### The Dirac delta doesn't discount

I took this course in Quantum Mechanics and Quantum Computation last term; it needed some serious effort (what's

*i*? don't ask Lacan, please) but it was a lot of fun. Umesh Vazirani was a fine lecturer as well, and in the end the whole experience sold me on online courses (at least for subjects with mathematical content; on Development Economics, my inner jury is still out).
As I worked through the course and read some of the supplementary material, I returned to my childhood hero Richard Feynman and ran into some of his great lectures on YouTube; here's one from 1964 at Cornell. (Fellow Cornellians: observe that Uris Hall is thankfully missing from the opening sequence; it didn't exist then.)

Man, what a teacher. The greatest ever.

Man, what a teacher. The greatest ever.

I was also introduced to the bra-ket notation of Paul Dirac. Elegant stuff: a perfect example of how good notation can both serve as a mnemonic and as a simplifier of tedious computations. (In economics I have also seen it change the results, but that's another, less interesting story.)

Dirac was by all accounts one of the greatest theoretical physicists ever. He won the Nobel Prize at the age of 31 "for the discovery of new and productive forms of atomic theory". Then young Dirac headed off to the Nobel banquet and delivered the following disquisition on economics:

"[W]e have an economic system which tries to maintain an equality of value between two things, which it would be better to recognize from the beginning as of unequal value. These two things are the receipt of a single payment (say 100 crowns) and the receipt of a regular income (say 3 crowns a year) all through eternity...May I ask you to trace out for yourselves how all the obscurities become clear, if one assumes from the beginning that a regular income is worth incomparably more, in fact infinitely more, in the mathematical sense, than any single payment?" (From Dirac's biography, The Strangest Man, by Graham Farmelo. Highly recommended btw.)

Coming from a physics genius, this is quite stunning in its stupidity. The most charitable thing I can say about the bloke is that he certainly wasn't a hyperbolic discounter. (Never mind.) I find particularly telling the following observations: (a) how winning the Nobel prize appears to confer intellectual "rights" over other disciplines that one just don't have the ability to exercise, but more importantly (b) how fundamentally "intuition" differs from field to field, so that a genius in one area can be a blithering idiot in another.

My utter awe of Paul Dirac came down by a couple of notches (small notches, granted).

Postscript: the above is an updated version of some notes in Facebook that I published in 2012. A couple of the comments were very interesting and I reproduce them here:

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