Thoughts on social models

[From Bill Powers (2009.09.20.0601 MDT)]

What I've been critical of, and have called "abstraction," may really be something else. I was thinking of prices, and the ideas that were being tossed around about their significance and the rules that govern them, when I saw what I think the problem is. It's simply that prices don't adjust themselves. Somebody has to do it, and when they do it's for a reason. There are no abstract principles that directly govern the setting of prices. The agent who is adjusting prices has been missing from the discussion, as have the reasons. What is being controlled by means of varying prices? Who is the agent doing the controlling, and for what higher purpose?

The nearest I've seen to this level of treatment in economics has been in discussions of indifference curves and the idea that consumers compare everything they might buy to everything else they might buy and select the one thing that has more utility than anything else -- a most unlikely story. There are certainly evaluations going on, and even comparisons, but not that way. Again, the problem is that of leaving out the agent, the controller. Nothing happens in the economy unless it's done by a person for a reason. A person, or type of person, or active agent, has to be behind every economic action. The economy is not driven by abstractions but by human reference signals, and it's organized by human perceptions and operated by human control systems.

Also, I've been thinking nostalgically about Isaac Asimov, one of the greatest of science fiction writers, whose Foundation trilogy inspired me long ago to think of complex projects in psychology. He called his psychology "psychohistory" and presented it as a sort of huge statistical analysis of galaxy-wide events that allowed the prediction of vast social processes, but I paid little attention to that part. I wanted to be Hari Seldon, the guy who figured it all out. And the images were wonderful. At a meeting of the Second Foundationers, the discussions centered on the Prime Radiant, which was a huge wall-sized screen on which the principals of psychohistory were displayed in fine detail, with controls that allowed scrolling the diagram and magnifying parts of it to allow examination of small parts of it and the equations that represented the analysis. A MODEL OF EVERYTHING!

Now, of course, we see that sort of thing every day on the weather reports where the commentator gestures on the touch-screen and drags parts of images around and expands them with well-practiced sweeping graceful movements -- an image straight out of the Matrix movies. Asimov was, like many science-fiction writers, envisioning a future and at the same time setting it up as a reference condition. Science fiction has been full of self-fulfilling prophecies.

Thus here I am trying to get the first few parts of the Prime Radiant organized so we can start building the ultimate model of everything. It's a project sufficiently large to be interesting, and it will need the best we can do to make it work. One day we will meet in a room with one wall covered by tiny boxes and microscopic equations that represent the work of thousands of contributors, and we will make a living by telling anyone who asks, "If you choose to follow THAT policy, THIS is what will happen." And the holographic image of old Bill Powers in his wheelchair -- Hari Seldon himself -- will appear and deliver his twice-a-century prediction of the next immense problem that will require your attention.

Best,

Bill P.

[From Rick Marken (2009.09.20.1015)]

Bill Powers (2009.09.20.0601 MDT)–

What I’ve been critical of, and have called “abstraction,” may really be something else. I was thinking of prices, and the ideas that were being tossed around about their significance and the rules that govern them, when I saw what I think the problem is. It’s simply that prices don’t adjust themselves. Somebody has to do it, and when they do it’s for a reason. There are no abstract principles that directly govern the setting of prices. The agent who is adjusting prices has been missing from the discussion, as have the reasons. What is being controlled by means of varying prices? Who is the agent doing the controlling, and for what higher purpose?

I did mention the agents involved in price determination when I said that prices are determined by a bid-ask interaction between controllers who have references for what they are willing to pay and what they want to get paid. Those references are set by higher order systems in each agent; there are surely many different references (goals) that are being satisfied by the selection of references for the bidding and asking price of goods and services. I assume, based on observation, that this bid-ask interaction between control systems results in fairly stable prices for goods and services. So I am not planning to model this price adjustment control process in my model of the economy, at least not right now. I still have to see what I’m going to do with you diagrams!

The nearest I’ve seen to this level of treatment in economics has been in discussions of indifference curves and the idea that consumers compare everything they might buy to everything else they might buy and select the one thing that has more utility than anything else – a most unlikely story. There are certainly evaluations going on, and even comparisons, but not that way. Again, the problem is that of leaving out the agent, the controller. Nothing happens in the economy unless it’s done by a person for a reason.

Ah, I see you are talking about conventional economists. Yes, they leave this out. In my economic modeling controlling will be central. As I’ve said before, an economy is, for me, control writ large (with the extra added attraction of specialization of production).

Thus here I am trying to get the first few parts of the Prime Radiant organized so we can start building the ultimate model of everything. It’s a project sufficiently large to be interesting, and it will need the best we can do to make it work. One day we will meet in a room with one wall covered by tiny boxes and microscopic equations that represent the work of thousands of contributors, and we will make a living by telling anyone who asks, “If you choose to follow THAT policy, THIS is what will happen.” And the holographic image of old Bill Powers in his wheelchair – Hari Seldon himself – will appear and deliver his twice-a-century prediction of the next immense problem that will require your attention.

I’m in;-)

Best

Rick

···


Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com

[Martin Taylor 2009.09.20.14.13]

[From Bill Powers (2009.09.20.0601 MDT)]

Also, I've been thinking nostalgically about Isaac Asimov, one of the greatest of science fiction writers,

Agreed -- also a great popularizer of science.

whose Foundation trilogy inspired me long ago to think of complex projects in psychology. He called his psychology "psychohistory" and presented it as a sort of huge statistical analysis of galaxy-wide events that allowed the prediction of vast social processes, but I paid little attention to that part. I wanted to be Hari Seldon, the guy who figured it all out. And the images were wonderful. At a meeting of the Second Foundationers, the discussions centered on the Prime Radiant, which was a huge wall-sized screen on which the principals of psychohistory were displayed in fine detail, with controls that allowed scrolling the diagram and magnifying parts of it to allow examination of small parts of it and the equations that represented the analysis. A MODEL OF EVERYTHING!

I'd be very surprised indeed if Hari Seldon's model did not express a chaotic system in which there are places at which an infinitesimal change in starting point lead to dramatic differences in future development. It takes very little nonlinearity in interacting systems to generate chaos. The point of the abstraction is to discover the dynamics, not to predict the future. The dynamics allow one to see where such bifurcations may be generated, and with what parameter values. For example, tight coupling of markets might be expected to lead to dramatic bubbles and crashes. Perhaps some "grit in the machine" such as transaction taxes that decrease with the length of time an item has been held might reduce the likelihood and intensity of such events. Or perhaps not. But modelling with different parameter values for things like such taxes might allow policy makers to say that if avoiding bubbles and crashes is a reference value for the perception of market stability, then setting a tax rate of x% declining at rate y per month might be a good (or bad) policy.

That's where I see the value of modelling, not so much in the prediction of what will happen though that can sometimes be useful, but in the analysis of the dynamics of the interacting control systems.

Martin

[From Bill Powers (2009.09.19.1322 mdt)]

Martin Taylor 2009.09.20.14.13 --

I'd be very surprised indeed if Hari Seldon's model did not express a chaotic system in which there are places at which an infinitesimal change in starting point lead to dramatic differences in future development. It takes very little nonlinearity in interacting systems to generate chaos. The point of the abstraction is to discover the dynamics, not to predict the future.

This is a pre-PCT view. When you attach a control system to a chaotic system (when it's not too big to handle, like the weather), the chaos disappears. You get chaos only when the system is running open-loop. When the butterfly in the antipodes upsets the weather in England, somebody would (if they could) introduce a much more direct effect that would cancel out the small disturbances caused by the butterfly's wings. In fact I read an article about exactly this: to cut down the chaotic turbulence in a stream, which was eroding the banks, some physicists used a sensor downstream and some sort of effector upstream and stabilized the flow. Wish I could recall the reference. I also read about something similar designed to prevent cavitation.

A pole balanced on end represents the classical "hypersensitivity to initial conditions." But only if you try to stand it on end and then let go. You can easily keep the pole from toppling over by standing it on end in the palm of you hand, and actively controlling it.

That's where I see the value of modelling, not so much in the prediction of what will happen though that can sometimes be useful, but in the analysis of the dynamics of the interacting control systems.

I suppose that might be interesting to a collector of facts about system dynamics. If you couldn't make predictions that way, however, you might have trouble attracting funding.

Best,

Bill P.

[From Bill Powers (2009.09.20.1336 MDT)]

Rick Marken (2009.09.20.1015) –

RM: I did mention the agents
involved in price determination when I said that prices are determined by
a bid-ask interaction between controllers who have references for what
they are willing to pay and what they want to get paid.

BP: I think that for most consumers, the bidding and the asking are
unconnected (or at least assymetrical) transactions. The bidding by the
consumer has to do with buying goods, and the consumer’s asking for
payment comes from applying for jobs. And most goods come with a price
tag that is not, in the normal market bazaar sense, negotiable. In fact
when it comes to buying things, the seller’s main means of bargaining is
to put a new price tag on items for sale. You can’t go to WalMart and say
“I’ll give you 15 cents less that what’s on this price tag.”
Elsewhere maybe you could, but not here very often. In a sense this is
still bidding and asking, but it’s a slow process. Of course you’re
assuming a slow process, so you can probably get away with it.

I see the seller as a control system trying to sell off the produced
goods at a price greater than their cost to the seller, or in
emergencies, for as little less than the cost as possible (Cabbage Patch
dolls). If there are too few customers at the existing price, the seller
lowers the price, which is a way of enticing more buyers and lowering the
inventory. You could say it’s implied bidding and asking, although not
face-to-face.

But few consumers are askers in transactions at WalMart, unless they’re
talking with a Human Resources person and applying for a job.

RM: So I am not planning to
model this price adjustment control process in my model of the economy,
at least not right now. I still have to see what I’m going to do with
your diagrams!

BP: Well, price appears in two places in those diagrams, but I didn’t
include any control system adjusting them. In Econ005, I proposed a
manager using adjustments of price to control inventory: if the inventory
was rising, the manager would reduce prices, and if it was falling,
increase them. Considering all the ads I get with the Sunday paper in
which many companies are frantically asking me to buy one and get one
free and all those tricks, it looks to me as if real managers really do
work this way.

The four control systems in my diagram are, I think, pretty basic. But in
Econ005 I got something wrong because when prices are lowered, the
consumer doesn’t buy more. I think the problem is that I allowed the
consumer to reach his reference level for goods, so even if the price is
lowered, the consumer doesn’t want more of them. If I restrict the wages
so the consumer can never come close to correcting the error, the problem
might be solved. But I’m also thinking that there may have to be two
kinds of goods, one essential for survival and the other more optional.
Then, on a limited budget, one would have to be sure the essential goods
were obtained first, with the number of optional goods obtained then
depending on price. Essential goods have to match their reference levels;
optional goods are not as important.

BP earlier: The nearest I’ve seen to this level of treatment in
economics has been in discussions of indifference curves and the idea
that consumers compare everything they might buy to everything else they
might buy and select the one thing that has more utility than anything
else – a most unlikely story. There are certainly evaluations going on,
and even comparisons, but not that way. Again, the problem is that of
leaving out the agent, the controller. Nothing happens in the economy
unless it’s done by a person for a reason.

RM: Ah, I see you are talking about conventional economists. Yes, they
leave this out. In my economic modeling controlling will be central. As
I’ve said before, an economy is, for me, control writ large (with the
extra added attraction of specialization of production).

BP earlier: Thus here I am trying to get the first few parts of the
Prime Radiant organized

RM: I’m in;-)

BP: See you on Trantor.

This picture is from sometime in the 1960s, maybe

1970s, I think. Cabin at Mount Meeker, Colorado, with my parents
and our kids. Mary made me the shirt, which I still have. That wine looks
so good… sigh.

678e9e.jpg

Best,

Bill P.

[Martin Taylor 2009.09.20.16.58]

[From Bill Powers (2009.09.19.1322 mdt)]

Martin Taylor 2009.09.20.14.13 --

I'd be very surprised indeed if Hari Seldon's model did not express a chaotic system in which there are places at which an infinitesimal change in starting point lead to dramatic differences in future development. It takes very little nonlinearity in interacting systems to generate chaos. The point of the abstraction is to discover the dynamics, not to predict the future.

This is a pre-PCT view. When you attach a control system to a chaotic system (when it's not too big to handle, like the weather), the chaos disappears.

No, it's not a pre-PCT view. Or at least I don't think it is. I was considering precisely the case of multiple interacting control systems when I wrote that. As you so often claim, there is no such thing as a "social control system" (it's a point I disputed in the Toronto CSG meeting, but that doesn't affect my position). Yes, you can use a control system to stabilize a dynamic system that would otherwise be chaotic. At least that's true if there's only one positive Lyapunov exponent. I suspect you probably need one control system for each positive Lyapunov exponent, though I don't know that to be true. In a system with as high a dimensionality as a set of even tens of interacting control hierarchy, I suspect you would need an equivalently high-dimensional social control system to stabilize against the tendencies toward chaos that are implicit in the nonlinearities of the interactions of the control systems.

You get chaos only when the system is running open-loop.

As far as I know, you never get chaos when a system is running open-loop. Chaos requires feedback.

When the butterfly in the antipodes upsets the weather in England, somebody would (if they could) introduce a much more direct effect that would cancel out the small disturbances caused by the butterfly's wings. In fact I read an article about exactly this: to cut down the chaotic turbulence in a stream, which was eroding the banks, some physicists used a sensor downstream and some sort of effector upstream and stabilized the flow. Wish I could recall the reference. I also read about something similar designed to prevent cavitation.

And for encryption based on chaos. Yes, it's beginning to be understood as a general phenomenon (though not really by me).

I think what you are saying in what follows that you get chaos only when the system within which the chaos is manifest does not have a control system outside it to monitor and alter the feedback that leads to the divergences. That could be correct, but in the social system I am considering, the control systems (individual people) are themselves part of the feedback system that leads to the chaos. You could think of "government policy" as the output part of a complicated control system that does the monitoring and altering of the choas-causing feedback, and to some extent I think that is its function. But this does not make it a pre-PCT view to consider the chaos implicit in the interactions among many control systems controlling in a non-linear way many interacting variables.

A pole balanced on end represents the classical "hypersensitivity to initial conditions." But only if you try to stand it on end and then let go. You can easily keep the pole from toppling over by standing it on end in the palm of you hand, and actively controlling it.

That pole is not a chaotic system, The boundary between its dynamic attractor basins is smooth and well defined. Not all systems with multiple dynamic modes are chaotic.

That's where I see the value of modelling, not so much in the prediction of what will happen though that can sometimes be useful, but in the analysis of the dynamics of the interacting control systems.

I suppose that might be interesting to a collector of facts about system dynamics. If you couldn't make predictions that way, however, you might have trouble attracting funding.

The kind of predictions I would hope to be able to make are of the kind: "If you want to avoid bubbles and crashes, make the tax on profits that come from quick flips of non-tangible possessions very high, but make the tax very low on transactions that involve long-held possessions". Not of the kind: "Joe has $10,000, and if he invests it in HyperStock, he will have $20,000 in three months".

The facts about the dynamics of the system are what should direct policies that affect how best to enable people to control their various perceptions. To predict perfectly, knowing how much money everyone individually can control, would be of no value if the perception (which is what such a prediction would be) cannot be related to both a reference value and a mechanism for effecting the desired change. And contrary to Rick, you can't do this by e-coli trial and error in a system with bifurcations, if one of your changes drives the system up a dynamic branch from which a policy reversal will not allow it to recover. Understanding the dynamics, and most particularly the bifurcation points of the dynamics, is what you need for determining the mechanisms by which to effect the (political) policy decisions.

Although it's not a chaotic system, the balancing pole can illustrate the problem with Rick's idea. Suppose you have only the ability to move the base of the pole in order to keep it upright, and you make a policy change to limit the speed of this movement (or to pass the data about the pole's inclination to a committee to consider before moving the base). The pole begins to fall several degrees. Now your reversal of the policy that caused this failure will not bring the pole upright again. Sorry. The e-coli approach won't work under that kind of dynamical regime. In an evolutionary sense, the e-coli approach would work in developing policies that would keep the pole upright if there were many poles and many generations of base-movers, but it won't work when you have only one opportunity to keep the pole upright. Still less will the e-coli work in a complicated chaotic environment when you can't re-set the initial conditions. Policies that will work in one part of the dynamic space may fail utterly in another part. The issue is to be able to determine where these bifurcations might be, and what policies might serve to enlarge "favourable" parts of the dynamic space, where "favourable" is a political question of who will be best placed to control their own perceptions.

I'm violating my own precept of keeping my interventions few and short. Too bad.

Martin

I find it odd to be on the side of arguing against the value of prediction in a discussion with you, who is so often on the other side of that argument.

Martin

[From Bill Powers (2009.09.21.0825 MDT)]

Martin Taylor 2009.09.20.16.58 --

BP earlier: This is a pre-PCT view. When you attach a control system to a chaotic system (when it's not too big to handle, like the weather), the chaos disappears.

MT: No, it's not a pre-PCT view. Or at least I don't think it is. I was considering precisely the case of multiple interacting control systems when I wrote that.

BP: OK then, before we go on with that, perhaps you'd better tell me why you think there is anything chaotic about human behavior. I don't really know why anyone thinks there is chaos in the brain, anyway -- my impression has been that the people who say that are just saying, in a fancy way, that that they don't understand what they're seeing. It's like saying a coastline is fractal. It takes a very generous imagination to conclude that coastlines look the same at all scales, and I think it takes the same thing to see chaos in the brain. But more to the point, what does it have to do with behavior? I don't see any chaos there.

BP earlier: You get chaos only when the system is running open-loop.

MT: As far as I know, you never get chaos when a system is running open-loop. Chaos requires feedback.

BP: Sorry, you're right. You need some sort of nonlinear oscillator, and that requires positive feedback. But control systems don't use positive feedback. Are you talking about malfunctioning control systems?

BP earlier: A pole balanced on end represents the classical "hypersensitivity to initial conditions." But only if you try to stand it on end and then let go. You can easily keep the pole from toppling over by standing it on end in the palm of you hand, and actively controlling it.

MT: That pole is not a chaotic system, The boundary between its dynamic attractor basins is smooth and well defined. Not all systems with multiple dynamic odes are chaotic.

BP: Yes, I understand that. I was referring to the hypersensitivity phenomenon, which seems to be a feature of chaotic systems but not only of such systems. I was illustrating how a control system can stabilize another system which, by itself, is unstable.

MT: The kind of predictions I would hope to be able to make are of the kind: "If you want to avoid bubbles and crashes, make the tax on profits that come from quick flips of non-tangible possessions very high, but make the tax very low on transactions that involve long-held possessions". Not of the kind: "Joe has $10,000, and if he invests it in HyperStock, he will have $20,000 in three months".

So you're talking about a prediction of the effect of applying negative feedback control to an otherwise unstable system. So am I, or I would hope to be able to do that some day.

The facts about the dynamics of the system are what should direct policies that affect how best to enable people to control their various perceptions. To predict perfectly, knowing how much money everyone individually can control, would be of no value if the perception (which is what such a prediction would be) cannot be related to both a reference value and a mechanism for effecting the desired change. And contrary to Rick, you can't do this by e-coli trial and error in a system with bifurcations, if one of your changes drives the system up a dynamic branch from which a policy reversal will not allow it to recover. Understanding the dynamics, and most particularly the bifurcation points of the dynamics, is what you need for determining the mechanisms by which to effect the (political) policy decisions.

I'm not really interested in either kind of predictions in the economic model, at least not at this stage. Anyway, you're assuming that the economic system is chaotic, and I haven't seen any evidence of that yet. I don't see anything chaotic in human behavior, either, though there do seem to be random components in it. But as I said in the "Essay on the Obvious," there is so much regularity and predictability in human behavior lying right on the surface that I don't see any advantage in ignoring that and digging down to find faint suggestions of mostly unpredictable regularities. I think we need to deal with the most obvious aspects of behavior first, as long as they're there for the taking. When we run out of that sort of thing perhaps we might want to recycle the mine tailings. But trying to deal with the subtle hints first is just going to make us look foolish when we realize what was really going on.

Best,

Bill P.

[Martin Taylor 2009.09.21.11.06]

[From Bill Powers (2009.09.21.0825 MDT)]

Martin Taylor 2009.09.20.16.58 --

BP earlier: This is a pre-PCT view. When you attach a control system to a chaotic system (when it's not too big to handle, like the weather), the chaos disappears.

MT: No, it's not a pre-PCT view. Or at least I don't think it is. I was considering precisely the case of multiple interacting control systems when I wrote that.

BP: OK then, before we go on with that, perhaps you'd better tell me why you think there is anything chaotic about human behavior.

I think you misunderstand. I have been talking about the high probability that chaotic dynamics is inherent in the interactions of large numbers of independent non-linear control systems, not in the dynamic behaviour of a single hierarchic control system.

Martin
(There. I managed to keep one message short!)