Saturday, August 22, 2009
Origin of Geometry:
Purchased at Talking Leaves Books for a graduate school course with Rodolphe Gasché. I think it was called something like, "The Idea of Europe." We read Husserl's The Crisis Of European Sciences and Transcendental Phenomenology to begin the class, as I recall. I don't remember much about reading the book, though I do remember feeling pleasure thinking about geometry.
I always got C's and D's in geometry in school. I pretty much got the same grades in everything. But I remember hating geometry in particular. Memorizing theorems bored me. Though when I read them now, I find the language of theorems quite interesting, even beautiful.
Every line is a set of points that can be put into a one-to-one correspondence with real numbers, with any point on it corresponding to zero and any other point corresponding to one.
If I have any interest in geometry, it is more a philosophical-historical-linguistic one.
The separation of concepts from things, which seems to begin with Euclidean geometry, fascinates me. That there is no such thing as a circle distinct from the conceptual plane, fascinates me. That the ability to conceptualize data that is distinct from nature and which is also, in essence, invisible, despite its infinite applicability to nature, fascinates me. That the very invisibility of geometrical data links its idealized state with the human invention of the divine, fascinates me.
I could sit around all day thinking about the language used to describe a circle. I once tried to write a poem (that didn't actually work out) in which I did just that. Here's an excerpt:
There are no circles
In nature, only more or less circular objects,
The circle itself exists
Only as a mathematical possibility
Within the confines of Euclidean geometry,
Which doesn’t prevent it from lending itself
To the contemplation of the beauty
And completeness of this simple closed curve
Dividing a plane into two parts,
“Interior” and “exterior,”
It’s “circumference” being the perimeter,
The inner portion known as the “disc,”
And the harmony of even the language
Used to describe it, as in “radius”
Which calls to mind the radiating rays
Of the sun, the great disc in the sky,
Or the circle’s many “chords,” line segments
Contained end to end within,
The “diameter” being a chord
Passing through the “center,” and the ratio
Of the circumference to the diameter,
Known as “π,” an “irrational” number
Describing perfection, which neither ends
Nor repeats, a “transcendental” number
That cannot be produced by the finite
Anyhow, here's an excerpt from Derrida:
If the usual factual study of history in general, and in particular the history which in most recent times has achieved true universal extension over all humanity, is to have any meaning at all, such a meaning can only be grounded upon what we can here call internal history, and as such upon the foundations of the universal historical a priori. Such a meaning necessarily leads further to the indicated highest question of a universal teleology of reason.
If, after these expositions, which have illuminated very general and many-side problem-horizons, we lay down the following as something completely secured, namely, that the human surrounding world is the same today as always, and thus also in respect to what is relevant to primal establishment and lasting tradition, then we can show in several steps, only in an exploratory way, in connection with our own surrounding world, what should be considered in more detail for the problem of the idealizing primal establishment of the meaning-structure "geometry."