Re: mathematical assumptions (Physics & Economics)

[Daljit Dhadwal]

The issue of whether the assumptions made in economics or any other 
science are "reasonable" depends upon one's philosophy of science. If 
"reasonable" is taken to mean realistic or plausible then the answer is no. 
Almost all models in Econ are set up as constrained maximization problems, 
and it's obvious that people don't figure out lagrangeans in their heads 
when they're deciding how many apples to buy at the market. Most 
economists and physicists fall into the instrumentalist/operationalist 
camp in the philosophy of science. This is the belief that theories are 
neither true nor false, but simply tools (i.e., instruments) used to make 
predictions about reality. Under this view, any assumption is reasonable 
as long as it allows one to make correct predictions. e.g., concave 
indifference curves predict that people will spend all of their income on 
one good, and we generally don't see that in real life and so concavity is 
an unreasonable assumption. The issue of whether an assumption is ad hoc 
under the instrumentalist worldview is mostly an aesthetic criterion. Since 
one can assume whatever one likes in order to generate predictions, there is no 
way to judge whether the assumption is ad hoc. Every discipline develops 
its own conventions about things like what constitutes "good" modeling 
techniques and what level of statistical significance is sufficient for 
counting something as a correct prediction. I think where economists and 
other instrumentalists get into trouble is when they decide that because 
their model makes correct predictions then the assumptions that they used 
to generate those predictions must be "reasonable" in the sense of 
representing reality. This is called the pragmatic conception of truth-- if it
works it must be true. This is when you get economists arguing 
absurd things like that people really, truly are rational maximizers or 
can actually form rational expectations.

Daljit Dhadwal

> I guess what I was origially wondering was not "Is math appropriate?" 
> But rather, given that math is appropriate, are the
> assumptions about rationality, preferences, convexity,
> continuity, inter alia, as well as some of the more ad
> hoc assumptions of many macro models as reasonable as
> the assumtions made in the king of all sciences? 

Re: mathematical assumptions (Physics & Economics)

[Christopher Auld]

On Wed, 13 Feb 2002, john hull wrote:

> Newtonian physics. However, if preferences are
> constant over time, then the conservation rule should
> be satisfied, right?  I think that is my weakest link.

Not quite.  The "conservation rule" Mirowski talks about
is the same beast as the integrability condition discussed
in any advanced micro text.  It is satisfied if consumer
choice is consistent with the Strong Axiom of Revealed
Preference.  But there exist rational preference relations
that do not satisfy the integrability/SARP condition.


Cheers,

Chris Auld  
Department of Economics 
University of Calgary
[EMAIL PROTECTED]

RE: mathematical assumptions (Physics & Economics)

[Robin Hanson]

Walt Warnick wrote:
>... the business cycle behaves strikingly like an automatic control
>system that has a positive feedback loop and damping. ...
>The parallel goes further. ... a stable automatic control system involving
>continuous feedback can become unstable if that same feedback is, instead,
>sampled.

Control theory is an application of single-agent decision theory, and since
economics is basically multi-agent decision theory, I'd say control theory
is closer to economics than to physics.  Of course one often needs to know
some details of the physics of the situation one is controlling, but usually
control problems are dominated by decision theory issues, not physics issues.


Robin Hanson  [EMAIL PROTECTED]  http://hanson.gmu.edu
Asst. Prof. Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-
703-993-2326  FAX: 703-993-2323

RE: mathematical assumptions (Physics & Economics)

[Warnick, Walter]

I am 1) an engineer by training with some heavy duty physics thrown in, and
2) a known economist sympathizer.  If there is a useful parallel between
conservation of energy and some principle of economics, I am not aware of
what that might be.

On the other hand, there is a lot of useful analysis in physics and
engineering that can be done without invoking conservation of energy.  Even
if a parallel to conservation of energy does not exist in economics, there
may still be other useful parallels to draw.

For example, the business cycle behaves strikingly like an automatic control
system that has a positive feedback loop and damping.  (By the way, analysis
of automatic control systems does not invoke conservation of energy.
Rather, the assumption is that an unlimited external source of energy is
always available--sort of like Simon's concepts from the Ultimate Resource.)
Elegant mathematical techniques (Laplace transform) are used to analyze
automatic control systems.

The parallel goes further.  A subclass of automatic control systems are
those that employ sampled feedback loops, rather than continuous feedback
loops.  It is well known that a stable automatic control system involving
continuous feedback can become unstable if that same feedback is, instead,
sampled.  The longer the sampling interval, the greater the potential for
introducing instability.  The potential instability derives from imperfect
knowledge between samples.  Other elegant mathematical techniques (not
Laplace transform) are used to analyze automatic control systems with
sampled feedback.  The parallel with economics is Von Mises' notion that the
business cycle is driven by imperfect knowledge.

Walt Warnick

-Original Message-
From: john hull [mailto:[EMAIL PROTECTED]]
Sent: Wednesday, February 13, 2002 8:46 PM
To: [EMAIL PROTECTED]
Subject: Re: mathematical assumptions (Physics & Economics)


Thank you all for your comments and suggestions.  I
appreciate them very much!  I just re-read the rules
for the armchair mailing list, and I hope this is not
too methodological or whatever.  Sorry about that!

I actually have read Mirowski's "More Heat Than Light"
and found it quite informative.  Interestingly,
Richard Feynman, of all people, blew Mirowski's
arguments out of the water (ex ante) with an almost
throw-away line in his Physics Lectures.  He asked
himself why was math an appropriate tool for studying
physical models.  His answer was merely that math is a
pre-packaged, internally consistent logic that
physicists can apply to the aformentioned models. 
Hmm.  By extension, that reasoning seemed to apply to
economics quite well.  It seemed to me that Mirowski's
thesis was that math, specifically the math used in
neo-classical economics, is an inappropriate tool for
economic study because economics lacks a conservation
rule analogous to the conservation of energy in
Newtonian physics. However, if preferences are
constant over time, then the conservation rule should
be satisfied, right?  I think that is my weakest link.

I hope that last paragraph hasn't made me to appear a
bonehead answering his own questions.  (I'm boneheaded
enough without doing that.)  I guess what I was
origially wondering was not "Is math appropriate?" 
But rather, given that math is appropriate, are the
assumptions about rationality, preferences, convexity,
continuity, inter alia, as well as some of the more ad
hoc assumptions of many macro models as reasonable as
the assumtions made in the king of all sciences? 
Obviously, I'm not really sure how to phrase the
question in the most clear manner.  I apologize for
that.

If this question is inappropriate for this forum,
please let me know.

Thanks again,
jsh 



--- "Seth H. Giertz" <[EMAIL PROTECTED]> wrote:
> I just checked out *More Heat Than Light: Economics
> as
> Social Physics:  Physics as Nature's Economics*,
> also
> by Philip Mirowski.
> 
> Here are a couple of quotes from the introduction
> that
> I found interesting:
> 
> "One rapidly discovers that the resemblances of the
> theories [of physics and economics] are uncanny, and
> one reason they are uncanny is because the
> progenitors
> of neoclassical economic theory boldly copied the
> reigning physical theories in the 1870s.
> ...Neoclassicals did not imitate physics in a
> desultory or superficial manner; no they copied
> their
> models mostly term for term and symbol for symbol,
> and
> said so.
> 
> "Neoclassical economics made savvy use of the
> resonances between body, motion, and values by
> engaging in a brazen daylight robbery:  The
> Marginalists appropriated the mathematical
> formalisms
> of mid-nineteenth century energy physics, ..., made
> them their own by changing the labels on the
> variables, and then trumpeted the triumph of a truly
> &

Re: mathematical assumptions (Physics & Economics)

[Robin Hanson]

As an economist who was once a physicist, I have to say that
there is quite a lot of difference between the kinds of
math economics and physics typically use.  Sure, they both
use calculus, but beyond that the similarities are scarce.

Differential equations across space and time dominate physics,
but have almost no place in economics.  In physics one almost
always knows the specific form of a function or differential
equation, while in economics one typically does not know the
specific functional forms, and so must reason in terms of
"convexity" etc., concepts that are foreign to most physicists.
Math of maximization dominates economics, but has only a side
supporting role in physics.  When physicists do maximize,
they almost never deal with non-interior solutions.  While
some basic concepts of information and probability are used in
thermodynamics, economists deal with these issues in far more
detail.


Robin Hanson  [EMAIL PROTECTED]  http://hanson.gmu.edu
Asst. Prof. Economics, George Mason University
MSN 1D3, Carow Hall, Fairfax VA 22030-
703-993-2326  FAX: 703-993-2323

Re: mathematical assumptions (Physics & Economics)

[john hull]

Thank you all for your comments and suggestions.  I
appreciate them very much!  I just re-read the rules
for the armchair mailing list, and I hope this is not
too methodological or whatever.  Sorry about that!

I actually have read Mirowski's "More Heat Than Light"
and found it quite informative.  Interestingly,
Richard Feynman, of all people, blew Mirowski's
arguments out of the water (ex ante) with an almost
throw-away line in his Physics Lectures.  He asked
himself why was math an appropriate tool for studying
physical models.  His answer was merely that math is a
pre-packaged, internally consistent logic that
physicists can apply to the aformentioned models. 
Hmm.  By extension, that reasoning seemed to apply to
economics quite well.  It seemed to me that Mirowski's
thesis was that math, specifically the math used in
neo-classical economics, is an inappropriate tool for
economic study because economics lacks a conservation
rule analogous to the conservation of energy in
Newtonian physics. However, if preferences are
constant over time, then the conservation rule should
be satisfied, right?  I think that is my weakest link.

I hope that last paragraph hasn't made me to appear a
bonehead answering his own questions.  (I'm boneheaded
enough without doing that.)  I guess what I was
origially wondering was not "Is math appropriate?" 
But rather, given that math is appropriate, are the
assumptions about rationality, preferences, convexity,
continuity, inter alia, as well as some of the more ad
hoc assumptions of many macro models as reasonable as
the assumtions made in the king of all sciences? 
Obviously, I'm not really sure how to phrase the
question in the most clear manner.  I apologize for
that.

If this question is inappropriate for this forum,
please let me know.

Thanks again,
jsh 



--- "Seth H. Giertz" <[EMAIL PROTECTED]> wrote:
> I just checked out *More Heat Than Light: Economics
> as
> Social Physics:  Physics as Nature’s Economics*,
> also
> by Philip Mirowski.
> 
> Here are a couple of quotes from the introduction
> that
> I found interesting:
> 
> “One rapidly discovers that the resemblances of the
> theories [of physics and economics] are uncanny, and
> one reason they are uncanny is because the
> progenitors
> of neoclassical economic theory boldly copied the
> reigning physical theories in the 1870s.
> ...Neoclassicals did not imitate physics in a
> desultory or superficial manner; no they copied
> their
> models mostly term for term and symbol for symbol,
> and
> said so.
> 
> “Neoclassical economics made savvy use of the
> resonances between body, motion, and values by
> engaging in a brazen daylight robbery:  The
> Marginalists appropriated the mathematical
> formalisms
> of mid-nineteenth century energy physics, ..., made
> them their own by changing the labels on the
> variables, and then trumpeted the triumph of a truly
> ‘scientific economics.’  Utility became the analogue
> of potential energy; and the Marginalist
> Revolutionaries marched off to do battle with
> classical, Historicist, and Marxian economists. 
> Unfortunately, there was one little oversight:  The
> neoclassicals had neglected to appropriate the most
> important part of the formalism, ... namely, the
> conservation of energy.” (pp 3 & 9)
> 
> >From skimming a couple of later chapters, it seems
> Mirowski also finds a close relationship with later
> 20th century economics and 19th century physics. 
> (He
> notes that on the surface Samuelson draws an
> analogous
> relationship between modern physics and modern
> economics, but when Mirowski digs deeper, he finds
> it
> to be simply a variation of 19th century physics in
> disguise.)  He seems to credit/blame Samuelson for
> much of the 20th century development – at least
> that’s
> what I gathered from reading a few pages here and
> there.  
> 
> Seth Giertz
> 
> --- "Ole J. Rogeberg" <[EMAIL PROTECTED]>
> wrote:
> > I can give you a completely opposite reference :-)
> > 
> > Philip Mirowski, in the Cambridge Journal of
> > Economics, nr. 8, 1984, pp. 
> > 361-379 has an article "Physics and the
> marginalist
> > revolution," where he 
> > argues that the similarities between the physics
> of
> > the 1800s and the 
> > economics of the 20th century results from
> > economists taking the 
> > mathematical models then in vogue and
> reinterpreting
> > them in economic 
> > terms. "Neoclassical economics is bowdlerised
> > nineteenth century physics." 
> > The second part of his argument is that this is
> not
> > reasonable.
> > 
> > The article was fun, whatever one may think of the
> > conclusions. Apparently, 
> > this is a major theme of Mirowski. I gather that
> > he's written on this 
> > subject elsewhere too. And been strongly
> criticised
> > by others, of course.
> > 
> > Ole
> > 
> > At 09:25 11.02.2002 -0800, you wrote:
> > >Dear all,
> > >
> > >I once heard about a paper by a physcist who
> > >juxtaposed the mathematical assumptions in
> > economics
> > 

Re: mathematical assumptions (Physics & Economics)

[Seth H. Giertz]

I just checked out *More Heat Than Light: Economics as
Social Physics:  Physics as Nature’s Economics*, also
by Philip Mirowski.

Here are a couple of quotes from the introduction that
I found interesting:

“One rapidly discovers that the resemblances of the
theories [of physics and economics] are uncanny, and
one reason they are uncanny is because the progenitors
of neoclassical economic theory boldly copied the
reigning physical theories in the 1870s.
...Neoclassicals did not imitate physics in a
desultory or superficial manner; no they copied their
models mostly term for term and symbol for symbol, and
said so.

“Neoclassical economics made savvy use of the
resonances between body, motion, and values by
engaging in a brazen daylight robbery:  The
Marginalists appropriated the mathematical formalisms
of mid-nineteenth century energy physics, ..., made
them their own by changing the labels on the
variables, and then trumpeted the triumph of a truly
‘scientific economics.’  Utility became the analogue
of potential energy; and the Marginalist
Revolutionaries marched off to do battle with
classical, Historicist, and Marxian economists. 
Unfortunately, there was one little oversight:  The
neoclassicals had neglected to appropriate the most
important part of the formalism, ... namely, the
conservation of energy.” (pp 3 & 9)

>From skimming a couple of later chapters, it seems
Mirowski also finds a close relationship with later
20th century economics and 19th century physics.  (He
notes that on the surface Samuelson draws an analogous
relationship between modern physics and modern
economics, but when Mirowski digs deeper, he finds it
to be simply a variation of 19th century physics in
disguise.)  He seems to credit/blame Samuelson for
much of the 20th century development – at least that’s
what I gathered from reading a few pages here and
there.  

Seth Giertz

--- "Ole J. Rogeberg" <[EMAIL PROTECTED]>
wrote:
> I can give you a completely opposite reference :-)
> 
> Philip Mirowski, in the Cambridge Journal of
> Economics, nr. 8, 1984, pp. 
> 361-379 has an article "Physics and the marginalist
> revolution," where he 
> argues that the similarities between the physics of
> the 1800s and the 
> economics of the 20th century results from
> economists taking the 
> mathematical models then in vogue and reinterpreting
> them in economic 
> terms. "Neoclassical economics is bowdlerised
> nineteenth century physics." 
> The second part of his argument is that this is not
> reasonable.
> 
> The article was fun, whatever one may think of the
> conclusions. Apparently, 
> this is a major theme of Mirowski. I gather that
> he's written on this 
> subject elsewhere too. And been strongly criticised
> by others, of course.
> 
> Ole
> 
> At 09:25 11.02.2002 -0800, you wrote:
> >Dear all,
> >
> >I once heard about a paper by a physcist who
> >juxtaposed the mathematical assumptions in
> economics
> >with the mathematical assumptions in physics.
> >Evidently the author found the assumptions in
> >economics to be quite reasonable.  I've never been
> >able to locate it.  Is anybody familiar with such a
> >work, or anything similar?
> >
> >Curiously,
> >jsh
> >
> >__
> >Do You Yahoo!?
> >Send FREE Valentine eCards with Yahoo! Greetings!
> >http://greetings.yahoo.com
> 


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