October 27, 2005

Proof of Excluded Middle.

Proof of Excluded Middle

The circle is open.
Kneel. Come inside.
What elegance, to deny:
the porcelain pitcher
is full, or the porcelain
pitcher is not full. The milk
breathes in tides,
like the moon with his ocean.
Come inside. Suppose
the pitcher is full: the white
porcelain sweats in meditation, one palm
open, one curled under to her
lotus belly. Between them
she offers up her possibility
to being emptied.
This will not do.
Come outside. The pitcher is not
full: the shadow
of her effort darkens her throat
past the bright muscles
of her open mouth. Between them
she sings the work
to her own fulfilling.
This will not do.

Come outside.
The moon is full, or
the moon is not full.
The pitcher holds his porcelain ocean,
or she does not. What elegance,
to know this, or not to know it.
Kneel. Or, do not kneel.
The circle is open.

The above poem is based on the proof in first-order logic of the tautology: 'p' or not 'p'. Tautologies are unique in first-order logic in that they can be proven without any premises (or, in other words, given any premises whatsoever). A key aspect of this proof is the role played by contradiction. Indeed, the proof itself takes this as its general form, which means in order to prove a statement, one assumes its opposite and derives the contradiction that follows from it. This proof is, in my opinion, one of the most amazing in all of first-order logic. Through the writing of this poem, I hoped to portray its beauty to those not naturally mathematically-minded.

Another unforeseen result was that I have happily been able to better define my goals for the poems I'm currently working on. Like the proof of excluded middle, it occurred to me as I wrote, there may be some truths which grow out of "nothing" (i.e. no premises, or any premises) only through a proof by contradiction--that is, only by assuming their opposites and running again and again into the contradictions and problems that result.

Most of this might not be interesting to most of you, but let me tell you, I was quite excited to stumble on this idea! In the end, it might be necessary to actually understand the proof of excluded middle itself (which requires subproofs within subproofs, a kind of circling deeper and deeper into imagined possibilities, only to run time and again into the same fundamental concept) in order to fully grasp what I'm talking about and how it relates to my series of poems. I just wanted to share this poem because to me, it is a perfect example of the "mystical" potential of left-brain analytical thinking, something which I think a lot of New Age practitioners sometimes tend to eschew or dismiss all too readily.


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At 7.1.06, Anonymous Helena said...

Hello, found your site through Witchvox.com, so glad that I stopped in. I was bit by the blogging bug a few years back and have grown to love it much.
Love the poem above, very unique and thought-provoking :)
Blessings, ~Helena

My Blog

At 22.1.06, Blogger Devon said...

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