[lbo-talk] Kuhn interviews Dirac

Chuck Grimes c123grimes at att.net
Sun Apr 8 12:21:47 PDT 2012


For listmembers who are interested in physical science and math, below is a link to Thomas Kuhn interviews with Paul Dirac in the 1970s. I had to wiki some of the more obscure references to figure out what they were generally discussing. Here is an extended excerpt. The link follows below. I would encourage anybody interested in these subjects, to look up famous people involved at this website. There might be an interview with some of your favorite historical people. I've been through Bohr, Bondi, Burbridge, and now Dirac.

http://www.aip.org/history/ohilist/4575_2.html

Kuhn: This connects with something you said last time that puzzled me a good deal, because I think in talking about the projective geometry with Fraser, you said that ever since then your own approach has been largely geometrical.

Dirac: Yes.

Kuhn: I was somewhat puzzled about this because I would myself have thought of your approach as being very often algebraic, but I probably wouldn't have even raised this except that as you may know Oppenheimer arrived in Copenhagen just before I left. He sends you his greetings. We were talking bit together about you and he came out, without my having raised this at all, with a remark about your immense facility as an algebraist. This has been somewhat my own feeling but runs dead counter to this remark of yours. I wonder if I could vex you by asking you to say a little bit more about what you' d had in mind.

Dirac: Well, I'm not altogether sure what is meant by 'algebraist'. If it means some- one who simply carries through masses of algebraic calculation without picturing what the equations mean, then I'm just no good at it. All this modern work about dispersion relations and reggi-poles and things like that I find very difficult to follow. It doesn't impress me strongly at all because I don't see the geometrical connections.

Kuhn: I would think of your peculiar q-number manipulations, for example, as being algebraic rather than geometric.

Dirac: Yes, but I only used them in an elementary way. Perhaps I didn't tell you that I kept up my connection with geometry some time after I came to Cambridge. There was a Professor Baker, a professor of geometry, who used to give tea parties on Saturday afternoons to people who were keen on geometry; after the tea someone would give a talk on some recent research work on none geometrical subject. I went to those tea-parties and absorbed quite a lot of geometry then. I talked once or twice myself. I remember I worked out a new method in projective geometry and gave a talk about that at one of these meetings. I never published this method. Well, that's a good deal about working with the geometry of four or more dimensions. Four dimensions were very popular then for the geometrists to work with. It was all done with the notions of projective geometry rather than metrical geometry. So I became very familiar with that kind of mathematics in that way. I've found it useful since then in understanding the relations which you have in Minkowski a space. You can picture all the directions in Minkowski space as the points in a three-dimensional projective space. The relationships between vectors, null-vectors and so on - - and you get at once just the relationships between points in a three-dimensional vector space. I always used these geometrical ideas for getting clear notions about relationships in relativity although I didn't refer to them in my published works.

Kuhn: Did this also give you techniques that were relevant to your approach to quantum theory whether relativistic or not?

Dirac: No. It doesn't connect at ail with non-commutative algebra.

Kuhn: It is all right to think of that as being algebraic.

Dirac: Yes, yes. But I don't think you'll find any heavy algebra in any of my work.

Kuhn: No. There is an awful lot of algebraic sense, though it's hard to know how to put that more precisely; but I think with many people who find the approach to a multiplication relation more general than XY, where these cannot be thought of as numbers, it suddenly gets away from them as a subject matter. You've clearly made this exception with ease and facility, at a time, I take it, when it wasn't the standard thing to do.

Dirac: Yes, I suppose. Non-commutative algebra was a rather strange idea in those days, although it shouldn't have been because of quaternions.



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