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

 

Revisiting "The Cloud of Unknowing"
Notes on a Universal Turing Machine (UTM) & the undecidable

Written in 1998 and revised January 2012

I hold a rather reverential view of the work of Alan Turing. He pioneered procedures that led me to explore new frontiers with algorithmic form.  His work 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, the decision problem.  By 1929 Gödel had shown that all formal systems are incomplete by their very nature so there will always be propositions that cannot be decided within any given formal system.  By 1935 Turing was drawn deeply into working on a procedure for all decidable propositions.  Such a procedure would be a universal algorithm able to decide all decidables.  What, we might ask, drew Turing so deeply into the decision problem.

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 "questioning-self" led me to interior trips I took even as as a child.  Lying on my back looking up at the star studded sky on summer nights was one of my greatest pleasures.  I could spend hours trying to figure out the idea of  the "infinity" they talked about in Sunday School.


Tarantula Nebula.    Credit: NASA / ESA
Close-up shot of part of the Tarantula Nebula, a small galaxy neighbouring the milky way, taken by Hubble.  In my memory, as a child, my view of the milky way back then would have been every bit as stunning as this NASA image of a neighboring galaxy  may be for us today. CLICK HERE FOR THE LARGER IMAGE & MORE DETAIL.

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"?  And there were other unknowns. Could I know something about me before I came to be me?  And I would get dizzy lying there and pondering my being there.  If I had never existed then I would never have thought about any of this in the first place. So it would have been OK not to exist because then you never would have been here to know about anything anyway.

Perhaps a similar seduction teased Alan Turing.  Could you know for sure that your algorithm will never halt?  If I understand correctly, his famous paper, outlining procedures for a universal algorithm, succeeds as a universal mime. The algorithm can 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” or worse . . .you can't even format the question.  

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 / revised  in January 2012

The original essay was written 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). RV

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