I think this is spot on - pre-1945 economists did think about equilibrium as the limiting point of some causal process, but as equilibria began to be described using increasingly complicated mathematics, they gradually gave up on describing the adjustment process, partly because it became hard to do so with the same level of mathematical sophistication. The result is that modern economics absolutely does think in terms of equilibrium without describing any process which reaches an equilibrium state, except perhaps in a handwaving fashion. If you'll forgive the self-promotion I have a recent paper about the problems with this (which incidentally cites this 'stack on p30!), very much in the spirit of Fisher's book: https://www.newyorkfed.org/research/staff_reports/sr1093
Thanks! Since alex mentioned Grossman-Stiglitz in a comment on your last post - section 5 of the paper discusses a particularly extreme example of the difference between equilibrium and homeostasis. Rational expectations models can have equilibria in which everyone learns the value of an exogenous random 'fundamental' by observing other people's behavior, even though *no-one* starts out with *any* information about this variable. Obviously no process can lead to this outcome, however resourceful and responsive the stylites are! But it's a consistent equilibrium: *if* everyone else knew the fundamental, I could observe it by watching them. A bit troubling if one wanted to use these models to think about how economic systems aggregate and transmit information...
The post leads me to recall an old book by MIT's Frank Fisher titled, "Disequilibrium Foundations of Equilibrium Economics." This was his attempt to apply the maths to the pths taken outside of equilibrium.
heh! I guess, "when you start taking them seriously"!
this is one of the rabbit holes which Nick Humphreys at Profile did such a good job steering me out of, but it's one of the big big themes of philosophy from Plato's Cave to Wittgenstein - the extent to which all you can ever talk about is representations of reality, but in order to live a practical life, you have to act as if the representations are the reality. IMO it's a shame that philosophers don't engage more with economics, business and management, because lots of these questions which seem forbiddingly abstract when you're talking about qualia or what it's like to be a bat, become terribly clear and real when you're talking about the extent to which a set of accounts represents the business reality.
One of the defining steps here is "intention/choice."
Equilibrium is a metaphor of physical systems, which will go the way the rules go.
Homeostasis is a metaphor of control systems, which go the way the control subsystems go - if they are simple subsystems, it simple, if they are complex, we have the possibility of the next concept being invoked. I don't know what word we have (is there one? Cyberstasis?) for the next level up, where choices are being made (either inside the control subsystem - one Stylite says "bugger this, I'm off to watch the football" and the ball is on the ground) or because someone decided to change the subsystem goals - maybe the blokes on poles could choose to hold the ball so high the cat can't get at it? Or that between them, it should for this year always bias to the right (as we look at the picture) to be followed by a shift to the left after Jan 2025.
In terms of the language and metaphor here -- I'm not that familiar with the economic or control theory side -- are you trying to distinguish between "static equilibrium" (e.g. an object at rest due to the balance of mechanical forces acting on it, like a lamp on its base on a table top, which is stable, or a pencil balanced on its tip, which is unstable) and "dynamic equilibrium" (e.g. a chemical reaction in which the forward and backward reactions occur at the same rate)?
In the former I would think of the system at hand being at single fixed point in its phase/state space, which is either stable (small perturbations result in the system eventually returning to the fixed point) or unstable (small perturbations drive the system away from the fixed point). In the latter I would think of the system being in a limit cycle in state space, which is again either stable or unstable, and I would think homeostasis in the biological sense corresponds to a kind of stable limit cycle.
one of the discussion items I am currently working on is the relationship between the place of ratio/reason in the world of analogies, and metaphor, where one of the ratios reaches zero (ratio/reason = zero then> metaphor wins, and if metaphor = zero, metaphor doesn't care), as if one has eaten the other, digested it, grokked, its very complex and I only have metpahors, but how do I go back? Phase/scale seems to re-assert numbers, but it is never clear.
Great post. I'd take my comment a step further. Mathematical models of human systems are clearly problematic, but the shift from math to metaphor is intrinsic to all applied mathematics. One of my favorite examples is from Nancy Cartwright: Newton's laws will give you a good prediction of where a bowling ball will land when you drop it off of a building. But what can they tell you about a dollar bill dropped from the same rooftop?
One of these days, I hope to write a book about the math-metaphor spectrum.
I think this is spot on - pre-1945 economists did think about equilibrium as the limiting point of some causal process, but as equilibria began to be described using increasingly complicated mathematics, they gradually gave up on describing the adjustment process, partly because it became hard to do so with the same level of mathematical sophistication. The result is that modern economics absolutely does think in terms of equilibrium without describing any process which reaches an equilibrium state, except perhaps in a handwaving fashion. If you'll forgive the self-promotion I have a recent paper about the problems with this (which incidentally cites this 'stack on p30!), very much in the spirit of Fisher's book: https://www.newyorkfed.org/research/staff_reports/sr1093
promote away! promote more! I love this stuff
Thanks! Since alex mentioned Grossman-Stiglitz in a comment on your last post - section 5 of the paper discusses a particularly extreme example of the difference between equilibrium and homeostasis. Rational expectations models can have equilibria in which everyone learns the value of an exogenous random 'fundamental' by observing other people's behavior, even though *no-one* starts out with *any* information about this variable. Obviously no process can lead to this outcome, however resourceful and responsive the stylites are! But it's a consistent equilibrium: *if* everyone else knew the fundamental, I could observe it by watching them. A bit troubling if one wanted to use these models to think about how economic systems aggregate and transmit information...
The post leads me to recall an old book by MIT's Frank Fisher titled, "Disequilibrium Foundations of Equilibrium Economics." This was his attempt to apply the maths to the pths taken outside of equilibrium.
I've read one or two things by FF and I'm not surprised, his stuff on general equilibrium was a real revelation for me.
Fisher also wrote this short essay which effectively summarizes his seminal book and other work on the topic: https://web.archive.org/web/20120725032805/https://economics.mit.edu/files/6988
I think that might have been the one that stuck in my mind so much, it's very good
When do metaphors become mental prisons?
heh! I guess, "when you start taking them seriously"!
this is one of the rabbit holes which Nick Humphreys at Profile did such a good job steering me out of, but it's one of the big big themes of philosophy from Plato's Cave to Wittgenstein - the extent to which all you can ever talk about is representations of reality, but in order to live a practical life, you have to act as if the representations are the reality. IMO it's a shame that philosophers don't engage more with economics, business and management, because lots of these questions which seem forbiddingly abstract when you're talking about qualia or what it's like to be a bat, become terribly clear and real when you're talking about the extent to which a set of accounts represents the business reality.
One of the defining steps here is "intention/choice."
Equilibrium is a metaphor of physical systems, which will go the way the rules go.
Homeostasis is a metaphor of control systems, which go the way the control subsystems go - if they are simple subsystems, it simple, if they are complex, we have the possibility of the next concept being invoked. I don't know what word we have (is there one? Cyberstasis?) for the next level up, where choices are being made (either inside the control subsystem - one Stylite says "bugger this, I'm off to watch the football" and the ball is on the ground) or because someone decided to change the subsystem goals - maybe the blokes on poles could choose to hold the ball so high the cat can't get at it? Or that between them, it should for this year always bias to the right (as we look at the picture) to be followed by a shift to the left after Jan 2025.
In terms of the language and metaphor here -- I'm not that familiar with the economic or control theory side -- are you trying to distinguish between "static equilibrium" (e.g. an object at rest due to the balance of mechanical forces acting on it, like a lamp on its base on a table top, which is stable, or a pencil balanced on its tip, which is unstable) and "dynamic equilibrium" (e.g. a chemical reaction in which the forward and backward reactions occur at the same rate)?
In the former I would think of the system at hand being at single fixed point in its phase/state space, which is either stable (small perturbations result in the system eventually returning to the fixed point) or unstable (small perturbations drive the system away from the fixed point). In the latter I would think of the system being in a limit cycle in state space, which is again either stable or unstable, and I would think homeostasis in the biological sense corresponds to a kind of stable limit cycle.
one of the discussion items I am currently working on is the relationship between the place of ratio/reason in the world of analogies, and metaphor, where one of the ratios reaches zero (ratio/reason = zero then> metaphor wins, and if metaphor = zero, metaphor doesn't care), as if one has eaten the other, digested it, grokked, its very complex and I only have metpahors, but how do I go back? Phase/scale seems to re-assert numbers, but it is never clear.
https://whyweshould.loofs-samorzewski.com/reaction-review-of-the-janus-point.html
Is it true that there are no exceedingly complex deterministic systems?
Great post. I'd take my comment a step further. Mathematical models of human systems are clearly problematic, but the shift from math to metaphor is intrinsic to all applied mathematics. One of my favorite examples is from Nancy Cartwright: Newton's laws will give you a good prediction of where a bowling ball will land when you drop it off of a building. But what can they tell you about a dollar bill dropped from the same rooftop?
One of these days, I hope to write a book about the math-metaphor spectrum.
I have to assume and hope you're familiar with Steve Keen and his blog here on Substack (link later). Exactly relevant to this post.
https://open.substack.com/pub/profstevekeen?utm_source=share&utm_medium=android&r=109of
Steve Keen, Building a New Economics (link when stupid app lets me paste it)