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==== Tumbling dice as a nomological machine ====
Markets, in the abstract, look like a [[nomological 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.
When we calculate probabilities — when we roll dice — we are in situations of ''known risk''. Even though dice ''trajectories'' are chaotic; even though no two rolls are identical,  all this intractable uncertainty is wiped out when the dice come to rest. At that stage we know the range of possible outcomes and their calculated probabilities. On a flat, hard surface, one side must come to rest face-up. There are six equal sides. We deduce each side has a ⅙ probability.
 
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 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>
 
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.”
 
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: 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.
 
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 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 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, 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.
 
But hold map and territory — model and reality — as an immutable dualism. We live in the territory, and to abstract from territory to map is to cross the mythical threshold from ordinary world to magical ''model'' kingdom. Unlike its fictional archetype<ref>Most famously outlined in [[Joseph Campbell]]’s {{br|The Hero with a Thousand Faces}}</ref> the model kingdom cannot change the real world. The less correspondence there is between the two, the greater the peril.
 
So the relationship between map and territory is fraught. Map, territory. Model, reality. Online, offline. Formal, informal. Narnia, the real world. The longer the stay in Narnia, the more we are persuaded by it: the more we build it out by reference to its own terms, its own logical imperatives. As we flesh out the theoretical and logical implications of our models without checking them back to the territory they originally meant to map, we are in danger of amplifying inadvertent implications of the buried ''differences'' between our maps and our models. The map of theoretical physics has long since parted from the point where practical comparison is even theoretically possible. There is ''no possible real world evidence'' for string theories, multiverses, dark energy or the cosmological constant. For some of these things, we are told, ''the very act of looking for evidence'' would destroy it. This is a skeptic-defeat device as powerful as anything found in religion. These are all pure functions of extrapolation from the model. If the model is wrong, all this fantastical superstructure, also, is wrong. Yet the whole superstructure the investment in it, the careers, the billion-dollar particle accelerators, the industrial academic complex behind it — these exist in the real world. These are, seemingly, reason enough to believe, notwithstanding the apparently, unfalsifiably bonkers things these things, with a straight face, tell us must be true.
 
This is not to say any of this higher order theoretical physics is not true or correct. We laypeople have no reason to doubt the maths . But mathematics is the business of internal logical consistency. It is a closed logical system; a linguistic game. It is the language in which we articulate the model. It has nothing to say about its relationship to the territory. Maths is a language: it is not science.
 
First, be sure you know which domain is which. Are you trying to fit the world to a model — as you do when flipping a coin or rolling dice — or a model to the world? Volatility calculations, Black-Scholes formulae, You can abstract fit real world to the model a normal distribution is a 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.


====Derivatives trading====
====Derivatives trading====
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