Tag: Determinism

O-Machines

In his dissertation, completed in 1938, Alan Turing sought “ways to escape the limitations of closed formal systems and purely deterministic machines” (Dyson, Turing’s Cathedral, p. 251) like the kind he’d imagined two years earlier in his landmark essay “On Computable Numbers.” As George Dyson notes, Turing “invoked a new class of machines that proceed deterministically, step by step, but once in a while make nondeterministic leaps, by consulting ‘a kind of oracle as it were’” (252).

“We shall not go any further into the nature of this oracle,” wrote Turing, “apart from saying that it cannot be a machine.” But, he adds, “With the help of the oracle we could form a new kind of machine (call them O-machines)” (“Systems of Logic Based on Ordinals,” pp. 172-173).

James Bridle pursues this idea in his book Ways of Being.

“Ever since the development of digital computers,” writes Bridle, “we have shaped the world in their image. In particular, they have shaped our idea of truth and knowledge as being that which is calculable. Only that which is calculable is knowable, and so our ability to think with machines beyond our own experience, to imagine other ways of being with and alongside them, is desperately limited. This fundamentalist faith in computability is both violent and destructive: it bullies into little boxes what it can and erases what it can’t. In economics, it attributes value only to what it can count; in the social sciences it recognizes only what it can map and represent; in psychology it gives meaning only to our own experience and denies that of unknowable, incalculable others. It brutalizes the world, while blinding us to what we don’t even realize we don’t know” (177).

“Yet at the very birth of computation,” he adds, “an entirely different kind of thinking was envisaged, and immediately set aside: one in which an unknowable other is always present, waiting to be consulted, outside the boundaries of the established system. Turing’s o-machine, the oracle, is precisely that which allows us to see what we don’t know, to recognize our own ignorance, as Socrates did at Delphi” (177).

The Language of Birds

My study of oracles and divination practices leads me back to Dale Pendell’s book The Language of Birds: Some Notes on Chance and Divination.

The race is on between ratio and divinatio. The latter is a Latin term related to divinare, “to predict,” and divinus, meaning “to divine” or “pertaining to the gods,” notes Pendell.

To delve deeper into the meaning of divination, however, we need to go back to the Greeks. For them, the term for divination is manteia. The prophet or prophetess is mantis, related to mainomai, “to be mad,” and mania, “madness” (24). The prophecies of the mantic ones are meaningful, insisted thinkers like Socrates, because there is meaning in madness.

What others call “mystical experiences,” known only through narrative testimonies of figures taken to be mantics: these phenomena are in fact subjects of discussion in the Phaedrus. The discussion continues across time, through the varied gospels of the New Testament, traditions received here in a living present, awaiting reply. Each of us confronts a question: “Shall we seek such experiences ourselves — and if so, by what means?” Many of us shrug our shoulders and, averse to risk, pursue business as usual. Yet a growing many choose otherwise. Scientists predict. Mantics aim to thwart the destructiveness of the parent body. Mantics are created ones who, encountering their creator, receive permission to make worlds in their own likeness or image. Reawakened with memory of this world waning, they set to work building something new in its place.

Pendell lays the matter out succinctly, this dialogue underway between computers and mad prophets. “Rationality. Ratio. Analysis,” writes the poet, free-associating his way toward meaning. “Pascal’s adding machine: stacks of Boolean gates. Computers can beat grandmasters: it’s clear that logical deduction is not our particular forte. Madness may be” (25). Pendell refers on several occasions to computers, robots, and Turing machines. “Alan Turing’s oracles were deterministic,” he writes, “and therefore not mad, and, as Roger Penrose shows, following Gödel’s proof, incapable of understanding. They can’t solve the halting problem. Penrose suggests that a non-computational brain might need a quantum time loop, so that the results of future computations are available in the present” (32).

Stochastic Music

The university library here in town dumps a collection of LPs from its listening room. Out with the old, in with the new. I encounter them in the bins at Goodwill. To them by chance led. The ones I come away with are remarkable: compositions by the likes of John Cage, George Crumb, Alvin Lucier, Pauline Oliveros, Iannis Xenakis, Karlheinz Stockhausen, and Krzysztof Penderecki. One pursues one’s education here or not at all, thinks the Narrator.

“To Xenakis—as, indeed, to most philosophers—” writes Bernard Jacobson in his liner notes to one of the Xenakis LPs, “chance itself is a scientific concept.”  The reference to “chance” catches my eye, given that “hap” (a Middle English word meaning chance) has been a preoccupation of mine of late.

“Central among the scientific laws [Xenakis] has applied to music,” continues Jacobson, “is Bernoulli’s Law of Large Numbers, which provides that as the number of repetitions of a given ‘chance’ trial (such as flipping a coin) increases, so the probability that the results will tend to a determinate end approaches certainty. Hence Xenakis’s use of the term ‘stochastic’ music, which means probabilistic in the sense of tending toward a certain goal.”

Xenakis’s approach intrigues me. Yet what interests me most about “stochastic music” and stochastic processes more generally is that, despite their probabilistic nature, their behavior and outcome is intrinsically non-deterministic.