In Progress: “Black Pillar”

I’m almost done with this second painting in the “black pillar” and “white pillar” series. I’ve put a coat of varnish on the inside/right side of the painting, so it will have a bit of a sheen or glimmer to it. I plan to do the same to the “White Pillar” too. I still haven’t decided if either painting needs any texts around time. My original thought was no, now I’m leaning toward “yes”, which means picking those texts and a contrasting color to paint them in.

Tree of Life Geometry, Revisited

I’m not entirely sure this will work. But here goes.  Thanks to Gordon’s recommendation to try out VINE, I was able to produce a trio of short videos today, including this one on the traditional geometry of the Tree of Life.  It’s fast, because Vine only allows six-second videos.  But it’s kinda cool, and if you watch it a few times, you can probably figure out how the geometry of the Tree fits together.  Enjoy!

Vine: Video of the Tree of Life

Update: Apparently you have to go to Vine’s website to view it, because I can’t embed it on a WordPress site.  Alas.  Enjoy anyway.

Tai Chi Y2D65: unfolding

I’m working on this pair of paintings called, appropriately enough, “Black Pillar” and “White Pillar”. They’re pretty much meditations on geometry, with the White Pillar holding three mandalas or roundels (I like roundel better, actually. It’s a more western word.) The three roundels on White Pillar are they in-yang symbol at the top, a square turned on its point in the middle, and two nested seven-pointed stars at the bottom. White Pillar, as a painting, is about 80% finished.

Last night I began laying out the detailed painting guides on “Black Pillar”. This is the bottom roundel on that pillar, a meditation on the number 8, and as you can see, it’s a pair of nested eight pointed stars (one is actually composed of two inter-locking squares) inside an octagon. It’s a considerable change in geometry from 2, and 3, deceptively simple and yet relying on what one learned from the earlier shapes and geometries. It’s an unfolding, of sorts, as larger numbers reveal much more complex patterns and allow greater interactions and relationships.

What does this have to do with tai chi?

Well, daily practice is an unfolding, of sorts. The natural habit of our minds and bodies is to ossify and tighten up, to reject new things, and to limit the adoption of new concepts or new technologies. I’m neither a painter nor a math teacher, nor a martial artist (once upon a time, I wouldn’t have said I was a magician either, but that title is growing on me).

In any case, what’s going on here is an unfolding. The creaks in my body rarely trouble me past the first two or three movements — I’m not reversing the aging of my body, but I’m slowing it down. Many of the creaks and pops that were ever present when I started, are gone.

Unfolding, in this instance, means breaking out of the shell. Letting the egg hatch. Pinocchio becoming a real, live boy. It’s growing up, in a sense. It’s growing out, in another sense. It’s delving deep, or reaching high… Some Christians use the prayer of Jabez, “O God, increase my territory.” And others remember the prophet Isaiah (I think it’s Isaiah), “enlarge the place of your tents, strengthen your cords, lengthen the stakes in the ground.”

A tent is useful only in potential when it’s stored in the bag. A human too tight in his skin is only partially useful. Or strong. Or happy. Or healthy.

I feel that I’m unfolding, these days.

Simple Gifts

It turns out that a dodecagon is fairly simple to produce from a circle crossed by a cross. The use of circles at the intersections of of the cross and circle can then be evolved into the dodecagon, and then into a twelve pointed star. How awesome!

Tai Chi Y2D50: underlying complexity

Today I did tai chi in a narrow hallway of a hotel room that I share with a colleague. We’re running an annual field trip. To say that we were tired last night is to miss the point. Exhaustion is closer to the correct idea.

It’s in this cramped space, under tight conditions, that I did tai chi this morning. And while I don’t always notice, I did notice today that I’m always doing tai chi under cramped space and tight conditions.

It’s part of the underlying complexity of any work, really. It has to fit into the matrix of your life: eating, sleeping, work, family obligations, personal issues. The Yin Yang has its own geometric architecture to suggest this— yes, it’s simple, just a white field and a black field. But there’s an underlying complexity — intersecting shaped and signs and symbols, ruled lines and curving arcs. The tai chi in the hotel hallway is fundamentally different than the work in the office. But it’s still an effort to connect with the form and shape of the work.

The matrix of our lives may sometimes feel like an imposition, but really it’s the meat of our work and our labor. The tai chi adds beauty and elegance to that life and work, and allows that life to go on longer, but it’s the emergent yin-yang sign, not the complex geometry that undergirds and scaffolds the emergent symbol. Balance, dynamic as it is, extrudes from the geometry and patterns of a life well-lived, not from a fully-realized tai chi practice.

The geometry of our lives is a tai chi. The forms and exercises are simply… A daily practice which helps make our lives straight-ruled, and our compasses properly set.

The Kavad of a Sacred Geometer

Suzanne Wind Gaskell has hit one out of the park on this exhibit at Wesleyan University. She’s built and illustrated the Kavad of a Sacred Geometer, a study of the geometry and training of a traditional, non-literate artisan in a mathematical tradition. I did not hear her talk, unfortunately, but this object is an occult and esoteric masterwork, as well as being a mathematical wonder.

A Kavad, for reference, is a storyteller’s box or shrine from India or Pakistan. It’s a small box, in this case somewhat smaller than a portable sewing machine case, that has a number of doors, drawers and compartments. In a traditional kavad, these panels are illustrated with scenes and characters from a storyteller’s repertoire. By degrees, the storyteller would open the box to an audience, and the audience members in appreciation would put money in the kavad’s bottom drawer. Once fully opened, the kavad could be a shrine of the Rig Veda or the Upanishads, a life of Muhammad or some Islamic saints.

Ms. Gaskell has taken this form — the kavad, for a non-literate storyteller to explain epic tales to a largely non-literate audience — and created a mathematical treatise. The kavad she’s designed and built is covered inside and out with mathematical proofs and complex geometric constructions; the money drawer is filled with almost-talismanic painted tiles showing traditional floor layouts and iterative techniques of geometrical layout. The inside panels explain points, lines, and circles, the vescia piscis and more. The innermost compartments show the relationship between a vibrating string and musical notation, and contain two dimensional and three dimensional explanations of the five platonic solids. Panels on the back and top demonstrate how the one side of a polygon iterates from a triangle to a square to a pentagon, all the way out to a decagon.

It’s singularly awesome. Awesome in the old sense of the word, “struck down or filled by a sense of awe”.

And of course, I want to build one. Because this is a storyteller’s tool par excellence, a simple cube that, when opened, reveals itself to be no less than a shrine of the building blocks of the universe. Figuring out what to put into a kavad, and figuring out how to build one, represents a deep mastery of many subtle and powerful matters.

Prototyping a Painting

My friend Daniel says its important to carry prototypes all the way to the end. That way you can see all the mistakes, and not just the ones that you made at the beginning. When I outlined my painting on canvas, I immediately realized that I hadn’t properly spaced the circles. As a result, I couldn’t follow the actual plan or outline of the Sefer Yetzirah, the tree of life. But, in the spirit of figuring out what it looks like when you do the geometry incorrectly, I realized a number of things.

One, the retraction of earth and the moon places the Moon sephirah in the place of power, not the sun. Thus daath or knowledge becomes a place of power unconnected to other realities. This is the realm of the invisible sun.

Second, the more regular geometry feels less organic, more structured. It’s not alive, exactly. It’s more balanced, but less energetic. The empty space is necessary for the work to flourish.

I’m going to keep working on this painting, but I suspect it won’t be a Tree of Life when I’m done.

Shapes on the board

A framework for design
Originally uploaded by anselm23

As you can see, those cut-out card stock shapes are taking form as a semi-public talisman — in the sense of an abstract but energetic reminder of a thought form — on this bulletin board in my school. I wish the shapes were larger, actually, and that I’d put the text in place a little more cleanly. But I wanted them to be readable at a distance.

While it may not be obvious to the teachers who read this blog, magical readers may notice that the colors and positions of some of the symbols are designed to reflect another model of another thought process — the Sefer Yetzirah, or “tree of life” in Kabbalah. Students of Kabbalah claim that the Tree is a perfect model of the universe, which can instruct anyone in the process of attuning one’s self to the mind of God. Whoa.

We don’t want to cause 15-year-olds to have that sort of experience, really, at least not while having a class on how to think through design problems. Maybe in their own religious education classes, sure. But not while they’re trying to learn how to operate a saw or a drill press.

But a lot of the principles of design run parallel to the concepts of the Tree. A problem has to be defined clearly before it can be solved; a problem has to be unpacked or brainstormed before it can be solved; visualizations of the problem’s possible solutions need to be imagined; something needs to be built; and very few people go it alone in design — so it’s important to keep asking others if they’ll help.

At the core of everything is the Sun — a source of creativity, of energy, of the constant question, “What next?” It’s a phenomenally difficult, perhaps impossible, question to get away from. No creative person can just sit back and let things happen — we have to be a source of the fire and energy we want to express in the world.

Because of the nature of design work, I couldn’t reflect the mindset of Kabbalah’s “lightning path” accurately, nor place the figures in exactly their order or associations in Kabbalah, but I made a point of trying to build up the associations in a way that would be recognizable to designers and thinkers, while still explainable to children. And if the children eventually want to learn the more esoteric aspects of Kabbalah… well. In a sense, the pump will have been primed.

The Frame of Design

The Frame of Design

Originally uploaded by anselm23

Some colleagues and I are in the process of assembling a glyph — a framework of talismans, if you will — designed to teach students about the design thinking process. If it educates parents at the same time, so much the better.

In order to make this bulletin board work, though, I needed to make the seven colored shapes that make up the core of the glyph — an equilateral triangle, a square, a pentagon, a hexagon, a heptagon, and octagon and a circle. They turned out ok, but I think I’m going to have to re-do the pentagon using a semi-super-secret technique, because the sides of the pentagon are not even/regular. All the same, I think they turned out well, and I look forward to putting the bulletin board together tomorrow.

Via Flickr:
This is a set of curious cut-outs I made tonight. I have to assemble a bulletin board tomorrow on design thinking at my school. I think of these as talismans for the project, and I constructed them by hand, geometrically, with ruler and compass.

Or this one!

Or how about this one? Here’s the steps for constructing a regular dodecagon – a twelve-sided figure, together with my solution.

Not bad for a first try. Is this a standard geometry curriculum anywhere, any more??

1. Draw a line AB.
2. Arcs AB and BA
3. Arc radius AB, center O
4. Circle center O-AB
5. Arcs radius OA, centers E, A, B, F.
6. Repeat arcs radius OA on new intersections.
7. Complete the figure.

You try it. Let me know if it works as well for you as it did for me.