1.) Supposedly the medieval Europeans thought Euclid's works were the same as the one we know as Eucleides of Megara, so olde books about geometry in Europe were by "Megarensis." They weren't the same dude: "Megarensis" was a contemporary of Plato; the great Euclid of high school geometry was closer to being contemporary with some of Plato's early students.
The Arabs got hold of Euclid and thought the name was made of ucli (the key) and dis (measure). At any rate, his Elements was the model of rationality ne plus ultra, and I'm writing this piece after pondering Euclid's influence on two philosophers, Vico and Spinoza, who were not the first to mimic the potent rhetorical form and structure of Euclid.
2.) In Peter Thonemann's review of three books for the TLS, note the story of the Malawi girl, who charged with learning how to set a dinner table English-style, experienced a steep learning curve, because the world she grew up in was curvilinear; there were no right angles. We had to learn the "order of things" we take for granted as "the way things are done." I also thought it interesting that with the Romans rolling through the peoples of Europe, they brought right angles and rectangles and ideas about straight lines and order with them, the Irish being the last to "convert," and it went along with Christianity.
There's a question of the "reading" of artefacts from the long-dead: if they built with right angles, was their social structure more authoritarian? Some think so. Others think what matters is the initial posit and then iterated forms that grew from there. Mikhail Okhitovich, Soviet sociological thinker of the 1930s, asserted that right angles originated with private land ownership, then extended to architectural forms, and represent a non-communistic mode of thought; because of this curvilinear forms in architecture were the best and most egalitarian form.
Before rigid hierarchical forms of State, what was often found were circular forms, which have a center but seem to resist hierarchy...on some level. Do Euclidean forms give rise to a form of thought that permeates a culture, and if so, is this idea mostly unconscious, part of the paideuma?
Many non-communist Left-ish thinkers have assumed that dwellings based on rectangles and 90 degree angles were somehow metaphors for artificiality, non-organicism, or simply convention, and living in "boxes" tended to encourage conformist social ideas and a stifling of creativity. Look at any fat book on great 20th century architects and buildings. Look at Buckminster Fuller.
3.) A pop kulch example of a leftist strain in American thought is found in this folk song: "Little Boxes." Boxes and conformity. Boxes and restraint. Boxes and the suburbs, Levittowns.
4.) The distaste for "boxes" runs in countless intellectual and aesthetic fields. While Nietzsche lays out with this probe: "Mathematics would certainly not have come into existence if one had known from the beginning that there was no exactly straight line, no actual circle, no absolute magnitude," and we are left to wonder, our contemporary Nassim Nicholas Taleb writes in his Bed of Procrustes, "They are born, then put in a box; they go home to live in a box; they study by ticking boxes; the go to what is called 'work' in a box, where they sit in their cubicle box; they drive to the grocery store in a box to buy food in a box; they go to the gym in a box to sit in a box; they talk about thinking 'outside the box'; and when they die they are put in a box. All boxes, Euclidean, smooth boxes." (p.31)
5.) Art critic Jed Perl wonders about the state of painting and painters in today's art world. At one time the rectangle frame of the painting was a given. The artist played an outre role in society. But now practically all competing media are either rectangle shaped (iPod/iPad/iPhone?), or text is read within a rectangular-ish frame (the screen you're using now?); further: images in the most popular media are dynamic inside a rectangular frame: TV, films, the camera frame. Could it be that the "degree of stabilizing supremacy of that rectangle has been undermined by the technology that surrounds us?," Perl asks. He knowns painters. It's his milieu. And Perl asserts that today's painter, because of the static image inside a rectangle, has been forced to go on the defensive or offensive, which presents a new hindrance. At the same time, Perl asserts that painting is not dead.
6.) In what appears to be an untitled poem, Tony Quagliano:
I read this poem about geometry
or was it poetics, or
some analogy among the three---
that sounds right
a poem about science and art
itself some artful connection
opting for the poem of course (being a poem) slyly
saying math's impure
or at least not pure enough
for one geometer not impressed by Euclid
or more impressed by non-Euclid
or some such twist
and what gets me, why I mention this at all, is
that the poem was good
though no one bled directly in it
words were clean, scientific
stitched in artful lines for the anthologist
and while a slashed wrist would have to wait
this poem of shadows, or math
or some connection in the courtyard of art
this fragile suture, poet to geometer, takes life
over your dead body
and it was good
which is why I mention this at all.
-p.65, Language Matters: Selected Poetry
7.) I remember reading about some hotshot engineering students - probably at CalTech? - and the problem of stacking oranges at the grocery store. Because of their roundness, there's far more non-used-up space (AKA "air") between oranges. How to maximize the number the oranges stackable? Well, you obviously make square oranges, using the Lego-mind. Easier said than done.
I hadn't thought much about shipping containers and how they have made the world seem far smaller and distance irrelevant until I read Andrew Curry's fine piece in Nautilus not long ago. "Invisible to most people, (shipping containers) are fundamental to how practically everything in our consumer-driven lives works." As for packing as much stuff into a space as efficiently as possible, it doesn't get much better than shipping containers. ("Invisible to most people...")
Score one for rectilinearity.
8.) One of the Prophets of Euclidean space and modern consciousness, Marshall McLuhan, in 1968:
The visual sense, alone of our senses, creates the forms of space and time that are uniform, continuous and connected. Euclidean space is the prerogative of visual and literate man. With the advent of electric circuitry and the instant movement of information, Euclidean space recedes, and the non-Euclidean geometries emerge. Lewis Carroll, the Oxford mathematician, was perfectly aware of this change in our world when he took Alice through the looking-glass into the world where each object creates its own space and conditions. To the visual or Euclidean man, objects do not create time and space. They are merely fitted into time and space. The idea of the world as an environment that is more or less fixed is very much the product of literacy and visual assumptions. In his book The Philosophical Impact of Contemporary Physics Milic Capek explains some of the strange confusions in the scientific mind that result from the encounter of the old non-Euclidean spaces of preliterate man with the Euclidean and Newtonian spaces of literate man. The scientists of our time are just as confused as the philosophers, or the teachers, and it is for the reason that Whitehead assigned: they still have the illusion that the new developments are to be fitted into the old space or environment.
-p. 347, Essential McLuhan, from an essay, "The Emperor's New Clothes," originally in Through the Vanishing Point: Space in Poetry and Painting, co-written with Harley Parker. McLuhan asserted in 1968 that "the artist is a person who is especially aware of the challenge and dangers of new environments presented to human sensibility." McLuhan thought artists were subversive because society expected the replication of existing orders and forms, but artists violated these expectations.
a.) In 1968 McLuhan may have been far more prophetic than he thought: not only are scientists still trying to come to terms with non-Euclidean findings in astrophysics, materials science, microbiology, subatomic physics (but I do see some inroads), but going back to Jed Perl's essay on the "state of the art" in painting 45 years later, McLuhan's "with the advent of electric circuitry"...and I think maybe painting, contra Perl, may be, if not dead, in the ICU, condition: critical.
b.) When I do that mental yoga which allows me into McLuhan's thought-space, I realize how intensely Euclidean my assumptions seem, as based on the idea of Gutenberg Man and the space of the literate reader of texts, for hours every day, decades on end, eyes decoding 26 symbols with punctuation, left to right, linear left to right, left to right (THIS), left to right, punctuation. In my conditioned assumptions of quotidian reality, objects "really do" fit inside of space and time. I want them to create space and time themselves, by power of their sheer Being, capital be. But most of the time: no. I have to work on it. How do I get out of Gutenberg Euclidean head space? Cannabis, film, walks in nature, animation, humor and surrealism, reading Joyce or Pound, get into the Korzybski-Zen level of the phenomenal event-level, pre-language, observing without hypnotizing and misleading "woids," and then careful consciousness of abstracting, watching myself abstract until It all melts, or something strange in science. You have your ways.
c.) For such a overwhelmingly "straight" Euclidean man, Prof. McLuhan's (whose personal politics were a sort of conservative Catholic with tinges of anarchy?) mind was, to me, reliably non-Euclidean and psychedelic. His deep immersion in James Joyce and Ezra Pound was probably a significant influence here, but there was so so so so much more. He was an absolute virtuoso with playing with metaphors and combining those ideas with others, if only just to see if they were thrilling and made anyone else want to think about some idea in some new way. I find this an anarchist strain in McLuhan's thought. (How about I take catholic idea about the senses and think about the new electronic media, like radio of TV? I can add ideas I copped from Thomas Nashe, Wyndham Lewis, Ezra Pound, Harold Innes, and anthropologists. And Finnegans Wake! And mythology, Poe, Einstein, and painting's figure/ground and the rise of the Renaissance's vanishing point? And then: Vico! And commercials and comic strips!? And Walter J. Ong...and and and...)
9.) Robert Anton Wilson's extensions of Timothy Leary's ideas of the evolution of "circuits" in the human mind drew heavily on Euclid for the first three "domesticated primate" aspects of all of us: the oral/biosurvival circuit is about approach/avoidance and is represented in Euclidean metaphor as "forward-back." The second circuit stage of development (according to the theory, we "imprint" all of these circuits), the anal/territorial circuit, is about up/down, and represents the deeper levels of any thinking about politics, whether within the family, local city, national, or international. Notice up/down fits well in Euclidean space-thought.
The third circuit is about right/left and for mammals like us, based on the bilateral symmetry of the body and the nervous system, which nature has seen fit to encourage a dominance of one side over the other, most people's left hemisphere's motor cortex encouraging right-handedness. Conceptual thought and left-right equations (think: algebra!) and logic all fall under the third circuit.
Although neuroscientific ideas about hemisphericalization in evolution and discrete modules of each of the brain's two hemispheres has moved away from a once-popular notion of the "holistic" right hemisphere and the "linear" left, these metaphors still seem to resonate. For Wilson, right-handedness and math and literacy in symbolic humans indicate a left-hemisphere domination (the left hemisphere controls the right side of the body) which has unconsciously biased "linear" and hierarchical forms in human history, which begins with writing. The right hemisphere, relatively "silent" and seemingly subdued by assumptions about "reality" made by the left hemisphere (especially in industrialized Western humans), has yet to harness the intuitive genius housed in the right hemisphere.
So much ink has been spilled over these ideas, once extremely popular but now seemingly in a slow descent. Nevertheless, these ideas live, as you may have noticed from a conversation within the past few months. Why?
Well, I think it's because there's still some truth to the right/left brain modularity-of-function idea, although it's not as simple as those who popularized the findings of the Sperry and Gazzaniga "split brain" experiments. Also: I think Wilson was on to something: "Right-hand dominance, and associated preferences for the linear left-lobe functions of the brain, determine our normal modes of artifact-manufacture and conceptual thought, i.e., third circuit 'mind.' It is no accident, then, that our logic (and our computer-design) follows the either-or, binary structure of these circuits. Nor is it an accident that our geometry, until the last century, has been Euclidean. Euclid's geometry, Aristotle's logic, and Newton's physics are meta-programs synthesizing and generalizing first brain forward-back, second brain up-down and third brain right-left programs." - Cosmic Trigger vol 1, pp.199-200
For Wilson (and Leary) there were relatively "new" circuits that have appeared in human evolution over the last 11,000 years or so. And they seem non-Euclidean, more organic, curvilinear, and more inclusive of a holistic, total-floating body sense, as if we were meant to move through space/time.
To be clear: Euclid and his forebears the Pythagoreans wormed their way into our paideuma due to the natural evolution of mammals on a rocky watery planet with an atmosphere conducive to carbon-based replicative life forms under the purview of a energy-source star at a Goldilocks distance. We got Euclidean forms because that's the way we evolve. Which may Beg the Q, but it's one of my favored narratives, and my entire brain, both hemispheres, seem to harmonically resonate with it.
[Further extrapolations from Wilson on this complex of ideas: see Illuminatus! Trilogy, pp.793-795; Prometheus Rising, pp.97-100; Schrodinger's Cat Trilogy, pp.342-347.]
10.) I grew up in boxy architecture, and when I first encountered this idea - about rectangles and 90 degree angles and conformity - I also found out we forgot how we did it, but at some point we had to learn to see in 3-D spatial terms. Supposedly some cultural anthropologists had gone into deepest darkest rain forest Africa and lived with and studied pygmies, whose complete environment was always giant trees and vines and moving through those living breathing green spaces, always canopied by jungle thickness as "ceiling."And when they were taken to a clearing at the edge of the forest and the anthropologists pointed to a man and a jeep far off in the distance, the natives thought they were seeing a tiny man. They had not learned to see over vistas of "open space."
So, I lay in bed and looked at the point where the ceiling meets the walls. Two walls meet at the "point" of the ceiling. And I tried to remember what it was like to not see that as a point in space. It's akin to many visual illusions or the Necker Cube you've all seen. It was fruitless. Until, one day...O! Such little things that thrill me. Aye: the corner was on a flat plane. And then it pointed out toward me...
I attest, I assert that when I enter buildings of a non-Euclidean build, my consciousness is altered. An inventory of memories and anecdotes would bore you and me, but I wonder if you have felt the same? I love round rooms. A spiral staircase can really get me going. On and on. But here's the thing: if I grew up in a non-Euclidean house, I strongly suspect that entering a Euclidean "tiny box" house would alter my conscious also. Because I think these represent the unfamiliar structure of space...
I hope I didn't come off like some un-hep "square" in this blogspew.