Template:M intro design Nomological machine

Nomological
/ˈnɒməˈlɒʤɪkᵊl (adj.)
Relating to or denoting principles that resemble laws, especially ones describing brute facts of the universe: things that are not explainable by theory, but are just “so”.

A term coined by philosopher of science Nancy Cartwright to describe the limited conditions that must prevail for scientific laws to work.

“It is a fixed (enough) arrangement of components, or factors, with stable (enough) capacities that in the right sort of stable (enough) environment will, with repeated operation, give rise to the kind of regular behavior that we represent in our scientific laws”

This is fancy way of saying it’s a model. So, for example, take Newton’s second law of motion, which describes the relationship between an object’s mass and the amount of force needed to accelerate it.

This is stated as F=ma which means the force (F) acting on an object is equal to the mass (m) of an object times its acceleration (a). This is an immutable law of physics which holds in all non-relativistic, non-quantum scales.

But the conditions in which it operates — zero friction, perfect elasticity, non-intertial frame of reference — circumstances which never exist in real life. So, a rolling ball with no force acting upon it will eventually stop. A crisp packet blowing across St. Mark’s square probably does still obey Newton’s laws of motion — once you have discounted all the contaminating effects of the real world, such as friction, convection and so on — but good luck calculating its trajectory using them in any case, so really it is impossible to know. We give Newton the benefit of a large and practically untestable doubt.

Cartwright’s point is that we are not justified in extrapolating laws that hold for nomological machines to the real world: it does not follow that the behaviour of apparatus in tightly-constrained, not-naturally occurring laboratory conditions give any great insight into the mechanics of a wind-blown crisp packet, or any of the other myriad quotidian physical effects we see and take for granted.

Tumbling dice as a nomological machine

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.

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 “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 engines 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 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.

But hold map and territory — model and reality — as an immutable dualism. Map, territory. Model, reality. Online, offline. Formal, informal. Narnia, the real world. We live in the territory: to abstract from territory to map is to cross a threshold from the ordinary world to a model realm. This is a mythical, metaphorical journey. It is the same as the hero’s journey into a magical world, as outlined in Joseph Campbell’s The Hero with a Thousand Faces. But unlike the fictional archetype, the magical model world 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. The longer we stay in Narnia, the more we fall under its spell: the more we build it out; the more we extrapolate from its own terms and logical imperatives the more impressive the model world seems to be. But if we flesh out these theoretical implications without grounding them back to the territory they are meant to map, we risk amplifying limitations in the model buried differences between the map and the territory.

The map of theoretical physics has long since departed from the theoretical possibility of such a practical re-grounding. There is no possible real-world evidence for string theories, the multiverse, dark matter or the cosmological constant — the cosmological constant exists only to account for a gap in the evidence. For some of these things the very act of seeking evidence would destroy it. This is quite the skepticism-defeat device, by the way. 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.