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Tyndall declared that he saw in Matter the promise and potency of all forms of life, and with his Irish graphic lucidity made a picture of a world of magnetic atoms, each atom with a positive and a negative pole, arranging itself by attraction and repulsion in orderly crystalline structure. Such a picture is dangerously fascinating to thinkers oppressed by the bloody disorders of the living world. Craving for purer subjects of thought, they find in the contemplation of crystals and magnets a happiness more dramatic and less childish than the happiness found by mathematicians in abstract numbers, because they see in the crystals beauty and movement without the corrupting appetites of fleshly vitality.
Preface to Back to Methuselah.
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript
The regional economies that existed in Europe, or even within a single realm such as France, still hadn’t become well integrated in these pre-modern times, and in general, there were no standardized monies backed by strong governments. Thus, like most Medieval and Renaissance arithmetic texts, the Pamiers manuscript includes many problems dealing with conversions between local currencies.
The practice of minting coins of silver, gold, and other precious metals had arisen many centuries earlier. However, each region tended to have its own coins. Weights and measures also varied from place to place, and even in a given location different units were used for different commodities, as we saw earlier in Section 5 on Barter Transactions. The confusing proliferation of local currencies, weights, and measures in France wasn’t swept away and replaced with a rational, unified, nationwide system until the Revolution of 1789.
Figure 8. “The Moneylender and His Wife” (1514) by Flemish painter Quentin Matsys. Musée du Louvre, Paris. (Image: The Yorck Project / Wikimedia Commons, licensed under the GNU Free Documentation License.)
In the above problem there is a twist, because more than just one ratio is given. But this was actually routine for money changers: typically, they knew the exchange rates for neighboring currencies, but to exchange more-distant currencies they had to build a chain out of such pairs of neighbors. Indeed, Perpignan, Montpellier, and Avignon are 3 cities strung along the Mediterranean coast in the order mentioned in the above problem, across a distance of roughly 150 miles, providing a nice geographical interpretation for the concept of “chain.” See if you can solve the problem by one of the methods discussed in Section 4.
It’s also interesting to note that the term denier mentioned in the above problem goes back to the time of King Charlemagne, who instituted a system of coins, weights, and measures around 800. The term is based on the Latin denarius, an ancient Roman silver coin that had ten times the value of an as, a coin of copper or bronze; the Latin root for “ten” is seen in denarius, as also in English words like decimal and dime. After the Norman conquest of England (1066), Charlemagne’s system of monetary units made its way across the Channel, where the silver denier eventually became known as the penny (plural pennies or pence); this is why the British penny was formerly always abbreviated “d” for denier. In turn, 12 deniers were equal to one sous, a coin mentioned earlier in Section 5 on Barter Transactions.
Monetary questions—including currency exchange, the money supply, and the alloying of precious metals—were complex enough that European mathematicians would sometimes advise rulers on this subject and write treatises about it. The entire Chapter 11 of Fibonacci’s Liber Abaci (1202) is concerned with “the alloying of monies.” Another prime example of this tradition is Nicole d'Oresme (1323-1382), a mathematician and religious philosopher of Norman origin who became both the chaplain and monetary advisor to French King Charles V. By 1355, Oresme had written an important treatise about money, De Origine, Natura, Jure et Mutationibus Monetarum. Paper money did not come into use in England until the 1690s, and in France not until the 1700s.
Schwartz, Randy K., "'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript," Loci (July 2012), DOI: 10.4169/loci003888