Template:M intro design Nomological machine: Difference between revisions

From The Jolly Contrarian
Jump to navigation Jump to search
No edit summary
No edit summary
Line 2: Line 2:
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”.
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.
A “[[nomological machine]]” is a term coined by philosopher of science [[Nancy Cartwright]] to describe the limited conditions that must prevail for scientific laws to work.
{{quote|
{{quote|
“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” <ref>{{author|Nancy Cartwright}}. {{br|The Dappled World – A Study of the Boundaries of Science}}. (Cambridge University Press, 1999)</ref>}}
“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” <ref>{{author|Nancy Cartwright}}. {{br|The Dappled World – A Study of the Boundaries of Science}}. (Cambridge University Press, 1999)</ref>}}


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.  
As a piece of marketing, this is a ''terrible'', obscurant — if technically accurate — label.<ref>Like academics, lawyers learn to use the arcane vocabulary of the [[power structure]] while on the lower rungs of the profession: it is a credentialing strategy and part of the tribal identification ritual. By the time they get high enough on the latter to influence how their underlings write they have often lost the ability to write clearly and simply. Cartwright is a brilliant thinker, but her writing is dense and hyper-academic.</ref> A better name would be “regularity machine”: a device designed to generate ''regularities'': to winnow out any chattering and crosstalk and produce the pure, untrammeled outcomes your theory predicts.


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.  
So, for example, take Newton’s second law of motion, ''F=ma''. The ''force'' (F) acting on an object is equal to its ''mass'' (m) times its ''[[acceleration]]'' (a).  


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|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.
This is an immutable law of physics.<ref>For all non-relativistic, non-quantum scales.</ref> But the conditions in which it holds — zero friction, perfect elasticity, a non-inertial frame of reference — never prevail in “the field”. In life, there is always friction, energy loss through heat, wind, and impurity. The neat formula, with all these unrealistic conditions, is a ''nomological machine''. If the universe does not seem to obey the law, we can blame shortcomings in observed criteria. The nomological machine is not properly represented.  


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.
A rolling ball with no force upon it will eventually stop. This is, so the theory goes, only because of the corruption of reality. So too, a [[crisp packet|crisp packet blowing this way and that across St. Mark’s square]]. Once you have discounted all the contaminating effects of the real world; the friction, convection, dust, drafts and so on, it still does, we ''assume'' obey Newton’s laws — but good luck proving that out. For every crisp packet, for every rolling ball, ''for every mass that ever accelerates in our imperfect human world'', we give Newton the benefit of a large and practically untestable doubt.


==== Tumbling dice as a nomological machine ====
But are we justified in extrapolating laws that hold for nomological machines to the real world? Do these imaginary regularity generators ''really'' tell us how wind-blown crisp packets, or any of the other myriad quotidian physical effects we see and take for granted every day, behave? Is this a ''conjuring'' trick?
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''.   
==== Tumbling dice as nomological machines ====
When we calculate probabilities — when we roll dice — we are in situations of ''known risk''. Even though their 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. We do ''not'' average the performance all dice, some of which yield probabilities of ⅐, others ⅕ and come out at about ⅙. ''Every individual die'' must, within minimal tolerance, yield a ⅙ probability. ''All'' dice must be 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]]”
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 illustrates 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.”  
 
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''.
But if, over time, our dice ''don’t'' yield the outcomed expect, we don’t conclude our probability calculations are 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.
The [[The map and the territory|“map” and “territory”]] are, thus, transposed: where usually the map 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.  
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 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.
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.

Revision as of 18:09, 16 January 2024

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 “nomological machine” is 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” [1]

As a piece of marketing, this is a terrible, obscurant — if technically accurate — label.[2] A better name would be “regularity machine”: a device designed to generate regularities: to winnow out any chattering and crosstalk and produce the pure, untrammeled outcomes your theory predicts.

So, for example, take Newton’s second law of motion, F=ma. The force (F) acting on an object is equal to its mass (m) times its acceleration (a).

This is an immutable law of physics.[3] But the conditions in which it holds — zero friction, perfect elasticity, a non-inertial frame of reference — never prevail in “the field”. In life, there is always friction, energy loss through heat, wind, and impurity. The neat formula, with all these unrealistic conditions, is a nomological machine. If the universe does not seem to obey the law, we can blame shortcomings in observed criteria. The nomological machine is not properly represented.

A rolling ball with no force upon it will eventually stop. This is, so the theory goes, only because of the corruption of reality. So too, a crisp packet blowing this way and that across St. Mark’s square. Once you have discounted all the contaminating effects of the real world; the friction, convection, dust, drafts and so on, it still does, we assume obey Newton’s laws — but good luck proving that out. For every crisp packet, for every rolling ball, for every mass that ever accelerates in our imperfect human world, we give Newton the benefit of a large and practically untestable doubt.

But are we justified in extrapolating laws that hold for nomological machines to the real world? Do these imaginary regularity generators really tell us how wind-blown crisp packets, or any of the other myriad quotidian physical effects we see and take for granted every day, behave? Is this a conjuring trick?

Tumbling dice as nomological machines

When we calculate probabilities — when we roll dice — we are in situations of known risk. Even though their 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. We do not average the performance all dice, some of which yield probabilities of ⅐, others ⅕ and come out at about ⅙. Every individual die must, within minimal tolerance, yield a ⅙ probability. All dice must be 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

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 illustrates 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.”

But if, over time, our dice don’t yield the outcomed expect, we don’t conclude our probability calculations are wrong: we throw out the defective dice.

The “map” and “territory” are, thus, transposed: where usually the map 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 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.

  1. Nancy Cartwright. The Dappled World – A Study of the Boundaries of Science. (Cambridge University Press, 1999)
  2. Like academics, lawyers learn to use the arcane vocabulary of the power structure while on the lower rungs of the profession: it is a credentialing strategy and part of the tribal identification ritual. By the time they get high enough on the latter to influence how their underlings write they have often lost the ability to write clearly and simply. Cartwright is a brilliant thinker, but her writing is dense and hyper-academic.
  3. For all non-relativistic, non-quantum scales.