Gianonni's was one of Feynman's favorite hangouts, and it seems that their placemats were one of his preferred items on which to work out whatever physics problems were occupying his mind at the moment. In his own words:
"There was a period when there were topless restaurants in town: You could go there for lunch or dinner, and the girls would dance without a top, and after a while without anything. One of these places, it turned out, was only a mile and a half away from my house, so I went there very often. I'd sit in one of the booths and work a little physics on the paper placemats with the scalloped edges, and sometimes I'd draw one of the dancing girls or one of the customers, just to practice." (Richard Feynman, "Surely You're Joking Mr. Feynman!", p. 309)
His colleagues and students were well aware of Feynman's fondness for doing work at Gianonni's, including his doctoral student Richard Sherman: "Sometimes Richard would suddenly say, "Let's knock off and go somewhere and fool around!" The usual place we went was a topless bar in Pasadena, called Gianone's (sic). There was always something happening at Gianone's in the afternoon, every day of the week. We'd walk in, grab a table. Feynman knew everybody there—all the ladies, Gianone the owner, and anybody who was a regular. He would go behind the bar and pick up an orange juice, because he never drank anything alcoholic. He would also grab a half-inch stack of those paper doilies, or place mats that they put down on tables in restaurants, and come back to the table. We might continue doing physics, or we might watch the ladies dancing on the stage. Frequently people would come by and chat, and this was the sort of entertainment that he liked. But it was kind of deceptive because, believe it or not, although this particular environment might not seem conducive to doing something like theoretical physics, over the years, Feynman actually did an enormous number of calculations in that place. " (Richard Sherman, in: Christopher Sykes, No Ordinary Genius: The Illustrated Richard Feynman, pp 100-101)
Distracted perhaps by the setting, Feynman's riffs here pertain mainly to his Operator Calculus, an elegant & powerful mathematical shorthand he had invented for QED, where proper ordering of noncommuting objects is essential; underlying formal work was published in a much-cited 1951 Physical Review paper the year he was in Brazil, before heading to Caltech. It is likely that Feynman's creation of Operator Calculus owes its inspiration, in part, to his learning Umbral ("shady"; i.e., from the "Dark Side") Calculus as a precocious Far Rockaway teenager fascinated by Faulhaber's Power Sums & the magical Bernoulli numbers encountered therein. Regrettably, not standard fare in college calculus courses these days...
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