Abstract comics and geometry--a modest proposal

This is going to be another one of my difficult posts, so let's begin with a pretty picture:

This is from Oliver Byrne's color-coded The First Six Books of the Elements of Euclid, 1847, which you can read for free here.   Ibn al Rabin (aka math professor Mathieu Baillif--I'm allowed to say that, right, Mathieu?  I don't think it's very much of a secret in the comics community) recommended it in his fascinating post on mathematical proofs as abstract comics. Ibn writes, "I was inspired by an incredible book of 1847 recently re-edited by Taschen: The elements of Euclid by Oliver Byrne. Anyone interested in abstract comics and/or mathematics should at least have a look at it."  I couldn't agree more.  As a matter of fact, I have bought the Taschen reprint since, and it's absolutely gorgeous. 

"Lode" by Veronica Graham

I got this in the mail a few weeks ago. Lode is a beautiful book, printed on semi-transparent vellum, so that at all time what you are seeing is not just the pattern printed on one page, but several designs superimposed, the ones on top the sharpest, the ones below more faded, in a strange parallel to something like atmospheric perspective. While the book's opening abstract compositions soon turn out to be topographical plans, which slowly become populated by houses, cattle, and so on, such abstract sequences are striking enough on their own to warrant being displayed here. Furthermore, I think they interestingly parallel my own attempts to find "found abstract comics," if you will, in Google Earth images--and so could easily have featured as an exhibit in the argument I tried to make about abstract comics and emergent systems.  It's a fascinating object, and highly recommended.  Given the transparent nature of the pages that I mentioned, simple scans won't do Lode justice, but that's the best I can do.  Here is the book's opening sequence:

And here is a sequence of pages from later in the book:

See more photos on Veronica's site.

Abstract Horror Comix by Mayhem

I have been viewing horror and mystery comics from 1955 through 1963. I have been mostly interested in the art of Steve Ditko. Looking up close at the inking and the faces, a whole abstract world started to develop. They inspired these spreads from my new project.

Three mathematical proofs

Hello everybody,

I recently had an exhibition in a small alternative art gallery in Geneva (Le Labo), and I took the opportunity to show three abstract comics that I recently made in which I try to convey the ideas of a mathematical proof into a totally wordless comic. I had already posted such a comic here in 2009, as you might recall:

http://abstractcomics.blogspot.ch/2009/12/pythagorus-comic.html

A lot of mathematical "proofs without words" do exist (there are even two books published containing the "best" ones), where mathematical results are proved using figures (single ones or a sequence), but there is almost always some kind of notation introduced into the figures to make the proof understandable. And of course, it is assumed that the reader has some kind of mathematical education, so as to understand the implicit steps of the proof.

My aim was to try to see whether the "intrinsic power of the sequence" (so to say) was enough to get rid of any kind of use of letters or typographical symbols, and to really break down the proofs in sufficiently many steps so that anybody, without mathematical education beyond "mandatory school" (I don't know how to call it, in Switzerland, it means roughly up to 15 years old), could in principle understand the proof. Of course you'd have to have some inclination towards abstract reasoning to really go through the whole story, but I tried to make it as self-contained as I could. But actually even my mathematicians friends had problems to really follow the reasoning, so I probably failed badly in my attempts.

Anyway, I thought it could be of some interest for the people here, so I post some pictures of these three pieces. I am really a terrible photographer and one of the pieces is like 2 meteres long, so it's impossible to really read anything, but at least it gives an idea of what I'm talking about.

The first piece is almost identical to my 2009 post and shows a proof of Pythagore's Theorem due to Thabit Ibn Qurra (826-901).

The second is a proof of an identity for sums of cubes:

 

And the third one is a comic rendering of a very nice proof of a theorem in "elementary" geometry that is due to Roger B. Nelsen. This theorem has the astonishing particularity of being both rather new (it was discovered in 2004) and quite simple (if you compare it with today's research).

By the way, I was inspired by an incredible book of 1847 recently re-edited by Taschen: The elements of Euclid by Oliver Byrne. Anyone interested in abstract comics and/or mathematics should at least have a look at it:

http://www.math.ubc.ca/~cass/Euclid/byrne.html

http://www.taschen.com/pages/en/catalogue/classics/all/06724/facts.byrne_six_books_of_euclid.htm

Sophie Taeuber-Arp

Six Distinct Spaces, gouache on paper, 1939.  Found via Pascal Blanchard

As I wrote on Facebook yesterday, in the comment thread to an update where I linked to the Christian Bonnefoi works posted yesterday:  "I'm not showing these necessarily as comics, any more than I show the Archies as abstract. I show a lot of stuff that would interest people who like abstract comics, even if it's not specifically AC."  What intrigues me here is not necessarily the sequence, but what Thierry Groensteen might dub the "iconic solidarity" of the panels, which is a feature of comics in addition, and complementary, to sequentiality.  See my earlier discussions (here for example) of iconostasis and sequential dynamism, and of the interdependence between the two; from that point of view, the title's claim of "distinctness" strikes me as intentionally ironic.

Christian Bonnefoi

top: Fioretti 3, "l'obscur," 1990. 

bottom:  from Fioretti 5 de la vie courante, 1987-1998, excerpt 1997-1998

each panel (in both images):  61 x 50 cm

Formal rhythm in comics: the case of the B&V limerick

My last theory/formal analysis post was very long, so I'll try to keep this one brief.  Here is a five-page story from Archie's Girls Betty and Veronica no. 118, October 1965, probably scripted by Tom Ruth (according to the GCD), definitely penciled by Dan DeCarlo (who, I'm guessing, had a lot to do with the breakdown and the layout), and inked by DeCarlo's brother, Vincent, who was DDC's regular inker at the time.

(I added the cover to fill out the 3 x 2 grid, and because it's cool.)

Note the way the first, second, and last pages end on a similar panel:  with Betty getting splashed with water, from a passing car or boat.  And while this is necessary for the strip's comic timing, notice also the visual similarities between the panels, which, echoing each other (the only partially-seen vehicles all coming in from the right, the water splashing diagonally up and to the left), make very clear visual rhymes.  (The visual rhymes, interestingly, continue in the first panels of pages 2 and 3.) The intermediary section, pages 3 and 4, while not so obviously "rhyming," is distinguished from the other two pages by the predominance of the green of Veronica's clothes (as opposed to the blue of water, predominant in 1, 2, and 5), and also provides a kind of rhyme-like echo as each page ends with a panel of Veronica alone.  (Also, notice how the framing section resumes with the return of Betty:  each of the two protagonists is basically associated with one of the rhyming sections, and form comes to echo--or is it, control and guide?--content.)

This five page story has a very clear formal rhythm:  with an aabba rhyme scheme, with a change of tenor between the framing sections and the middle section, it has the structure of a limerick--though a visual one.  You may know about the OuLiPo, the literary movement that explores writing based on pre-determined constraints (taking, for example, its cue from early poetic forms such as the rondeau or the sestina); and you may have heard of its comics equivalent, the OuBaPo.  If not, as it happens, in the new issue of Words Without Borders, Matt Madden provides an introduction and translates some examples from the French.  (Scroll down.)  What's fascinating is that, without the benefit of such theory, DeCarlo and his associates achieved a similar formal rigor--and produced, as far as I'm concerned, some of the most visually compelling work of this kind.  (The piece I would most closely compare it to is Madden's own visual sestina, "The Six Treasures of the Spiral," in his comic A Fine Mess 2, from 2004).  Maybe it's time for the OuBaPo to enlist him as an honorary plagiarist by anticipation, alongside Verbeek, Spiegelman and the rest?  (I would also nominate Kirby, but that's a post for another time...)

Abstract Cartoon Strip Anthology

I have just published a 48 page book of my Abstract Cartoon Strips, many of which you have seen on this blog. The price is 8.95 and the digital version is free.Thank you to everyone on this blog for inspiration and support. Click the link below.

Abstract Cartoon Strip Anthology by James Mahan AKA Mayhem

two pages - digital book / asemic writing

Gianpaolo Pagni, from "Senza Nuvole"

"Senza Nuvole," a collection of rubber stamp drawings, was published as issue 22 (June 2011) of Un Sedicesimo (Corraini Edizioni). Here is Gianpaolo's website.

Jean-Pierre Pincemin

Jean-Pierre Pincemin, untitled, 1967

oil on unprimed canvas

285 cm x 220 cm

Comics-painting

I've been experimenting the past few years with making comics-paintings. Generally, these have been more figurative (like, abstracted figures?), but lately it's been more abstract. Here is the one I finished this morning; thought I should share. 18"x24" mixed media on paper. The background for all of this is a torn up and collaged section of the manga "Violence Jack." I was going with the idea of deconstructing something and reconstructing it as a way to explore its form.