Friday, December 9, 2011

Box algebra: logic as abstract comics / abstract comics as logic

From here. This "box algebra" or "box arithmetic" is adapted from G. Spencer-Brown's Laws of Form (1969), one of the strangest books ever written, about which I'm going to have to post some day in much more detail.

EDIT: afterthought. Maybe I should briefly explain why I'm posting this here, beyond the possibly fortuitous resemblance of its diagrams to abstract comics. Or maybe, I should explain that I don't think that resemblance is all that fortuitous. Yes, "Laws of Form" essentially rewrites, with supposedly only one sign (actually two, the marked and the unmarked space) the laws of Boolean logic. But, before getting to that level, you can see it as simply a formal exercise, whereby arbitrary rules are established for the manipulation of a simple form (and its absence), together with spatial notions of juxtaposition and containment. The simple rules allow for the transformation of one spatial structure into another. Then these transformations can be enchained, to either complicate or reduce those structures. We are talking about a set of formal constraints, basically, that help create a sequence of structures made up of rectangles and lacks. It's pretty clear how each structure in a"logical" sequence can be seen to correspond to a panel, and there even is a kind of "narrative" logic to how you get from the first structure in a chain to the last; this narrative logic is purely formal, but it has a clear directionality, leading to the final intended structure (the "theorem" it is trying to "prove").

This logic of transformation can be appreciated rationally, as a model for logical development; but it can also be appreciated aesthetically. (And, perhaps, deep down, mathematics is always appreciated aesthetically; after all, mathematicians probably use the word "beautiful" to describe a proof more often than artists or critics use it to describe a work of art.) And maybe that aesthetic appreciation--in being an appreciation of the rules of transformation of form, and how they are manipulated--is the very same thing as that rational appreciation; there is no difference.

In the same way, it seems to me, abstract comics can--and often do--establish a formal narrative arc by establishing a kind of formal logic, that leads from first panel to last, though one that is most often perceived only intuitively, not based on strict and clear rules. Nevertheless, it's nice to see for once the rules being made explicit.

Well, maybe not just once--here is an exercise I created based on formal constraints:

And here is a comic by Ibn al Rabin/Mathieu Baillif, which seems to be based on a very clear development of only a few formal rules (which makes sense, since Mathieu in his day job is a mathematician):


  1. Super ! Cela m'a l'air fort passionnant et intéressant ; tiens, m'en vais approfondir ton lien (et regarder si le livre en question a été traduit en français…).

    En parlant de mathématiques et de bande-dessinée abstraite, il y a dans le numéro de la revue DMPP consacré à Verbeek un pastiche "abstrait"* et arithmétique des upside-down.

    *enfin… plutôt concret -- au sens d'"art concret".

  2. Voici un bon article au sujet du bouquin:
    Mais, a vrai dire, pour en jouir vraiment du point de vue esthetique, vous devriez obtenir le livre meme, pas un sommaire. J'imagine que ce n'est pas si difficile de lire meme pour quelqu'un qui ne parle pas l'anglais parfaitement, ou bien c'est aussi difficile que pour quelqu'un qui le parle fluemment.

    DMPP, je ne connais pas. T'as un lien?

  3. Pour DMPP :
    (ce numéro vaut surtout le coup pour les planches de Verbeek -- car assez rares en France -- et la planche dont il est question ci-dessus. Et puis pas sûr que ce numéro soit facilement trouvable… Je peux te scanner la planche en question, et te l'envoyer par mail, si tu veux ?)
    Sinon il y a une interview du gars qui gère la revue sur : (il est question de Lev Youdine, élève de Malévitch et, entre autres, dessinateur de livre suprématistes pour enfants)

    Pour le livre Laws of Forms, apparemment, il n'existe qu'en anglais et en allemand… (donc j'essayerai de me procurer la version anglaise un de ces quatre).
    Merci pour l'article -- je vais lire ça.

  4. the ibn al rabin's comic's link is dead…

  5. I was drawing when I was supposed to be learning algebra...

  6. You probably got it by osmosis, though.

  7. I doodled a lot in class too, sometimes brazenly, right under the eyes of the teacher. I got away with it because I actually really liked math, and whenever I was asked a question I could answer it correctly--despite continuing to doodle.


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