Monday, 20 January 2014

The mathematics of mediocrity

I think it was the late seventies. I was walking and chatting with Bill Blackburn through Mount Royal, an old and affluent Calgary community -- pausing now and again to look at a mansion  or so that Bill could spit in front of its gate. A few days earlier I had been reading a passage in some book describing experiments involving planarian worms abilities to learn the route through a maze to find water or food at its end. After the worm reached its target, it would be picked up and placed at the entrance again and its performance was recorded for each pass. The worms would build up to about an 80% efficiency rating but if the experiment went on much past that then the worm  would get less efficient again and eventually would just lie at the entrance until it died, apparently, of boredom.  I told this to Bill and said that I thought that it must also mean that planarian worms must have a rudimentary intelligence. Bill disagreed strongly, saying that many of his students did not even have a rudimentary intelligence.

It is fairly common, in numismatics and archaeology to deal with percentages. Quite often in the ancient world very similar things are not quite the same in some of their measurements. Weights and alloys in numismatics have long been considered to be very important and that attention has been passed down to modern archaeology. There are, of course, different statistical methods and one can even use a variety of them in the same project to tease out of the data the results that one wants. If one method doesn't work after a set or two, then just switch to one that does. In this way, apparent truths can be seen to dutifully follow one's hypothesis.
There are lies, damn lies - and statistics
              Mark Twain (who attributed its origin to Benjamin Disraeli)

Katherine Gruel, in Le tresor de Trebry, Cotes-du-Nord, 1er siecle avant notre ere: Contribution a l'histoire du monnayage des Coriosolites suggests that the Coriosolite tribe of NW France had been reducing the silver content in their coins by about 2% from class to class, save for a 25% reduction at about the start of Class IV. I could buy the latter -- one in four would not tax the abilities of Celtic moneyers in the middle of the first century BC. At the time of that publication, it was thought that all of the classes of Coriosolite coins followed one after another. I was later able to prove that three different mints were involved and at one point, all three were likely in operation at the same time. One of these mints ("Class II") was not even Coriosolite, but Unelli. (Hooker, Notes on part of the Le Catillon Hoard purchased by the Société Jersiaise in 1989. Ann. Bull. Soc. Jersiaise, 1993, 26 (1); Celtic Improvisations: An Art Historical Analysis of Coriosolite Coins, BAR International Series 1092, Archaeopress, Oxford, 2002)

 A 2% devaluation taxed my credulity. For a start, I doubt that the Coriosolites had the means or the motives to do such a thing, but most importantly, the classes were an arbitrary classification imposed on the coinage in modern times. Besides, I already had determined that the coinage was produced whereby each coin was a unit of account. The coins were paid out, in quantities, to military commanders for the hire of their troops to fight the Romans in the Gallic Wars. In using such small devaluation percentages, adjusting the weights of the blanks, al marco was the usual method employed. Adjusting the weights al pezzo was only rarely done in ancient times (see previous link), and I could see no evidence of either on the coins (some people display their ignorance of numismatic methodologies by imagining that we can do our work entirely from looking at illustrations of museum-held coins!). The situation was thus: the moneyers had been presented with certain amount of bullion and were told to make X numbers of coins from it. This bullion was not just ingots or casting pellets of refined silver, copper and tin, but was (or included) various scrap metal likely dug up from founders or personal hoards. Much later, the coins were again deposited in a sort of founders hoard awaiting transportation to the metalworks at Hengistbury in England so that the silver could be recovered through cupellation. This industry seems to have been closed, through a Roman police action in about 10-15 AD. The Durotriges (the tribe who ran the Hengistbury industry) were forced to devalue their own currency to pathetic cast copper coins. As these staters were also used as units of account, they were unable to hire outside forces to defend themselves from the Romans after Claudius landed in England, but supplies were in short supply, anyway, because of an agreement between Caesar and Cassivellaunos (I'll have a post on that later), and they had already been reducing the silver content of their coins. A similar situation happened much earlier with the coinage of Lesbos.

What actually happened, in the manufacture and later distribution and deposition of Coriosolite coinage was as follows: The workmen started, in each series, to adjust the alloys fairly carefully. It was not terribly important to get each batch of alloy just right as the commanders would get thousands of them. They were not used to buy goods in shops, so exact weights and intrinsic values were not that useful for the purpose, it would all average out in the end. After a while, the repetitive task took its toll. Whether planarian worms or some university students have a rudimentary intelligence is open for debate, but certainly these Coriosolite moneyers had more intelligence than, at least, the worms. The moneyers would, now and again, see that one of the pile of metals was going down faster than it should to maintain the intended alloy ratio and would correct that by using a bit less of it in the next batch of blanks. There were also other mistakes, In the nineteenth century, Sir John Evans recorded one Coriosolite coin that had a silver content of only only 4.1%, while the tin content was excessively high at 11.66%. Evidently, some scrap potin (high tin bronze) coins had got thrown in the silver pile because of their pale colour.

Now for the juicy part: Gresham's law shows that bad money drives out good (if you were a Roman emperor paying your troops, it would also usually lead to assassination!) In modern times, almost bovine complacency has taken over in these matters in our slow evolutionary path toward shark-intelligence. So imagine yourself back about two thousand years going through a bunch of coins that have been valued by unit of account. A few extra percentage points of silver, even as much as about ten percent in the alloy might not look very different from the rest, but a coin that had a very large percentage of silver would be quite noticeable. You know that you can make a profit on that so you remove it at once. Should you see one that had virtually no silver, you would let it remain. You might even exchange one of your own baser coins for an average one in the batch you were sending to be recycled.

Two thousand years later, someone finds a hoard of these coins and their alloys all go into the mental melting pot where they are averaged out to determine some monetary policy. The sample was corrupted even before they were buried and archaeology is not a science: if you depend on the wrong scientific method, your study will also become corrupted. All of the highest silver content coins had been culled before the hoard was buried and what had survived was mistaken for what had been created. This is why there appeared to be a 2% reduction "class by class". If you used clustering methods, instead, as I show in the above chart, the truth of the matter might well reveal itself. I could have done better if I had been able to plot them, exactly, on their timeline -- coin by coin, but I was only working from book data. My series X does not show the effect very clearly because of the rarity of the earliest of these, a major devaluation probably around the end of "class Vb" and the experimental effect of the initial minting of the earliest of Series X -- which are exceptionally rare. It also does not work very well for my Series Z, which are Unelli and found in Coriosolite territory in very small numbers. The latter have existed in vast numbers in the poorly recorded Normandy hoards of the nineteenth century and the recycling hoards in Jersey. Series Y, however, shows it quite clearly.

It's a lot more work to do this sort of thing properly, and I didn't have the coins on hand, but there is enough to show the general trend. Mediocrity is the state of being average. If you rely too much on averages, then you might well end up with a mediocre result!

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