottle. It looks like a fancy bottle, and you can buy one as a novelty gift for a mathematician. I don’t need one but do thank you for thinking of me. MathWorld shows another representation, a figure-eight-based one which looks to me like an advanced pasta noodle. But it doesn’t look anything like a bottle.

Eric the Circle for the 31st of August, this one by JohnG, is a spot of wordplay. The pun here is the sine of an angle in a (right) triangle. That would be the length of the leg opposite the angle divided by the length of the hypotenuse. This is still stuff relevant to circles, though. One common interpretation of the cosine and sine of an angle is to look at the unit circle. That is, a circle with radius 1 and centered on the origin. Draw a line segment opening up an angle θ from the positive x-axis. Draw it counterclockwise. That is, if your angle is a very small number, you’re drawing a line segment that’s a little bit above the positive x-axis. Draw the line segment long enough that it touches the unit circle. That point where the line segment and the circle intersect? Look at its Cartesian coordinates. The y-coordinate will be the sine of θ. The x-coordinate will be the cosine of θ. The triangle you’re looking at has vertices at the origin; at x-coordinate cosine θ, y-coordinate 0; and at x-coordinate cosine θ, y-coordinate sine θ.

Bill Griffith’s Zippy the Pinhead for the 1st of September is its usual sort of nonsense, the kind that’s up my alley. It does spend two panels using arithmetic and algebra as signifiers of intelligence, or at least thoughtfulness.

My other Reading the Comics posts should appear at this link. Other essays with On The Fastrack are at this link. The essays that mentioned Randolph Itch, 2 am, are at this link, and I suppose this will be the last of them. We’ll see if I do succeed in retiring the tag. Other appearances by Saturday Morning Breakfast Cereal are at this link. The strip comes up here a lot. Eric the Circle comics should be at this link. And other essays with Zippy the Pinhead mentions should be at this link. Thank you.

## Reading the Comics, July 11, 2018: GoComics Hardly Needs Me Edition

The first half of last week’s comics are mostly ones from Comics Kingdom and Creators.com. That’s unusual. GoComics usually far outranks the other sites. Partly for sheer numbers; they have an incredible number of strips, many of them web-only, that Comics Kingdom and Creators.com don’t match. I think the strips on GoComics are more likely to drift into mathematical topics too. But to demonstrate that would take so much effort. Possibly any effort at all. Hm.

Bill Holbrook’s On the Fastrack for the 8th of July is premised on topographic maps. These are some of the tools we’ve made to understand three-dimensional objects with a two-dimensional representation. When topographic maps come to the mathematics department we tend to call them “contour maps” or “contour plots”. These are collections of shapes. They might be straight lines. They might be curved. They often form a closed loop. Each of these curves is called a “contour curve” or a “contour line” (even if it’s not straight). Or it’s called an “equipotential curve”, if someone’s being all fancy, or pointing out the link between potential functions and these curves.

Their purpose is in thinking of three-dimensional surfaces. We can represent a three-dimensional surface by putting up some reasonable coordinate system. For the sake of simplicity let’s suppose the “reasonable coordinate system” is the Cartesian one. So every point in space has coordinates named ‘x’, ‘y’, and ‘z’. Pick a value for ‘x’ and ‘y’. There’s at most one ‘z’ that’ll be on the surface. But there might be many sets of values of ‘x’ and ‘y’ together which have that height ‘z’. So what are all the values of ‘x’ and ‘y’ which match the same height ‘z’? Draw the curve, or curves, which match that particular value of ‘z’.

Topographical maps are a beloved example of this, to mathematicians, because we imagine everyone understands them. A particular spot on the ground at some given latitude and longitude is some particular height above sea level. OK. Imagine the slice of a hill representing all the spots that are exactly 10 feet above sea level, or whatever. That’s a curve. Possibly several curves, but we just say “a curve” for simplicity.

A topographical map will often include more than one curve. Often at regular intervals, say with one set of curves representing 10 feet elevation, another 20 feet, another 30 feet, and so on. Sometimes these curves will be very near one another, where a hill is particularly steep. Sometimes these curves will be far apart, where the ground is nearly level. With experience one can learn to read the lines and their spacing. One can see where extreme values are, and how far away they might be.

Topographical maps date back to 1789. These sorts of maps go back farther. In 1701 Edmond Halley, of comet fame, published maps showing magnetic compass variation. He had hopes that the difference between magnetic north and true north would offer a hint at how to find longitude. (The principle is good. But the lines of constant variation are too close to lines of latitude for the method to be practical. And variation changes over time, too.) And that shows how the topographical map idea can be useful to visualize things that aren’t heights. Weather maps include “isobars”, contour lines showing where the atmospheric pressure is a set vale. More advanced ones will include “isotherms”, each line showing a particular temperature. The isobar and isotherm lines can describe the weather and how it can be expected to change soon.

This idea, rendering three-dimensional information on a two-dimensional surface, is a powerful one. We can use it to try to visualize four-dimensional objects, by looking at the contour surfaces they would make in three dimensions. We can also do this for five and even more dimensions, by using the same stuff but putting a note that “D = 16” or the like in the corner of our image. And, yes, if Cartesian coordinates aren’t sensible for the problem you can use coordinates that are.

If you need a generic name for these contour lines that doesn’t suggest lines or topography or weather or such, try ‘isogonal curves’. Nobody will know what you mean, but you’ll be right.

Ted Key’s Hazel for the 9th is a joke about the difficulties in splitting the bill. It is archetypical of the sort of arithmetic people know they need to do in the real world. Despite that at least people in presented humor don’t get any better at it. I suppose real-world people don’t either, given some restaurants now list 15 and 20 percent tips on the bill. Well, at least everybody has a calculator on their phone so they can divide evenly. And I concede that, yeah, there isn’t really specifically a joke here. It’s just Hazel being competent, like the last time she showed up here.

Mark Anderson’s Andertoons for the 11th is the Mark Anderson’s Andertoons for the week. And it’s a bit of geometry wordplay, too. Also about how you can carry a joke over well enough even without understanding it, or the audience understanding it, if it’s delivered right.

Rick DeTorie’s One Big Happy for the 11th is another strip about arithmetic done in the real world. I’m also amused by Joe’s attempts to distract from how no kid that age has ever not known precisely how much money they have, and how much of it is fairly won.

Bill Griffith’s Zippy the Pinhead for the 11th is another example of using understanding algebra as a show of intelligence. And it follows that up with undrestanding quantum physics as a show of even greater intelligence. One can ask what’s meant by “understanding” quantum physics. Someday someone might even answer. But it seems likely that the ability to do calculations based on a model has to be part of fully understanding it.

I have even more Reading the Comics posts, gathered in reverse chronological order at this link. Other essays with On The Fastrack tagged are at this link. Other Reading the Comics posts that mention Hazel are at this link. Some of the many, many essays mentioning Andertoons are at this link. Posts with mention of One Big Happy, both then-current and then-rerun, are at this link. And other mentions of Zippy the Pinhead are at this link.

## Reading the Comics, March 5, 2018: If It’s Even Mathematics Edition

Many of the strips from the first half of last week are ones that just barely touch on mathematical content. I’m not sure how relevant they all are. I hope you like encountering them anyway.

Bill Griffith’s Zippy the Pinhead for the 4th of March offers “an infinite number of mathematicians walk into a bar” as a joke’s setup. Mathematics popularizers have a small set of jokes about infinite numbers of mathematicians, often arriving at hotels. They’re used to talk about how we now understand infinitely large sets. There’s often counter-intuitive or just plain weird results that follow. And presenting it as a joke works surprisingly well in introducing the ideas. There’s a kind of joke that is essentially a tall tale, spinning out an initial premise to as far and as absurd a consequence as you can get. In structure, that’s not much different to a proof, a discussion of the consequences of an idea. It’s a shame that it’s hard to make jokes or anecdotes about more fields of mathematics. Somehow infinitely large groups of people are funnier than, say, upper-bounded nondecreasing sequences.

Mike Baldwin’s Cornered for the 4th has a bit of fraction-based wordplay. I’m not sure how mathematical this is, but I grinned.

Bill Amend’s FoxTrot for the 4th has Jason try to make a “universal” loot box that consists of zeroes and ones. As he says, accumulate enough and put them in the right order and you have any digital prize imaginable. Implementation is, as joked, the problem. Assembling ones and zeroes at random isn’t likely to turn up anything you might care about in a reasonable time. (It’s the monkeys-at-typewriters problem.) If you know how to assemble ones and zeroes to get what you want, well, what do you need Jason’s boxes for? As with most clever ideas by computer-oriented boys it shouldn’t really be listened to.

Mark Pett’s Lucky Cow rerun for the 4th has Neil make an order-of-magnitude error estimating what animal power can do. We’ve all made them. They’re particularly easy to make when switching the unit measure. Trying to go from meters to kilometers and multiplying the distance by a thousand, say. Which is annoying since often it’s easiest to estimate the order of magnitude of something first. I can’t find easily an estimate of how many calories a hamster eats over the course of the day. That seems like it would give an idea of how much energy a hamster could possibly be expected to provide, and so work out whether the estimate of four million hamsters to power a car is itself plausible. If someone has information, I’d take it.

Jonathan Lemon’s Rabbits Against Magic for the 4th is a Rubik’s Cube joke. Also a random processes joke. If a blender could turn the faces of a cube, and could turn them randomly, and could run the right period of time … well, yeah, it could unscramble a cube. But see the previous talk about Jason Fox and the delivery of ones and zeroes.

Mark Tatulli’s Lio for the 5th is a solid geometry joke. I’ve put more thought into whether and where to put hyphens in the last three words of that sentence than is worth it.

Steve Sicula’s Home and Away rerun for the 6th has the father and son happily doing some mathematics. It’s in the service of better gambling on sports. But at least they know why they would like to do these calculations.

I thought my new workflow of writing my paragraph or two about each comic was going to help me keep up and keep fresher with the daily comics. And then Comic Strip Master Command decided that everybody had to do comics that at least touched on some mathematical subject. I don’t know. I’m trying to keep up but will admit, I didn’t get to writing anything about Friday’s or Saturday’s strips yet. They’ll keep a couple days.

Bill Amend’s FoxTrot Classicsfor the 29th of January reprints the strip from the 5th of February, 1996. (The Classics reprints finally reached the point where Amend retired from daily strips, and jumped back a dozen years to continue printing.) It just mentions mathematics exams, and high performances on both is all.

Josh Shalek’s Kid Shay Comics reprint for the 29th tosses off a mention of Uncle Brian attempting a great mathematical feat. In this case it’s the Grand Unification Theory, some logically coherent set of equations that describe the fundamental forces of the universe. I think anyone with a love for mathematics makes a couple quixotic attempts on enormously vast problems like this. Or the Riemann Hypothesis, or Goldbach’s Conjecture, or Fermat’s Last Theorem. Yes, Fermat’s Last Theorem has been proven, but there’s no reason there couldn’t be an easier proof. Similarly there’s no reason there couldn’t be a better proof of the Four Color Map theorem. Most of these attempts end up the way Brian’s did. But there’s value in attempting this anyway. Even when you fail, you can have fun and learn fascinating things in the attempt.

Carol Lay’s Lay Lines for the 29th is a vignette about a statistician. And one of those statisticians with the job of finding surprising correlations between things. I think it’s also a riff on the hypothesis that free markets are necessarily perfect: if there’s any advantage to doing something one way, it’ll quickly be found and copied until that is the normal performance of the market. Anyone doing better than average is either taking advantage of concealed information, or else is lucky.

Matt Lubchansky’s Please Listen To Me for the 29th depicts a person doing statistical work for his own purposes. In this case he’s trying to find what factors might be screwing up the world. The expressions in the second panel don’t have an obvious meaning to me. The start of the expression $\int exp\left(\frac{1}{N_0}\right)$ at the top line suggests statistical mechanics to me, for what that’s worth, and the H and Ψ underneath suggest thermodynamics or quantum mechanics. So if Lubchansky was just making up stuff, he was doing it with a good eye for mathematics that might underly everything.

Rick Stromoski’s Soup to Nutz for the 29th circles around the anthropomorphic numerals idea. It’s not there exactly, but Andrew is spending some time giving personality to numerals. I can’t say I give numbers this much character. But there are numbers that seem nicer than others. Usually this relates to what I can do with the numbers. 10, for example, is so easy to multiply or divide by. If I need to multiply a number by, say, something near thirty, it’s a delight to triple it and then multiply by ten. Twelve and 24 and 60 are fun because they’re so relatively easy to find parts of. Even numbers often do seem easier to work with, just because splitting an even number in half saves us from dealing with decimals or fractions. Royboy sees all this as silliness, which seems out of character for him, really. I’d expect him to be up for assigning traits to numbers like that.

Bill Griffith’s Zippy the Pinhead for the 30th mentions Albert Einstein and relativity. And Zippy ruminates on the idea that there’s duplicates of everything, in the vastness of the universe. It’s an unsettling idea that isn’t obviously ruled out by mathematics alone. There’s, presumably, some chance that a bunch of carbon and hydrogen and oxygen and other atoms happened to come together in such a way as to make our world as we know it today. If there’s a vast enough universe, isn’t there a chance that a bunch of carbon and hydrogen and oxygen and other atoms happened to come together that same way twice? Three times? If the universe is infinitely large, might it not happen infinitely many times? In any number of variations? It’s hard to see why not, but even if it is possible, that’s no reason to think it must happen either. And whether those duplicates are us is a question for philosophers studying the problem of identity and what it means to be one person rather than some other person. (It turns out to be a very difficult problem and I’m glad I’m not expected to offer answers.)

Tony Cochrane’s Agnes attempts to use mathematics to reason her way to a better bedtime the 31st. She’s not doing well. Also this seems like it’s more of an optimization problem than a simple arithmetic one. What’s the latest bedtime she can get that still allows for everything that has to be done, likely including getting up in time and getting enough sleep? Also, just my experience but I didn’t think Agnes was old enough to stay up until 10 in the first place.

## Reading the Comics, December 30, 2017: Looking To 2018 Edition

The last full week of 2017 was also a slow one for mathematically-themed comic strips. You can tell by how many bits of marginally relevant stuff I include. In this case, it also includes a couple that just mention the current or the upcoming year. So you’ve been warned.

Mac King and Bill King’s Magic in a Minute activity for the 24th is a logic puzzle. I’m not sure there’s deep mathematics to it, but it’s some fun to reason out.

John Graziano’s Ripley’s Believe It Or Not for the 24th mentions the bit of recreational group theory that normal people know, the Rubik’s Cube. The group theory comes in from rotations: you can take rows or columns on the cube and turn them, a quarter or a half or a three-quarters turn. Which rows you turn, and which ways you turn them, form a group. So it’s a toy that inspires deep questions. Who wouldn’t like to know in how few moves a cube could be solved? We know there are at least some puzzles that take 18 moves to solve. (You can calculate the number of different cube arrangements there are, and how many arrangements you could make by shuffling a cube around with 17 moves. There’s more possible arrangements than there are ones you can get to in 17 moves; therefore, there must be at least one arrangement that takes 18 moves to solve.) A 2010 computer-assisted proof by Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge showed that at most 20 face turns are needed for every possible cube to be solved. I don’t know if there’s been any success figuring out whether 19 or even 18 is necessarily enough.

Bill Griffith’s Zippy the Pinhead for the 26th just mentions algebra as a thing that Griffith can’t really remember, even in one of his frequent nostalgic fugues. I don’t know that Zippy’s line about the fifth dimension is meant to refer to geometry. It might refer to the band, but that would be a bit odd. Yes, I know, Zippy the Pinhead always speaks oddly, but in these nostalgic fugue strips he usually provides some narrative counterpoint.

Larry Wright’s Motley Classics for the 26th originally ran in 1986. I mention this because it makes the odd dialogue of getting “a new math program” a touch less odd. I confess I’m not sure what the kid even got. An educational game? Something for numerical computing? The coal-fired, gear-driven version of Mathematica that existed in the 1980s? It’s a mystery, it is.

Ryan Pagelow’s Buni for the 27th is really a calendar joke. It seems to qualify as an anthropomorphic numerals joke, though. It’s not a rare sentiment either.

Jef Mallett’s Frazz for the 29th is similarly a calendar joke. It does play on 2017 being a prime number, a fact that doesn’t really mean much besides reassuring us that it’s not a leap year. I’m not sure just what’s meant by saying it won’t repeat for another 2017 years, at least that wouldn’t be just as true for (say) 2015 or 2019. But as Frazz points out, we do cling to anything that floats in times like these.