I don’t think my standards for mathematics content in comic strips are seriously lowering, but the strips do seem to be coming pretty often for the summer break. I admit I’m including one of these strips just because it lets me talk about something I saw at an amusement park, though. I have my weaknesses.
Harley Schwadron’s 9 to 5 (July 25) builds its joke around the ambiguity of saying a salary is six (or some other number) of figures, if you don’t specify what side of the decimal they’re on. That’s an ordinary enough gag, although the size of a number can itself be an interesting thing to know. The number of digits it takes to write a number down corresponds, roughly, with the logarithm of a number, and in the olden days a lot of computations depended on logarithms: multiplying two numbers is equivalent to adding their logarithms; dividing two numbers, subtracting their logarithms. And addition and subtraction are normally easier than multiplication and division. Similarly, raising one number to a power becomes multiplying one number by the logarithm of another, and multiplication is easier than exponentiation. So counting the number of digits in a number might be something anyway.
Steve Breen and Mike Thompson’s Grand Avenue (July 25) has the kids mention something as being “like going to an amusement park to do math homework”, which gives me a chance to share this incident. Last year my love and I were in the Cedar Point amusement park (in Sandusky, Ohio), and went to the coffee shop. We saw one guy sitting at a counter, with his laptop and a bunch of papers sprawled out, looking pretty much like we do when we’re grading papers, and we thought initially that it was so very sad that someone would be so busy at work that (we presumed) he couldn’t even really participate in the family expedition to the amusement park.
And then we remembered: not everybody lives a couple hours away from an amusement park. If we lived, say, fifteen minutes from a park we had season passes to, we’d certainly at least sometimes take our grading work to the park, so we could get it done in an environment we liked and reward ourselves for getting done with a couple roller coasters and maybe the Cedar Downs carousel (which is worth an entry around these parts anyway). To grade, anyway; I’d never have the courage to bring my laptop to the coffee shop. So I guess all I’m saying is, I have a context in which yes, I could imagine going to an amusement park to grade math homework at least.
Wulff and Morgenthaler Truth Facts (July 25) makes a Venn diagram joke in service of asserting that only people who don’t understand statistics would play the lottery. This is an understandable attitude of Wulff and Morgenthaler, and of many, many people who make the same claim. The expectation value — the amount you expect to win some amount, times the probability you will win that amount, minus the cost of the ticket — is negative for all but the most extremely oversized lottery payouts, and the most extremely oversized lottery payouts still give you odds of winning so tiny that you really aren’t hurting your chances by not buying a ticket. However, the smugness behind the attitude bothers me — I’m generally bothered by smugness — and jokes like this one contain the assumption that the only sensible way to live is a ruthless profit-and-loss calculation to life that even Jeremy Bentham might say is a bit much. For the typical person, buying a lottery ticket is a bit of a lark, a couple dollars of disposable income spent because, what the heck, it’s about what you’d spend on one and a third sodas and you aren’t that thirsty. Lottery pools with coworkers or friends make it a small but fun social activity, too. That something is a net loss of money does not mean it is necessarily foolish. (This isn’t to say it’s wise, either, but I’d generally like a little more sympathy for people’s minor bits of recreational foolishness.)
Marc Anderson’s Andertoons (July 27) does a spot of wordplay about the meaning of “aftermath”. I can’t think of much to say about this, so let me just mention that Florian Cajori’s A History of Mathematical Notations reports (section 201) that the + symbol for addition appears to trace from writing “et”, meaning and, a good deal and the letters merging together and simplifying from that. This seems plausible enough on its face, but it does cause me to reflect that the & symbol also is credited as a symbol born from writing “et” a lot. (Here, picture writing Et and letting the middle and lower horizontal strokes of the E merge with the cross bar and the lowest point of the t.)
Berkeley Breathed’s Bloom County (July 27, rerun from, I believe, July of 1988) is one of the earliest appearances I can remember of the Grand Unification appearing in popular culture, certainly in comic strips. Unifications have a long and grand history in mathematics and physics in explaining things which look very different by the same principles, with the first to really draw attention probably being Descartes showing that algebra and geometry could be understood as a single thing, and problems difficult in one field could be easy in the other. In physics, the most thrilling unification was probably the explaining of electricity, magnetism, and light as the same thing in the 19th century; being able to explain many varied phenomena with some simple principles is just so compelling. General relativity shows that we can interpret accelerations and gravitation as the same thing; and in the late 20th century, physicists found that it’s possible to use a single framework to explain both electromagnetism and the forces that hold subatomic particles together and that break them apart.
It’s not yet known how to explain gravity and quantum mechanics in the same, coherent, frame. It’s generally assumed they can be reconciled, although I suppose there’s no logical reason they have to be. Finding a unification — or a proof they can’t be unified — would certainly be one of the great moments of mathematical physics.
The idea of the grand unification theory as an explanation for everything is … well, fair enough. A grand unification theory should be able to explain what particles in the universe exist, and what forces they use to interact, and from there it would seem like the rest of reality is details. Perhaps so, but it’s a long way to go from a simple starting point to explaining something as complicated as a penguin. I guess what I’m saying is I doubt Oliver would notice the non-existence of Opus in the first couple pages of his work.
Thom Bluemel’s Birdbrains (July 28) takes us back to the origin of numbers. It also makes me realize I don’t know what’s the first number that we know of people discovering. What I mean is, it seems likely that humans are just able to recognize a handful of numbers, like one and two and maybe up to six or so, based on how babies and animals can recognize something funny if the counts of small numbers of things don’t make sense. And larger numbers were certainly known to antiquity; probably the fact that numbers keep going on forever was known to antiquity. And some special numbers with interesting or difficult properties, like pi or the square root of two, were known so long ago we can’t say who discovered them. But then there are numbers like the Euler-Mascheroni constant, which are known and recognized as important things, and we can say reasonably well who discovered them. So what is the first number with a known discoverer?
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