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Every fair die has the same characteristics. It is not just that on some some dice the probability is more like ⅐, on others now like ⅕ but, on average, dice work out at all about ⅙. Every die must, within tolerance, behave exactly the same way. Therefore probabilities are a valid means of predicting behaviour. | Every fair die has the same characteristics. It is not just that on some some dice the probability is more like ⅐, on others now like ⅕ but, on average, dice work out at all about ⅙. Every die must, within tolerance, behave exactly the same way. Therefore probabilities are a valid means of predicting behaviour. | ||
====Dice rolling as a nomological machine==== | ====Dice rolling as a nomological machine==== | ||
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]]”:<ref>This is a ''terrible'', typically ''academic'' label. No doubt it is etymologically accurate, but it is forbidding to a lay reader. Academics, like lawyers, tend to do this while they train and occupy the junior rungs as a self-credentialising device. By the time they sit on the higher rungs, they don’t know any different way of writing.Cartwright is a brilliant thinker, but her writing is dense and hyper-academic. </ref> a carefully designed, constrained, hermetically-sealed simple system, designed to generate a specific theoretical outcome. If over time our dice don’t yield | 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]]”:<ref>This is a ''terrible'', typically ''academic'' label. No doubt it is etymologically accurate, but it is forbidding to a lay reader. Academics, like lawyers, tend to do this while they train and occupy the junior rungs as a self-credentialising device. By the time they sit on the higher rungs, they don’t know any different way of writing.Cartwright is a brilliant thinker, but her writing is dense and hyper-academic. </ref> a carefully designed, constrained, hermetically-sealed [[simple system]], designed to generate a specific theoretical outcome. If over time our dice don’t yield the ⅙ outcome we want, we don’t conclude the ⅙ outcome is wrong: ''we throw out the'' ''dice''. | ||
The “map” and | 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 be 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. | ||
The machined dice and the flat, constrained surface con which they fall are not meant to represent our actual reality. They are aspiring to the desired statistical model. They seek to emulate an idealised platonic form. A “loaded” die is a ''flawed'' [[nomological machine]]. So is a surface like sand which allows a die to rest on its corner. If you get bad results with a [[nomological machine]] you don't chuck out the theory: you chuck out the equipment. | The machined dice and the flat, constrained surface con which they fall are not meant to represent our actual reality. They are aspiring to the desired statistical model. They seek to emulate an idealised platonic form. A “loaded” die is a ''flawed'' [[nomological machine]]. So is a surface like sand which allows a die to rest on its corner. If you get bad results with a [[nomological machine]] you don't chuck out the theory: you chuck out the equipment. | ||