Subject: Re: Metastable oscillators
From: "Benjamin J. Tilly " <>
Date: Sun, 02 Mar 2003 21:47:35 +0500

"Stephen J. Turnbull" <> wrote:

> >>>>> "ben" == Benjamin J Tilly <" <>> writes:
>     ben> Stable versus unstable is a local criterion.  Stability does
>     ben> not imply that the system won't fall over if it is stressed
>     ben> properly, and most stable equilibria indeed can be forced to
>     ben> fall over.
> Of course you are mathematically correct.  That's why I mentioned the
> "design range."  I know that open sets are "large" but if you tell the
> engineers "it's stable as long as you stay within an open set
> containing an 0.1-sigma tolerance of the mean" you'll get some funny
> looks.

Actually engineers deal with the notion of design
tolerances all of the time.  You might need to say it in
terms that they are familiar with, but they know the

Incidental trivia.  Control theory was developed in
Russia before the US.  What made "rocket science" so hard
in the Sputnik era for the US is that we had not way to
figure out whether a rocket would fall apart other than
to build it and cross our fingers.  The Russians by
contrast could figure out what would fail on paper.  (Or
so claimed the engineer turned math prof that I took my
last differential equations course from.)

>     ben> Note that there is also no real distinction between natural
>     ben> and artificial equilibria.  Both tend to be only locally
>     ben> stable, and both routinely go through catastrophic
>     ben> adjustements.
> The distinction I made _is_ a real distinction.  Many control systems
> are intended to optimize something, and usually that requires banging
> up against some constraint.  And there's nothing that guarantees that
> a system behaves smoothly in a case where a moving constraint makes
> the current "steady state" infeasible, as far as I know.

I see your point, but don't think that it is always that
clear in practice.  Many natural phenomena have temporary
equilibria that change routinely.  People come along and
expect it to remain the same.  It doesn't.  People then
enforce the equilibrium that they want.  See the course
of the Mississippi for instance.

>     >> There is as yet not even one generally accepted dynamical model
>     >> embedding Nash equilibria.
>     ben> Is the lack of a generally accepted dynamical model evidence
>     ben> that it is hard to produce one that is mathematically
>     ben> acceptable, or evidence that a dynamic system has sufficient
>     ben> additional features that it is hard to agree on how much of
>     ben> the system can be included/excluded?
> It's evidence that it is all too easy to produce many dynamic models
> that are mathematically acceptable.  However, not even "backward
> induction" (dynamic programming) in pure strategies is entirely
> uncontroversial on behavioral grounds!

In that case then it is fine to assert the plausibility
of one when waving your hands about really general
stuff.  But the controversial issues have to be dealt
with before you can test the quantitative models that
would let us do more useful things.  Like perform
actual calculations.  (Yeah, far simpler said than done.
I know well...)

>     >> Consider: the markets where we insist on controlling prices
>     >> (labor, housing, agricultural products) are precisely with ones
>     >> with rather unsatisfactory quantity outcomes.
>     ben> Actually with agriculture we control both price and quantity
>     ben> - we guarantee a minimum quantity and then offer farmers
>     ben> direct support of some kind for the resulting low prices.
> That's just plain wrong.  We simply guarantee the farmers a high
> price.  In some cases we also subsidize the consumers, but I know of
> no program in which minimum quantities are guaranteed.  It's never
> necessary.  There are "soil bank" programs which attempt to guarantee
> a _maximum_, but they always fail when the farmers (who always feel
> they're undervalued) both sell in the market (usually, but not always,
> a different crop, often enough also soil-banked---they're the
> overpriced ones, after all) and collect their redundancy payments too.

I don't think that it is wrong in principle.  Public
policy is based on the _need_ to have minimum
quantities.  That need is met without explicitly putting
quotas in, but you can guarantee that any democracy
which failed to meet an invisible quota would take
drastic action.  (Yes, I am aware of the situation in
India right now.  That is only the second incident of
famine in a democracy that I know of since WW II.  The
other being a famine among the inuit in Canada that was
resolved by the drastic effort of directly subsidising
the whole population.)

>     ben> Predictable inflation rates may not affect the real economy
>     ben> to a first approximation, but boy oh boy do the higher order
>     ben> effects matter!  Consider the difference between inflation
>     ben> and deflation to see what I mean.
> Predictable inflation does not affect the economy in equilibrium at
> all, except to the extent that people can't do division.  Only if the
> inflation is unbalanced or unpredictable does it have effects.  This
> is actually fairly well verified empirically for countries whose
> historical inflation rates stay under 15%.
> Deflation is another matter because it is basically impossible for
> nominal interest rates to go below zero (holding cash is always an
> alternative, and if it's not, the financial system implodes).

I knew both things, hence my comment about higher order
effects that kick in when inflation is near 0.
(Deflation is merely a negative interest rate.)

>     ben> Arguing for inaction when appropriate actions seem to be
>     ben> obvious is always hard.  It becomes harder still when
>     ben> subsequent events demonstrate that action was, after all,
>     ben> justified.  See British inaction in the face of the Irish
>     ben> Potato Famine, motivated by the belief that intervention now
>     ben> would just cause a later, larger famine.  Given the
>     ben> subsequent history, this conclusion is dubious.
> Huh.  Of course you have a citation on tap?
mentions it.

The problem was a blight that wiped out the potato crop
several years running.  While Britain probably could not
have prevented it, Britain could have alleviated the
problems far more than it did.  Britain did not, in part
because of its belief in laissez-faire economics.

Remember that this was the era of Malthus.  Famines like
the one that happened in Ireland were regarded as
inevitable.  Also remember that this was the era which
was hesitant to take action to guarantee clean water
supplies because people should be free to decide whether
they wanted to pay for that.  (A policy that suddenly
reversed after Prince Albert died of typhoid...)

>     ben> Um.  Control systems are often designed to manage otherwise
>     ben> predictable natural catastrophes.
> Economic catastrophes are by definition man-made, and the goal of
> economic control systems seems never to be containment of the
> disaster, but rather to return to unsustainably high levels of pork
> for everybody.

Good point. :-)

>     ben> I am bothered by people who are so convinced of the rightness
>     ben> of their rational models that they can comfortably disregard
>     ben> the human consequences.  But I am also wise enough to not
>     ben> lightly disregard their reasoning...
> Milton Friedman, in person, even when speaking to a large audience,
> was nowhere near as smug about the human consequences as he comes off
> in his books.  He still was convinced enough of his models to advocate
> never caving in to the temptation to "do good."  I think that he's
> pretty representative of the breed.  It's the dialectical materialists
> who have historically been explicit about neglecting human consequences.

I am glad that he is not as smug as he comes across in
his writing.  I disagree with him on the value of "doing
good" if only for the personal psychological benefits...

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