One of the most celebrated papers ever written was the report by Cooley and Tukey in the 1960s on the so-called Fast Fourier Transform (FFT). The FFT reduced the number of computations required to compute a discrete Fourier transform. One ot the characteristics of the FFT was that it required the user of the algorithm to operate on a dataset containing a number of points equal to a power of 2.
It is important to note that there are now a variety of algorithms available for computing Fourier Transforms (FTs) on data sets having other lengths. The fact that programs such as Excel, and many others, do not allow you to perform FTs on data lengths that are not powers of 2 is a holdover from earlier times. It is also a tribute to the lasting influence of the Cooley-Tukey algorithm. While all data lengths do not have a Fast transform available, many do. Also, slow transforms can be done on nearly any length data set. As long as you do not need to be doing a lot of FTs, modern computers can handle the computing if programmed to do so AND you won’t necessarily be an old man or woman by the time they are finished.
I gave this background more as an introduction to John Tukey one of the authors of this influential paper. I had the good fortune to meet John Tukey in the late 80’s early 90’s and I think he is a nice person to tell a story about to give students a better picture of scientists and mathematicians. As I have remarked elsewhere on this site, people have strange ideas about what it means to be a scientist and the nature of their work. Most are normal people who have been blessed with scientific or mathematical abilities.
I met John Tukey when he came to Seattle as a consultant for the Health Effects Institute. The Health Effects Institute is a combined USEPA and Automobile Industry fund which was created to fund health effect research. They were the first to audit MY notebooks; a story for another day. I was working for Jane Koenig at the time as a technician and she was applying for funding from HEI to support some studies of the health effects of air pollution. There were some statistical questions related to sample size etc. (actually, I do not remember exactly what the problem was) raised by a reviewer of the grant. HEI brought in John Tukey to resolve the disagreement between the group I worked for and the HEI reviewers.
In the time before he came to visit my boss’s lab, I spent a good bit of time teaching myself Fourier transforms mostly from papers in the literature (and a few IEEE publications). The idea was to do some measurements of pulmonary mechanics using the analysis of waveforms. For those on there way to medical school there is a model of the lungs based on the behaviour of RLC (resistor-inductor-capacitor) circuits. C is related to the size of the lung, I to the inertia of air moving in the airways, and R the resistance of the airways. The lab was interested in airway resistance as a measure of the effect of air pollution on lungs. Having fought my way (slowly) through the FT papers, I was immediately interested when I heard John Tukey would visit. I would get to meet the man in the papers I had been reading!
John Tukey was quite an old man at the time. We never talked any “shop.” What I remember about him was that he really liked to read mysteries. I discovered he had a love of used bookstores. He told me that whenever he travelled he always liked to make the rounds of the local bookstores to see if there were any mysteries he had not read. I have always had a similar love of books (particularly used books). At the time there were a number of reasonable used bookstores in the district around the University of Washington. I remember spending some time telling John Tukey how to get to all of them. He listened intently, took some notes and took off. He didn’t want to wait for me to show him around, caught a cab, and came back later that evening.
He wasn’t quite what I expected. I am not sure what I was expecting, but an old gentleman who loved mysteries didn’t quite fit my picture of what the co-discoverer of the FFT would be like. It was nice to have met him. I still think of him occasionally as I am looking through used bookstores while on my travels, something I do whenever I can.
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