Infinition: Thinking-Fractal

May 1, 2009

I wrote a poem a while back called “Axiom: A Mathematics of Poetry” in which I parody the opening chapters of G. Spencer-Brown’s The Laws of Form. The first line introduces a new concept that I created called “infinition”:

It shall be taken as given the idea of infinition. The idea of infinition stands in direct opposition to the idea of definition.

Then, as in chapter one of the Spencer-Brown book, I provide a definition:

Infinition is the act of making indefinite or unclear. That is to say, while some uses of language attempt to clarify, others attempt to obfuscate.

The poem then continues with instructions to make a poem, introducing “canons,” “conventions,” and “principles” much like The Laws of Form does in its opening chapters; these kind of “mathematical” moments attempt to define poetry from its moment of creation. Interspersed within these various defining moments are “infinitions,” poetic moments that obfuscate, that use metaphor and imagery to open up or make blurry what the definitions try to distinguish or clarify.

I later realized that this concept of infinition, which I playfully created for the purposes of this poem, could be introduced in the context of electracy as a simple analogue of electrate thinking. If electracy is a kind of thinking that emerges from or opposes (to some extent) literacy, and literate thinking has as its modus operandi the goal of defining, distinguishing, and clarifying, then “infinition” can be seen perhaps as a kind of electrate definition.

Or, to phrase it as Greg Ulmer might, infinition is to electracy as definition is to literacy.

As a kind of image-thinking, or thinking through or via images, electracy invites the kind of ambiguity that literacy loathes. Ulmer’s work (in Internet Invention: From Literacy to Electracy for example) steers us toward this kind of thinking that is already happening, that is at the core of inventive thinking, as in Einstein’s “wide image” of the compass:

Part of the value of Einstein as a paradigm is that his theories are imaged by a compass. The story of his compass becomes a parable for our own search , in that we must find our equivalent of the compass–the scene that we recognize as having this guiding role in our orientation to the world and to life. (27)

For Ulmer, “invention is an ecological process” and therefore we must attend to the various institutions of our lives (family, career, entertainment, community) in order to tune in to potential new ideas that can emerge from cross-over (in the way that metaphor suggests “crossing over” or “carrying across”). His books provide “heuretics” for invention, and they work: using his CATT(t) method back in his graduate theory course in 1987, I independently discovered the image of the rhizome (for me imaged as a watermelon) as a model of thinking differently, before knowing anything about Deleuze and Guattari.

If we are to think of infinition imagistically, then, I would offer the Koch snowflake as a model of a kind of “fuzzy definition” or “fuzzy logic” or “thinking-fractal.” The idea is to start with an equilateral triangle and then to let each of the sides open out into an increasingly elongated boundary. It’ll be quicker for you to get the idea if you see the animations at the Wikipedia entry for the Koch snowflake. Here is a boundary of infinite length, which seems to be a contradiction: if something is bounded, it is typically finitely bounded, enclosed by a measurable boundary.

So the question, then, is how can this fractal curve help us to think differently? Can the model of the Koch snowflake open up thought, make it an act of infinition?

Don’t get me wrong: there is a place for definition. But there is also a place for infinition.

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