# 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.

## Author: Joseph Nebus

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

## 4 thoughts on “Reading the Comics, October 11, 2018: Under Weather Edition”

1. If you feed a cold and starve a fever — what do you feed the cold? Hope you feel better soon.

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1. I don’t know what helps a cold. I usually spend my time being cranky and puttering around the house, but I do that anyway.

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1. Oh, thank you.

So I was a 17-year-old working in Walden Books. Customer came up with a test-prep book wanting to know about the 10% discount sticker: was the discount taken on the price before the sales tax (6%) was calculated, or was the sales tax calculated and then 10% taken off the total? And he wanted me to know that the law directed that the discount be taken before tax was calculated. I could not say with authority how the registers calculated things. But I did know that, for the thing which mattered, it didn’t make any difference. Whether you took $15.95 [ book price ] times 0.90 [ ten percent discount ] times 1.06 [ six percent sales tax ] first, or whether you took$15.95 times 1.06 times 0.90 you got the same figure, $15.22. He was skeptical, but I showed him on a calculator how it worked out, and he let me ring it up. So the thing is, while we could enter a price by the UPC code, we just used the laser scanner and let the machine ring things up. And on this particular book, for some reason, the UPC code had the book price as$16.95, even though the suggested cover price was $15.95. So the machine rang it up as$16.17 and he insisted, see? SEE?

I tried to explain what the mistake was — you can see the UPC code price on a book; it’s in the digits on the upper right of the bar code — and rang up the correction to this. But I know he never, ever believed me.

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