I am not a numbers person, but reading Alan Turing’s “Computing Machinery and Intelligence” (NMR), and watching The Imitation Game has me thinking about numbers, what they mean, and what we make of them. The excerpt in the New Media Reader was first published in 1950 and teems with binaries. Turing’s original conception of the “Imitation Game” juxtaposes man to woman (can a human interrogator differentiate between the two using only written questions?), and then (hu)man to machine (can a machine convince the interrogator of its humanity?). Further on he invokes other dualities: black-white, human-animal, discrete state-continuous state machines, stimulus-response, abstract-concrete, and even chess-English (as illustration of the latter). Reading Turing think through the arguments against and for “machines that can learn” I was struck by his consistent invocation of binary logic and syllogism, especially when the discussion extended to the emotions and initiative — aspects of learning and humanity less easily explained in this framework. It seemed at time as though the very humanity of humans might be overridden by a kind of behaviorism that would level the playing field for machines to win the Imitation Game.
And then I remembered the magic of fibonacci sequences and the golden section, Turing’s interest in them, and the ways these values and relationships inform some of the most beautiful expressions of art and nature. Sunflowers, anyone?
SunFlower: the Fibonacci sequence, Golden Section by Luca Postpischl (https://flic.kr/p/24oVY3)
CC license 2.0 https://creativecommons.org/licenses/by-nc-nd/2.0/legalcode
Or Bartok’s 1926 piano sonata? (See and hear the structural elements comprising the first five numbers in the fibonacci series (1-2-3-5-8) at the beginning of the piece?
Turing may have used binary frameworks to make a case for thinking machines, but he found the more elusive and pervasive relationships, in nature and numbers even more compelling.