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The following brief essay was written in preparation for a session at ISEA 98 in Manchester, UK. For that symposium I created a series of works as homage to Alan Turing whose work at Manchester was seminal to the evolution of the computer. About 15 originals from this series, The Manchester Illuminated Universal Turing Machine, were shown at the Manchester Metropolitan University as part of the ISEA '98 exhibitions (December 1998). Because of an airline strike I was unable to attend the sessions for my presentation on the illuminated UTM's. However the works were shown then and later were included in a London retrospective (2001) as part of a hard copy show  to mark the launching of the Digital Art Museum's presence on line: www.dam.org.  RV

The Cloud of Unknowing, 1998. Algorithmic pen & ink drawing. 11.5" by 14.5 ". 

THE “CLOUD OF UNKNOWING” REVISITED:
Notes on a Universal Turing Machine (UTM) and The Undecidable

I hold a rather reverential view of the work of Alan Turing. He pioneered procedures that led me to new frontiers with algorithmic form generators. His work has also awakened meditation on the mystery of undecidables in my spiritual journeys. The mathematician’s adventure with undecidable propositions parallels, in some ways, the spiritual struggle with concepts of transcendent existence.

The concept we call a Universal Turing Machine (UTM) grew from Turing’s interest in Hilbert’s Entscheidungsproblem that was essentially a question as to whether an algorithm for solving all problems whatsoever was possible. By 1929 Gödel had shown that all formal systems are incomplete by their very nature so there will always be propositions that cannot be proven within any given formal system.  By 1935 Turing was drawn deeply into the question as to whether there was an algorithm rigorous enough to prove an undecidable proposition to be undecidable. What, we might ask, drew Turing so deeply into this question of the undecidable?

Let me diverge for a moment. Pondering the undecidable takes me back to younger years when I first wrestled with the baffling limits of “reason”. Wonderment with my own "questioning-self" led me to interior trips I took as a child. Lying on my back looking up at the sky I could spend hours trying to figure out the idea of "infinity" that we learned in Sunday school. How would it "be" to exist without beginning or ending?  Thinking about this question made me strangely dizzy. Try as I might, I could never  hold  "forever and ever without end" in my head.  Would this kind of  existing be somehow outside of "now" since I couldn’t hold it in my head?  And there were other unknowns. Could I know something about me before I came to be me? Would there be no me after I died? And I would get dizzy lying there wondering about how all this came to be and whether there might be some way of being beyond me? 

Perhaps a similar seduction with non-decidable logical propositions drew Alan Turing into the question of the universal problem solver. If I understand correctly, his famous paper, outlining procedures for a universal problem solving algorithm, succeeds as a universal mime. It is able to execute any procedure that is computable because it can mime any computable procedure. However,  a properly coded "undecidable" remains "undecidable" for a universal mime. This gets to be something like the "God" question - you will never know! The decidability of the  proposition remains “undecidable”.  

Recently I had been reading The Cloud of Unknowing, which was written by an unknown spiritual master (probably an English monk) in the late 14th Century. The "Cloud of Unknowing" refers to the author's experience of what stood between himself and knowledge of the God he sought. While not a believer myself,  I would tend to view his "Cloud of Unknowing" as the cloud between myself and understanding the mystery of self or anything that exists whatsoever. So the "Cloud of Unknowing" hovers over the meta-undecidable, the "Undecidable of undecidables", the mystery of our own being here!

A similar cloud hovers over a Universal Turing Machine. 

On the one hand a UTM has the cool logical recipe to assist us in deciding the decidable. It is the marvelous machine enabling my form generators with a magnificent power. If I do it right it helps me unveil new frontiers of form - delightful surprises and marvelous adventures. So, given well-formed procedures (algorithms) and suitable hardware, a UTM can monitor corporate inventories, fly an airplane, and locate my position on the earth.

But, alas, it cannot cope with a single undecidable. The haunting meta-question remains – can we ever be sure that an undecidable is indeed undecidable?  So the "Cloud of Unknowing" hovers over a "UTM" just as surely as it hovers over all of us!

Roman Verostko. Minneapolis, February 1998

See also my essay on "ILLUMINATING  A  UNIVERSAL TURING MACHINE".

 * Turing’s thesis addressing the Entscheidungsproblem can be found at: http://www.abelard.org/turpap2/tp2-ie.asp