标签: omomorphic

I never met Richard Feynman but I am glad to say that I played a small role in preserving what he had to say, especially stories about events in his past. I first encountered Feynman’s physics books when I was in college in the late ‘60s. A picture in the forward of the book showed Feynman playing bongo drums. What kind of a physicist could this be, I wondered to myself. As decades passed, I encountered people who had taken a course from Feynman, usually at CalTech, including physics professor Julian Noble. Walter Thorson, a theoretical chemist who went through school the CalTech-MIT route and taught for many years at the U. of Alberta in Edmonton, is another. In one of our roving discussions, I recall Walter telling me about Feynman’s teaching style and his ability to do contour integrals in the most non-obvious ways. It was hard for Feynman, as brilliant as he was, to teach minds of ordinary brilliance. The former Feynman student who stands out to me the most was a friend of mine and fellow homesteader in the jungle here in Belize who, sadly, died of cancer a few years ago at the age of 51. Mark Ludwig had a doctorate in particle physics. For his PhD thesis, he had worked out by a different means one of the classic math derivations of modern physics. I marveled that it had not been worked out as he did it long before, but it was not a simple feat. Mark went to MIT, and according to his PhD chemist father, was there less than two years. He had gone through all the undergraduate math and physics and was wondering what to do next. A friend of his was going to Cal Tech, but it was long past the deadline for submission of admission applications as a student. On the letters of recommendation of his physics teachers at MIT he got into graduate school at Cal Tech without having obtained a degree from MIT. The only university degree he ever had was a PhD. Later, he dropped out of the hallowed halls of science at CalTech, in part because of what he observed as the dilution of the pursuit of scientific truth by a pursuit of money by his professors. Then there was a bizarre incident that shattered his hard-headed scientific-materialist outlook. In the Pasadena newspaper, an occult group ran an advertisement guaranteeing a “psychic experience” or your money back. Mark rose to such challenges and, determined to get to the bottom of the ruse, responded to the ad - but he did not ask for his money back. I asked him what happened. He responded: “They told me things that only I knew that they could not possibly have known and in enough detail to convince me that there is more going on in the universe than can be explained on the basis of physics alone.” He subsequently returned home and spent time studying the wider picture of reality, continuing it after returning to a physics school that was not as demanding as CalTech or MIT so that he could do both physics and continue “studies of everything” at the same time.   While at CalTech, Mark was one of only two students who dared to take for credit among a class full of auditors Feynman’s course in advanced mathematical methods for physics. The other was Stephen Wolfram who is known for his contributions to symbolic computing of mathematics. Like Thorson, Mark was also not entirely impressed with Feynman’s teaching style, though he was interacting with someone of similar ability. One of Feynman’s colleagues at Cal Tech was the father of Ralph Leighton. Ralph was a school teacher and young friend of Feynman. Both of them had an interest in drumming, and they had drumming sessions together and even built drums. At these sessions, the raconteur (story-teller) Feynman would tell of events from his past. The younger Ralph began to realize that these stories were extraordinary - a goldmine of tales! He brought his tape recorder - an ordinary machine and not of studio quality - to tape them. He then transcribed them into what became the longest top-selling book on the New York Times best-seller list at that time, titled Surely You’re Joking, Mr. Feynman: Adventures of a Curious Character. I later wrote to Ralph that the subtitle was ambiguous in that it could be taken two different ways. He and Feynman had already thought about it and knew of three different meanings. Later in life, while the Soviet Union still existed, Feynman had an interest - kind of a fetish curiosity - about Tannu Tuva, an obscure part of the Soviet Union in Central Asia. The capital city was Kyzyl, and lacking any vowels, Feynman thought that it just had to be an interesting place, a country with a capital having a name with no vowels. (Russian head of state, Vlad Putin, recently disappeared for a week to Tuva on vacation, and did some fishing.) Ralph was Feynman’s co-laborer in the effort to go there. Feynman got a California license plate that said “TOUVA” on it and was trying to devise means of going to the place that was off-limits by the Soviets. He offered to give physics lectures in Moscow, to which the Soviets agreed, and then he could visit Tuva. No, Feynman objected; Tuva first, then the lectures. It was declined. Leighton wrote a book on the project, Richard Feynman’s Last Journey: Tuva or Bust! (W.W. Norton, 1991). Before I tapped into Leighton’s Friends of Tuva website, I had gone to an IEEE conference in Miami, Florida on signal processing and had run across Alan Oppenheim who taught DSP at MIT. At Tektronix, I took his videotape course and was impressed by his mastery of the subject and his ability to deliver highly-refined lectures. I met and talked with him at the conference. (Small world: his sister and my brother Kenneth were working together in heart surgery in Portland, Oregon over that summer while Ken was in medical school.) Oppenheim had developed an extension of linear filtering he called homomorphic filtering. In one of his videotape lectures he explained it and then played an aria of Enrico Caruso from an old 78 rpm vinyl record that had been filtered. It was memorable; Caruso’s tenor voice was filtered out from the background orchestra and it was as though he were singing a capela, with no hint of an orchestra behind him or of scratches on the record. Years later, Ralph began to offer through his Friends of Tuva website audiotape copies of his better recordings. I bought a copy of each of them and was keen to get others of lesser quality. I wrote to Ralph, with homomorphic filtering impressed on my memory, and suggested that he talk with Oppenheim about the tapes. In February 1995 he wrote back on a postcard: “Al Oppenheim has sent me some sound-reduced tapes that are promising. He’s definitely the guy with the know-how. Thanks for the lead!” Some complications arose for Ralph’s purposes and he later wrote a note saying: “MIT’s solution (algorithm) was not well suited for the job, but “Sonic Solution’s No-Noise” did the trick. Thanks for the impetus to get it done!” Oppenheim had referred him to a sound lab in Utah that accomplished the task. The “tapes” are available in digital format and can be downloaded for a very modest price (some free) from Welcome to Feynman Online! Feynman’s safecracker story - one of his best, about how he picked the lock on a safe that contained all of the detailed secrets of the atomic bomb - has also been put in cartoon form as a “Two-Fisted Science” booklet from Gemstone Publishing, P.O. Box 469, West Plains, MO 65775; tel.: 417-256-2224; Two-Fisted_Science@umich.edu I end with a final story about Feynman from another of his students. An acquaintance of mine, Don Page, a physicist at the U. of Alberta at the time of telling of this story, was reminded that during his physics PhD candidacy exam, after failing to give a good explanation of quantum emission from black holes shortly after Stephen Hawking’s prediction of it (when he had been working on the problem himself before Hawking and so in principle, he wrote, could have made the prediction himself “if only I had been much more competent”) was humiliated by being told by Feynman: “Quantum mechanics was invented in 1926. Now it is 1972. You should learn quantum mechanics.” But, he wrote, my embarrassment was mollified somewhat when other members of the committee said, “Dick, Dick, it’s 1973.” Dennis Feucht has his own laboratory, Innovatia, on a jungle hilltop in Belize, where he performs electronics research, technical writing, and helps others with product development. He wrote a four-volume book-set on analog circuit design, has completed a book on transistor amplifier design and is working on a book on power electronics.