Someone has asked me why this blog is Magic, maths and money.
In 1902 two sociologists, Marcel Mauss and Henri Hubert wrote ‘Outline of a general theory of magic’ where they identified that
The magician is a person who, through his gifts, his experience or through revelation, understands nature and natures …Owing to the fact that magicians came to concern themselves with contagion, harmonies, oppositions, they stumbled across the idea of causality, which is no longer mystical even when it involves properties which are no way experimental [Mauss and Hubert, 1902 (2001), pp 94–95]
The origins of magic in primitive societies is the idea that there is some sort of causal link between a ritual and a phenomenon and as such, the individual can control nature, making it less unpredictable.
Recently, the history of science has identified one of the motivations for scientists in Europe during the sixteenth and seventeenth centuries was a desire to find hidden mechanisms of cause and effect, mechanism that they could then employ to control the universe [Dear, 2001, p 52], [Henry, 2008, Chapters 5], [Hall, 1962, p 159]. The belief that these hidden mechanisms actually existed was inspired by what would now be considered as magical beliefs [Dear, 2001, p 25], [Henry, 2008, Chapter 4] and as the historian of science, John Henry, puts it
By their very nature, these mechanisms were uncommon and had to be discovered and the process of exploration in the world was replicated by experimentation in the laboratory.The history of magic since the the eighteenth century has been the history of what was left to the tradition after major elements of natural magic had been absorbed into natural philosophy. [Henry, 2008, p 57]
In the ‘general theory of magic’ book, Mauss and Hubert distinguish magic and science by observing that magic is based on belief in a set of rituals [Mauss and Hubert, 1902 (2001), p 114]. A person will only consult a magician if they have faith in the actions that the magician will perform. Science is not based on belief in its theorems, the equivalent of magic’s rituals, but on a belief in the process by which science is created. Science is a process that creates rituals, not simply a collection of rituals. This is a subtle point, but the effect is that magic is necessarily static, a contemporary astrologer would have more authority if they claimed to be experts in ancient knowledge. On the other hand, science is necessarily dynamic, we trust modern science’s explanations of the universe more than those of the Babylonians.
While magic and science are distinguished by static or dynamic belief, Mauss and Hubert distinguish magic and religion by hidden and open belief
Where religious rites are performed openly, in full public view, magical rites are carried out in secret. …and even if the magician has to work in public he makes an attempt to dissemble: his gestures become furtive and his words indistinct. [Mauss and Hubert, 1902 (2001), p 29]
The suggestion is, for science to be reputable and maintain a divide with magic, it needs to be carried out, like religion, in the open. As soon as either science or religion takes place out of the public arena, they risk degenerating into magic.
The choice of the word ‘magic’ is to highlight that financial mathematics needs to be a process of developing and refining theories, not simply of adopting sets of rituals (like pricing assets using risk neutral valuation), and that it needs to be conducted in a public forum. The public should be familiar with the “equations that blow up Wall Street” before the explosions.
This might seem a little metaphysical, non-scientific, but then isn’t this why financial mathematics is not just interesting. For example, with concerns of a U.S. default, the price of gold keeps climbing – but why gold?
Around 4,000 years ago, people started making ornaments out of electrum (an alloy of gold and silver), copper and gold [Diamond, 1998, pp 362–363], metals found naturally (i.e. without processing) in nature. Metals have an almost unique, natural, physical property; they reflect light. The only other material that stone-age humans would have come across that reflected light would have been water, so to these people gold would appear to combine the essence of both water and the sun, the basis of life [Betz, 1995], [Landes, 1999, pp 70–73]. Imagine the awe that humans would have felt the first time they spotted a nugget of gold sparkling in a river bed, here was an object that seemed to captured and store life-giving sunlight, the ‘tears of the Sun’ as the Incas said. In the medieval period, European alchemists believed that metals were produced by some mechanism involving rays from different ‘planets’: gold from the Sun, silver from the Moon, mercury from Mercury, copper from Venus, iron from Mars, tin from Jupiter and lead from Saturn.
In ancient Babylon, Egypt and Greece, temples became associated with stores of metals, gold for the Greeks, silver for the Babylonians and copper for the Egyptians. It seems that these metals had developed a religious significance and become important as temple offerings. Consequently followers of the religion would look to acquire the metal, to enable them to make an offering, and so the metal became the commodity in the most universal demand. [Pryor, 1985] Athens treasury was in the Temple of Athena, and Jesus cast the money-lenders, exchanging worldly Roman money for divine shekels, out of the Temple.
The earliest tokens used as ‘money’ were not specific weights of a certain metal but roughly cut pieces of metal with an official stamp on them [Ingham, 2004, p 98] – monopoly money as it were. The emergence of money, in the sense of coins, in Greece coincides with the emergence of mercenary troops, the term ‘soldier’ is derived from the word for a Roman gold coin, solidus. A simple economic model developed, states paid soldiers in gold, who then spent it in the community. The government then recovered the gold by taxing the merchants and innkeepers that the soldiers had paid for food and lodgings. This model would survive and drive colonialism until the modern age. A power, such as Alexander’s Greece, Imperial Rome, Napoleonic France or Industrial Britain, would take control of a region through force of arms. They would then demand tax from the conquered nation, which would have to be paid in currency specified by the coloniser. The conquered nation could only obtain the currency by exchanging their produce for the specified currency. For example, in the 1920s the British taxed Kenya at a rate of about 75% of wages, while the Belgians did not tax the Congo – they relied on forced, rather than ‘free’ wage labour [Ingham, 2004, p 76].
In the 1920’s, John Maynard Keynes became obsessed with the origins of money [Ingham, 2004, p 209, Note 16]. In neo-classical economic analysis, money is a consequence of exchange, and from money comes banking and then the ‘credit relations’ between borrowers and lenders, pretty much as Aristotle had conceived things. However, at the start of the twentieth century, anthropologists studying primitive societies observed that cultures that had not developed money, tokens to facilitate exchange, none the less, lent and borrowed.
One of the most studied examples of these sorts of systems was that of indigenous people around Vancouver in North Western Canada. A young man would lend five blankets to an older, richer person, for a year and they would be repaid with ten blankets. A similar situation existed in the Southwestern Pacific were strings of shells were lent by a young man, sometimes to an unwilling borrower, at very high rates of interest. The value of the shells was was purely ceremonial, they bought entry to the fraternities of adult men [Homer and Sylla, 1996, pp 22–23]. In fact many cultures had systems where by a gift had to be reciprocated by a greater gift in return [Mauss, 1924 (2001)] and it could be disastrous to be given a present, since it would require the return of more han what was given. What these very primitive societies had done was create credit-debit relationships, reciprocity, which played a critical role in gluing society together by creating bonds between the rich and poor, the old and young. [Sahlins, 1972 (2003], [Mauss, 1924 (2001)]
The anthropologist Marcel Mauss summed up the research in a paper on 1923, ‘An essay on the gift: the form and reason of exchange in archaic societies’
The evolution in economic law has not been from barter to sale, and from cash sale to credit sale. On the one hand, barter has arisen through a system of presents given and reciprocated according a time limit. …On the other hand, buying and selling arose in the same waywith the latter according to a fixed time limit, or by cash, as well as by lending. For we have no evidence that any of the legal systems that have evolved beyond the phase we are describing [primitive society] (in particular, Babylonian law) remained ignorant of the credit process that is known in every archaic society that still survives today. [Mauss, 1924 (2001), pp 46–47]
Keynes knew that he Babylonians had established credit relations. There was a Babylonian prototype of the Bill of Exchange from a time when the Babylonians did not use coins and in the 1930 Treatise on Money Keynes, like Mauss, argued that money did not, in fact, originate in the market place, rather it was created by the state or community ‘the age of money had succeeded to the age of barter as soon as men had adopted a money of account’ [Keynes, 1971, p 4]. Here, ‘money of account’ is the generally accepted medium by which debts are settled, for example the Babylonians settled debts, typically tax debts or loans from temples, in either grain or an amount of silver, and this medium was defined by the state and based on trust in credit relations, the state theory of money or money as a ‘social relation’.
O. Betz. Considerations on the real and the symbolic value of gold. In G. Morteani and J. P. Northover, editors, Europe: Mines, Metallurgy and Manufacture, chapter 2, pages 19–28. B. B. Price, 1995.
J. M. Diamond. Guns, Germs and Steel: A short history of everybody for the last 13,000 years. Vintage, 1998.
S. Homer and R. Sylla. A History of Interest Rates. Rutgers University Press, 3rd edition, 1996.
J.M. Keynes. The collected writings of John Maynard Keynes. Vol. 5 : Treatise on money 1: The pure theory of money. Macmillian, 1971.
M. Mauss. The Gift: Form and Reason for Exchange in Archaic Societies. (Routledge), 1924 (2001).
F. L. Pryor. The origins of money. Journal of Money, Credit and Banking, 9(3):391–409, 1985.
M. Sahlins. Stone Age Economics. (Routledge), 1972 (2003)