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.

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:

  • Michael Chwe Of course, some physicists are great intellects, but I think our overall social awe of the field has a lot to do with the PR surrounding the atomic bomb, etc.
  • Michael Chwe Hi Debraj---you should take a look at the following paper by William Press and Freeman Dyson, both very distinguished, on the repeated prisoners' dilemma. I think that most of the paper is wrong.
  • Abhay Puri He would not be the only physicist to have struggled with economics.
    Planck is believed to have said to Keynes that he had thought of studying Economics but didn't because it was too difficult. Some might mischievously attribute this to properties of the dismal science but according to Hilbert, even physics is too difficult for physicists 
  • Debraj Ray Hi Michael, I'll definitely look at the Press-Dyson paper. But having no clue about discounting is of a different order of magnitude. By the way, I have been reading some (very basic) quantum mechanics so there is little doubt in my mind about how smart these guys are.
  • Debraj Ray Abhay, the Planck line to Keynes sounds like a polite nod from P to K! As for Hilbert, he's probably right because the short-cuts these physicists too were astounding (but in the end, apparently correct...).
  • Abhay Puri Keynes polite nod back to Planck goes: 
    "Professor Planck of Berlin, 
    Berlin, the famous originator of the Quantum Theory, once remarked to me that in early life he, had thought of studying economics, but had found it too difficult ! Professor Planck could easily master the whole corpus of mathematical economics in a few days. He did not mean that! But the amalgam of logic and intuition and the wide knowledge of facts, most of which are not precise, which is required for economic interpretation in its highest form, is, quite truly, overwhelmingly difficult for those whose gift mainly consists in the power to imagine and pursue to their furthest points the implications and prior conditions of comparatively simple facts which are known with a high degree of precision." 

    Not much of that seems right to me ... but then I'm not an economist. Or a physicist  
    But I love the phrasing anyway.

    Btw, I believe Dirac was often contentious on /any/ subject in his non-mathematical 
    expression. He's stark about poetry, too for example.


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