Overcoming the problem with FFT
The problem to distinguish a nuclear test from an earthquake. Every day
around the world, there are close to 300 earthquakes with a magnitude of
three or greater. Seismometer signal depends not only on the yield of
the device but also on how deep it was buried. For a given yield, deeper
explosions appear smaller. So, scientists wanted a method to reliably
determine whether a given signal was a bomb or an earthquake, all the
information needed was indeed present in the seismometer signal but the
method to extract the information was needed. We had to find how much of
different frequencies were present which meant Fourier transform of the
signal needed to be taken. At the speed of 1960s computers, this
calculation would take unrealistic amount of time and was not a
practical solution to the problem. John Tukey American mathematician and
statistician knew a way to compute discreet Fourier transforms with many
fewer computations. It would mean that the calculation that would’ve
taken over three years could be done in just 35 minutes. This has aptly
become known as the Cooley-Tukey Fast Fourier Transform algorithm.
Richard Lawrence Garwin (born April 19, 1928) is an American physicist
learnt this method to run the FFT algorithm without disclosing that it
was to detect underground Soviet nuclear tests.
Cooley and Tukey published the algorithm in a seminal 1965 paper and its
use immediately took off, but it was too late to secure a comprehensive
nuclear test ban. At the peak in the mid-1980s, 70,000 nuclear warheads
were already in existence. If only this algorithm was found 5 years
prior a comprehensive test ban could have been reached, stopping the
nuclear arms race before it even started. Even more unfortunate thing is
that FFT algorithm was already discovered all the way back in 1805 by
Mathematician Carl Friedrich Gauss to determine the orbit of newly
discovered asteroids and he never thought to publish that first insight.
The reason his breakthrough was not widely adopted was because it only
appeared after his death in volume three of his collected works and it
was written with non-standard notation in a 19th century version of
Latin.