“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.

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.

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.