Sunday, June 7, 2009

The Business Mathematics Connection

Niall Ferguson's "The Ascent of Money" is a highly entertaining history of business that seeks to explain how business practice has had a profound effect on human history. The title of documentary series is a deliberate pun on the influential BBC TV series "The Ascent of Man" from the 1970s. This series presented a grand overview of the history of human civilisation, in which commerce was barely mentioned, where as Greek mathematics and Galileo's trail by the church were described in great detail. Apparently, a young Niall felt that something was missing and decided that once he had become a world famous economic historian he would have his revenge ! I, for one, enjoyed the pun !

In one episode, Ferguson traced the history of lending, arguing that the fortune generated by the business innovations of the Medici family and other Italian businessman effectively funded the Renaissance. This claim may somewhat under estimate the importance of artistic and scientific ideas but is certainly an effective counterbalance to the traditional dis-taste and dis-interest that many historians have shown towards the influence of commerce on human affairs.

Of particular interest to me, was Ferguson's emphasis on the impact of the introduction of "Arabic" numerals to Europe (which we now know came from India) on the ability for traders to effectively barter and exchange currency and goods. As Ferguson explained, Roman numerals, was practically useless for large commercial transactions and that Southern European traders found the counting systems used by their counterparts from the Muslim world to be far more practical. In this way, business lead a revolution in mathematics.

This link between business and mathematical innovation is profound. The very business of counting in groups of numbers (binary, decimal or duodecimal) is almost certainly linked to the growth trade in the ancient world. The concept of exponential functions is similarly linked to the development of interest calculations and banking practices in the late middle ages. It is also well established that basic concepts of probability and statistics were developed in a business context, in particular, around the complicated calculations of insurance and risk assessment in the 19th century. This interaction between business and mathematical innovation continued in the 20th century with the development of game theory and other techniques of discrete mathematics.

I'm personally not surprised by this profound link. In my own experience in small business, the back and forward of everyday commerce is a fertile ground for innovation and new ideas. The atmosphere is very different from academia, where often new ideas can be squashed by petty snobbery's, ideological positions, intellectual fashions and just plain conservatism. In business, the attitude often is, if it works, than lets use it ! This, of course, means that lots of mediocre ideas also fly but that's part of territory.

I look forward to the next episode of Ferguson's "The Ascent of Money" and learning more about the link between "dirty money" and mathematics !

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