Dave,
I'd rather replace von Neumann's automata quotation (third one in
your list) with the following one, which seems to my view much more
important from the viewpoint of (a very big part of) 20th century
mainstream economics (automata are, or will presumably be, a matter
of 21st century economics):
<<As a mathematical discipline travels far from its empirical source,
or still more, if it is a second and third generation only indirectly
inspired by ideas coming from "reality", it is beset with very grave
dangers. It becomes more and more purely aestheticizing, more and
more purely l'art pour l'art. This need not be bad if the field is
surrounded by correlated subjects, which still have closer empirical
connections, or if the discipline is under the influence of men with
an exceptionally well-developed taste. But there is a grave danger
that the subject will develop along the line of least resistance,
that the stream, so far from its source, will separate into a
multitude of insignificant branches, and that the discipline will
become a disorganized mass of details and complexities. In other
words, at a great distance from its empirical source, or after much
"abstract" inbreeding, a mathematical subject is in danger of degeneration.>>
(John von Neumann 1961 [1947], "The mathematician", in: Taub A.H.
(ed.), John von Neumann. Collected works, Oxford: Pergamon Press,
1961-63, vol. I, p. 9).
Nicola Giocoli
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