Michael Perelman wrote:
Second, any analysis based on labor would call out for
both impossible quantification and more difficult
mathematics. Utility, however, seemed to permit
economists to avoid the need for quantification, while
seeming to simplify mathematical complexities.
Finally, utility seemed to be capable of fitting in
with the type of models that economists were using in
their quest to emulate physics with its mathematics of
maximization.
Michael:
are you implying that there are potentially interesting mathematical and
modeling problems related to a study of labor? what is the "impossible
quantification"?
re/ utility: was this more or less an attempt to copy at least the
outlook of lagrangian and hamiltonian methods from physics?
i still remember the set of lectures in grad school where we were
introduced to the details of these methods: the most boring part of grad
school [**]. but i remember it because i remember thinking how stupid
was this notion that "nature took the path of least action". but as
physicists and applied mathematicians we had little interest in the
quasi-religious aspects of the theory. and i always thought the nail was
put to coffin when my teach showed us the problem of the "second
variation" ... it turns out these "least" principles are not
necessarily strictly maxima or minima ... nature, it appears, does not
abhor saddle points. when i saw that, i knew the whole teleological
thing was a crock of beans. in fact, i was sitting here trying to
remember the name "least action" because i have been trained to think of
it as a "stationarity principle". equivalence of Lagrange's equations
with Newton's formulation of mechanics requires only stationarity,
extremism need not apply.
of course, Lagrangian and Hamiltonian techniques went on to conquer
physics. but not because of their maximization properties, but because
they exhibited deep transformational characteristics.
Les
[**] Feynman, in his famous Lectures on Physics, attempts to make
something of this minimization, and its the least interesting aspect of
his book. ok, i am biased.
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