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and analytical
picture
of the interdependence of the many elements in the causation of
prices, but also to employ the mechanism as an instrument of investigation and by it,
study some complicated variations which could scarcely successfully be followed
without its aid.”
10
Without the machine to illustrate the factors that influence prices,
in other words, it would have been more difficult not simply to picture their influence
upon each other but also to investigate the more “complicated variations” of their
interrelations.
The drawings, descriptions, and three-dimensional machine that Fisher presented as
“analogues” for an economy seeking equilibrium seem to constitute relatively simple
mimetic representations. That is, in helping the student visualize the economy as analo-
gous to a water-filled tub containing a system of linked and differently weighted floating
cisterns, these representations seem simply to point to and quantify things that exist in
the material world. While some of the things Fisher mentions could be quantified,
however, this was not true of all of the items he lists. Thus one could measure and
presumably record “the quantities of each commodity consumed by each individual
during the year” and, conceivably, “the given total quantities of each commodity con-
sumed by the whole market”; but “the marginal utility of money to each individual” had
to be inferred, based on the theoretical assumptions about what makes one “point” or
“degree” of utility marginal and why this matters. Then, too, the economy does not exist
in the same physical form that Fisher's machine did, cisterns floating in water constitute
a poor representation of desire (“utility”), and even the equilibrium that was thought
to establish prices was a theoretical assumption about an idealized state that economic
processes never actually, or permanently, achieve. The mechanism to which Fisher
applied mathematical interpretations, then, existed at one remove, at least, from eco-
nomic transactions conducted by actual economic actors; and the mathematical equa-
tions he used to convey the more “complicated variations” of all of the interrelated
factors did not simply refer to or add up actual sales, purchases, prices, or quantities
of money in circulation (much less the desire that motivated these transactions) but,
instead, created an abstract—but useable—analog for these factors.
Even if this analog could help the reader visualize the interrelationships that con-
nected economic elements, then, neither the drawings nor the machine solved all of
the challenges involved in Fisher's ambition to depict the entire economy. His analog
machine
was
able to solve two, related problems. By inventing a unit by which the
economist could “measure” the movements that stood in for quantities of desire, which
Fisher called the “util,” he was able to assign numerical values to what other economists
