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Now every fair die has these same characteristics. It is ''not'' just an average across all dice: that some some dice yield probabilities of ⅐, others ⅕ but, on average, they shake out at about ⅙. ''Every individual die'' must, within minimal tolerance, yield a ⅙ probability. ''All dice are functionally identical''. | Now every fair die has these same characteristics. It is ''not'' just an average across all dice: that some some dice yield probabilities of ⅐, others ⅕ but, on average, they shake out at about ⅙. ''Every individual die'' must, within minimal tolerance, yield a ⅙ probability. ''All dice are functionally identical''. | ||
Therefore, when we roll dice to ''determine'' an outcome we do not build a statistical model that predicts a ⅙ probability: we build the dice to yield that outcome. A die is part of what [[Nancy Cartwright]] would call a “[[nomological machine]]” | Therefore, when we roll dice to ''determine'' an outcome we do not build a statistical model that predicts a ⅙ probability: we build the dice to yield that outcome. A die is part of what [[Nancy Cartwright]] would call a “[[nomological machine]]” | ||
The [[The map and the territory|“map” and “territory”]] are, thus, transposed: it turns out that the “real-world” dice are the map, the theoretical probability is the territory. The map is, as far as engineering permits, ''identical'' to the territory. It need not take the form of | By way of side-note this is a ''terrible'', if accurate, label. “[[Nomological]]” means “denoting principles that resemble laws, especially ones describing brute facts of the universe”, so it is spot on, but it is intimidating to a lay reader. It sounds, and is meant to sound, ''clever''.<ref>Academics and lawyers, learn to do this sort of thing while they train and occupy the junior rungs: using arcane vocabulary of the power structure is part of the early tribal identification ritual, and a self-credentialing device. By the time they sit on the higher rungs in a position to write clear, simple prose, specialists often can’t. They literally don’t know any other way. Cartwright is a brilliant thinker, but her writing is dense and hyper-academic.</ref> | ||
A “nomological machine” is a carefully designed, constrained, hermetically-sealed and [[simple system]]. It is specifically designed to generate the outcome predicted by an existing theory. It is a means of articulating the theory. Rolling dice generate probabilities. We can roll dice and say, look: just as probability theory predicts, over time each side comes up one-sixth of the time. | |||
Now note that if, over time, our dice ''don’t'' yield that outcome, we don’t conclude the ⅙ outcome is wrong: ''we throw out the defective dice''. | |||
The [[The map and the territory|“map” and “territory”]] are, thus, transposed: it turns out that the “real-world” dice are the map, the theoretical probability is the territory. The map is, as far as engineering permits, ''identical'' to the territory. It need not take the form of dice: it could be any contraption that reliably yields a ⅙ probability. Now each of us has a [[difference engine]] in our pocket, we could generate the same outcome with a random number-generator. | |||
Machined dice and the flat, constrained surface on which they fall are not meant to represent “the real world”. They aspire to an idealised platonic utopia, free of friction and caprice, where abstract objects behave yield obediently to the expected statistical outcome: ⅙. | Machined dice and the flat, constrained surface on which they fall are not meant to represent “the real world”. They aspire to an idealised platonic utopia, free of friction and caprice, where abstract objects behave yield obediently to the expected statistical outcome: ⅙. |