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Unforgeable Costliness

Introduction

Unforgeable costliness is ubiquitous and fundamental to civilization. Unforgeably costly phenomena serve as proxy measures of value -- ways to estimate value that cannot be observed directly. By costly we mean that the observer is interested in determining the cost to produce the phenomenon, and by unforgeable we simply mean that a crucial property of the proxy measure is the difficulty of faking this cost. No technology has been invented that is perfectly unforgeable in this regard, but the goal has been met sufficiently to make various proxy measures based on cost important to civilization.

We will briefly describe two examples (and link to articles which discuss them at depth). We will think about how unforgeability is maintained, and under what incentives such a cost measure may be expected to reflect value. Finally, since much of our civilization may be rapidly moving online, we will confront the question -- can computer bits be made unforgeably costly?
Ostrich-eggshell beads, Kenya Rift Valley, 40,000 B.P. (Courtesy Stanley Ambrose)

Collectibles

Detail of necklace from a burial at Sungir, Russia, 28,000 BP. Interlocking and interchangeable beads. Each mammoth ivory bead may have required one to two hours of labor to manufacture. [W97] How did money evolve? See here for the full story. In brief, an artifact useful for other things, such asa flint for cutting, could also be used as a collectible. As a collectible, it had an added value beyond cutting -- it reduced the transaction costs of wealth transfers. Later, once institutions involving wealth transfer became sufficiently important, collectibles were manufactured just for their collectible properties. What are these properties? For a particular commodity to be chosen as a valuable collectible, it would have had, relative to products less valuable as collectibles, been more secure from accidental loss and theft (this often meant carrying on the person, as with jewelry, and also being resistant to decay when buried), and easier for the observer to accurately (despite attempts at fraud) determine the costliness from simple observations. Such a sequence led from beads, in necklaces and bracelets, made from ostrich eggshells (40,000 BC), ivory (30,000 BC), rare stone (25,000 BC), and finally metals (9,000 BC). Coins (600 BC) made observation easier by adding a stamp of approval from the tax collecting authority -- if the tax collector was willing to take them, so was everybody else. Nowadays we simply trust in the awesome revenue generating potential of tax collection to back our fiat currencies, which then can take any form (paper, plastic, computer bits).

Silver ring and coil money from Sumer, c. 2,500 B.C. Note the standard size of cross-sections. Many of the pieces had a standard weight, ranging from one-twelfth of a shekel to sixty shekels. To assay a ring or coil, it could be weighed and cut at random locations. (Courtesy Oriental Institute, University of Chicago)

Time

The main alternative to the time wage is the piece rate wage. This must be accompanied by penalties and rewards for variable quality, since the piece rate wage provides incentive to produce quantity at the expense of quality. Measuring more or a greater variety of qualities increases complexity, and so increases dispute and the unpredictability of the labor relationship. To collapse this complexity into manageable proportions, a general proxy measure is needed that doesn't have such a pathological incentive effect on quality.

Late Medieval Europe mastered a general proxy measure for for labor. Time measures sacrifice -- the amount of time the laborer cant spend in other pursuits family, recreation, or anything else the worker might prefer to labor. Mechanical clocks, bell towers, and sandglasses provided the world's first fair and fungible measure of sacrifice. So many of the things we sacrifice for are not fungible, but the employer and employee can arrange their relationship around the measurement of the employee's sacrifice rather than his hard-to-observe results. Thus was the modern time-rate wage born, and along with it the technology to measure it with much more accuracy and integrity than had previously been attained.

The Labor Theory of Value

Once one discovers the idea of unforgeable costliness, it readily brings to mind that old problem child of economics, the labor theory of value. Ricardo, Smith, and other early economists used this theory as one of several ways of attempting to predict or account for market prices (which under a competitive equilibrium, the model of modern economics, accurately reflect value). Their use simply reflected the role of unforgeably costly proxy measures themselves in the overall economy. Gold-backed currencies and the time wage (getting its big boost during the Late Middle Ages in Europe) both played huge roles then (during the early Industrial Revolution), as the time rate wage still does today.

Karl Marx and Friedrich Engels, inspired by their hatred of their own society, by Romantic notions of the inherent dignity of labor, and by the time wage method of accounting for labor in Engels' factory, gave new life to the labor theory of value as a morally correct belief system and criticized capitalists for taking surplus value which rightfully, so they said, belonged to labor. The theory had historical and cultural appeal, because for many relationships, included for precious metals that backed money in Marx's day, and the time wages of the working class, the unit of measure was based on unforgeable costliness -- all of which could be tied back to labor (the costs of mining gold, the costs of making the equipment to mine the gold, etc.). The labor theory of value may even have instinctive appeal, related to the instinctive appeal of collectibles. However, the labor theory has some obvious problems. If some workmen come dig a hole in my backyard, and fill it up again, what value have they produced? What if they dig a hole in my backyard, and fill it up again taking pictures all the while -- so that the hole is unforgeably costly -- have they produced value? The filled-in hole is useless as far as my own needs go. Nor does it have collectible value unless I can somehow use the evidence of costliness to store and trade wealth. This isn't as entirely unthinkable as it sounds. The Yap of the South Pacific once moved vast stones by boat, from the island on which it was quarried, to islands without that kind of rock. They used ownership of the resulting fixed stones to store and trade wealth. Alas, collectibes technology advances just as any other, and Yap stones and holes in my backyard just don't cut it any more. The hole is, therefore, quite worthless, regardless of how long and hard the workmen toiled to complete the job. There is no inherent value in labor just because it's hard work or takes time. Credible evidence of labor may, however, in the context of other institutions or incentive mechanisms, provide a very good proxy measure of value -- unforgeable costliness.

Such problems with the labor theory of value were dimly recognized by most economic thinkers all along, but it took the marginal revolution (Marshall, Walras, Menger, etc.) and the idea of prices as communicating knowledge residing in both the consumer and the laborer (Menger, Mises, Hayek, etc.) to put the stake in the heart of the labor theory of value. Nevertheless, such theories go to far if they dismiss the importance of proxy measures of labor as proxy measures of value in certain very important areas such as for collectibles and time wages. Quite the contrary, such measures have been and continue to be crucial to our civilization. Western economics, recoiling in horror from Marx, has neglected study of crucial areas such as the time wage, and the source of value of precious metals, namely they have until now failed to discover and study the idea of unforgeable costliness.

Bit Gold -- Unforgeable Costliness on a Computer?

The rapidly increasing importance of computers and their networks raises the question -- can unforgeable costliness occur online? Specifically, can computer bits be made unforgeably costly?

In 1992, computer scietists Dwork and Naor proposed combating spam with "client puzzles" -- problems that a computer must solve in order to send e-mail. In our terminology, it must cost the computer something to send e-mail, and this cost must be demonstrated to the remote computer unforgeably. Dwork and Naor proposed problems that take a long time on a computer to solve. For the normal user this would be no problem your computer cranks through the problems, every night for a month, entitling you to send e-mail to (say) 30,000 recipients in that month -- 1,000 for every day. If a spammer wants to send 100,000 e-mails every day a typical amount he must buy or rent 100 computers to do so. It gets to be pretty expensive for spammers. More detailed designs and software for this have been produced by Adam Back and others.

I have proposed using such a scheme to generate bank-independent online money -- bit gold. Current digital cash schemes suffer from the need for a trusted third party to issue digital bearer notes, worthless (like a piece of paper or plastic) in themselves, but redeemable for government fiat currency or a collectible. With bit gold, the piece of cash would itself be unforgeably costly, like a piece of jewelry or a non-fiat coin. In other words, bit gold would be online collectibles, unforgeably costly bits, money not dependent on trust for its value.

Bit gold essentially involves combining an unforgeable benchmark function, unforgeably linked (as with a cryptographic hash chain), with digital timestamping and secure property titles. The bits are public knowledge, but with the property title system the public securely agrees on who owns them. The property title system resembles that for the Internets Domain Name System (DNS), which essentially involves the ownership of bits as names. For the bit gold property titles, however, the dependence on third parties is reduced and far more distributed.

Such schemes are all based on what I call an unforgeable ("one-way") benchmark function, a computer program that produces a string of bits. These bits can be later be verified as having been produced by a certain very large number of CPU cycles (or, alternatively, by consuming large amounts of computer memory). Unfortunately, it is impossible using classical computers to make such function secure against novel computer architectures. As long as people are using normal processors such as the Intel architecture, all those generating bits are on a level playing field. However, other architectures (such as certain supercomputers) might be more efficient than the desktop PC at producing unforgeably costly bits. Worse, producers of bit gold could develop custom architectures that radically lower the prices. This is because the variability in costs between architectures would be much higher, than say, for the best gold mines versus the marginal gold mines. The mathematical theory behind the dependence of benchmark function costs on computer architecture this is explained here.