The German Genius

miles up. The outline of Italy is the same but many details are now visible that weren’t before—estuaries, small bays, tiny off-shore islands. Again, what transformation has taken place, what has changed, and what has stayed the same, and how can that change/staying-the-same be represented mathematically? This last example was not available in Klein’s day because aerial photography didn’t exist, but the problem, mathematically, is now known as “fractals” and shows how far ahead of his time Klein was. It presaged chaos theory.
    Under Klein’s leadership Göttingen became a mecca to which students from many lands, especially America, flocked. 39 The French had led the way at the turn of the nineteenth century, at the École Polytechnique, embracing the work of Joseph-Louis Lagrange, Gaspard Monge, and Jean-Victor Poncelet. The research and inspiration of Gauss, Riemann, and Klein ensured that that leadership passed to Germany. It held that lead—at least in theoretical terms—until the advent of Hitler. 40

The Rise of the Laboratory: Siemens, Hofmann, Bayer, Zeiss
     
    N o one better illustrates the changes taking place in Germany in the nineteenth century than Werner Siemens. As just one indicator, he became Werner von Siemens in 1888. Born in 1816, the fourth of fourteen children of a tenant farmer in Lenthe, near Hanover, Werner had to leave his Gymnasium in 1834 without taking his examinations because of the family’s precarious financial situation, so that he could join the Prussian army and gain some engineering training in that way. He had the foresight, while at school, to drop Greek and take extra lessons in mathematics and land surveying.
    He said later that the three years he spent at the Berlin Artillery and Engineering School were the happiest of his life. Among his teachers was Martin Ohm, brother of the physicist Georg Ohm. 1 While at the school Werner started to produce the first of the inventions at which he was to prove so adept. The earliest concerned gilding and plating silver, a process he sold to a German silver manufacturer.
    He became interested in the theory of the conservation of energy (he was familiar with the work of both Mayer and Helmholtz) and this fanned his interest in engines (he published some of his early ideas in Poggendorff’s Annalen )—all of which meant he was one of the first to appreciate the great importance of telegraphy. 2 His time in the army had taught him, among other things, the need for rapid, reliable communication, and so in 1847 he produced a pointer telegraph, which was notable for its reliability, this dependability laying the foundation for the Siemens & Halske Telegraph Construction Company, which he founded jointly with Johann Georg Halske, himself a mechanic, in Berlin that same year. 3
    Once he had a reliable telegraph, Siemens saw its many possibilities. He laid the first long subterranean wire, from Berlin to Grossbeeren, almost twenty miles to the southwest. He recognized that the invention of guttapercha in Britain would enable the lines to be insulated, which meant that telegraph wires could be spread across the world, even in America following the Civil War. An underground line from Berlin to Frankfurt am Main came next, Frankfurt being where the German National Assembly was meeting. The line was buried to keep it safer at times of political trouble. 4
    In 1851 Siemens announced what would become his greatest invention—the dynamo-electrical machine. 5 He clearly foresaw the exceptional growth of power engineering, with Siemens & Halske repeatedly introducing new applications for electric current: in 1879 the first electric railway was presented at the Berlin Trade Fair, and the first electric street-lights were installed in Berlin’s Kaisergalerie; in 1880 the first electric elevator was built in Mannheim; in 1881 the world’s first electric streetcar went into service in Berlin-Lichterfelde; in 1886 the first electric trolley bus made its appearance; in 1887 the Berlin Mauerstrasse power station opened; in 1891 the first electric drills were made; and in 1892 the electricity meter, indicating the widespread acceptance of electrical machines, was installed. The name Siemens became synonymous with Elektrotechnik , a word coined by Siemens himself. 6
    In 1879 he helped found the Elektrotechnischer Verein (Engineering Society), one of whose aims was the introduction of faculties for electrical engineering at the technische