Feynman's cognitive style (Information Processing blog)Because I pretty much share all the features that Hsu calls "Feynman's cognitive style" and because I find Hsu's comments fundamentally misguided, skewed, and unflattering, I decided it is important enough to respond.
Hsu starts as follows:
I have always felt that Feynman was cognitively a bit "lopsided" – much stronger mathematically than verbally. This might be partially responsible for his way of learning – it was often easier for him to invent his own solution than to read through someone else's lengthy paper. (Personality factors such as his independent streak, and his strong creativity, also play a role.) But this often left him with gaping holes in knowledge.Feynman had a habit of rediscovering all the insights and physics that he would rely upon in his research – and thinking about Nature in general. Incredibly enough, Stephen classifies this habit as "lopsidedness", borderline illiteracy, and a vice. Sorry, Steve, but you only represent the group think of average scholars who mostly parrot others and are doing okay with that, scholars whose work is derivative at best and whose confirmations can't really be viewed as independent ones because their writing is always a borderline plagiarism.
Feynman was a charming and articulate speaker who could formulate sentences clearly. He knew how to read, too. But the true reason why he preferred to rediscover things and avoid reading other people's papers is that it is a safer, scientifically cleaner way to collect knowledge. It is a way that not everyone can afford because many other people would simply be incapable of rediscovering all the physics (and Feynman was ultimately unable to rediscover things in physics above a certain level, e.g. string theory, too).
But the scientists who can do it in their actual work like that – and Feynman was an example – should do it.
Hsu is making fun out of Feynman's ignorance of some terminology used by the average researchers, of the fact that he hasn't read some papers by Schwinger and Tomonaga with whom Feynman shared the Nobel prize. But Hsu is completely missing all the reasons why it was the right approach for Feynman.
First of all, science is not the process of learning what other people wrote about Nature. Science is not the process of learning how things are called, either. Science is the process of learning how Nature works. This is no detail; it's been a fundamental insight of Feynman since his childhood (and mine, too); recall the monologue about the name of the bird. You may learn the name of the bird in all the languages (I haven't accurately memorized a single one of them) but you will know nothing whatever about the bird.
Feynman preferred the method of rediscovering everything not because he was lopsided but because he was smarter and especially much more certain about the conditions for science to be solid than pretty much everyone else. Moreover, most of the things people write contain lots of wrong or at least redundant rubbish and it may be either uncomfortable or a waste of time to read too much of that.
Even more importantly, it is critical for a scientist to verify "simpler" examples of statements and insights (theoretical as well as experimental insights) that he or she is going to generalize in his or her work. I don't think this is some subjective feature of a personality or an individual cognitive style. It is really an important quality benchmark for all the science above a certain quality threshold.
To remind you of a context in which Feynman stressed that this "reproduction" or "rediscovery" is extremely important, let me quote from Cargo Cult Science, Feynman's 1974 Caltech commencement speech included in Surely You're Joking, Mr Feynman:
Other kinds of errors are more characteristic of poor science. When I was at Cornell, I often talked to the people in the psychology department. One of the students told me she wanted to do an experiment that went something like this—it had been found by others that under certain circumstances, X, rats did something, A. She was curious as to whether, if she changed the circumstances to Y, they would still do A. So her proposal was to do the experiment under circumstances Y and see if they still did A.If you're making fun out of this "reproduction" or "rediscovery", you don't really know what science is, Steve.
I explained to her that it was necessary first to repeat in her laboratory the experiment of the other person—to do it under condition X to see if she could also get result A, and then change to Y and see if A changed. Then she would know the the real difference was the thing she thought she had under control.
She was very delighted with this new idea, and went to her professor. And his reply was, no, you cannot do that, because the experiment has already been done and you would be wasting time. This was in about 1947 or so, and it seems to have been the general policy then to not try to repeat psychological experiments, but only to change the conditions and see what happened.
Nowadays, there's a certain danger of the same thing happening, even in the famous field of physics. I was shocked to hear of an experiment being done at the big accelerator at the National Accelerator Laboratory, where a person used deuterium.
Steve's paragraph about Feynman's lopsidedness continues as follows:
In contrast, Schwinger had at age 17 an encyclopedic understanding of what was known about quantum electrodynamics – he had read and mastered all of the literature as a high school kid!I remember similar discussions about "Feynman vs Schwinger" a decade ago. I have nothing against Schwinger, he was a smart and hard worker, but no doubts about it, I was defending Feynman's approaches. Someone (outside Harvard) suggested that I was obliged to defend Schwinger when I was at Harvard. I think that I have replied that Harvard would have to add a dozen of zeroes to the pennies it was giving me to change my views about these rather fundamental questions about the philosophy of science. I may have been using Schwinger's office but the Linux workstation in my office just happened to be named feynman.harvard.edu.
Most children learn how to read. Whoever can read may read lots of books or papers. It is downright silly to sell this "achievement" as a culmination of the mankind's intellectual efforts, Steve. Schwinger isn't an example but there have been many people who have read pretty much everything that was written in the field they cared about but they were still complete idiots. Marx and Lenin might be listed as damn good examples. They have read a lot – including texts by their ideological opponents – but they were still unable to understand rudimentary issues such as the reasons why communism cannot work. Similar individuals are still hyped by contemporary intellectuals who are as subpar as Marx and Lenin were (if not more so).
Steve is missing the "pragmatic" factor behind Feynman's decision not to read papers doing similar things as he understood:
Feynman: No. No. I don’t think I read the paper. But this must be understood – I don’t mean anything disparaging. If Schwinger hadn’t been in the front yard at Pocono, or next to me, I wouldn’t have known what he did either. I got the same as everybody else. If you can do it yourself, why learn how somebody else does it? So I don’t know precisely what the relation of Tomonaga’s and Schwinger’s work is or the relation of his and mine. I think the relation of Tomonaga’s work to my work is very small. I mean, I think he’s gone around much closer the direction that Schwinger went.Exactly. When you can derive something yourself, why would you learn another man's method to do the same thing? This is really common sense and this common sense is a principal sensible reason behind the things that Steve is stupidly making fun of.
And science is something different than the history of science. Feynman was in the former business.
In fact, it is not really true that Feynman was a chronic "non-reader" of other people's papers. Many of you may remember that Feynman has stated that there was a period in which he was reading all papers published in Physical Review. There weren't too many, he thought.
Path integral vs creation/annihilation operator
Feynman would be thinking about all derivations in quantum field theory in terms of his path integral approach – something he would develop already in the case of non-relativistic quantum mechanics. The path integral is perfectly fine to calculate the answer to any physical question in any quantum theory that was calculable by any method at that time. Nevertheless, Feynman's preference for the path integral is the reason for some additional stupid laughter by Steve Hsu.
The average instructors prefer to teach quantum mechanics in the operator formalism – and the mediocre and subpar ones prefer not only the operator approach but the operator approach in the Schrödinger picture. However, the Heisenberg picture is arguably more physically justified even if one uses some operator approach. And Feynman's path-integral approach is at least equally justifiable and equivalent.
In fact, for technical reasons, Feynman's approach is superior for all modern theories – theories with some gauge symmetries. The path integral makes the treatment of gauge symmetries natural, unified, automatic, and compatible with the Lorentz symmetry. All the calculations that depend on gauge symmetries may also be translated to the operator approach but the required calculations are much more messy. This messiness is unnecessary.
The very interview shows that Feynman was able to read a paper using the operator approach and find a mistake in it, too. So it wasn't an example of any "gap in physics knowledge". The main justification for Steve's laughter are the creation and annihilation operators, however:
When someone explained the action of a creation operator on the vacuum, Feynman reportedly objected "How can you create an electron? It disagrees with conservation of charge!" :-)Feynman was obviously thinking about the real-world process of creating a single electron or annihilating one; his thinking was "process-based", in this sense. And he's completely right: you can't do nothing else than to create a single electron (or annihilate a single electron) because it would violate the charge conservation law. And indeed, Nature never does it. The terms in the Lagrangian always do several things at the same moment (create an electron-positron pair while destroying a virtual photon, for example) which is needed for the charge conservation law to be upheld. These terms in the Lagrangian may be understood as (sums of) products of creation and annihilation operators but this decomposition of the interaction terms to individual "atoms" proceeds along a seemingly very different philosophy in the path-integral approach.
The formalism using creation and annihilation operators seems universally important, elegant, and unavoidable to most of us – to some extent, even to me – because we were educated in this way. But as far as physics predictions go, there's nothing "essential" about it that one couldn't do otherwise (with the path-integral tools, for example).
The harmonic oscillator has some energy eigenstates, some spectrum that happens to be equally spaced. You may treat the harmonic oscillator problem on par with all other generic potentials that don't admit a simple solution in terms of creation and annihilation operators. You may still be aware of the special features of the harmonic potential. And in the application of the harmonic oscillators to quantum field theory, you may avoid all these concepts by calculating the scattering amplitudes via the path-integral approach directly.
Feynman was really using this approach to calculate and to think about all the physics problems and the only reason why someone may make fun of it is stupidity combined with lots of group think. If one can do all the quantum physics calculations using path integrals, there is really no point of learning another man's toolkit that doesn't achieve anything that you can't do comparably effectively and naturally.
If you have mastered the path-integral approach but not the operator approach to quantum mechanics, it is legitimate to consider the learning of the operator approach to be as unnecessary if not stupid as learning another human language.
I personally find it natural to think in terms of creation and annihilation operators in many contexts – much of physics may be approximated by "some kind of a harmonic oscillator" with some extra cherries on a pie and the creation/annihilation operators are among the most natural mathematical tools that "solve" this omnipresent physical problem – but I am not blinded enough to overlook the fact that physics may work without mentioning any of these operators, too.
Just like Feynman was used to avoiding creation and annihilation operators, many people remain pretty much ignorant of the path-integral perspective on most quantum phenomena and calculations in quantum physics. The only reason why they tend to think or say that this is less funny than Feynman's avoidance of the creation and annihilation operators is group think. There are just many people who were trained to use the same "language" for the calculation of the scattering amplitudes. But their being numerous is no rational or scientific argument in favor of the superiority of their "language" just like 1+ billion of speakers doesn't make Chinese a superior language or a must (and sorry, U.S. readers, similar comments hold for English as well – I guess that for Steve Hsu, these remarks may be triply inconvenient: one because Chinese is not fundamental, second one because English is not, either, and the third one because languages are not the focus of knowledge).
So I view Steve's criticism of Feynman's "cognitive style" – which actually contains many principles of the scientific method that Feynman considered essential and indisputable – to be a lopsided, libelous, superficial, and rationally unjustifiable testimony of the mediocrity of the present era.
And that's the memo.
P.S.: Steve Hsu wrote another blog post, Feynman and the secret of magic, as a reaction to the blog entry above. I wrote a comment over there, too.