Tuesday, March 13, 2012

The differences are enormous

Luis Alvarez laid it out bluntly:

The world of mathematics and theoretical physics is hierarchical. That was my first exposure to it. There's a limit beyond which one cannot progress. The differences between the limiting abilities of those on successively higher steps of the pyramid are enormous.

See also Out on the tail. People who work in "soft" fields (even in science) don't seem to understand this stark reality. I believe it is because their fields do not have ready access to right and wrong answers to deep questions. When those are available, huge differences in cognitive power are undeniable, as is the utility of this power.


Nick Metropolis on von Neumann. See also his classic essay The Age of Computing.

Metropolis interview: ... Fermi and von Neumann overlapped. They collaborated on problems of Taylor instabilities and they wrote a report. When Fermi went back to Chicago after that work he called in his very close collaborator, namely Herbert Anderson, a young Ph.D. student at Columbia, a collaboration that began from Fermi's very first days at Columbia and lasted up until the very last moment. Herb was an experimental physicist. (If you want to know about Fermi in great detail, you would do well to interview Herbert Anderson.) But, at any rate, when Fermi got back he called in Herb Anderson to his office and he said, "You know, Herb, how much faster I am in thinking than you are. That is how much faster von Neumann is compared to me."


Herman Goldstine on von Neumann:

Goldstine interview: ... If you ever look at Gauss' collected works, you'll see Gauss also loved to calculate. You just find in Gauss' works huge calculations that he undertook. It was a form of recreation. Von Neumann loved to do these things. It was a kind of being in touch with reality in a peculiar way. He would live to play mathematical games, such as the question of whether the numbers on a box car were prime or composite. He did calculations in his head that nobody else could do. He loved to do things like that. It was just part of his make-up. So calculation was not something abhorrent. Again, if you look in Gauss' collected works, you'll find all kinds of tabular things that he did. In fact, it was probably relaxing for each one of them to turn to calculation just for the fun of it.

... I think they were very alike. I think different people's minds are differently constituted. I never particularly noticed any geometrical interests on von Neumann's part. He once told me he knew nothing about topology. Of course these have got to be taken as relative things. When he said he didn't know anything about topology, that probably meant he knew more than most people. But I think he loved to calculate. If you look at his book on quantum mechanics you'll find a number of things that you might conceivably do by other methods, he did do them by not numerical calculation, but by algebraical calculation. He was masterful at it. He could take the most elaborate formulas and manipulate them down until they were a couple of terms. This he loved. This was part of his virtuosity. You know, there was just nothing he liked so much as to do that.

Both interviews are worth reading in their entirety. See also Only he was fully awake.

31 comments:

Joey said...

I agree that in soft fields there is less recognition of the value of intelligence because the phenomenon in question doesn't bite back, so to speak, if your theories are wrong. For example, if my theory about the influence of Ovid on Paradise Lost is wrong, nothing happens. On the other hand, if my theory about quantum chemistry is wrong, the real world will bite back.

The somewhat arbitrariness of critical judgment prevents people in literary studies from moving forth. I wonder if I'm the only humanities major who reads this blog? I find it irritating when political whims get in the way of serious analysis. It's not that we can't move forward in the study of literature, it's just that professors in general do not want to.

These problems are not insurmountable, of course. If they were, I would have no involvement with a field as "soft" as my own. But scrupulous self-honesty is required, and one has to approach problems with an eye for truth and a willingness to let the object of analysis bite back and tell you you are wrong.

...As an aside, it's impossible for me not to be jealous of Jon Von Neumann's memory. Specialists in a field often have well-above-average memory for their subject matter, but Neumann apparently could perfectly recall tons of literature, and he was a professional mathematician. I often regale friends with my recall for poetry (I've got about 150 pages in store, or so), but I would easily by outdone by Von Neumann, who probably viewed poetry as essentially a pastime.

steve hsu said...

>> But scrupulous self-honesty is required, and one has to approach problems with an eye for truth and a willingness to let the object of analysis bite back <<

I agree 100%. Unfortunately, as career advancement and social prestige become more important later in life, this becomes harder and harder.

Joey said...

Quite true, and something I am worried about. I have considered becoming an English professor, but have thought that my political views (I'm only liberal-humanist, not Marxist), my acceptance of evolutionary psychology, and my belief in firm objectivity would make it hard to earn the respect of my colleagues or get tenure. I may simply take it on faith, though, that some people somewhere will appreciate a more sober, rationally-minded approach to literature, that they will stick up for me, and that therefore I will survive the hordes of postmodernists eager to defenestrate me.

steve hsu said...

You may need to learn to hold your tongue in certain circumstances ;-)

Joey said...

I could learn to make them sound more extreme and ridiculous than they really are in certain contexts. Unlike physicists, who are attracted to raw brainpower, humanities types are attracted to affectation. Bombasticity! The Avant-Garde! New terms!

Sam H said...

It seems von Neumann is the genius's genius. I wonder what his IQ was, in terms of V and M.

steve hsu said...

My wife has a PhD from Berkeley and is a professor of comp lit. I know exactly what you mean ;-)

Joey said...

I have to admit I am really surprised to learn that you are married to a literary critic, given your humorous jabs at the humanities. Surely she objects! 

Perhaps your genes will combine to produce bizarre multilingual sci-fi novelists.

Jean Huiskamps said...

I read (popular) philosophy, history and literary criticism just for fun and I think that those fields of study can be approached just as rigorously as the "hard" sciences. For example this series of lectures on literature:

The Modern Scholar: A Way With Words, Part II: Approaches to Literature by Professor Michael D.C. Drout
http://www.amazon.com/The-Modern-Scholar-Approaches-Literature/dp/B001ED186C/ref=sr_1_6?s=books&ie=UTF8&qid=1331665398&sr=1-6

demonstrates that this "soft" field of study can be approached in a structured, humble and rigorously truth seeking manner. It compares very well with the (popular) books that I read about mathematics and physics.

And even physics has it's unscientific deviations if I may believe Woit and Smolin (I will never be able to read the primary sources).
And even quite verifiable scientific facts can be held up for years by question of prestige and status. See for example the unnecessary delays in the decoding of Linear B and the Mayan scripts. Here the outsiders were right after all.

So it may be that social and cultural factors play just as strongly in the "hard" and "soft" sciences. And I see many practitioners of the "soft" sciences using clear scientific attitudes.

steve hsu said...

>> So it may be that social and cultural factors play just as strongly in the "hard" and "soft" sciences. <<

Your comments are correct but it's a question of degree. The problems that Woit and Smolin indicate are real but are caused by lack of experimental ability to probe quantum gravity (string theory). Under these circumstances physics can become almost as bad as the standard situation in the humanities. But it is an anomaly.

steve hsu said...

Familiarity breeds contempt ;-)

Just kidding.

Jean Huiskamps said...

I'm just a random office worker but I feel compelled to defend literary criticism. I listen with great pleasure to literary professors from English, American and German universities discussing an analyzing Conrad, Shakespeare, Kafka, Musil etc. I have a great respect for their analytic skills. Their views enhance my enjoyment of literature. And in their lectures I hear very little bombasticity. For example: it is very enlightening to hear a detailed analysis how Kafka builds his surreal atmospheres from "normal" building blocks. Maybe I'm just lucky to miss all the pretentiousness :-)

Anonymous said...

As a scholar in the humanities who regularly follows this blog, I find your remark to be truly fascinating. No one in my field has ever mentioned the experience of having to come to grips with the existence of a clear and objective hierarchy of cognitive ability (at least at a certain level of professional achievement - there are obvious differences in ability and motivation among undergrads and graduate students).

This is worrisome for at least three reasons: 1) There is a fairly clear professional hierarchy, but where self-promotion and political strategy play at least as strong a role as mental prowess and genuine productivity. Is this not the case outside of the humanities? 2) In the absence of clear benchmarks of intellectual achievement and genuine problem-solving, even the best of humanities scholars will tend to stagnate in a no-man's-land of speculative assertions, with no unambiguous feedback to bring home to them just how tough a particular problem is. There is no sense of failure and therefore no greatness. The tragedy is not only that a Von Neumann in the humanities will essentially remain at the level of a Fermi - or a Herbert Anderson - in the humanities, but that each individual
scholar will remain ignorant of how far they could have truly progressed. 3) Unfortunately, most attempts at introducing the methodology of the hard sciences into the humanities have had laughably simplistic results. They lack true rigour because they fail to come to grips with the nature of their object.

So we are kind of stuck. The situation would be tolerable enough if only we weren't additionally submerged in fadishness of all kinds and fashionable close-mindedness...

Commander_Ga said...

Steve, when do you think science will be able to easily create people with greater than von Neumann intelligence?  When this happens life will get ugly for all of us without the same kind of brains. But it has to happen for the good of the species. I just want to know if I'll have to worry about competing with these upstarts for my job!

JustinLoe said...

 I am a skeptic in medium term, i.e. the next 50 years. Past that point, anything is possible. In the interim, we should be more concerned about the human race blowing itself up, rather than genetic engineering.

As anything becomes technologically practicable and is beneficial, it will be done. Certainly we must rely on our own intellects as a species and not "providence", or some such, to safeguard our progress. In that sense, genetic engineering will be a moral imperative in the future.

tractal said...

I admire your optimism, but look through any English faculty at a top school and the Marxists +radical feminists+post-modernists+race theorists=75%+. There is a reason Harold Bloom calls it Stalinism without Stalin. These people can't think and they don't listen. 

Stephen S said...

I continue to enjoy your series about von Neumann. I can't wait until we can clone Gauss, Euler, vN, etc. The era of genetic engineering will be even better. (I can't imagine why non-world history geniuses think this would be a bad idea. The world hasn't exactly been made worse off by these sorts.)

~

Recognizing that there is a hierarchical structure to human endeavor is one of the hallmarks of maturity. There is nothing sadder than a grown man who refuses to recognize when somebody is better at something than he is. Physics seems like it provides a nice respite from the self-serving delusion you see everywhere in this respect. Perhaps that's why Steve likes MMA, as well? --> It's hard to pretend you deserved to win the fight when you got CTFO'd.

LaurentMelchiorTellier said...

There's a popular stereotype that smart people are evil, but psychopathy correlates strongly with low IQ, and interestingly, also correlates with lack of monetary success. Of course, it was recently established that Wall Street vastly outrepresents in terms of psychopaths, so the stereotype has a meaningful origin:

http://www.huffingtonpost.com/2012/02/28/wall-street-psychopaths_n_1307168.html I don't think it's obvious that we should be at all nervous about the advent of smart people, however. I suspect that they are more likely to give you a job, than take it.

Joey said...

Hey, I only said "some people somewhere"!

matmcinn said...

Sorry, I'm not getting all the von Neumann love. vN was undoubtedly far more intelligent than Schroedinger, Heisenberg, Fermi et al.... and yet his actual achievements were trivial by comparison. Surely he is the most outstanding examplar of the strange fact that IQ is *not* actually the most important thing in physics? We could clone an army of vNs and just produce a whole lot of clever but fundamentally trivial contributions to things like computer "science"....

Sam H said...

Just BS about your views until you get tenure. 

Joey said...

I don't think it was trivial that Von Neumann basically invented the field of Game Theory. He did a bunch of other pretty important things too. I agree that the Von Neumann love is a little over-the-top, probably because, as I said below, physicists often seem to drool at the sight of pure intelligence, and Von Neumann more than Schroedinger, Heisenberg, or Fermi seems to just breath brainpower. But he was nevertheless an extremely important mathematician and scientist and one not unreasonable to "love."

Abett Tabett said...

It´s very hard to accept your limitations as a prospective theoretical physicist with only 140ish IQ (perfect score RAPM) . It's a narcissist injury that not all people accept graciously.
How Von Neumann would have scored on the IMO? Something like a gold at 9 years old maybe?

brown_slacker said...

True! To paraphrase Grigori Perelman, Math is about depth, not speed.  Also, why the quotation marks for the science in computer science (unless the intent is to provoke)?

David Coughlin said...

I didn't know Metropolis was a physicist.

hobelman said...

As for no geometrical interests on Von Neumann's part what about his book on Continuous Geometry? Speaking of exceptional memories it is said that Euler had memorized the entire text of the Aeniad.
I not sure exactly where I would rank Von Neumann among the mathematicians of the twentieth century but I'm amazed that anybody would describe his mathematical accomplishments as trivial as one commentator here did. Isn't the duality between compact and discrete abelian groups pretty remarkable?

Ene Dene said...

There is so much proof that IQ is nowhere near "everything" that it fascinates me how come so much smart people are trying to prove otherwise. IQ is a measure of subset of needed abilities, nothing more. It's like a jumping ability for a basketball player, it's nice if you can jump 1.5m, but that doesn't make you a good basketball player, in fact you're nowhere near.

Ene Dene said...

Average chess grandmaster has a more impressive record as far as the memory is concerned.

Also in Islam if you know the K'uran from first to last page, you get an Hafiz title, the ability is not that uncommon.

prasad said...

How many rungs should one put between the average Physics professor at MIT and Fermi?

LabanTall said...

"There's a limit beyond which one cannot progress. The differences
between the limiting abilities of those on successively higher steps of
the pyramid are enormous."

Or as someone said in the 30s : 

"The leaders of thought have reached the horizons of human reason, but all the wires are down and they can communicate with us only by unintelligible signals..."

DAB said...

Steve, what's your impression of how most physicists psychologically contend with the fact that they have colleagues who are much smarter?

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