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Now here is the thing. When we calculate probabilities — when we roll dice — we are in situations of known risk. | Now here is the thing. When we calculate probabilities — when we roll dice — we are in situations of ''known risk''. We don’t know exactly how this particular event will turn out, but we know the range of possible outcomes and the calculated probability of each. No matter how deft our technique, no matter how surprising or extraordinary their trajectory, the dice must come to rest showing one of six equally-sized faces uppermost. No two throws are the same. The trajectory is chaotic, but all this intractable uncertainty is wiped out when the dice come to rest. None of it matters. All that matters is the average. By that we can set our watches. | ||
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==== | |||
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 the 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 a ⅙ outcome we don't throw out the statistical model: we throw out the ''dice''. | |||
The | The “map” and territory ” are transposed: the dice are the map, the theoretical ⅙ probability is the territory. The map is, as far as engineering permits, ''identical'' to the territory. Now each of us has a difference engine in our pocket, we don’t even need physical dice: we could generate the same outcome, with a random number generating app. | ||
Likewise, if, inside your nomological machine there is a mischievous imp who catches and places the die as it sees fit, the conditions for your probabilistic calculation do not prevail. There | 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. | ||
Likewise, if, inside your nomological machine there is a mischievous imp who catches and places the die as it sees fit, the conditions for your probabilistic calculation do not prevail. There must be no interfering causal agency. | |||
“Nomological machines” are highly constrained, artificial environments. If all their conditions are not satisfied, we can expect the world to behave differently without validating the machine. This is how, as [[Nancy Cartwright]] put it “the laws of physics lie”. | “Nomological machines” are highly constrained, artificial environments. If all their conditions are not satisfied, we can expect the world to behave differently without validating the machine. This is how, as [[Nancy Cartwright]] put it “the laws of physics lie”. | ||