Specific cycles, trust minimization, and the kula ring

While responding to Ian Grigg's comment to my previous blog entry on kula, I came up with what is the most rigorous explanation for the two-collectible cycle that I've seen. The explanation neatly incorporates two patterns I've talked about in the past, namely (1) the literal circulation of collectibles in specific cycles to minimize non-coincidence transaction costs in a bilateral monopoly economy, and (2) trust minimization in institution design.

Secure and accurate time sources

Broadcasts using sound or radiation, from sources such as radio, bell towers, and astronomical phenomena, must send out the same value to every receiver. A remote beacon such as a pulsar has perfect security: the access structure is any party, and its complement, the attack structure, is the empty set. For human controlled broadcasts, the attack structure consists only of the broadcaster and the access structure is any receiver.

Natural broadcasts are thus immune to the problem (known in computer science as the Byzantine Generals problem) of a transmitter sending different values to different receivers. Indeed, distributed network researchers have gone to great lengths to recreate this simple property on the Internet with logical broadcast protocols. The results are incomplete and very inefficient compared to physical broadcasts.

Nature provides clocks that are oblivious to the malicious intentions of any outside parties and many orders of magnitude more accurate than random delays that face attackers on the Internet. If critical Internet servers were synchronized to natural clocks in a secure and timely fashion, they would be immune to attacks that relied on uncertainties in timing. Here are some comparisons of the stability (error creep) in good natural clocks. Pulsars overtake atomic clocks in accuracy after about 4 months.

Oscillator Stability	1 sec	1 day	1 month
Quartz	10^-12	10^-9	10^-8
Rubidium	10^-11	10^-12	10^-11
Cesium Beam	10^-10	10^-13	10^-13
Hydrogen Maser	10^-13	10^-14	10^-13
Pulsar	10^-11	10^-12	10^-13

Commercial payments at the Muslim zenith

In the 19th century spectacular Jewish burial caches ("geniza"), totalling over 10,000 items, including over 7,000 documents, were unearthed in old Cairo. Study of these items has shed light on the status of commercial payments in Islamic society (and Jews living within it) before the development of full bills of exchange, deposit banking with loans, and so in 14th century Europe. The Muslim world connected that European world to the highly evolved ancient civilizations, almost unbroken from Sumer to Phoenicia and Persia to the Muslim Caliphate. At the time of the Geniza documents Muslim trading networks spanned much of the globe, from Indonesia to Spain.

Among the finds dating from the Muslim zenith between the 10th and 12th centuries:

Cases, or sealed purses containing a specific number of coins. These had been in use since at least ancient Phoenicia for paying with specific weights of gold or silver. A widely trusted entity (coin exchangers, government mint or treasury officers, or individual merhants) would deposit a specific weight and purity of jewelry or coins in the purse, and seal it. Cases relieved the recipient of having to weigh the coins, substituting trust in the sealer of the purse. Cases remained in common use with the onset of coinage, since coins wore out, depreciating below their face value, and merchants wanted payment by weight, not face value. A widely trusted entity (exchange or government officers, or individual merhants) would deposit a specific weight and purity of jewelry or coins in the purse, and seal it. In Europe cases were far less common. This may be due to less security on the road, or because many Italian and some German cities more frequently reminted worn coins than did the caliphate. In other parts of Europe where coin quality was poor, bank notes and bills of exchange later became the preferred medium of exchange. Cases are still used in modern diamond dealing to avoid tedious re-assaying of the diamonds.

Suftaja, or demand notes at a distance. These were used, like the later European bills of exchange, to transfer money over long distances. Under Muslim law, a suftaja was a "loan of money in order to avoid the risk of transport." Suftaja had been in widespread use at least since ancient Persia. Unlike many bills of exchange, they were payable in coin (by weight) on demand rather than on a specific date. They cost a fixed fee rather than interest, although the fee could vary depending on the distance between cities without violating usury laws.

Hawala, or an order to pay. This was similar to a modern check, but more cumbersome. Hawala was an order to a third party to pay the recipient in coin. In legal form, it was a delegation of a debt from the maker to the payer, and had to be made before a notary to verify the payer's assent.

Three big differences between Muslim commercial payments at their zenith and the later European practices that gave birth to the industrial revolution and modern capitalism were:

(1) The Muslims did not combine deposit banking with loans of deposits. One consequences was no market for commercial paper by which the ongoing costs of a business (especially wages and overhead) could be financed.

(2) Perhaps related to (1), the lack of large commercial organizations such as the later Dutch and British India companies. For example, Arab trading ships , while common from the Mediterranean to Indonesia, tended to be owned by individuals.

(3) Stricter enforcement of usury laws (perhaps also the cause of (1)). This was also a problem in Europe until the 14th century Genoese, among others, developed contracts based on bills of exchange that essentially mimicked loans with interest but without overtly charging interest. The saftaja and hawala by contrast were more rigid forms that could not be varied to hide interest without attracting the wrath of clerics.

Despite the advances they later made, it's clear that Europe did not come up with their 14th century commercial innovations from scratch. Rather, Italy and the Hanseatic cities, and later the Dutch and the English, stood on the shoulders of giants -- on commercial practices, institutions, and techniques that had been evolving in the Middle East since the clay commercial documents of ancient Sumer.

Metabolite schedule

Chief Justice Roberts has recused himself from Metabolite, so there will be eight justices deciding the case including Stevens. Here is the schedule:

Laboratory Corp. of America Holdings v. Metabolite Laboratories, Inc., Supreme Court No. 04-607: Briefing schedule through January 2005; hearing February-April 2006; decision by June 2006.

Although the case may be decided on narrower grounds, it's possible that this case could have profound implications for software and business method patents, especially if Justice Stevens' methodology in the 1978 case Parker v. Flook is applied here. I describe a clarified version of this methodology in a paper on the origin of U.S. software patents I wrote earlier this year. Here is a brief summary of that methodology and of Metabolite.

Augustus' solar timekeeper

The University of Oregon is recreating a famous Roman sundial from 10 B.C. which doubled as a clock and calendar. A few decades earlier the Roman comic writer Plautus put into the mouth of an idle character a complaint against shared standards of time and scheduling:

“The gods confound the man who first found out

How to distinguish the hours. Confound him too,

Who in this place set up a sundial,

To cut and hack my days so wretchedly

Into small pieces! When I was a boy,

My belly was my sundial – only surer,

Truer, and more exact than any of them.

This dial told me when ‘twas the proper time

To go to dinner, when I ought to eat;

But nowadays, why even when I have,

I can’t fall to unless the sun gives leave.

The town’s so full of these confounded dials!”


As I described my article "A Measure of Sacrifice," the Romans recognized astronomical time as a measure of sacrifice, but it was the medieval bell and clock makers who gave us our modern sense of precise shared time. Precise and objectively measured time used as measure of sacrifice is one of the patterns of integrity basic to modern civilization. I describe some of the latest research in securely sharing time and determining the order of events on the Internet in "Advances in Distributed Security."