The Computable Artist — On Turing and Michelangelo

“A Great science fiction detective story”
- Ian Watson, author of The Universal Machine 

Days to Centenary:  162

Turing and the Art of Classical Computability [12pp., download PDF here] sounds like the name of yet another derivative paper, maybe a survey or a restatement of established mathematical principles.

No, Turing-ites!

Because its author, Robert Irving Soare, who has written several papers in honour of the Alan Turing Year, is using the word “art” in the way you and I would use it when visiting a gallery. He means art as in a skill, but also art as in an aesthetic endeavor.

Soare, who is  the Paul Snowden Russell Distinguished Service Professor of Mathematics and Computer Science at the University of Chicago, writes:

Mathematics is an art as well as a science. It is an art in the sense of a skill as in Donald Knuth’s series, The Art of Computer Programming, but it is also an art in the sense of an esthetic endeavor with inherent beauty which is recognized by all mathematicians.

In his essay, Soare asks why Turing receives so much credit with respect to the issue of computability when Alonzo Church, as he puts it “got it right and … got it first.”

Soare answers this question by reference to Turing’s mathematical artistry through a side-trip into classical art and a comparison of Donatello, to whom he likens Church, and Michelangelo, whom he compares to Turing.

Michelangelos '"David" (detail)

Soare’s argument is entertaining and enlightening, and will probably be so even for those who don’t end up convinced by his argument, so I recommend reading the paper yourself.  At twelve pages, it’s admirably economical and will more than reward the short time it takes to read it.

Michelangelo's Pietà, completed when he was twenty-four, the same age as Turing when he published his "On computable numbers with an application to the Entscheidungsproblem."

Soare insists — as many commentators have done in relation to scientific disciplines that can be practiced in a theoretical manner, such as mathematics and physics — that math is not simply a matter of getting the right result, but of doing so in a way that is elegant and that may therefore be judged aesthetically:

Mathematicians are not assigned projects like building bridges. Like artists, they choose which problems to work on according to taste and beauty. Like artists, what they produce is evaluated on the basis of beauty as well as mathematical results. The greatest results are those arising from a completely new vision and a profound intuition into the area.

I’m not a mathematician and therefore not in much of a position to judge the relative aesthetics of Turing’s work myself, but if it does constitute great art that bears comparison with Michelangelo I wouldn’t be much surprised.

Great art can be judged by many particulars, but one of its hallmarks is its capacity to be endlessly fecund, and with all of the things that have flowed from  Turing’s brief period of creation his work is certainly that.

Podcasting Alan Turing, Review 3: Groks Science Show, “Alan Turing”

Days to Centenary: 252

This is the third in a series of reviews of English-language podcasts that relate to Alan Turing (all of which are available for free through iTunes). With any luck I will review them all before the centenary arrives — cross your fingers. (Earlier reviews: Number 1, Number 2)

Source: Groks Science Show

Title: Alan Turing

Running Time: 30:03 (Turing section runs from 10:00 to 26:53)

Format: Audio only

Sound Quality: 5/5 stars

Available here (scroll down to episode 287 from March 29, 2006)

Groks Science Show is a weekly science radio show and podcast hosted by Dr. Charles Lee, Dr. Frank Ling and Dr. Elise Covic. Each episode features an interview with a leading scientist, researcher, or industrialist. Interviewees have included familiar figures like Brian Cox and a variety of other less well known but equally compelling guests. A personal favourite of mine is quantum computation pioneer David Deutsche.

This episode includes an interview with David Leavitt, author of The Man Who Knew Too Much, a biography of Alan Turing (not to be confused with other things entitled The Man Who Knew Too Much, like the collection of G.K. Chesterton mysteries or the movie with Peter Lorre). The interview begins at the 10:00 mark, after other material that was breaking science news when the show aired (2006), but that isn’t any more (although it isn’t without some interest).

Leavitt would be an interesting subject for a better interviewer. In addition to providing a brief summary of Turing’s significance, he emphasizes his book’s examination of Turing’s work through the lens of his sexual orientation. He also provides some examples of the book’s specific contents, for instance saying that (despite not being a mathematician) he attempts to explain Turing’s first important paper “On computable numbers, with an application to the Entscheidungsproblem” [pdf] by following the specific proof used by Turing, which he describes as being needlessly complex but inherently interesting, rather than by using a more efficient or elegant proof as he says some authors have chosen to do.

The episode concludes with Leavitt submitting to the show’s “Grokatron 5000″ — a segment created perely for fun — in which he is asked to rate various persons as a pass or fail on the Turing Test, which means that for each he must answer the question “would this person be interpreted as human in the course of a Turing Test or might they ever be mistaken for a homo artificialis”? He argues that Michael Jackson passes — could not be mistaken for a machine — because he’s “inimitable,” and George W. Bush passes because “nothing as intelligent as a machine could utter the remarks [he makes].”

I’m sorry to give a thumbs down to Groks — the hosts seem like nice guys and it’s a long-running science radio show, which is an achievement not to be dismissed as trivial. But a review is little help to anyone reading it if it refuses to be critical. If these reviews are to have any justification it must lie primarily in saving people who read them from having to spend hours sorting through everything on iTunes to find a good show related to Turing — I’m supposed to do that for you. So, to paraphrase a position so often taken by my favourite film critic, Mark Kermode: this podcast is not terrible, it just isn’t very good.

The interview is simply not well done. As a source of information, nothing in this podcast matched this single disputatious paragraph from a review of Leavitt’s book in The Independent:

David Leavitt, the American gay novelist, has no mathematical background, though he makes considerable efforts to cover Turing’s work with a condensation of other books. He has not found new sources, nor used the recently released codebreaking documents; his summary of Turing’s Enigma work is particularly thin. His focus lies in applying his interpretation of sexual politics to Turing’s texts.

Now, them’s fightin’ words, but whether one ultimately agrees or disagrees with The Independent’s assessment of Leavitt’s book, it is informative — it assists you in deciding whether it would be worth buying the book, or merely checking it out of the public library, or bypassing it altogether.

Leavitt himself injects some information into his Groks interview, but this ends up being a thin substitute for a well conducted interview. An interviewer who is doing his or her job should do things that the person being interviewed can’t accomplish effectively on their own or are unwilling to do, like challenge them on their interpretation of the facts, point out lacunae in their arguments, or examine their work from a perspective they haven’t thought of before. The Independent does this and Groks doesn’t.

I have briefly sampled other (especially more recent) episodes of this show, and while I have reservations about some of them, they tend to be better than this one, their lack of Turing-ness or Turing-osity notwithstanding.

So my bottom line is threefold:

(1) if you want to know more about Leavitt’s book, look to other sources;

(2) if you want a new science podcast to listen to, try Groks, but listen to an episode other than this one;

(3) if you want to listen to a Turing podcast, try one of the other ones that have been reviewed here, or that are reviewed here in the future.

Until next time.