The scale of the British Empire and the dominance of British industry ensured that in 1890 nearly two-thirds of the telegraph lines in the world were owned by British companies, which controlled 156,000 kilometers of cables. But the influence of the system extended far beyond the British Empire. The growth of the new global communication networks meant, as the writer Max Nordau noted in 1892, that the simplest villager now had a wider geographical horizon than a head of government a century before. If he read a paper he 'interests himself simultaneously in the issue of a revolution in Chile, a bush-war in East Africa, a massacre in North China, a famine in Russia'. Within major cities, tram systems, and suburban and underground railways began to speed up traffic, just as the main roads were becoming clogged with horse-drawn cabs and carriages, automobiles and omnibuses. In 1863 the world's first underground railway, the Metropolitan, opened in London, and was soon extended, but steam locomotives posed many problems, and the cut-and-cover method of construction soon ran out of roads that could be dug up, and London turned to boring deeper lines for 'tube' trains powered by electricity, the first of which was opened in 1890. Above ground, the electric tramway system devised by Werner von Siemens began running in Berlin in 1879, and soon spread to many other countries.

Spiral-like shapes crop up regularly in nature. There’s a particular kind of spiral, called a logarithmic spiral that was familiar to Wren. Logarithmic spirals were first mentioned by the German artist and engraver Albrecht Durer, and studied in great detail by the mathematician Jacob Bernoulli – he gave them the name “spira mirabilis”, or “miraculous spiral”. In a logarithmic spiral, the distance r from the centre is a power of the angle we’ve moved through (or conversely the angle is a logarithm of the distance, hence the name). This means that the gap between consecutive rings of the spiral is increasing each time. One example of a logarithmic spiral, shown below, is r= 2 θ/360(where we are measuring our angles in degrees). With every complete revolution, the distance of the spiral from the origin doubles. It crosses the x -axis at 1, 2, 4, 8, 16 and so on. Keen to recapture the initiative from the British, the French government organized an International Conference on Time in 1912, which established a generally accepted system of establishing the time and signaling it round the globe. The Eiffel Tower was already transmitting Paris time by radio signals, receiving calculations of astronomical time from the Paris Observatory. At 10 a.m. on 1 July 1913, it sent the first global time-signal, directed at eight different receiving stations dotted around the world. Thus, as one French commentator boasted, Paris, 'supplanted by Greenwich as the origin of the meridians, was proclaimed the initial time centre, the watch of the universe'. The coming of wireless telegraphy had indeed signaled the death-knell for the remaining local times.You can play with the effects of different shaped lenses – spherical, parabolic, and hyperbolic – using Lenore Horner’s Geogebra simulation at https://www.geogebra.org/m/Ddbpxd5X Wren was educated at Oxford and later held the Savilian chair in astronomy there, as well as his Gresham professorship in London. These roles and others place him right at the heart of an exceptionally active and exciting community of scientific thinkers. The group around Gresham College included not just Wren as Gresham Professor of Astronomy but also Robert Hooke, who was Gresham Professor of Geometry at a similar time. Wren was not just a founder member of the Royal Society (which arose out of weekly meetings at Gresham beginning in November 1660) but served as its president. And he was an active contributor in meetings – if perhaps not in subscription fees, which he had to be chased to pay up. In short, he was a key contributor to the scientific and mathematical thought of the time. We can see this, not just from his own work, but by the amount he is mentioned in the writing of others, giving credit to him for certain ideas. For example, when Isaac Newton introduces the idea of a force governed by an inverse square law in his Principia Mathematica, he says that one example is the force governing the motion of the planets “as Sir Christopher Wren, Dr. Hooke, and Dr. Halley have severally observed”. Wren’s name appears seven times in the Principia. In fact, the leading architectural historian John Summerson (1904-1992) wrote that if Wren had died at thirty, he would still have been a “figure of some importance in English scientific thought, but without the word “architecture” occurring once in his biographies”. Wren’s contributions to astronomy are the subject of a lecture by the current Gresham Professor of Astronomy, Katherine Blundell, which you can watch online: today I want to explore his mathematical contributions. The portrait of Christopher Wren is from the National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw06939/Sir-Christopher-Wren Allan H Brooks/ New Control Tower Newcastle Airport/Image use permitted under CC BY-SA 2.0 https://commons.wikimedia.org/wiki/File:Newcastle_International_Airport_Control_Tower.jpg

We’ve got a huge range of 100% genuine luxury watches from leading brands such as Rolex, Tag Heuer, Omega and Breitling, all individually assessed and valued by our expert buyers.Wren’s solution of Kepler’s problem manages to relate the areas into which the semicircle must be divided to lengths of specific circle arcs. These are then equated to carefully positioned “stretched” or “prolate” cycloids – which of course Wren already knew how to find the length of, from his own earlier work. And so he was able to solve Kepler’s problem. His solution was published by John Wallis in a 1659 treatise on the cycloid (which also included Wren’s rectification of the cycloid). If your Latin is tip-top, you can give it a read: John Wallis: Tractatus duo, prior de cycloide et corporibus inde genetis: posterior, epistolaris in qua agitur de cissoide. In a 1668 letter, the English mathematician John Wallis said that although the challenge of Kepler’s problem had been issued to the French mathematicians almost a decade previously, “there is none of them have yet (that I hear of) returned any solution”. Take that, Jean de Montfort! Numerous technical obstacles had to be overcome in creating a universal system of standard time. In 1872, when the first transatlantic cable, the transmission of messages revealed that Paris was half a second further away from London than had previously been thought. Trying to fix a precise difference in longitude between Paris and Berlin, engineers noted that signals were slowed by mechanical and other factors such as the 'non-instantaneity of the transmission of the electric flux'. Despite such technical problems, and overcoming a bitterly fought rearguard action by the French, who eventually abstained on the decisive motions, in 1884, delegates from 25 states met in Washington to agree on the standardization of world time. Sailors had already synchronized time using chronometers set by longitudinal measurements based on the Greenwich Meridian, reflecting British dominance of seaborne mercantile traffic, and this was the standard adopted at the Washington conference, which divided the world into 24 time-zones by longitude, treating the meridian as the zero line, dividing the Eastern from the western hemisphere.