Famously, Scott McCloud defined comics as follows:

… juxtaposed pictorial and other images in deliberate sequence, intended to convey information and or produce an aesthetic response in the viewer. (Understanding Comics, p. 9)

McCloud’s definition has been criticized for: being too formal, lacking sensitivity to historical or tradition-bound factors, being too broad, being nothing more than an ingredient in McCloud’s ersatz history of comics, etc., etc. In later work, McCloud (following Eisner) suggests the snappier, albeit even more theoretically suspect, term “sequential art”.

There is one aspect of both the earlier definition and the later euphemistic technical term that has not received the attention is probably deserves, however – the role of the concept ‘sequence’ in both. The question I would like to ask is: Must the individual panels (or other pictorial content) in a comic constitute a sequence?

In the mathematical world, a sequence is a linearly ordered (finite or infinite) collection of objects. In particular, given any sequence of objects, and any two distinct objects a and b in the sequence, either a is earlier that b, or b is earlier than a (and not both).

Now, on the mathematical understanding of sequence, comics need not be sequences. I have included three examples in this post – a Quimby Mouse strip (by Chris Ware), a page from Rabbithead (by Rebecca Dart), and a strip by Tymothi Godek. We could just decide that McCloud was using the term “sequence” loosely, and that he would have no problem including these examples as comics. And in terms of evaluating McCloud’s work, that’s probably the right thing to do (he isn’t a mathematician, after all!) But there is another question that now arises: If comics need not be sequences in the mathematical sense, then what sorts of mathematical structures can be instanced by panel arrangements within comics? Notice that the Chris Ware strip uses ‘trails’ – that is, arrows telling us which panel or panels occur next. Although this sort of structural sign-posting was common in the early days of comics, before many of the conventions governing panel arrangement and panel reading were in place, they now typically appear only in very complex comics where the reader would get hopelessly confused otherwise (again, see the Quimby Mouse strip above).

So: Is there some natural mathematical characterization of the sorts of panel arrangements that can be coherently and unambiguously used in comics? Are there more such coherent panel arrangements when we allow the unrestricted use of trails? Do trails allow us to make any arrangement intuitive and understandable? As a partial answer to the second and third question, it is worth noting that trails seem to allow us to construct comics whose structure is any planar graph (or, at least, any planar graph that will fit on the page or screen). But beyond this, the questions are wide open.

About roytcook

Roy T Cook is associate professor of philosophy at the University of Minnesota - Twin Cities. He works in the philosophy of logic, the philosophy of mathematics, and the aesthetics of comics. He is the co-editor (with Aaron Meskin) of The Art of Comics: A Philosophical Approach (Wiley-Blackwell 2012)

5 responses »

  1. Barbara Postema says:

    Thanks for that thought-provoking question, Roy!
    When it comes to comics and sequences, I like Thierry Groensteen’s use of the term. Chapter Two of _The System of Comics_ is actually devoted entirely to the sequence, and he defines it as “a story segment of any length, characterized by a unity of action and/or space. The sequence allows itself to be converted into a synthetic statement that … produces a global meaning that is explicit and satisfying” (111). Groensteen contrasts the sequence of images to the series. Sequence is continuous, though it has no set length, and is tied to narration, while a series of images can be scattered throughout a text, and the images connect to one another thematically or symbolically, such as for example all the panels with clocks, calendars (and an egg timer), in Seth’s _Clyde Fans_, which set up the theme of passing time. These uses of the terms sequence and series are certainly not mathematical, in some ways I think they are almost opposite to the mathematical definition of the words, but I think they are very useful in comics studies.

  2. Your post raises a lot of questions, Roy. But one that strikes me as very important you ask near the end of the post: ‘Do trails allow us to make any arrangement intuitive and understandable?’

    Could you say more about what you mean? How do you define/differentiate ‘intuitive’ and ‘understandable’? For me, trails can make any comic understandable. If the reader is able to discern the path that the artist has created, then the reader can follow the thread of the story (action, narrative, what have you).

    But I think that’s different from intuitive. I think that if a comic has (to have) trails in it, then it is in fact most definitely not intuitive. For me, this points to the question of conventions and how comics conventions act as sign posts for readers to follow. If the comic as rendered doesn’t use enough of those conventions, then reading the comic becomes much less intuitive, hence the desirability of extra signs (in this case, trails).

    Sequencing is, as you point out, the ordering of units (in some sense). For me, the presence of trails helps create sequence and also nods to the fact that most comics need to be read in a sequence to make sense.

  3. Barbara Postema says:

    Roy’s post, and especially Frank’s comment, also remind me of an essay by Joseph Witek, “The Arrow and the Grid,” in which he writes precisely about the matter of trails. It’s in _A Comics Studies Reader_. I think one of his points is that comics artists used to be more concerned about readers being able to read the right sequence, guiding readers through with numbered panels and arrows and the like. As the form has matured and (presumably) readers have become more sophisticated, these kinds of signposts are not usually used or necessary anymore, except for in some circumstances like the three examples Roy gives in his illustrations.

  4. roytcook says:

    Qiana: Groensteen’s use of the terms (amongst other things) is what actually got me thinking about this. Now, I am not going to argue for the claim that Groensteen (or, equally likely, his English translators) is misusing the terms ‘series’ and ‘sequence’ (as much as I believe this). The point, though, is that these terms do have precise mathematical meanings as well, and it is interesting to explore the mathematical properties of actual and possible panel arrangements in order to see how (if at all) their graph-theoretic properties might affect the storytelling possibilities, etc. So I don’t deny that Groensteen’s usage is useful, and highlight important, content-relative patterns of connection between panels. But I think it is worth asking whether the more precise mathematical notions have any use in studying how these arrangements create meaning as well.

    And this brings us to Frank’s comment. First off, I am not sure that trails will make ANY comic understandable or intuitive. Imagine 100 panels numbered 1 – 100, where, for panel number n, that panel leads via a trail to (i) each panel that is labelled with a multiple of a factor of n if n is composite, or (ii) each panel numbered with a multiple of n-1, if n is prime. Even with trails, I am not sure that much intuitively un-patterned complexity would be understandable in any sense!

    Further, I am not convinced that “if a comic has (to have) trails in it, then it is in fact most definitely not intuitive.” Here’s an example: Let’s say that two panels are ‘accessible’ to each other if there is a gutter of even width separating the border of one panel from the border of another (points of intersection where gutters ‘meet’ don’t count). Then it is a mathematical theorem that there is no panel arrangement involving four panels where each of the four panels is accessible from the remaining three. So, as a result, there is no way to draw four panels where each panel ‘leads directly’ to each of the other three without trails, and this is a mathematical, not aesthetic, fact! (Note that, in the ‘circular’ comic above, one can ‘move’ from any panel to any other in a sequence of steps, following the balloon tails, but one can’t ‘move’ directly from the 1st panel to the 4th).

    As a result, I think that Witek’s story in the article mentioned by Barbara is incomplete. It is certainly true that trails originally evolved in order to lead the reader unambiguously through the story in the ordered intended by the creator(s), and these disappeared due to (i) the conventions for panel arrangement and ordering become more developed, and to a lesser extent (ii) creators allowing for more ambiguity in their panel ordering. But I think that trails have begun resurfacing in the work of Ware and others, however, in part because of the realization that certain formal arrangements of panels just are not possible without them, no matter how clever the panel arrangement.

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