The Austrians’ most emphatic defense against all possibility of solutions to their Vienna Problem holds that economic calculation, or computation, is not really a mathematical problem at all (Hayek's direct assertions to the contrary notwithstanding).
Hayek’s 1945 AER paper on The Uses of Knowledge in Society.1 begins by taking Professor Schumpeter to task for having credited Pareto and Barone with solutions to economics’ calculation problem, finding nothing could not be more clear than that Pareto's optimum only states the criteria for solution, to which Hayek finds Barone adding nothing of interest.
This paper divides what is now known as the Vienna problem between 1) formulating a soluble set of the inevitably complicated, non-linear simultaneous equations with which to specify Pareto’s optimum, and 2) the problem of the utilization of knowledge which is not given to anyone in its totality but which certainly must enter any equations for the over-arching, singular criteria synthesized by Pareto. Hayek treats the second aspect of the computation problem through almost the entire length of his paper, while only returning the first aspect in order to dismiss the mathematics of economic calculation as no more than a useful preliminary to the study of the main problem in his closing sentence.
Hayek clearly states economics’ main problem in terms of the necessarily fragmentary information available to each individual: what social processes could possibly resolve masses of distributed, incomplete, and unorganized data into a logical relationship which can be meaningfully asserted only of propositions simultaneously present to one and the same mind? His extensive account of these social processes leads to, in our reading, nothing but despair:
On the one hand, he cannot cognize that singular state around which economic systems seem to organize except as the handiwork of some sort of governing economic homunculus who focuses economic data so that it might be given order. Variations on the phrase single mind occur ten times, and extensions of the word central occur fourteen times, in a paper of 5500 words. Other searches are no less suggestive.
Yet Hayek knows that no such homunculus exists, nor could such a creature possibly exist.Thus the Austrian School could not be more correct in that Hayek’s specification of the Vienna problem arrives couched in his inability to conceive of how the information necessary to perform economic calculation might be assembled for examination by any single mind. And indeed: if the economy were directed by the intelligence of a solitary economic homunculus, seated somewhere beyond material actuality, then we would certainly be at pains to account for how this creature assembles the necessary data.
Having once again arrived at a contradiction to the ongoing fact of objective economic calculation, we again return to ponder the observational premises by which we are shunted off to this point of despair. Where is it written that information must be focused before it can be acted-upon? Why cannot the data necessary for economic calculation be operated-on in situ? This would certainly be the operative premise if the macro economy were viewed as a mind in its own right as opposed to a mélange composed by the diffuse individual actions individual actions of all humanity.
If we view the economy as an organism governed by a thought process, then we leave behind any requirement that its requisite data need to be focused in order to be acted upon. Economic activity itself is the thought process through which structure is given to distributed economic data: focusing these data in an expression of general optimality IS the economic process of pure capitalism; and cells in an input/output are analogous to nodes in an extended meta-mind, rather like the individual residents of a self-organizing insect colony. Focus does not, cannot, and need not occur outside of economic activity itself.
SFEcon's boundary conditions are composed by the utility parameters with which Hayek states the Vienna problem. Given no more than the shapes of the economy's production and utility tradeoffs, the SFEcon program will efficiently emulate all the activities of asset creation and distribution that culminate in a steady-state of asset levels that instantiates Pareto optimality. Observing this process, you will see the model internally generating prices and everything else Hayek thought necessary to economic calculation. Once again, the calculations are not in any way centralized: they are, rather, replicated at each cell of the I/O context, somewhat in analogy to object-oriented programming.
Continuing this impulse into economic science would set the task of macroeconomic theory as 1) understanding market prices as fragmentary epitomes of the current economic state, such that 2) the isolated responses of petty economic actors to these prices always direct the economy toward a singular state characterized by Pareto’s criteria. The problem of the utilization of knowledge which is not given to anyone in its totality is ultimately the solution to economics’ non-computability problem: the exertions needed to solve this mere mathematical preliminary to the study of the main problem reveal how distributed economic knowledge is utilized.
Here we have conveniently (and perhaps shamelessly) defined the object of theoretical
materialism as the goal SFEcon has already reached. A given sector in our I/O structure
operates only on knowledge of its own technical tradeoffs. The
price of a given commodity is computed from nothing more than that
commodity’s current rate of supply and the commodity’s current
marginal valuations among the sectors that use it. The sectors do not know
what one another are doing; and the markets know nothing of one another’s prices. There is
simply no homunculus to whom these scattered data might be presented; yet the system nonetheless
converges to a stable optimum.