Re: mathematical assumptions (Physics & Economics)
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)
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)
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)
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 > 'scientific economics.' Utility became the analogue > of potential energy; and the Marginalist > Revolutionaries marched off to do battle with > classical, Historicist, and Marxian economists.
Re: mathematical assumptions (Physics & Economics)
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
