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On alternating Fridays, Michael Carlisle examines the world “outside” sequential art to find… more sequential art. Expect mathematics, a bit of madness, and a dash of pessimistic optimism.

by Michael Carlisle

Hi. My name is Mike, and currently I’m an academic.

(“Hi, Mike!”)

Some day I hope to get out with a Ph.D.

In mathematics.

Already you’re wondering, why is this guy here?

I want to share an idea with you. What are the sequential arts? These are, in the McCloudian sense,

Yes, there’s argument about this definition. However, I’m a mathematician, and so I, like the esteemed Mr. McCloud, like to start with understandable (and general) definitions.

I will now proceed to give a most unmathematical argument.¹

I think most people agree that debate is an art form of a sort. The medium is language; the canvas is the topic of discussion and your opponent’s view. While this could be considered sequential in that there is a sequence of play (making it like a game) – turns taken, each segment a discrete unit of rhetoric blended with fact (truth values to be verified). However, I would relegate debate to the realm of performing (or performance) art, rather than sequential, as the live aspect is a primary player, temporality secondary.

The focus on sequential art is on its discrete spatial quality. Regardless of the physical representation, sequential art is named so for the fact that its experience-timing is reader’s-choice, as opposed to creator’s-choice (as with “recorded” or “live” media). Debate, TV, music, etc. in the way they are intended to be experienced are not sequential arts.²

What am I getting at? First, I am deducing that, if we agree that debate is an art, its written counterpart is as well. As opposed to debate, the art of the written argument is, at its base, sequential. Therefore, persuasive writing is a sequential art.

I haven’t been known for my own persuasiveness, but I’m claiming that what you just read, paragraphs = panels if you really wish, is a piece of sequential art.

Yes, I know, I’m getting technical on the “and other images”-means-letters-means-words end of things.

Let’s get a bit more symbolic. I would bet that most mathematical expressions, like or , for most people, are a bit more “like pictures” than, say, words. Now, the body of work referred to as “abstract art” has a large quantity of symbolic objects that have meanings³. The body of mathematical symbols, along with graphics, etc. convey a very particular meaning based in the field of study.

Unfortunately, most people think math is dry, technical, and boring. If you haven’t spent enough time to get to the good stuff, it is. This isn’t math’s problem, it’s math education’s problem, which is a different story altogether; “real” mathematics is all about being clever in a pure problem-solving space. Math is thinking hard about abstract notions, coming up with analogies, some tricks, a eureka or two, cutting the chaff, and building it all into a concise structure.

This brings us to the crux of the argument: from basic definitions, to supporting propositions and their proofs, to theorems, a work of mathematics – in the form of a series of logical arguments, displayed via words, symbols, and graphics, and laid out in a logical sequence – is a sequential art.

Reading a mathematical text in sequence does not exactly involve a temporal sequence. The notion of “time”, the physical process of cause and effect, is replaced by a “logical” cause and effect. Following an argument is something done in time by the reader; the work itself’s “narrative time” is actually “logical time”.

(These aren’t new ideas to mathematicians; I just don’t think most of them think of their work in these terms.)

I posit that the current way math is taught fails many students, and that by exploiting the “sequential artness” of math, the unfolding of a logical sequence in a more “panelized” fashion, might aid in teaching. This certainly wouldn’t be a cure-all; there are many other aspects of mathematics education that need examining, and my statements here help more for higher-level math than the lower-level material one sees in K-8. I’m also not saying that educators don’t put pictures along with their text, since a large amount of math education relies on the blending of pictures, symbols, and words. What I am saying, though, is that if math is a sequential art, would it not help if it was portrayed as such?

Larry Gonick‘s series of books and the recently-translated Manga Guides
have been a good starting point, but I’m not saying that math needs to be comics. (Not to mention that most I’ve found are about statistics, not spread out nicely across many fields of math.) I’m saying that math itself is a sequential art, and this fact needs to be used to its advantage.⁴

There are a number of issues to be explored here: the necessity of a particular sequence (for example, certain supporting ideas can be put in many different orders and still have the work be cohesive); whether or not a “story narrative” should be woven into the “logical narrative” and actually maintain both good storytelling and good pedagogy; how to test retention; and, of course, much more.

Hopefully you’ve stuck with me and aren’t bored to tears by now, so I’ll give a simple example that should be understandable just how it is. You’ve probably seen it before, but not exactly presented in this way. Granted, not all mathematical ideas can be presented as such, but if someone is clever in both the math and the layout, this methodology can certainly help.

This proof of the Pythagorean Theorem simply couples some words, symbols, and pictures, and as long as you know what an area is, and that the two small (it’s acute) angles in a right triangle add up to a right angle, it’s pretty self-contained, and a hell of a lot easier to understand than the first one they give.

More examples will be forthcoming as I find or construct them.

[1] I wrote a paper on a topic similar to this a few years back… with a very different result.

[2] This covers the “silent-film-sans-soundtrack-is-n-frames-per-second-and-so-a-sequential-art” argument.

[3] Apparently… I haven’t studied art history. Why am I here?

[4] Karen Green touched on the idea (in her own comment thread) of a calculus comic, something I’ve wanted to sit down and write for some time now. Maybe someday……..

Michael Carlisle is a mathematics Ph.D. candidate at the City University of New York’s Graduate School and University Center (“Graduate Center”), where he earned a certificate in Interactive Technology and Pedagogy. When not teaching or researching probability, rambling on about dystopian films and surrealist animation, or non-ironically calculating the odds of finishing his thesis instead of doing it, he volunteers with the Sequential Art Collective and New York Center for Independent Publishing. He has more data than you.