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{{d|Nomological|/ˈnɒməˈlɒʤɪkᵊl|adj|}}
{{d|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”.
'''{{helvetica|Philosophy}}''': 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.
Philosopher [[Nancy Cartwright]] coined the term “[[nomological machine]]” to describe the limited conditions that must prevail for scientific laws to work. A nomological machine:
{{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>}}
“... 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>}}


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 bottom rungs of the profession as a means of climbing up it: it is a credentialing strategy and part of the tribal identification ritual. By the time they get high enough to influence how the upcoming generations write, they have often forgotten how to write clearly and simply themselves. Cartwright is a brilliant thinker, but her writing is dense and academic.</ref> A better name would be “regularity machine” or even just a ''model'': a device designed to generate ''regularities'' predicted by the theory by filtering out the inconvenient chattering, debris and crosstalk we get in real life, to extract the pure, untrammelled outcomes your theory predicts.
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 bottom rungs of the profession as a means of climbing up it: it is a credentialing strategy and part of the tribal identification ritual. By the time they get high enough to influence how the upcoming generations write, they have often forgotten how to write clearly and simply themselves. Cartwright is a brilliant thinker, but her writing is dense and academic.</ref> A better name would be “regularity machine” or even just a ''model'': a device designed to generate ''regularities'' predicted by the theory by filtering out the inconvenient chattering, debris and crosstalk we get in real life, to extract the pure, untrammelled outcomes your theory would predict if  the planet’s cussedly intractable ''impurities'' didn’t get in the way.


A “nomological machine” is a hermetically-sealed [[simple system]], carefully designed to generate the specific outcome a scientific theory predicts. It is not a means of proving the theory so much as ''articulating'' it.  
A “nomological machine” is a hermetically-sealed [[simple system]], carefully designed to generate the specific outcome a scientific theory predicts. It is not a means of proving the theory so much as ''articulating'' it.  
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The nomological machine might be something like this: a perfectly elastic one kilogramme ball, in a frictionless vacuum, to which we apply a force of one Newton, which therefore accelerates at 1 metre per second squared.  
The nomological machine might be something like this: a perfectly elastic one kilogramme ball, in a frictionless vacuum, to which we apply a force of one Newton, which therefore accelerates at 1 metre per second squared.  


The conditions in which this machine operates — zero friction, perfect elasticity, a non-inertial frame of reference — never prevail “in the wild”. In life, there is always friction, interference and inexactitude. We can never be sure of our measurements — was it ''exactly'' a Newton? — whether the force was applied perfectly flush, nor whether the speedo was correctly calibrated. We we expect the prediction to be “near enough” but don’t expect accuracy to the micrometre.  It is too hard to calculate, and we don’t have the data in any case.  
The conditions in which this machine operates — zero friction, perfect elasticity, Euclidean [[Space-time|spacetime]], a non-inertial frame of reference, no other interfering causal effects — never prevail “in the wild”. In practice, there is ''always'' friction, interference, [[Unknowns|unknown]]<nowiki/>s and inexactitude. We can never be sure of our measurements — was it ''exactly'' a Newton? Was the force was applied perfectly flush? Was the speedo was correctly calibrated? Being pragmatic folk, we we expect the prediction to be “near enough” but don’t expect accuracy to the micrometre.  It is too hard to calculate, and we don’t have the data in any case.  


Newton’s neat formula, with all these unrealistic conditions, is a ''nomological machine''. If the observed universe does not seem to quite come up to brief, we blame shortcomings in our observations and the lack of conditions required to satisfy the model. The nomological machine is not properly represented.  
Newton’s neat formula, with all these unrealistic conditions, is a ''nomological machine''. If the observed universe does not quite come up to brief, we put its shortcomings down to observational errors and the lack of conditions required to satisfy the model. The nomological machine is not properly represented.  


It is said that, when calculating trajectories during the Apollo programme, NASA scientists used Newtonian mechanics rather than Einstein’s more accurate calculations, because the relativistic maths was too hard to do on a slide rule, the effects would have been swamped by the margin for error in data observations, and it was safer and easier to make mid-course corrections in any case.<ref>This would please [[Gerd Gigerenzer]].</ref>
Most of the time, this does not matter. It is said that, when calculating Apollo module trajectories, NASA scientists used Newton rather than Einstein, because the relativistic maths was too hard, the effects would have been swamped by the margin for error in data observations, and it was safer and easier to just make mid-course corrections in any case.<ref>This would please [[Gerd Gigerenzer]]. There is a real lesson here for business managers techno-futurists.</ref>


A rolling ball with no force upon it will eventually stop. This is, so the theory goes, only because of the corruptions 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 — all of which are subject to their own equally scientific, equally certain laws, just in this case uncalculated — it still does, we ''assume'' obey scientific canon — but good luck proving it. For every lunar module, crisp packet, or every rolling ball, ''for every mass that ever accelerates in our imperfect human world'', we give our models the benefit of a large and practically untestable doubt. We assume that observed divergence is purely a function of lack of data and calculating wherewithal.
A rolling ball with no force acting upon it will eventually stop. This, so the theory goes, is only because of the corruptions 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 — all of which are subject to their own equally scientific, equally certain laws, just in this case uncalculated — it still does, we ''assume'' obey scientific canon — but good luck proving it. For every lunar module, crisp packet, or every rolling ball, ''for every mass that ever accelerates in our imperfect human world'', we give our models the benefit of a large and practically untestable doubt.  
 
We presume that observed divergence is purely a function of lack of data and calculating wherewithal.


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, or are we just taking this on trust? Is this a ''conjuring'' trick? To find out, read Cartwright’s book. By way of hint, it is called, {{br|How the Laws of Physics Lie}}.
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, or are we just taking this on trust? Is this a ''conjuring'' trick? To find out, read Cartwright’s book. By way of hint, it is called, {{br|How the Laws of Physics Lie}}.
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''All'' dice, to count as dice, are functionally ''identical''. Hold this thought: statistics is designed to work on populations ''that are functionally identical''.
''All'' dice, to count as dice, are functionally ''identical''. Hold this thought: statistics is designed to work on populations ''that are functionally identical''.


==== Map and territory as an immutable dualism: crossing and recrossing the threshold ====
==== Map and territory as an immutable dualism: crossing and re-crossing the threshold ====
But hold [[The map and the territory|map and territory]] — model and reality — as an immutable dualism.  [[The map and the territory|Map, territory]]. [[Models.Behaving.Badly|Model, reality]]. [[Great delamination|Online, offline]]. [[Informal systems|Formal, informal]]. Narnia, the real world.  
But hold [[The map and the territory|map and territory]] — model and reality — as an immutable dualism.  [[The map and the territory|Map, territory]]. [[Models.Behaving.Badly|Model, reality]]. [[Great delamination|Online, offline]]. [[Informal systems|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, [[metaphor]]ical journey. It is the same as the hero’s journey into a magical world, as [[Joseph Campbell]] outlined it {{br|The Hero with a Thousand Faces}}.<ref>meta-irony: Campbell’s theory is of course a model, a carefully filtered [[monomyth]]ical  model of the countless fables, legends and morality tales — all doubtless, per the model, similar but, in the analog particular, different, that he found in the oral and cultural traditions he surveyed.</ref> As we cross it we abstract from an intractable, analog actuality to a simplified digital essence, in the process giving up a colossal weight of “extraneous” information. What counts as extraneous is determined by the model. But unlike the fictional archetype, the magical model world cannot change the real world. Things that are true in the model kingdom are not necessarily true in the mundane world. Crossing back over the threshold, the lossed information is not restored. We can extrapolate, interpolate, approximate to emulate that information, and substitute something like it — in each case using the mathematical tools and amulets and swords we discovered in the magical model realm — but should we cross back to the mundane, the magic would drain away.
 
Maddeningly the magic often seems to work, sort of, in ordinary use, but it is hard to tell whether this is magic, or if it is just behaving like a normal, non-magical sword. (I once had an electric bike and it took me a week to realise the motor wasn't working. That kind of thing). It is only on those rare occasions when a normal sword won’t do — when you could really use a special sword, that  you find it isn’t magic. This can be a “Wylie Coyote hanging in mid air off the cliff” situation.


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, [[metaphor]]ical journey. It is the same as the hero’s journey into a magical world, as outlined in [[Joseph Campbell]]’s {{br|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.
There is a great temptation to steal back into the magical kingdom, where the magic works. And, the longer we stay there, in Narnia, the more we fall under its spell: the more we build out our book of magical incantations; the more we extrapolate from its own terms and logical imperatives the more impressive the model world seems to be.  But the magical world is our own creation: the spells work because we define the rules and customs and principles therein. We are building our own memory palace.


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.  
We flesh out these theoretical implications without grounding them back to the territory they were originally supposed to be representing, we risk amplifying the variance between this simple magic all world and the complex, ornery world outside. As we push back the “limitations” of the model we cannot see the buried ''differences'' between this increasingly fantastical map and the boring old 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.
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.
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 working out an internal logical consistency.<ref>Bertrand Russell explicitly set out to formulate the complete set of mathematical axioms at the beginning of the 20th century with ''Principia Mathematica'', and was fairly disappointed by Kurt Gödel proving it to be [[undecidability|logically impossible]].</ref> Mathematics is a closed logical system; a linguistic game. It is the language in which we articulate our scientific and financial models. But it is the language of science, not itself a science. It has nothing to say about the territory.  
 
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 real-world events to confirm to normal distributions, standard deviations, and confident probabilities they must meet the criteria of the [[nomological machine]]. All potential events must known and independent of each other and our observation of them.  


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.
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.
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