## Reading the Comics, May 23, 2020: Parents Can’t Do Math Edition

This was a week of few mathematically-themed comic strips. I don’t mind. If there was a recurring motif, it was about parents not doing mathematics well, or maybe at all. That’s not a very deep observation, though. Let’s look at what is here.

Liniers’s Macanudo for the 18th puts forth 2020 as “the year most kids realized their parents can’t do math”. Which may be so; if you haven’t had cause to do (say) long division in a while then remembering just how to do it is a chore. This trouble is not unique to mathematics, though. Several decades out of regular practice they likely also have trouble remembering what the 11th Amendment to the US Constitution is for, or what the rule is about using “lie” versus “lay”. Some regular practice would correct that, though. In most cases anyway; my experience suggests I cannot possibly learn the rule about “lie” versus “lay”. I’m also shaky on “set” as a verb.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th shows a mathematician talking, in the jargon of first and second derivatives, to support the claim there’ll never be a mathematician president. Yes, Weinersmith is aware that James Garfield, 20th President of the United States, is famous in trivia circles for having an original proof of the Pythagorean theorem. It would be a stretch to declare Garfield a mathematician, though, except in the way that anyone capable of reason can be a mathematician. Raymond Poincaré, President of France for most of the 1910s and prime minister before and after that, was not a mathematician. He was cousin to Henri Poincaré, who founded so much of our understanding of dynamical systems and of modern geometry. I do not offhand know what presidents (or prime ministers) of other countries have been like.

Weinersmith’s mathematician uses the jargon of the profession. Specifically that of calculus. It’s unlikely to communicate well with the population. The message is an ordinary one, though. The first derivative of something with respect to time means the rate at which things are changing. The first derivative of a thing, with respect to time being positive means that the quantity of the thing is growing. So, that first half means “things are getting more bad”.

The second derivative of a thing with respect to time, though … this is interesting. The second derivative is the same thing as the first derivative with respect to time of “the first derivative with respect to time”. It’s what the change is in the rate-of-change. If that second derivative is negative, then the first derivative will, in time, change from being positive to being negative. So the rate of increase of the original thing will, in time, go from a positive to a negative number. And so the quantity will eventually decline.

So the mathematician is making a this-is-the-end-of-the-beginning speech. The point at which the the second derivative of a quantity changes sign is known as the “inflection point”. Reaching that is often seen as the first important step in, for example, disease epidemics. It is usually the first good news, the promise that there will be a limit to the badness. It’s also sometimes mentioned in economic crises or sometimes demographic trends. “Inflection point” is likely as technical a term as one can expect the general public to tolerate, though. Even that may be pushing things.

Gary Wise and Lance Aldrich’s Real Life Adventures for the 19th has a father who can’t help his son do mathematics. In this case, finding square roots. There are many ways to find square roots by hand. Some are iterative, in which you start with an estimate and do a calculation that (typically) gets you a better estimate of the square root you want. And then repeat the calculation, starting from that improved estimate. Some use tables of things one can expect to have calculated, such as exponentials and logarithms. Or trigonometric tables, if you know someone who’s worked out lots of cosines and sines already.

Henry Scarpelli and Craig Boldman’s Archie rerun for the 20th mentions romantic triangles. And Moose’s relief that there’s only two people in his love triangle. So that’s our geometry wordplay for the week.

Bill Watterson’s Calvin and Hobbes repeat for the 20th has Calvin escaping mathematics class.

Julie Larson’s The Dinette Set rerun for the 21st fusses around words. Along the way Burl mentions his having learned that two negatives can make a positive, in mathematics. Here it’s (most likely) the way that multiplying or dividing two negative numbers will produce a positive number.

This covers the week. My next Reading the Comics post should appear at this tag, when it’s written. 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, October 19, 2018: More Short Things Edition

At least, I’d thought the last half of last week’s comics were mostly things I could discuss quickly. Then Frank and Ernest went and sprawled on me. Such will happen.

Before I get to that, I did want to mention that Gregory Taylor’s paneling for votes for the direction his mathematics-inspired serial takes:

You may enjoy; at least, give it a try.

Thaves’s Frank and Ernest for the 18th is a bit of wordplay. There’s something interesting culturally about phrasing “lots of math, but no chemistry”. Algorithms as mathematics makes sense. Much of mathematics is about finding processes to do interesting things. Algorithms, and the mathematics which justifies them, can at least in principle be justified with deductive logic. And we like to think that the universe must make deductive-logical sense. So it is easy to suppose that something mathematical simply must make logical sense.

Chemistry, though. It’s a metaphor for whatever the difference is between a thing’s roster of components and the effect of the whole. The suggestion is that it is mysterious and unpredictable. It’s an attitude strange to actual chemists, who have a rather good understanding of why most things happen. My suspicion is that this sense of chemistry is old, dating to before we had a good understanding of why chemical bonds work. We have that understanding thanks to quantum mechanics, and its mathematical representations.

But we can still allow for things that happen but aren’t obvious. When we write about “emergent properties” we describe things which are inherent in whatever we talk about. But they only appear when the things are a large enough mass, or interact long enough. Some things become significant only when they have enough chance to be seen.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 18th is about mathematicians’ favorite Ancient Greek philosopher they haven’t actually read. (In fairness, Zeno is hard to read, even for those who know the language.) Zeno’s famous for four paradoxes, the most familiar of which is alluded to here. To travel across a space requires travelling across half of it first. But this applies recursively. To travel any distance requires accomplishing infinitely many partial-crossings. How can you do infinitely many things, each of which take more than zero time, in less than an infinitely great time? But we know we do this; so, what aren’t we understanding? A callow young mathematics major would answer: well, pick any tiny interval of time you like. All but a handful of the partial-crossings take less than your tiny interval time. This seems like a sufficient answer and reason to chuckle at philosophers. Fine; an instant has zero time elapse during it. Nothing must move during that instant, then. So when does movement happen, if there is no movement during all the moments of time? Reconciling these two points slows the mathematician down.

Patrick Roberts’s Todd the Dinosaur for the 19th mentions fractions. It’s only used to list a kind of mathematics problem a student might feign unconsciousness rather than do. And takes quite little space in the word balloon to describe. It’d be the same joke if Todd were asked to come up and give a ten-minute presentation on the Battle of Bunker Hill.

Julie Larson’s The Dinette Set for the 19th mentions the Rubik’s Cube. Sometime I should do a proper essay about its mathematics. Any Rubik’s Cube can be solved in at most 20 moves. And it’s apparently known there are some cube configurations that take at least 20 moves, so, that’s nice to have worked out. But there are many approaches to solving a cube, none of which I am competent to do. Some algorithms are, apparently, easier for people to learn, at the cost of taking more steps. And that’s fine. You should understand something before you try to do it efficiently.

John Atkinson’s Wrong Hands for the 19th is the Venn Diagram joke for the week. Good to have one around.

This and my other Reading the Comics posts are available at this link. The essays mentioning Frank and Ernest should be at this link. For just the Reading the Comics posts with Saturday Morning Breakfast Cereal content try this link. Essays which talk about things raised by Todd the Dinosaur are at this link. Posts that write about The Dinette Set are at this link. And the essays based on Wrong Hands should be at this link. And do please stick around for more of my Fall 2018 Mathematics A-To-Z, with another post due tomorrow that I need to write today.

## Reading the Comics, October 11, 2018: Under Weather Edition

I ended up not finding more comics on-topic on GoComics yesterday. So this past week’s mathematically-themed strips should fit into two posts well. I apologize for any loss of coherence in this essay, as I’m getting a bit of a cold. I’m looking forward to what this cold does for the A To Z essays coming Tuesday and Friday this week, too.

Stephen Beals’s Adult Children for the 7th uses Albert Einstein’s famous equation as shorthand for knowledge. I’m a little surprised it’s written out in words, rather than symbols. This might reflect that $E = mc^2$ is often understood just as this important series of sounds, rather than as an equation relating things to one another. Or it might just reflect the needs of the page composition. It could be too small a word balloon otherwise.

Julie Larson’s The Dinette Set for the 9th continues the thread of tip-calculation jokes around here. I have no explanation for this phenomenon. In this case, Burl is doing the calculation correctly. If the tip is supposed to be 15% of the bill, and the bill is reduced 10%, then the tip would be reduced 10%. If you already have the tip calculated, it might be quicker to figure out a tenth of that rather than work out 15% of the original bill. And, yes, the characters are being rather unpleasantly penny-pinching. That was just the comic strip’s sense of humor.

Todd Clark’s Lola for the 9th take the form of your traditional grumbling about story problems. It also shows off the motif of updating of the words in a story problem to be awkwardly un-hip. The problem seems to be starting in a confounding direction anyway. The first sentence isn’t out and it’s introducing the rate at which Frank is shedding social-media friends over time and the rate at which a train is travelling, some distancer per time. Having one quantity with dimensions friends-per-time and another with dimensions distance-per-time is begging for confusion. Or for some weird gibberish thing, like, determining something to be (say) ninety mile-friends. There’s trouble ahead.

Zach Weinersmith’s Saturday Morning Breakfast Cereal for the 10th proposes naming a particular kind of series. A series is the sum of a sequence of numbers. It doesn’t have to be a sequence with infinitely many numbers in it, but it usually is, if it’s to be an interesting series. Properly, a series gets defined by something like the symbols in the upper caption of the panel:

$\sum_{i = 1}^{\infty} a_i$

Here the ‘i’ is a “dummy variable”, of no particular interest and not even detectable once the calculation is done. It’s not that thing with the square roots of -1 in thise case. ‘i’ is specifically known as the ‘index’, since it indexes the terms in the sequence. Despite the logic of i-index, I prefer to use ‘j’, ‘k’, or ‘n’. This avoids confusion with that square-root-of-minus-1 meaning for i. The index starts at some value, the one to the right of the equals sign underneath the capital sigma; in this case, 1. The sequence evaluates whatever the formula described by $a_i$ is, for each whole number between that lowest ‘i’, in this case 1, and whatever the value above the sigma is. For the infinite series, that’s infinitely large. That is, work out $a_i$ for every counting number ‘i’. For the first sum in the caption, that highest number is 4, and you only need to evaluate four terms and add them together. There’s no rule given for $a_i$ in the caption; that just means that, in this case, we don’t yet have reason to care what the formula is.

This is the way to define a series if we’re being careful, and doing mathematics properly. But there are shorthands, and we fall back on them all the time. On the blackboard is one of them: $24 + 12 + 6 + 3 + \cdots$. The $\cdots$ at the end of a summation like this means “carry on this pattern for infinitely many terms”. If it appears in the middle of a summation, like $2 + 4 + 6 + 8 + \cdots + 20$ it means “carry on this pattern for the appropriate number of terms”. In that case, it would be $10 + 12 + 14 + 16 + 18$.

The flaw with this “carry on this pattern” is that, properly, there’s no such thing as “the” pattern. There are infinitely many ways to continue from whatever the start was, and they’re all equally valid. What lets this scheme work is cultural expectations. We expect the difference between one term and the next to follow some easy patterns. They increase or decrease by the same amount as we’ve seen before (an arithmetic progression, like 2 + 4 + 6 + 8, increasing by two each time). They increase or decrease by the same ratio as we’ve seen before (a geometric progression, like 24 + 12 + 6 + 3, cutting in half each time). Maybe the sign alternates, or changes by some straightforward rule. If it isn’t one of these, then we have to fall back on being explicit. In this case, it would be that $a_i = 24 \cdot \left(\frac{1}{2}\right)^{i - 1}$.

The capital-sigma as shorthand for “sum” traces to Leonhard Euler, because of course. I’m finding it hard, in my copy of Florian Cajori’s History of Mathematical Notations, to find just where the series notation as we use it got started. Also I’m not finding where ellipses got into mathematical notation either. It might reflect everybody realizing this was a pretty good way to represent “we’re not going to write out the whole thing here”.

Norm Feuti’s Retail for the 11th riffs on how many people, fundamentally, don’t know what percentages are. I think it reflects thinking of a percentage as some kind of unit. We get used to measurements of things, like, pounds or seconds or dollars or degrees or such that are fixed in value. But a percentage is relative. It’s a fraction of some original quantity. A difference of (say) two pounds in weight is the same amount of weight whatever the original was; why wouldn’t two percent of the weight behave similarly? … Gads, yes, I feel for the next retailer who gets these customers.

I think I’ve already used the story from when I worked in the bookstore about the customer concerned whether the ten-percent-off sticker applied before or after sales tax was calculated. So I’ll only share if people ask to hear it. (They won’t ask.)

When I’m not getting a bit ill, I put my Reading the Comics posts at this link. Essays which mention Adult Children are at this link. Essays with The Dinette Set discussions should be at this link. The essays inspired by Lola are at this link. There’s some mention of Saturday Morning Breakfast Cereal in essays at link, or pretty much every Reading the Comics post. And Retail gets discussed at this link.

## 20,000: My Math Blog’s Statistics

I reached my 20,000th view around here sometime on the final day of 2014, which is an appealingly tidy coincidence. I’m glad for it. It also gives me a starting point to review the blog’s statistics, as gathered by WordPress, which is trying to move us to a new and perfectly awful statistics page that shows less information more inconveniently.

The total number of page views grew from 625 in October to 674 in November all the way to 831 in December 2014, which just ties my record number of viewers from back in January 2013. The number of unique visitors grew from October’s 323 to November’s 366 up to 424 total, which comes in second-place to January 2013’s 473. I don’t know what I was doing in January 2013 that I’m only gradually getting back up to these days. The number of views per visitor went from 1.93, to 1.84, back up to 1.96, which is probably just a meaningless fluctuation. January 2013 had 1.76.

My most popular articles — with 25 views or more each — were Reading The Comics posts, mostly, with the exceptions being two things almost designed to be clickbait, although I mean them sincerely:

1. Reading the Comics, December 14, 2014: Pictures Gone Again? Edition, in which I work out one of the calculus-y expressions and find it isn’t all that interesting.
2. Reading the Comics, December 5, 2014: Good Questions Edition, in which I figured out a Dark Side Of The Horse comic was using a page of symbols from orbital perturbation problems.
3. Reading the Comics, December 27, 2014: Last of the Year Edition?, which it wasn’t, and which let me talk about how Sally Brown is going to discover rational numbers if Charlie Brown doesn’t over-instruct her.
4. Reading The Comics, December 22, 2015: National Mathematics Day Edition, which celebrated Srinivasa Ramanujan’s birth by showing a formula that Leonhard Euler discovered, but Euler’s formula is much more comic-strip-readable than any of Ramanujan’s.
5. What Do I Need To Pass This Class? (December 2014 Edition), which gathered and reposted for general accessibility the formula and the charts so people can figure out what the subject line says. Also what you need to get a B, or A, or any other desired grade. (Mostly, you needed to start caring about your grade earlier.)
6. How Many Trapezoids I Can Draw, my life’s crowning achievement. (Six. If you find a seventh please let me know and I’ll do a follow-up post.)

The country sending me the most readers was, as ever, Bangladesh with 535 viewers. Well, two viewers, but it’s boring just listing the United States up front every time. The United Kingdom (37) and Canada (33) came up next, then Argentina (17), which surprises me every month by having a healthy number of readers there, Australia (12), Austria (11), and the Netherlands (10), proving that people in countries that don’t start with ‘A’ can still kind of like me too. The single-reader countries this month were the Czech Republic, Greece, Macedonia, Mexico, Romania, and South Africa. That’s far fewer than last month; of November’s 17 single-reader countries only Romania is a repeat.

Among search terms that brought people here were popeye comic computer king — I don’t know just how that’s going to end up either, folks, but I’m guessing “not that satisfyingly”, since Bud Sagendorf was fond of shaggy-dog non-endings to tales — and which reindeer was in arthur christmas (they were descendants of the “Original” canonical eight, though Grand-Santa forgets some of the names), daily press, “the dinette set” answer for december 11, 2014, and solution to the comic puzzle, “the dinette set”. in the daily press, december 12, 2014, and answer to the comic puzzle, “the dinette set”. in the daily press, december 12, 2014, which suggests maybe I should ditch the pop-math racket and just get into explaining The Dinette Set, which is admittedly kind of a complicated panel strip. There’s multiple riffs around the central joke in each panel, but if you don’t get the main joke then the riffs look like they’re part of the main joke, and they aren’t, so the whole thing becomes confusing. And the artist includes a “Find-It” bit in every panel, usually hiding something like a triangle or a star or something in the craggly details of the art and that can be hard to find. Mostly, though, the joke is: these people are genially and obliviously obnoxious people who you might love but you’d still find annoying. That’s it, nearly every panel. I hope that helps.