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Chapter ten begins the exploration of the French case of neo-Roman mimesis and its particular deployment of ruin scenes. The author argues that French imperial mimesis consists of three acts, bookended by the Napoleonic conquest of Egypt in 1798 as the first act of French imitation staged among Egypt’s Roman ruins, and the occupation of Rome in 1806, with its designs for the restructuring of the ancient metropole, as the third act. The chapter ends with Joseph Fourier’s introduction to the Description de l’Égypte as a Napoleonic manifesto in the vein of Augustus’s Res Gestae. Fourier rewrites the conquest’s failure as anticipating the success of France’s future ventures. In the process, Fourier rediscovers empire’s time as the time before the end.

This chapter takes a look at the origins of the carbon dioxide theory of climatic change. In 1938, Guy Stewart Callendar, a British steam engineer and amateur meteorologist, had explained to the Royal Meteorological Society that by burning fossil fuel, humans were adding carbon dioxide to the atmosphere. Since carbon dioxide traps rising heat rays, he argued, adding more would be bound to warm the Earth. During and after World War II, carbon dioxide levels in the atmosphere did rise as humans burned more fossil fuel, but global temperatures fell. Callendar estimated that twenty years should provide enough data to test his theory. Over the years, scientists assembled a mountain of evidence that confirmed Callendar's theory. Callendar was right about carbon dioxide, but his timing was off. This chapter examines the work of Jean Baptiste Joseph Fourier, Claude Pouillet, and Jozef Stefan that shed light on the greenhouse effect and greenhouse warming.

This chapter traces the roots of the idea of deep time, one of the most fundamental and surprising discoveries about the Earth during the twentieth century. In September 1846, William Thomson, then age twenty-two, applied for the chair in natural philosophy at the University of Glasgow. Before an appointment could become official, the applicant had to write and deliver, in Latin, an essay assigned by the faculty. Thomson's topic was De caloris distributione per terrae corpus: “The distribution of heat within the Earth.” The title echoed that of Joseph Fourier's book on heat flow, The Analytical Theory of Heat. The implications of Fourier's mathematics, first encountered by Thomson at age sixteen, would occupy him for sixty-eight years, until his death in 1907. By then he was known as Lord Kelvin. This chapter also looks at the emergence of geology as a true science and the rise of uniformitarianism by focusing on the works of James Hutton and Charles Lyell.

With the advent of the Napoleonic Expedition to Egypt in 1798, Egypt came fully into European awareness. Although the expedition was primarily military and colonial in intent, and although it ultimately failed, it also brought unprecedented attention to ancient Egypt with the discovery of the Rosetta Stone and publication of the great Description de l’Égypte. Napoleon took with him a large commission of scholars, or savants, that included such luminaries as the artist Vivant Denon and mathematician Joseph Fourier, who documented ancient Egypt to an unprecedented degree. Egyptian antiquities began to flood into Europe and especially into the British Museum after the British appropriated most of those that the French had assembled in Egypt.

This chapter analyzes the law of facility of errors. All the early applications of the error law could be understood in terms of a binomial converging to an exponential, as in Abrahan De Moivre's original derivation. All but Joseph Fourier's law of heat, which was never explicitly tied to mathematical probability except by analogy, were compatible with the classical interpretation of probability. Just as probability was a measure of uncertainty, this exponential function governed the chances of error. It was not really an attribute of nature, but only a measure of human ignorance—of the imperfection of measurement techniques or the inaccuracy of inference from phenomena that occur in finite numbers to their underlying causes. Moreover, the mathematical operations used in conjunction with it had a single purpose: to reduce the error to the narrowest bounds possible. With Adolphe Quetelet, all that began to change, and a wider conception of statistical mathematics became possible. When Quetelet announced in 1844 that the astronomer's error law applied also to the distribution of human features such as height and girth, he did more than add one more set of objects to the domain of this probability function; he also began to break down its exclusive association with error.

Chapter 2 looks at the development of algorithms for estimating the value of Pi and analysing waveforms. Early estimates for Pi – the ratio of a circle’s circumference to its diameter – were produced in Babylonia. The ancient Greek mathematian, Archimedes, produced improved estimates by means of a clever algorithm which used polygons to approximate the dimensions of a circle. Later, the Chinese mathematician Zu Chongzhi and his son used a similar method to produce an estimate that would stand as the most accurate for 900 years. With the decline of ancient Greece, Persia took on the mantel of leadership in mathematics from the 8^th to 11^th centuries. Al-Khawrzmi’s texts ultimately propagated knowledge of algorithms to the West. In 18^th century France, Joseph Fourier proposed that waveforms could be decomposed into their constituent simple harmonics. The resulting algorithm became the key to signal analysis in today’s electronic communication systems.

This chapter discusses the historical development of the theory of global warming. The origins of our understanding that gases in the atmosphere influence climate can be traced back to 1824, when a French polymath named Joseph Fourier recognized that atmospheric gases trapped heat, raising the surface temperature enough to allow us to inhabit the planet. In 1896, Swedish chemist and eventual Nobel Prize winner Svante Arrhenius calculated that if the amount of carbon dioxide gas in the atmosphere were to double, global temperatures would rise 5–6°C (9–11°F). By 1960 the greenhouse effect had evolved from theory to observational fact to dimly perceived threat. Research showed that it was possible to measure carbon dioxide concentrations accurately and that they were rising.