Comments on: Why not von Neumann?

By: Ron Maimon

Ron Maimon — Sun, 02 May 2010 23:35:47 +0000

What isn’t often appreciated about Feynman is that he managed the computational department at Los-Alamos in his early twenties, arranging stacks of calculation cards that contained solutions of partial diffential equations running through a mill of secretaries with hand-calculators. He was always therefore conscious of the actual practical aspects of calculations, and this influenced his formulations of problems— he often stated the results algorithmically as opposed to algebraically. This computational point of view was taken to an extreme by Feynman’s collaborator Wolfram, but it is reflected in many of Feynman’s works of the 50′s and 60′s (for instance, the path integral and He4 work, which is formulated in terms of ground state properties, including the imaginary time connection with stochastic processes, which allows the ground-state properties to be more efficiently solved by Monte-carlo on a probabilistic computer than the naive diagonalization of an enormous dimensional matrix, or the diagrams, which reduce the algorithmic complexity of internal propagators by unifying the antiparticle and particle propagators, which are separate in the old fasioned perturbation theory).

By: Scott Aaronson

Scott Aaronson — Sat, 30 Sep 2006 03:42:06 +0000

Maybe a better question is: why didn't von Neumann invent classical computational complexity theory? As you mentioned, that would certainly have been a first step toward inventing quantum computing! My own answer is simply that (1) von Neumann had a huge amount on his plate, and (2) he died in 1957. (Indeed, it was while he was dying in a hospital that Gödel sent him his famous letter about P vs. NP. But we don't know if von Neumann ever even saw this letter, let alone thought about it.) Some of von Neumann's papers from the fifties show that he was aware of computational scaling as an issue, and of polynomial scaling being better than exponential scaling. Probably, this was one of many things that he died before he was able to follow up on. Interestingly, Feynman did not have a particularly good appreciation of complexity -- if you read his Lectures on Computation, complexity never appears even once! And even in his famous 1982 talk on quantum computers, complexity only appears as one of many issues to be considered.

By: Matthew Leifer

Matthew Leifer — Thu, 28 Sep 2006 03:53:04 +0000

Indeed, they’ve been having trouble filling that positon for some time.

By: William

William — Thu, 28 Sep 2006 03:36:34 +0000

At some point in my university career I was torn. I was interested in theoretical computer science, pure math (particularly functional analysis) and quantum mechanics. I decided the natural career path was to become John von Neumann. It’s not an easy job, but I hear there is an opening.