[Humanist] 22.610 an exemplary approach to a difficult job
Humanist Discussion Group
willard.mccarty at mccarty.org.uk
Wed Mar 11 07:27:11 CET 2009
Humanist Discussion Group, Vol. 22, No. 610.
Centre for Computing in the Humanities, King's College London
Submit to: humanist at lists.digitalhumanities.org
Date: Tue, 10 Mar 2009 12:47:59 +0000
From: Willard McCarty <willard.mccarty at mccarty.org.uk>
Subject: a recommendation
Allow me to recommend to your attention two small portions of John von
Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior,
3rd edn (Princeton, 1953), available in toto from the Internet Archive's
fine collection of texts. Many here will know that this is not a book
for the mathematically timid, but the portions of it I'm recommending
have no maths at all. These are the prefatory Technical Note (pp. ix-x)
and section 1, "The Mathematical Method in Economics", esp on the
"Difficulties of the application of the mathematical method" and
"Necessary limitations of the objectives" (pp. 3-6, mostly).
The first, technical note, is a model of how to address an audience a
significant part of which you anticipate will be ignorant of your subject or
some aspect of it but at the same time highly intelligent and eager to
learn. The authors target a reader "moderately versed in mathematics" and
with that person in mind describe the level of knowledge involved and
provide throughout the progress of their argument a way of acquiring the
necessary practice. Emphasis is given to purely verbal discussions and
analyses. For the reader not interested in the maths, they mark those
sections that the non-mathematical reader is most likely to want to skip.
The second portion is notable for the judicious choice of modest objectives
and for the strongly articulated belief that in time more will be possible.
The following will illustrate:
> The great progress in every science came when, in the study of
> problems which were modest as compared with ultimate aims, methods
> were developed which could be extended further and further....
> It seems to us that the same standard of modesty
> should be applied in economics. It is futile to try to explain - and
> systematically at that - everything economic. The sound procedure is
> to obtain first utmost precision and mastery in a limited field, and
> then to proceed to another, somewhat wider one, and so on. This would
> also do away with the unhealthy practice of applying so-called
> theories to economic or social reform where they are in no way
> We believe that it is necessary to know as much as possible about the
> behavior of the individual and about the simplest forms of exchange.
> Economists frequently point to much larger, more
> "burning" questions, and brush everything aside which prevents them
> from making statements about these. The experience of more advanced
> sciences, for example physics, indicates that this impatience merely
> delays progress, including that of the treatment of the "burning"
> questions. There is no reason to assume the existence of shortcuts.
> A fortiori it is unlikely that a mere repetition of the tricks which
> served us so well in physics will do for the social phenomena too.
> The probability is very slim indeed, since it will be shown that we
> encounter in our discussions some mathematical problems which are
> quite different from those which occur in physical science. (pp.3-6)
I find the mention of need for a different kind of mathematics to be
intriguing, esp since at the very end of von Neumann's last work, the
Silliman Lecture published as The Computer and the Brain (1955), he wrote,
> Thus the outward forms of our mathematics are not absolutely relevant
> from the point of view of evaluating what the mathematical or logical
> language truly used by the central nervous system is. However, the
> above remarks about reliability and logical and arithmetical depth
> prove that whatever the system is, it cannot fail to differ
> considerably from what we consciously and explicitly consider as
> mathematics. (p. 82)
Willard McCarty, Professor of Humanities Computing,
King's College London, staff.cch.kcl.ac.uk/~wmccarty/;
Editor, Humanist, www.digitalhumanities.org/humanist;
Interdisciplinary Science Reviews, www.isr-journal.org.
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