Joan Robinson is an interesting case. Part of the question here actually is one involving language. Math in its various forms is a kind of language, maybe several kinds of language. It is completely true that virtually every mathematical argument can be expressed in verbal language. Putting it in equations or figures may be offputting to some, but is quicker and usually clearer, as verbal presentations often become muddied and ambiguous.
Joan Robinson made it a practice never to write down equations. However, she in fact made many arguments that were highly mathematical, e.g. in her discussion of the Cambridge capital theory debates. One might say her approach is better, but it was certainly mathematical, even if may not have appeared to be so on the surface. She is as guilty as the rest of us, and so was Keynes (and so was Marx too).
Another famous example was John Stuart Mill. It is a rather curious fact that he discovered nonlinear programming, a fairly high-powered mathematical technique (now rather passe) that has been much used in economics. It was in Chapter 18 on International Values (exchange rates) in one of the later editions of his Principles of Political Economy. The whole discussion is entirely verbal with nary an equation or a graph.
I view it as a matter of taste whether or not one uses the longer (and sometimes misleading) verbal presentations or uses equations. Usually I prefer to have equations, figures, and a hopefully reasonably coherent verbal explanation as well, although I cannot swear that my explanations are always as clear as they might be.
I do think that chaos theory provides certain understandings that were not there before, e.g. how something that is actually deterministic may appear to be random. This has some rather heavy duty implications, but I shall not go on about them here and now. This was not understood prior to chaos theory, although you may perhaps not consider it to be a matter of interest.
And, finally there is a much deeper and more difficult philosophical question regarding the nature of the reality of mathematical arguments. Is there a Platonic reality that math inhabits or is it all an illusion? I know Marxist physicists who nevertheless believe in the ultimate Platonic nature of math reality. This may be why in efforts to communicate with other species on other planets we send them things like the decimal expansion of pi. When Einstein wrote that E = MC squared, was he just constructing a useful statement or was he really penetrating the Mind of God (it appears that he himself thought the latter).
When a mathematician writes down the proof of a theorem that has never been proven before or even realized, has he "discovered" it or has he "invented" it? Barkley Rosser -----Original Message----- From: Doug Henwood <dhenwood at panix.com> To: lbo-talk at lists.panix.com <lbo-talk at lists.panix.com> Date: Sunday, February 18, 2001 4:34 PM Subject: Re: Volatitily as social flaring
>J. Barkley Rosser, Jr. wrote:
>
>> If you are implying that the only use of such analysis is to
>>make money, well, I am not going to do that, although there are
>>plenty of people who are using such approaches to try to do so.
>>But, frankly, I thought it would be preferable to make an ironic
>>wisecrack rather than go through all this stuff again.
>
>What I said was that I understand pursuing this sort of analysis if
>your goal was to beat the market and make money. What I didn't
>understand is what chaos theory tells you that simpler forms of
>analysis don't. I still don't.
>
>Clearly, I like social statistics. I think they can tell you a lot.
>But they're forms of description that illuminate social reality in
>ways that prose doesn't necessarily. Income distribution stats can
>tell you something about whether the rich are getting richer, and the
>poor are getting poorer. Empirical work like Card and Krueger's on
>the minimum wage is also extremely useful; it refuted, fairly
>strongly, conventional claims about the minwage's job-destroying
>powers.
>
>>I am not, however, going to get
>>into a general discussion of math in econ other than
>>to say that you really cannot seriously do econ today
>>without math.
>
>Well, yes. But that says more about how the discipline polices itself
>than anything about the intellectual contribution of math. Aside from
>serving as the token of initiation, heavy math gives the practitioner
>of conventional economics the illusion of mastery over complex
>material. It's also helped depoliticize the practice of economics and
>to isolate it from other disciplines.
>
>Somehwere Joan Robinson said that econ likes to think of itself as
>the hardest of the social sciences, but next to physics it's like
>astrology. Have things really changed that much in the 40 or so years
>since she said that?
>
>Doug
>