Astral Science in Early Imperial China, a forthcoming book by the historian Daniel P Morgan, shows that in ancient China, as in the Western world, the most valuable type of mathematics was devoted to the realm of divinity – to the sky, in their case (and to the market, in ours). Just as astrology and mathematics were once synonymous in the West, the Chinese spoke of li, the science of calendrics, which early dictionaries also glossed as ‘calculation’, ‘numbers’ and ‘order’. Li models, like macroeconomic theories, were considered essential to good governance. In the classic Book of Documents, the legendary sage king Yao transfers the throne to his successor with mention of a single duty: ‘Yao said: “Oh thou, Shun! Theli numbers of heaven rest in thy person.”’
China’s oldest mathematical text invokes astronomy and divine kingship in its very title – The Arithmetical Classic of the Gnomon of the Zhou. The title’s inclusion of ‘Zhou’ recalls the mythic Eden of the Western Zhou dynasty (1045–771 BCE), implying that paradise on Earth can be realised through proper calculation. The book’s introduction to the Pythagorean theorem asserts that ‘the methods used by Yu the Great in governing the world were derived from these numbers’. It was an unquestioned article of faith: the mathematical patterns that govern the stars also govern the world. Faith in a divine, invisible hand, made visible by mathematics. No wonder that a newly discovered text fragment from 200 BCE extolls the virtues of mathematics over the humanities. In it, a student asks his teacher whether he should spend more time learning speech or numbers. His teacher replies: ‘If my good sir cannot fathom both at once, then abandon speech and fathom numbers, [for] numbers can speak, [but] speech cannot number.’
Modern governments, universities and businesses underwrite the production of economic theory with huge amounts of capital. The same was true for li production in ancient China. The emperor – the ‘Son of Heaven’ – spent astronomical sums refining mathematical models of the stars. Take the armillary sphere, such as the two-metre cage of graduated bronze rings in Nanjing, made to represent the celestial sphere and used to visualise data in three-dimensions. As Morgan emphasises, the sphere was literally made of money. Bronze being the basis of the currency, governments were smelting cash by the metric ton to pour it into li. A divine, mathematical world-engine, built of cash, sanctifying the powers that be.
The enormous investment in li depended on a huge assumption: that good government, successful rituals and agricultural productivity all depended upon the accuracy of li. But there were, in fact, no practical advantages to the continued refinement of li models. The calendar rounded off decimal points such that the difference between two models, hotly contested in theory, didn’t matter to the final product. The work of selecting auspicious days for imperial ceremonies thus benefited only in appearance from mathematical rigour. And of course the comets, plagues and earthquakes that these ceremonies promised to avert kept on coming. Farmers, for their part, went about business as usual. Occasional governmental efforts to scientifically micromanage farm life in different climes using li ended in famine and mass migration.
Like many economic models today, li models were less important to practical affairs than their creators (and consumers) thought them to be. And, like today, only a few people could understand them. In 101 BCE, Emperor Wudi tasked high-level bureaucrats – including the Great Director of the Stars – with creating a new li that would glorify the beginning of his path to immortality. The bureaucrats refused the task because ‘they couldn’t do the math’, and recommended the emperor outsource it to experts.
There are some interesting references and interviews of people in the article.
Why would skeptical astronomers question the emperor’s faith in their models? In a phone conversation, Daniel Hausman, a philosopher of economics at the University of Wisconsin, put it bluntly: ‘If you reject the power of theory, you demote economists from their thrones. They don’t want to become like sociologists.’
George F DeMartino, an economist and an ethicist at the University of Denver, frames the issue in economic terms. ‘The interest of the profession is in pursuing its analysis in a language that’s inaccessible to laypeople and even some economists,’ he explained to me. ‘What we’ve done is monopolise this kind of expertise, and we of all people know how that gives us power.’
Every economist I interviewed agreed that conflicts of interest were highly problematic for the scientific integrity of their field – but only tenured ones were willing to go on the record. ‘In economics and finance, if I’m trying to decide whether I’m going to write something favourable or unfavourable to bankers, well, if it’s favourable that might get me a dinner in Manhattan with movers and shakers,’ Pfleiderer said to me. ‘I’ve written articles that wouldn’t curry favour with bankers but I did that when I had tenure.’