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AM Turing: Automatic Elegy — installation, performance, and ritual

22 June, 2012, at Chapel Performance Space (installation at 7 PM, concert at 8 PM)

Alan Turing. The father of computer science and artificial intelligence, and a significant contributor to other brainy academic disciplines: mathematics, philosophy, and biology. A shy, but affable, man “of the professor type” who enjoyed science and mathematics, party games and chess, sharing a pint, and who kept fit through competitive long-distance running and biking. A true war hero, who was awarded the Order of the British Empire in 1945. A man who also lived conflicting secret lives, openly gay when being gay was illegal, and sworn to secrecy by the British Foreign Office as critical to World War II codebreaking efforts. In the end, he was a tragic figure, paying the ultimate price for his secrets when he seemed to stylishly and deliberately take his own life.

a portrait of alan turingJune 2012 is the centenary of Alan Turing’s birth, and many artists are responding to this event by commemorating his life with art. My own contribution to this body of work will consist of a ritualized performance set within a biographically-focused abstract installation, which will be performed in Seattle’s Chapel Performance Space on the eve of his birthday. (7PM on 22 June, 2012)

The installation will consist of artifacts, emotional, physical and intellectual, that are drawn from Turing’s life, interpreted as a series of 41 chalkboards. Some will be physical items, others written or drawn. An ambient soundscape consisting of gentle mechanical sounds and synthesized electronic drones will accompany these chalkboards, along with other, more enigmatic, sounds: mathematical structures, historical conversations, and simple machines. The performance, which will take place within the installation, will include spoken word, music, field recordings, and ritual movement, all based upon mathematical and philosophical structures from Turing’s life work.

The three mathematical and philosophical structures that form the backbone of the piece are the Universal Turing Machine, the Turing test, and Turing patterns. Although the music, visual images, and choreography that occur as part of the ritual can be fully enjoyed without previous knowledge of Turing’s intellectual output, the pieces will directly reflect his work on the Riemann hypothesis, on algorithms, on cryptanalysis, on group theory, on digital computing, on x-ray crystallography, on logic, and on mathematical biology. There are lots of good web resources where you can learn more about these topics; I hope that the entries lower on this page will also help to provide context.

The blog posts below record my ongoing collaborations in preparation for this event. Thanks to everyone who has helped, and especially to Geoff Shilling, Perri Lynch, Beth Glosten, Jim Bennett, Erika Chang, Linda Strandberg, Dean Moore and David Krueger!

am turing: automatic elegy

turing installation and concertOur June 22nd performance and installation was a success, and audience reactions were very gratifying. I will edit video excerpts and post at some point, but in the meantime, besides posting a few photos of the event, I want to credit members of the cast and those who provided artistic input. Thank you all. This piece could never have happened without you!

geoff shilling weaving

Fiber artist Geoff Shilling, who was weaving the state machine in the room at the event, also wove the large portrait of Turing and built the chalkboards that made up the set. This job was immense, and he did it in less than 3 months, without complaint.

puzzles by beth glosten
Beth Glosten, who played the bouncer at the door, chalked many of the boards, wrote the 13 scavenger hunt clues, and stage managed the production. (If that weren’t enough, she also provided valuable input and moral support at home as the piece came into focus.)

Perri Lynch, who helped run the house at the event, provided 8 beautiful chalkboards based on details of the zeta calculator blueprint and also gave me valuable basic crash course in chalkboard marking techniques.

David Krueger, Erika Chang, Linda Strandberg, Markdavin Obenza, and Josh Haberman sang beautifully, and Dean Moore contributed percussion that was both sensitive to the context and appropriately unusual. All six of them also performed whatever strange stage actions I requested without complaint. (David Krueger and Erika Chang also helped immensely by contributing muscle to setup and teardown.)

Jim Bennett as the Prof
Jim Bennett played the Prof perfectly, gave much input on the piece along the way, and then, to top it off, humped the set in and out of the building along with Geoff, David, and myself.

the tape of turing's life

Finally, thanks to John Forsen for his videography talents, Audrey Guidi for her photographic ones, and to Steve Peters and the Wayward Music Series for providing such a perfect venue for this piece.

The set, when broken down, fits on two shipping pallets. Where should we perform this piece next? Bletchley Park, do you copy?

turing among the machines

One of the defining characteristics of Alan Turing was his pairing of supremely abstract thinking with a very real-world interest in the nuts and bolts of machines. He enjoyed hands-on physics, chemistry, and biology experiments his entire life, and had already begun his life-long adventures with computing machines with analog devices when he recognized and formalized the design advantages of digital technology.

Turing portrait in progressIt is entirely natural to think of Turing’s deepest emotional relationship as being the one which he had with The Machine. He formalized what we mean by a “binary computing machine”, as well as the universal nature of such a machine. He knew that machines had the capacity to possess their own intelligence (and their own set of fallibilities) far before that was fashionable, and spoke of them in that light from day one. (He probably went further, thinking of all life as mechanical, but this is only implied in his writings.) He would often solve new problems by sketching or prototyping: his output started with devices such as his childhood Foucault pendulum, continued with advanced devices of his own design including a gear-driven analog calculator, a binary electronic adder, and an electronic voice scrambler, and culminated with the first flush of true general-purpose computers in the 1940s and early 1950s, for which he was a central influence.

In this installation, I have chosen one of the oldest and most universal technologies, the loom, to stand in as the ritual presence of The Machine. When I first encountered the machines described by Turing in On Computable Numbers, my mind immediately went to the motion of a shuttle, whose oscillatory movements resemble the movement of the turing machine head across its tape. The tape itself also seems symbolically linked: the fabric being created from warp and weft seems similar to the output being created from “state” and “mark”. Because of this, I have chosen to weave the sounds and outputs of looms into the performance. They come and go, and are produced by both live weaving in the room, as well as by the triggering of electronic field recordings.

Geoff Shilling has also created a woven portrait of Turing which will sit with us in the room, invoking his presence. If you examine the portrait closely, you will see that it is composed of letters (symbols) from the Fraktur family of fonts, which is the same font that Turing used to represent the workings of his universal machines on paper. It is a beautiful piece, and a beautiful tribute.

introduction to the ACE report

diagram from Turing ACE report

From Turing’s Proposal for Development in the Mathematics Division of an Automatic Computing Engine (ACE):

“Calculating machinery in the past has been designed to carry out accurately and moderately quickly small parts of calculations which frequently recur. The four processes addition, subtraction, multiplication and division, together perhaps with sorting and interpolation, cover all that could be done until quite recently, if we except machines of the nature of the differential analyser and wind tunnels, etc. which operate by measurement rather than by calculation.

It is intended that the electronic calculator now proposed should be different in that it will tackle whole problems. Instead of repeatedly using human labour for taking material out of the machine and putting it back at the a ppropriate moment all this will be looked after by the machine itself. This arrangement has very many advantages.

(1) The speed of the machine is no longer limited by the speed of the human operator.
(2) The human element of fallibility is eliminated, although it may to an extent be replaced by mechanical fallibility.
(3) Very much more complicated processes can be carried out than could easily be dealt with by human labour.

Once the human brake is removed the increase in speed is enormous. For example, it is intended that multiplication of two ten figure numbers shall be carried out in 500 μs. This is probably about 20,000 times faster than the normal speed with calculating machines.”

the weaving commences

While I’ve been slacking off, Geoff Shilling has fortunately remained busy, continuing to fabricate wooden pieces for the installation. He’s now starting on the woven pieces, including a rendering of the famous portrait shown in this post. Look carefully at the characters that he is using for the half-toning; they will be familiar to anyone who has read the original article on computable numbers! Writing custom rendering code is just another in his long list of skills.

I hope that this work is self-explanatory

A bombe cribAn obscure paper, but a wonderful view into Turing’s mind and the practical problems associated with cracking the Enigma daily: CRITIQUE OF RUNNING SHORT CRIBS ON THE U. S. NAVY BOMBE. The snarky jabs at builders who don’t really understand the day-to-day operation of the system will be very familiar to anyone who designs a lot of code. (Note that this paper is freely available only for a limited time. The Cryptologia paywall will rise again at the end of the year.) The first paragraph really sets the tone. The gem that provided my title is near the bottom:

“We are reather surprised to hear that you are able to find the keys, given that a message when deciphered says VVVBDUUU. Our experience shows that with a ‘crib’ as short as 8 letters there are always far too many sets of keys consistent with the data, so that whatever method may be used for discovering the dkeys, the time required to test these solutions out further becomes prohibitive. To illustrate this I have enciphered VVVBDUUU with a random chosen key viz wheel order 457, English Ringstellung RWH, pre-start window position SZK and Stecker A/P, B/Y, C/L, E/Q, F/X, K/R, M/W, N/T, O/V, S/Z, giving YFZONMTY. I then imagined that

Y  F  Z  O  N  M  T  Y
V  V  V  B  D  U  U  U

was a crib that I had to solve, but that I knew the wheel order and Ringstellung: I tried out the hypothesis that the pre-start window position was the right one (SZK) and also the five which follow it (allowing correctly for turnovers) viz TAL, TAM, TBN, TBO, TBP, and found that with pre-start TBP there is a solution with V/J, F/G, Z/H, Y/E, U/X, M/L, T/K, D/P and either B/S and O/W or B/W and O/S. The ‘unsteckered alphabets’ for the relevant positions of the machine are shown in Fig 1, and the working in Fig 2. I hope that this work is self-explanatory. Each column of letters consists of steckers of the letters VFZYUMT which imply one another on account of the crib.”

sonification of Turing’s work

Computer codeAlan Turing is among the handful of thinkers who formulated the concept of algorithmic computation. Every task that we perform with a computer begins with an algorithm, and yet this concept, which we now take for granted, was not yet formalized in the 1930s. This simple, yet immensely impactful, contribution is why I’ve chosen to create an algorithmic soundscape as the backdrop for our upcoming installation/performance. I like to think of Turing, along with Alonzo Church, as the modern muses who inspire all algorithmic arts and sciences. In honor of the centenary of Turing’s birth, I am creating an elegy for him.

There are several parts to this Turing elegy: a physical installation (which also functions as the setting for performances), a continuous ambient soundscape which surrounds the visitor upon entering the room, and finally, a brief ritualized performance in which Turing-inspired works will be presented using sound, spoken word, and movement. I’ve been working on both the physical set and the sonic ambience lately, and thought that I’d post a little bit about the methods that I’m using to create the soundscape.

There are three basic layers to this soundscape: live sounds produced by human performers, synthesized electronic sounds, and the sounds of machines (both live and via field recordings). All of the sounds relate to Turing’s life and his work, and many of them are based on either pure mathematics or realized Turing machines. All are created and/or performed using algorithms. In order to preserve the freshness of the live experience, I am not going to go into too much blog detail before the actual performance, but I will say that the live sounds will include humans operating simple machines, thinking, engaging in academic dialog, and chanting introspectively. Field recordings include turing machines, looms, and machines of Turing’s own creation.

The electronic portion of the soundscape is composed of algorithmically produced sonifications of Turing’s scientific output. Turing’s work included not only his very significant work on computability, but also forays into disparate subjects including group theory, logic, number theory, and mathematical modeling. I am currently in the process of transforming several specific results — his work on the Riemann hypothesis, his biological model for morphogenesis, and some of the examples from the Entscheidungsproblem paper — into electronic sounds using the Supercollider programming language for digital synthesis.

(Click to read more of the gory details)

fabrication has begun

Long-time collaborator Geoff Shilling and I did an intensive three days in his shop last week, and our installation is definitely starting to take shape. 41 blackboards, complete with road cases, ready for chalking. Geoff, who is a fiber artist, will also be participating in the live portion of this event as well as creating pieces for it!


a taste of programming the Mark I


Besides containing math that helped to advance work on the Riemann Hypothesis, Turing’s paper “Some Calculations of the Riemann Zeta Function” also contains a great snapshot of what it was like to program the first generation of electronic computers. I’ll start with the widely-quoted introduction to the paper, which I’ve annotated a bit:

“In June 1950 the Manchester University Mark I Electronic Computer was used to do some calculations concerned with the distribution of the zeros of the Riemann zeta-function. It was intended in fact to determine whether there are any zeros not on the critical line in certain particular intervals. The calculations had been planned some time in advance, but had in fact had to be carried out in great haste. If it had not been for the fact that the computer remained in serviceable condition for an unusually long period from 3 p.m. one afternoon to 8 a.m. the following morning it is probably that the calculations would never have been done at all. As it was, the interval 2π632 < t < 2π642 was investigated during that period, and very little more was accomplished.

(Click to read more of the gory details)

the zeta zero approximator

A blueprint
The Turing Digital Archive contains a single tantalizing blueprint image for an elaborate gear-driven mechanical calculator that Turing proposed to build in 1939, which would have helped to make progress in verifying the Riemann Hypothesis. It was to be a very special-purpose device for adding up sine components in the various ratios needed to perform calculations using the Riemann-Siegel theta function, which was a new development in the 30’s.

Table of values from blueprint
The table in the blueprint contains the ratios he would need for mechanical linkage, although as Bill Casselman points out, the table actually contains several calculation errors which would have eventually caused some problems. [My personal favorite is the column for ratios in log base 8.]

From Turing’s application to the Royal Society: “It is proposed to make calculations of the Riemann zeta-function on the critical line for 1,450 < t < 6,000 with a view to discovering whether all the zeros of the function in this range of t lie on the critical line. An investigation for 0 < t < 1,464 has already been made by Titchmarsh. The most laborious part of such calculations consists in the evaluation of certain trigonometrical sums
An intermediate equation
In the present calculation it is intended to evaluate these sums approximately in most cases by the use of apparatus somewhat similar to what is used for tide prediction. When this method does not give sufficient accuracy it will be necessary to revert to the straightforward calculation of the trigonometric sums, but this should be only rarely necessary. I am hoping that the use of the tide-predicting machine will reduce the amount of such calculation necessary in a ratio of 50:1 or better. It will not be feasible to use already existing tide predictors because the frequencies occurring in the tide problems are entirely different from those occurring in the zeta function problem. I shall be working in collaboration with D. C. MacPhail, a research student who is an engineer. We propose to do most of the machineshop work ourselves, and are therefore applying only for the cost of materials, and some preliminary computation.”

Although this physical machine was never finished, due to the arrival of World War II, Turing continued to putter with the Riemann Hypothesis throughout his career via the zeta function, eventually becoming the first person to use an electronic computer to calculate zeroes, and thereby extending the upper limit for known zeroes to t < 1540. [Minuscule by today’s standards, but not bad for work done with paper tape in raw base 32 on a machine with a little over 25,000 bits of memory!] He also devised what is now called “Turing’s method” for easier computational analysis of the function. These exploits are detailed in his papers “A method for the calculation of the zeta-function” and “Some calculations of the Riemann zeta-function,” which are both widely referenced in contemporary math papers.

obituary quotations

“It was a great loss to natural science as well as to mathematics when, on June 8, at the age of 41, he was found dead in his house at Wilmslow in Chesire.” — Kings Report 1954 [No mention of his wartime achievements, of his sexuality, or of suicide.]

“Turing took a particular delight in problems, large or small, that enabled him to combine mathematical theory with experiments he could carry out, in whole or part, with his own hands. He was ready to tackle anything which combined these two interests. His comical but brilliantly apt analogies with which he explained his ideas made him a delightful companion.” — DR ALAN TURING An Appreciation, Manchester Guardian 11 June 1954

“For those who knew him here [at Sherborne] the memory is of an even-tempered, lovable character with an impish sense of humour and a modesty proof against all achievement. You would not take him for a Wrangler, the youngest Fellow of King’s and the youngest F.R.S. [Fellow of the Royal Society], or as a Marathon runner, or that behind a negligé appearance he was intensely practical. Rather you recollected him as one who buttered his porridge, brewed scientific concoctions in his study, suspended a weighted string from the staircase wall and set it swinging before Chapel to demonstrate the rotation of the Earth by its change of direction by noon, produced proofs of the postulates of Euclid, or brought bottles of imprisoned flies to study their “decadence” by inbreeding. On holidays in Cornwall or Sark he was a lively companion even to the extent of mixed bathing at midnight. During the war he was engaged in breaking down enemy codes, and had under him a regiment of girls, supervised to his amusement by a dragon of a female. His work was hush-hush, not to be divulged even to his mother. For it he was awarded the O.B.E. He also adopted a yound Jewish refugee and saw him through his education. Besides long distance running, his hobbies were gardening and chess; and occasionally realistic water-colour painting.

In all his preoccupation with logic, mathematics, and science he never lost the common touch; in a short life he accomplished much, and to the roll of great names in the history of his particular studies added his own.” — The Sherbornian, Summer Term 1954