After Cranwell, Whittle transferred to Hornchurch in Essex to a fighter squadron, and then in 1929 moved on to the Central Flying School at Wittering in Sussex as a pupil instructor. All this time he had been doggedly worrying how to create a new kind of engine, most of the time working on an amalgam of a petrol engine and a fan of the kind used in turbines. While at Wittering, he suddenly saw that the solution was alarmingly simple. In fact, his idea was so simple his superiors didn’t believe it. Whittle had grasped that a turbine would drive the compressor, ‘making the principle of the jet engine essentially circular.’69 Air sucked in by the compressor would be mixed with fuel and ignited. Ignition would expand the gas, which would flow through the blades of the turbine at such a high speed that not only would a jet stream be created, which would drive the aircraft forward, but the turning of the blades would also draw fresh air into the compressor, to begin the process all over again. If the compressor and the turbine were mounted on the same shaft, there was in effect only one moving part in a jet engine. It was not only far more powerful than a piston engine, which had many moving parts, but incomparably safer. Whittle was only twenty-two, and just as his height had done before, his age now acted against him. His idea was dismissed by the ministry in London. The rebuff hit him hard, and although he took out patents on his inventions, from 1929 to the mid-193os, nothing happened. When the patents came up for renewal, he was still so poor he let them lapse.70
In the early 1930s, Hans von Ohain, a student of physics and aerodynamics at Göttingen University, had had much the same idea as Whittle. Von Ohain could not have been more different from the Englishman. He was aristocratic, well off, and over six feet tall. He also had a different attitude to the uses of his jet.71 Spurning the government, he took his idea to the private planemaker Ernst Heinkel. Heinkel, who realised that high-speed air transport was much needed, took von Ohain seriously from the start. A meeting was called at his country residence, at Warnemünde on the Baltic coast, where the twenty-five-year-old Ohain was faced by some of Heinkel’s leading aeronautical brains. Despite his youth, Ohain was offered a contract, which featured a royalty on all engines that might be sold. This contract, which had nothing to do with the air ministry, or the Luftwaffe, was signed in April 1936, seven years after Whittle wrote his paper.
Meanwhile in Britain Whittle’s overall brilliance was by now so self-evident that two friends, convinced of Whittle’s promise, met for dinner and decided to raise backing for a jet engine as a purely business venture. Whittle was still only twenty-eight, and many more experienced aeronautical engineers thought his engine would never fly. Nonetheless, with the aid of O. T. Falk and Partners, city bankers, a company called Power Jets was formed, and £20,000 raised.72 Whittle was given shares in the company (no royalties), and the Air Ministry agreed to a 25 percent stake.
Power Jets was incorporated in March 1936. On the third of that month Britain’s defence budget was increased from £122 million to £158 million, partly to pay for 250 more aircraft for the Fleet Air Arm for home defence. Four days later, German troops occupied the demilitarised zone of the Rhineland, thus violating the Treaty of Versailles. War suddenly became much more likely, a war in which air superiority might well prove crucial. All doubts about the theory of the jet engine were now put aside. From then on, it was simply a question of who could produce the first operational jet.
The intellectual overlap between physics and mathematics has always been considerable. As we have seen in the case of Heisenberg’s matrices and Schrödinger’s calculations, the advances made in physics in the golden age often involved the development of new forms of mathematics. By the end of the 1920s, the twenty-three outstanding math problems identified by David Hilbert at the Paris conference in 1900 (see chapter 1) had for the most part been settled, and mathematicians looked out on the world with optimism. Their confidence was more than just a technical matter; mathematics involved logic and therefore had philosophical implications. If math was complete, and internally consistent, as it appeared to be, that said something fundamental about the world.
But then, in September 1931, philosophers and mathematicians convened in Königsberg for a conference on the ‘Theory of Knowledge in the Exact Sciences,’ attended by, among others, Ludwig Wittgenstein, Rudolf Carnap, and Moritz Schlick. All were overshadowed, however, by a paper from a young mathematician from Brünn, whose revolutionary arguments were later published in a German scientific journal, in an article entitled ‘On the Formally Undecidable Propositions of Principia Mathematica and Related Systems.’73 The author was Kurt Godei, a twenty-five-year-old mathematician at the University of Vienna, and this paper is now regarded as a milestone in the history of logic and mathematics. Gödel was an intermittent member of Schlick’s Vienna Circle, which had stimulated his interest in the philosophical aspects of science. In his 1931 paper he demolished Hilbert’s aim of putting all mathematics on irrefutably sound foundations, with his theorem that tells us, no less firmly than Heisenberg’s uncertainty principle, that there are some things we cannot know. No less importantly, he demolished Bertrand Russell’s and Alfred North Whitehead’s aim of deriving all mathematics from a single system of logic.74
There is no hiding the fact that Gödel’s theorem is difficult. There are two elements that may be stated: one, that ‘within any consistent formal system, there will be a sentence that can neither be proved true nor proved false’; and two, ‘that the consistency of a formal system of arithmetic cannot be proved within that system’.75 The simplest way to explain his idea makes use of the so-called Richard paradox, first put forward by the French mathematician Jules Richard in 1905.76 In this system integers are given to a variety of definitions about mathematics. For example, the definition ‘not divisible by any number except one and itself’ (i.e., a prime number), might be given one integer, say 17. Another definition might be ‘being equal to the product of an integer multiplied by that integer’ (i.e., a perfect square), and given the integer 20. Now assume that these definitions are laid out in a list with the two above inserted as 17th and 20th. Notice two things about these definitions: 17, attached to the first statement, is itself a prime number, but 20, attached to the second statement, is not a perfect square. In Richardian mathematics, the above statement about prime numbers is not Richardian, whereas the statement about perfect squares is. Formally, the property of being Richardian involves ‘not having the property designated by the defining expression with which an integer is correlated in the serially ordered set of definitions.’ But of course this last statement is itself a mathematical definition and therefore belongs to the series and has its own integer, n. The question may now be put: Is n itself Richardian? Immediately the crucial contradiction appears. ‘For n is Richardian if, and only if, it does not possess the property designated by the definition with which n is correlated; and it is easy to see that therefore n is Richardian if, and only if, n is not Richardian.’77