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The first lecture- ‘Introduction’. What do you remember about it?
I remember having regarded the task of having to give that first lecture with some distaste, for the simple reason that it appeared to represent a tremendous self-indulgence: lecturing per se, invariably risks being an imposition on the listener. One cannot always be certain that the listener cares very much what the lecturer is talking about.
In this particular case, only a handful of students had subscribed to the course through the formal channels, and yet the class was packed for the introductory. One could not help the impression that the remainder of the attendees (those who hadn’t subscribed) were testing the waters. I would have been significantly more self-assured of our ability to turn them into subscribers if I weren’t lecturing,- if I were,  rather, answering questions that were uppermost in their minds. However, this was the first day of the course and none of the students were altogether clear on what exactly it was intended to address. As a result, I was compelled to invent my own questions, guessing rather clumsily what the average student may be expected to ask on encountering the title of the course.
And so, I addressed the questions: ‘Why talk about “physics” in a course about “computational” modeling?’ and ‘Of what use is this material to a practicing engineer/programmer/…etc.?’

Let’s get into it. You begin with Richard Feynman.
That’s right. Richard Feynman strikes many as being, in some sense, a key figure in engineering. Throughout the Feynman Lectures he made decisions about emphasis and style based on the fact that his audience included engineers. He contributed, in varying degrees of participation, to a number of major engineering projects in his life- ones that produced the atom bomb, nanotechnology, protective measures for the space shuttle, computer networks etc. And he spent the last stage of his life working, with considerable involvement, on computing. This characterisation of his legacy is likely to be controversial to some, but there is an unmistakable style in his approach to problems that is highly suggestive of the engineer.
  And it can be recognised elsewhere- regardless of time and cultural environment. I recall once having remarked, years ago, in conversation with an eminent scientist, on the great difference in the styles of Riemann and Fourier while discussing the same thing- trigonometric series. The scientist responded, simply: “It is true…Riemann thought like a mathematician, whereas Fourier had the mind of an engineer.” Similarly, the great computer scientist Donald Knuth often speaks of scientists of the distant past who had the ‘soul’ of a computer scientist, despite living centuries before the invention of computers: he mentions Abel, and the ancient Babylonians as examples.
  I should say that I don’t think very much like an engineer, by my own assessment. As such, my characterisation of Feynman and his intellectual family must take the form of a tourist’s impressions of an intriguing, strange culture.

And what were your impressions? How did you characterise Feynman and co.? I assume you discussed them in order to ‘inspire’ or ‘nudge’ the students into adopting their approach to science- or at least comparing their own ideas with Feynman’s?
  I decided to dedicate the better part of the first lecture to a quick study of Feynman’s style, (illustrated with a couple of problem solving exercises) because that appeared to encompass a significant part of the “engineering outlook on life”, which the students had been continuously exhorted to adopt. A rough study of this would, I had hoped, give some substance to this exhortation, and then leave them to decide how they preferred to respond to it.
  What was this “outlook”? Broadly speaking, it was an approach to work that emphasized “detachment”, or more concretely, “the exploitation of abstraction”. Scientific models abstract away details and leave behind a set of abstract concepts and relations between these concepts. More often than not, the concepts can be made to correspond to certain variables and the relations to equations. The solution of any problem then reduces to working with these as though we were engaged in pure mathematics.
  Now this summary of the engineer’s outlook will again be controversial, for the reason that there is a tremendous gulf between the psychological profile of an engineer and that of a ‘pure’ mathematician, between the profiles of a  Feynman or Fourier and those of a Riemann or Kronecker. But there is a certain species of mathematician who perfectly fits this profile, and blurs the line between the two. By this I mean the mathematician who has a strong inclination to the practice of mathematics as a game. The Lexicon Encyclopedia entry for mathematics explains: “Mathematics is variously considered a language, an art, a science, a tool, and a game. (Emphasis mine)” A hypothesis suggests itself that each of these approaches to mathematics corresponds to a distinct “style”, and a distinct “psychological profile.” The mathematician who has a strong preference for the last  of these, shares a great deal of this thinking (perhaps close to all of his profile) to that of an engineer. The mathematicians closer to our own time who seem to come to mind include Knuth, John von Neumann, Martin Gardner, John Conway, Ronald Graham and John Nash. In the past, we had Lewis Carrol, Edwin A. Abbott and a few others.
  Naturally this is a coarse generalisation, as there are several different types of engineers with distinct styles, and we would do them ill to pigeonhole them. For instance, can we find anything significant in common between the styles of Isambard Brunel and Thomas Edison? Similarly, there are approaches to mathematics which blur the lines between the Lexicon Encyclopedia taxonomy above. For example, Wittgenstein would have said that there is no difference between the “game” approach and the “language” approach- he would say they both involved playing what he called a language-game.
  But those of us outside of this breed must begin somewhere, and this abstraction serves as a startlingly good point of departure....