The Ancient Greeks (Archimedes being an honourable exception) have a reputation for having been only interested in pure studies, and despising practical applications (which may well have helped the Romans take over.)
Recently we were treated to a BBC programme entitled How Britain Won the Space Race, a rather over-ambitious title one might think. Probably viewer bait, but it did treat a significant contribution, namely that of Sir Bernard Lovell, the pioneering British radio astronomer who set up the Jodrell Bank Observatory, whose Mark I telescope was the only one in the world able to track Sputnik’s booster rocket by radar, locating it just before midnight on 12 October 1957.
It also tracked the US Pioneer 5 interplanetary probe (160) and the Soviet lunar lander Luna 9 and listened in on its facsimile transmission of photographs from the Moon’s surface. The photos were sent to the British press and published before the Soviets themselves had made the photos public.
Between 1958 and 1963, it was the main component of Britain’s Four-minute warning system designed to detect and track incoming Soviet missiles, while continuing to be used for astronomical research. Bernard Lovell was unhappy with this, saying:
It was known only to a very few people that I had been approached by the Chief of the Air Staff, who told me we had the only instrument in the world that could detect a Soviet missile. I simply wanted to do research, but events wouldn’t allow me to.
According to the programme, though, it was the existence of the Soviet space and missile programmes that freed up government funding for Jodrell Bank. Ingratitude, maybe?
Another interesting article was The unplanned impact of mathematics (Nature 475, 166–169 (14 July 2011) doi:10.1038/475166a). An edited snippet from this:
«In 1998, mathematics was suddenly in the news. Thomas Hales of the University of Pittsburgh, Pennsylvania, had proved the Kepler conjecture, showing that the way greengrocers stack oranges is the most efficient way to pack spheres. A problem that had been open since 1611 was finally solved! On the television a greengrocer said: “I think that it’s a waste of time and taxpayers’ money.” I (= the author) have been mentally arguing with that greengrocer ever since: today the mathematics of sphere packing enables modern communication, being at the heart of the study of channel coding and error-correction codes.»
Now the E8 lattice is the densest packing of spheres in 8-dimensions. The author continues:
« . . . but is it useful? In the 1960s an engineer called Gordon Lang believed so. Lang was designing the systems for modems and was busy harvesting all the mathematics he could find. He needed to send a signal over a noisy channel, such as a phone line. The natural way is to choose a collection of tones for signals. But the sound received may not be the same as the one sent. To solve this, he described the sounds by a list of numbers. It was then simple to find which of the signals that might have been sent was closest to the signal received. The signals can then be considered as spheres, with wiggle room for noise. To maximize the information that can be sent, these ‘spheres’ must be packed as tightly as possible.
In the 1970s, Lang developed a modem with 8-dimensional signals, using E8 packing. This helped to open up the Internet, as data could be sent over the phone, instead of relying on specifically designed cables. Not everyone was thrilled. The master geometer Harold Scott MacDonald Coxeter, who had helped Lang understand the mathematics, said he was “appalled that his beautiful theories had been sullied in this way”.»