The German Genius

thousands of meters per second. This brought about the objection from several others that his assumptions and calculations could not be right, since otherwise gases would diffuse far more quickly than they were known to do; he therefore abandoned that approach, introducing instead the concept of the “mean free path,” the average distance that a particle could travel in a straight line before colliding with another one. 24
    Others were attracted by Clausius’s efforts, in particular James Clerk Maxwell in Britain, who published “Illustrations of the Dynamical Theory of Gases” in the Philosophical Magazine in 1860, making use of Clausius’s idea of the mean free path. However, where Clausius had assumed that every particle in a gas traveled at the same average velocity, Maxwell relied on the new science of statistics to calculate a random distribution of particle velocities, arguing that the collisions between particles would result in a distribution of velocities about a mean rather than an equalization. (Just what these particles were was never settled, not then, though Maxwell was convinced their very existence “was proof of the existence of a divine manufacturer.”) 25
    The statistical—probabilistic—element introduced into physics in this way was a very controversial and yet fundamental advance. In his 1850 paper Clausius had drawn attention in the second law of thermodynamics to the “directionality” of the heat flow—heat tends to pass from a hotter to a colder body. He had not at first bothered with the implications of the irreversibility or otherwise of processes, but in 1854 he argued that the transformation of heat into work and the transformation of heat from a higher temperature into heat of a lower temperature were in effect equivalent and that in some circumstances they could be counteracted—reversed—by the conversion of work into heat, where heat would flow from a colder to a warmer body. This, for Clausius, only emphasized the difference between reversible (man-made) and irreversible (natural) processes: a decayed house never puts itself back together, a broken bottle never spontaneously reassembles.
    It was only later, in 1865, that Clausius proposed the term “entropy” (from the Greek word for “transformation”) for the irreversible processes whereby the tendency for heat to pass from warmer to colder bodies was also described as an instance of the increase in entropy. In doing this Clausius now emphasized the directionality of physical processes, and he described the two laws of thermodynamics as follows: “The energy of the universe is constant” and “The entropy of the universe tends to a maximum.” Time, in some mysterious way, had become a property of matter. 26
    For some people, the second law had a much greater significance than even Clausius thought. Another Briton, William Thomson, Lord Kelvin, thought that the irreversibility that was such a feature of the second law—the dissipation of energy—also implied a “progressivist cosmogony,” one that moreover underlined the biblical view about the transitory character of the universe. Thomson drew the implication from the second law that the universe, known by then to be cooling, would “in a finite time” run down and become uninhabitable. Helmholtz had also noticed this implication of the second law, but it was only in 1867 that Clausius himself, who had by then moved back to Germany from Zurich, acknowledged the “heat death” of the universe. 27
    T HE A PPEARANCE OF “S TRANGENESS” IN P HYSICS
     
    The statistical notions aired by Clausius and Maxwell attracted the attention of the Austrian physicist Ludwig Boltzmann. 28 Boltzmann (1844–1906) was born in Vienna during the night between Shrove Tuesday and Ash Wednesday, a coincidence which, he half-jokingly complained, helped to explain his frequent and rapid mood swings, which tossed him between unalloyed happiness and deep depression. The son of a tax official, Boltzmann was appointed professor of mathematical physics at the University of Graz in 1869 at the age of only twenty-five. Later he worked with Robert Bunsen at Heidelberg and with Helmholtz in Berlin. In 1873 he joined the University of Vienna as professor of mathematics and remained there until 1902 when he committed suicide during one of his depressions.
    Boltzmann’s main achievement lay in two famous papers, describing in mathematical terms the velocities, spatial distribution,