Re: Mirowski and critiques

[enilsson@xxxxxxxxxxxxxxx (Eric Nilsson)]

A reply from the overheated wet blanket.

J. Galbraith writes:

>Do new theories require new maths? In principle, they may not. But it seems
>quite evident that a new math can have a powerful effect on the
>development of a progressive research program around a new theory, and
>therefore new theories based on a mathematical framework, or metaphor, will
>have a powerful evolutionary advantage over non-mathematical constructs.

I think this is possibly true: the use of new math might contribute to new
thinking by permitting the thinker to not bring along (unconsciously) ideas
associated with old maths.

However, I wonder how much faith should be placed on new math as a good tool
faciliting the production of new ideas.

A number of issues come to mind, but I'll only deal with one:

Assume there are two new maths: M1 and M2.  Assume that M1 leads to new
ideas NI1 and M2 leads to new ideas NI2.  Further, assume that there is a
lag between the use of a particular math (M1 or M2) and the discovery of the
associated new ideas (NI1 or NI2).

Given that different maths lead to different new ideas (NI1 or NI2) and that
these new ideas are only discovered with a lag (tomorrow), how are we to
decide which math to select today?  We commit ourselves to a particular
methodology (M1 or M2) without knowing where it is leading us.  J. Galbraith
(if I read him correctly) seems to be saying that the newness is the key and
so it really doesn't matter whether we use M1 or M2 (and, so, whether we end
up at NI1 or NI2).  The key, he seems to be saying, is the new ideas we get
are different from neoclassical ideas.

Seeing new maths as tools to help us gain insight is one thing, but putting
so much weight on new math as a key to the development of a research program
seems to be something else.  Granting math the right to guide the
development of our thinking seems a bit much.

Eric Nilsson
Department of Economics
California State University, San Bernardino
enilsson@xxxxxxxxxxxxxxx
909-880-5564