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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''.
-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 rolling die on a flat surface is what [[Nancy Cartwright]] might call a “[[nomological machine]]”
-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>
+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.
+A “nomological machine” is carefully designed, constrained, hermetically-sealed: a [[simple system]] designed to generate the specific outcome an existing theory predicts. It is not a means of proving a theory so much as articulating it. It may be abstract and not even possible in the real world. Rolling fair dice on a flat surface illustrate probabilities. We can co-opt them for a game of monopoly, as a means of generating a random outcome. 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''.
+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.
+The [[The map and the territory|“map” and “territory”]] are, thus, transposed: where usually the have is the abstract simplification of an intractable real world territory, here the “real-world” dice is the map of the territory of a theoretical probability. But it is a map on a 1:1 scale: as far as engineering permits, ''identical'' to the territory. Its [[substrate]] need not take the form of dice: it could be any contraption that reliably yields a ⅙ probability. Now we all carry [[difference engine]]s in our pocket, we could get 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.
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 A “loaded” die is a ''flawed'' [[nomological machine]]. So is a surface like sand which allows a die an ambiguous resting place upon its edge. If, over time you get don't get the ⅙ outcome you expect you don't chuck out the probability theory: you chuck out the dice.
-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 probabilis1tic calculation do not prevail. There must be no interfering causal agency.
+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 calculations do not prevail. There must be no interfering causal agency.
-“[[Nomological machine|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 machine|Nomological machines]]” are highly constrained, artificial environments. If all their conditions are not satisfied in the real world, and we find the world does not obey the model, this does not invalidate the model. This is how, as [[Nancy Cartwright]] put it “the laws of physics lie”.
-In any case, these are the circumstances in which the rules of probability prevail. Should the universe “misbehave” then the conditions required for the [[nomological machine]] cannot be present.
+In any case, the circumstances in which the laws of probability hold are highly limited and very artificial. Should the universe “misbehave” then the conditions required for the [[nomological machine]] cannot be present.
 Boy, did I get side-tracked.
-Normal distributions standard deviations, and confident probabilities require a complete [[nomological machine]] where all potential events are known, are independent, and there is no intervening agency that can upset the observed behaviour of the system. If you have all that all risks can be calculated and probabilities assigned.
+For events in the real world to confirm to normal distributions, standard deviations, and confident probabilities they must meet the criteria of a nomological machine. All potential events must known, and be independent of each other and our observation of them. If a motivated agent intervenes it can upset the observed behaviour of the system. If you have all that all risks can be calculated and probabilities assigned.
 Markets, in the abstract, look just like such a machine. There is a bounded environment, a finite trading day and a limited number of market participants and financial instruments which one can buy or sell. In the modern days of computerised trading everything is very clean, tidy observable, unitary and discrete.