Aren’t we just passing around digital versions of the tallies we’ve been using for almost 1,000 years?

with nothing more than a notched wooden stick. So what’s the problem? Aren’t we just passing around digital versions of the tallies we’ve been using for almost 1,000 years? Aren’t mortgages, whether prime or subprime, just a modern version of paying for houses with fraud-resistant sticks?

Photograph courtesy of the National Archives UK; transcription at makezine.com/go/tallystick

The roots of the current financial meltdown can be found in John von Neumann’s model of general economic equilibrium, first developed in 1932. Von Neumann elucidated the behavior of an expanding, autocatalytic economy where “goods are produced not only from ‘natural factors of production,’ but ... from each other,” and he proved the coexistence of equilibrium and expansion using the saddle-point topology of convex sets.

Some of his assumptions — such as “the natural factors of production, including labour, can be expanded in unlimited quantities” and that “all income in excess of necessities of life will be reinvested” — appeared unrealistic to others at the time, less so now that Moore’s Law and the zero-cost replication of information are driving today’s economy. Other assumptions, like an invariant financial clock cycle, are conservative under the conditions now in play.

Von Neumann, who made seminal contributions to digital computing, left a number of distinct monuments to his abbreviated career, among them his Theory of Games and Economic Behavior (with Oskar Morgenstern) and his Theory of Self-Reproducing Automata (with Arthur Burks). Synthesis between these 2 regimes is now advancing so quickly that no unified theory of the economics of self-reproducing systems has been able to keep up. Periodic instability should come as no surprise. We may be on the surface of a balloon. Or in the saddle of a dynamic equilibrium — we hope.

The unlimited replication of information is generally a public good (however strongly music publishers and software developers disagree). The problem starts, as the current crisis demonstrates, when unregulated replication is applied to money itself. Highly complex

And in the beginning, there were tally sticks. This collection of 13th-century Exchequer “stocks” is stored at the National Archives in London.

computer-generated financial instruments (known as derivatives) are being produced, not from natural factors of production or from other goods, but purely from other financial instruments.

When the Exchequer splits the tally stick in two, the king keeps the gold, and you keep one half of the stick. Derivatives are the equivalent of splitting off (and selling) further copies of the same stick — or the “clipping” and debasing of coinage that led Isaac Newton to spend the later part of his life reforming the financial system as master of the Royal Mint.

The result is a game of musical chairs that follows von Neumann’s model of an expanding economic equilibrium — until the music stops, or we bring in Isaac Newton, whichever comes first.

George Dyson, a kayak designer and historian of technology, is the author of Baidarka, Project Orion, and Darwin Among the Machines.

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