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Complexity is a Real Factor

In my latest column for AIER, I steal Paul Romer’s idea of using simple arithmetic to explain the enormous challenge that markets meet in bringing about productive arrangements of the world’s multitudinous inputs. A slice:

When I was young, the number of family members gathered for our family’s Thanksgiving dinner was about 20 – a large dinner gathering, yes, but nothing out of the ordinary. Yet the number of different ways to arrange the seating of a mere 20 people around a dinner table is – drumroll! – 2,432,902,008,176,640,000.

A number this large has no non-scientific name. It is inconceivably high and unimaginably humongous. It’s just a bit larger, by a mere several thousand trillion, but roughly equivalent to this number: 2,428,272,000,000,000,000 – which is the number of seconds (as in “60 seconds in a minute”) there are in 77 billion years. Note that astronomers estimate the universe’s age to be 13.8 billion years.

I didn’t write the above to impress you with my knowledge of advanced arithmetic or my ability to google “How old is the universe?” I wrote the above to make a point about the economy.

Solving economic problems – creating value – requires discovering how to arrange inputs productively. The number of inputs available for use is not 20 or even 20,000; it’s in the billions. Therefore the factorial operation means that the number of possible ways to arrange these billions of inputs is indescribably far beyond human comprehension. Yet only a minuscule fraction of these ways has any prospect of being productive. Almost all possible arrangements are useless or even dangerous.

One among these countless arrangements is gin mixed with turpentine and anchovies, but the resulting martini would be terrible. How best to discover the vanishingly small number of productive arrangements out of the sprawling and gigantic number of possible arrangements?

Obviously, relying on random chance will not do. Equally futile would be reliance on what on the surface appears to be the opposite of random chance: central planning. No human being or committee could possibly even survey and list all of the possible different arrangements of billions or inputs. Much less could any individual genius, or agency of geniuses, discover from this vast list of possibilities which of these arrangements are most useful compared to the uncountably large number of other possible arrangements.

Given the puniness of the human mind relative to the incalculable number of possible different arrangements of an economy’s inputs, to turn over to government the responsibility for choosing how resources should be allocated is, in effect, to rely upon random chance.


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