I apologize for not writing as thoughtfully about the comics this week as I’d like, but it’s been a bit of a rushed week and I haven’t had the chance to do pop-mathematics writing of the kind I like, which is part of why you aren’t right now seeing a post about goldfish. All should be back to normal soon. I’m as ever not sure which is my favorite comic of the bunch this week; I think Bewley may have the strongest, if meanest, joke in it, though as you can see by the text Candorville gave me the most to think about.
Ryan Pagelow’s Buni (December 31) saw out the year with a touch of anthropomorphic-numerals business. Never worry, 4; your time will come again.
Daniel Beyer’s Long Story Short (January 1) plays a little on the way a carelessly-written Z will morph so easily into a 2, and vice-versa, which serves as a reminder to the people who give out alphanumeric confirmation codes: stop using both 0’s and O’s, and 1’s and I’s, and 2’s and Z’s, in the same code already. I know in the database there’s no confusion about this but in the e-mail you sent out and in the note we wrote down at the airport transcribing this over the phone, there is. And now that it’s mentioned, why is the letter Z used to symbolize snoring? Nobody is sure, but Cecil Adams and The Straight Dope trace it back to the comics, with Rudolph Dirks’s The Katzenjammer Kids either the originator or at least the popularizer of the snoring Z.
Darrin Bell’s Candorville (January 2) opens with Lemont pondering, and moping, about data being put into the Drake Equation. This is probably the most pop-culturally famous equation about astrophysics, since it touches the great question of “are there other intelligences in the universe” and inspires the subsidiary “well, so where is everybody?” question. The Drake Equation tries to estimate how many intelligences there might be out there by, essentially, multiplying the number of stars there are by the chance any star will produce an intelligent species, which is an expectation value problem. It’s named for Dr Frank Drake (born in 1930 and still with us), who presented it in the early 1960s to one of the first professional conferences on extraterrestrial intelligences. (You might also know Drake as one of the designers of the Pioneer plaque and the golden record sent on Voyager 1 and 2.)
The number of stars is tolerably easy to get good results on; the probability of any star producing an intelligent species … well, that’s harder to say. We can list a string of things that seem likely to be required for an intelligent species to form, such as, a star having planets that can support life, and a planet capable of supporting life actually having life, and life developing intelligence; but what the chances of each of those things are is not really clear since we’ve got only one data point. We can make some guesses, and try to work out implications of those guesses and whether those implications lead to unsustainable conclusions at least, and now and then we get some fresh and very useful data. A generation ago, we couldn’t offer more than hypotheses about how common planets are; now, we have good reason to think that a star has to be doing something pretty wrong not to have planets, and a good number of planets that look a lot like Earth, down to having atmospheres, are known to exist.
The Drake Equation comes in for a lot of criticism, I suppose because in its canonical form it gets written as a series of probabilities multiplied together — probability a star has planets, times probability a planet has life, times probability life gets to intelligence, et cetera — and this form contains within it the assumptions that we can estimate all these probabilities, and that each of these is an independent event. I tend to be friendly towards the Drake Equation, basically because I would like to have an estimate of how many intelligences there are in the universe and I know of no substantially different way to make an estimate. The estimates right now are lousy, owing to a want of data, but if we could have more credible estimates of, for example, how likely life is to form on a suitable planet, then our estimate of the number of intelligences would get better. And if the Drake Equation should prove to be hilariously wrong or inapplicable, well, I don’t know how to discover that it is except by studying its parts and showing how it models the real universe too poorly to use. Even if it is wrong, it seems likely a good starting point for study.
Samson’s Dark Side Of The Horse (January 3) plays on a book of mathematics problems as something that made Horace’s childhood “not easy”. The problems’ author, “Lucien Kastner”, turns out to be a Monty Python reference, though their Kastner was an archeologist who wasn’t particularly tall. Horace pops in again with insomnia on the 5th of January, and some mixing of sleep numbers and counted sheep.
Ruben Bolling’s Super Fun Pak Comix (January 3, rerun from sometime) features an installment of Chaos Butterfly, calling on the iconic representation of deterministic chaos. The idea that infinitesimally small changes even in a system that could be perfectly predicted if we had perfect data can produce major differences also pops up in Anthony Blades’s Bewley (January 5) with the kid, Tonus, averting the butterfly-created disaster. Maybe. That’s the nagging problem about chaos theory; it suggests that it’s plausible to make changes even in massive systems like the world’s weather, but also that it’s impossible to tell whether you’ve made things better or worse.
David Hoyt and Jeff Knurek’s Jumble (January 3) shows off a mathematics teacher and so it won’t surprise you has a mathematics-based play on words for the answer. (If you need a hint, as ever, look at the cartoon panel.)
Zach Weinersmith’s Saturday Morning Breakfast Cereal (January 3) shows off something that’s happened to every mathematics major and probably every physics major, among other things: the calculation that proves to be agonizingly difficult because you overlooked something simple early on.
The particular mathematical bit being described here applies to the study of fields, which is when a swath of space is covered by something that’s got magnitude and maybe direction; I think the easiest-to-understand physical example is to think of studying the speed of particles of water in a moving stream. The curl of a field is a measure of the field’s rotation; imagine placing a little wooden chip on the surface of the water and watching how quickly or slowly it then spins. The gradient is a measure of how much the speed of the water is changing, and in what direction it’s changing the fastest. And, indeed, for a scalar field — where you’re interested in only the speed of the water, not in its direction — the curl of the gradient of this field is zero.
Saturday Morning Breakfast Cereal turns up again the 4th of January with the claim that mathematicians make the worst parents, as one explains to her kid that yes, 2 + 2 equals 4, but can you prove that’s a unique solution? This isn’t a problem in arithmetic, but in algebra you start to see problems in which there can be multiple solutions, like when a parabola intersects a line. By the time you get to calculus or to differential equations you can have literally infinitely many solutions, and maybe even several different families of infinitely many solutions. This can be a sign that you haven’t got a precise enough idea of what you wanted to solve, and that you need to add some requirements to finding your solution. Alternatively, it might mean that you’ve solved a problem which can be applied to more cases than you originally expected, which can be a wonderful discovery.
Phil Dunlap’s Ink Pen (January 5) talks a bit about quantum physics, which is of course heavily mathematical, and about some alleged resemblances between the field and ancient mythology. I’m more used to seeing claims that very abstract representations of the universe, like various aspects of quantum physics, have things in common with Asian mythologies or philosophies or religions, particularly Buddhism, so it’s probably worth mentioning this: no they do not. There may be some aesthetically pleasing parallels, but that follows from how the things humans look for in theoretical physics — simplicity, symmetry, unity of structure, mystery — are the things humans have always looked for in systems of thought. (By “mystery” I mean “things that look contradictory, even paradoxical, but that can be resolved with enough thought”.) We will see some similarities for the same reasons that the food of a very different land and a very different era will turn out to have salt and a couple spices, just like it does back home. It is worth learning mythology because of the insight it gives you into how people understood their world, and because it improves your understanding of human culture, and because there are many grand and emotionally resonant stories to be found in mythologies; it will not help you understand quantum physics, except in the way that learning things probably helps you become a better thinker even in other fields.
Mark Litzler’s Joe Vanilla (January 5) uses the icon of a blackboard full of mathematical symbols as shorthand for “this thing that’s gotten so complicated even we who created it don’t know what to do with it”.