Thursday, January 24, 2013

Learn to solve every problem that has been solved

Feynman had that on his final blackboard. Crazy? Even for Feynman? An admirable ambition, nonetheless.

At what point did this become impossible for even the smartest human alive? What if we amend it to Learn to solve every important problem that has been solved? (For some threshold of importance...)




Feynman's TO LEARN list:

Bethe Ansatz, Kondo Effect, 2-D Hall Effect, "accel. temp" = Unruh Effect?, Non-linear classical Hydrodynamics

Do I know anyone well-acquainted with all of these topics? I can think of a few people who come close ...

While it may be impossible to achieve Feynman's goal, I'm surprised that more people don't attempt the importance threshold-modified version. Suppose we set the importance bar really, really high: what are the most important results that everyone should try to understand? Here's a very biased partial list: basic physics and mathematics (e.g., to the level of the Feynman Lectures); quantitative theory of genetics and evolution; information, entropy and probability; basic ideas about logic and computation (Godel and Turing?); ... What else? Dynamics of markets? Complex Systems? Psychometrics? Descriptive biology? Organic chemistry?

37 comments:

Bobdisqus said...

Hello Steve

With a world population around 7B and a smart fraction (>3σ) of around 9.5M who are the one in a billion intellects out on the tail of the tail, and why don’t they stand out more from the more pedestrian of their 9.5M peers? What does that lack of clear standouts say about the possibilities that I will bounce my super smart spell checked grandchildren on my knee? Is there an IQ threshold even for math and physics?

http://images.angelpub.com/2010/31/5477/world-population-1800-2100.png

LondonYoung said...

While I don't disagree about non-normality in the tails, in a Gaussian world :
If you have a group of at least +1 SD's, 14% of them are at least +2
If you have a group of at least +2 SD's, only 6% of them are at least +3
By the time you are in the elite +6 SD group, only 0.3% of those lofty intellects qualify for the +7 club.
So, I propose that the +7's have so little impact on the world compared to the +6's because their extra SD of "whatever it is" does not make up for the 300:1 advantage the "just +6's" have over them ...

gide07 said...

The very smartest people can be pedestrian in some ways. Big differences in subtest scores are more common the higher the IQ.

gide07 said...

And there was some "maladjustment" for Terman's smartest of the smart.

gide07 said...

"Learn to solve every problem that has been solved"

Did Feynman write that when he was very young. Like 13? No. It was his final blackboard. If you're life's purpose is to be super smart or super sophisticated how smart could you be?

"...genetics...Descriptive biology? Organic chemistry?"

Compared to vaccines and antibiotics all other human accomplishments since the Romans developed plumbing are lame and stupid. LY will want to put distillation on the list.

stevesailer said...

Von Neumann was said to be the last man to understand all the major fields of mathematics.

steve hsu said...

This is sort of how I think of it. At least the top 5 or so kids per graduating class are +4ish (top by brainpower, not necessarily GPA, although the two are correlated) -- this is even consistent with test scores in the old days when the SAT ceiling was pretty high. The top couple of kids on campus at any moment might be qualitatively different from these +4s -- maybe they'll go on to do something really special ;-)

http://calteches.library.caltech.edu/584/2/Putnam.pdf

Paul said...

"What I cannot create, I do not understand" reminds me of McCarthy: “Whatever in creation exists without my knowledge exists without my consent.”

Cornelius said...

I've found this to be the case as well, although physicists, philosophers and economists come across as the most well-rounded among the high IQ types. Economists seem to have a lower IQ ceiling though. Engineers and classicists seem very lopsided.

I can only estimate based on what I know about the averages in different fields, but I think I'm close to 4 on verbal-analytic, between 3 and 4 on math and slightly below 3 on spatial.

Paul said...

I think you covered it pretty well. My question is this: what percentage of Americans 22+ would you guess are meaningfully proficient in even *one* of these areas?

tractal said...

Demonstrated mastery of at least one of these should be required for a bachelors degree. Would go along way against the vacuous humanities curriculum often found at lesser institutions. If you're really learning so much about Shakespeare and Milton it shouldn't be hard for you to grasp basic mathematical logic or statistics.

David Coughlin said...

By when in your life?

LondonYoung said...

just before you die?

gide07 said...

Do you wear +4s when you golf?

gide07 said...

What is an intellectual? The way it's used most frequently today intellectuals are most conspicuously lacking in real life experience and understanding of technology and its history. The engineer cum executive seldom has anything interesting to say. So even the smartest are stupid and the whole thing goes over a cliff.

gide07 said...

What about building a house?

gide07 said...

You should volunteer for Steve's looking for non-existent genetic correlates of IQ study.

gide07 said...

"Of making many books there is no end, and much study is a weariness of the flesh."

Keith Power said...

Good to see Feynman was learning right till the end. On the CS side I think being able to write simple programs and know a few key data structures and algorithms is far more useful than knowing about Godel or Turing's work, they don't make much difference in practice. I'm reminded of:

"A human being should be able to change a diaper, plan an
invasion, butcher a hog, conn a ship, design a building, write a sonnet,
balance accounts, build a wall, set a bone, comfort the dying, take
orders, give orders, cooperate, act alone, solve equations, analyze a
new problem, pitch manure, program a computer, cook a tasty meal, fight
efficiently, die gallantly. Specialization is for insects."— Robert Heinlein, Time Enough for Love

Cornelius said...

I want to. I lost the official copy of my GRE scores, but I'm considering taking them again or paying for a professionally administered IQ test; it's worth it for what BGI is offering.

David Coughlin said...

Hmm, now that I think about, it would be hard to exclude the Poincare Conjecture and Fermat's Last Theorem from even a just-the-most-important list, and gaining fluency in them is a couple of decades of work. So I'm going to flip Steve's question, which problem's do you omit if you are really smart and want to maximize the breadth of your fluency?

David Coughlin said...

Also, I don't think it is a dismal situation for the really smart. You probably have 60 or 70 intellectually vital years, and that is a LONG time if you are a devoted student. That's the trade, though, how much are you willing to be the student and how much are you driven to be the professor?

gide07 said...

It's vainglory. The really smart would never try.

"There is nothing better for a man, than that he should eat and drink, and
that he should make his soul enjoy good in his labour."

tractal said...

People can usually tell when someone is clearly smarter than them, so if we say that threshold is 1 SD difference Steve is plausibly right about limited perspectives. Looking at it from the other point of view: could you easily distinguish a -1 from a -2? I wouldn't be surprised if you could estimate intelligence by an individuals relative IQ range sensitivity.

David Coughlin said...

I think Zeno's Paradox prevents this from happening.

David Coughlin said...

Post-structuralists, philosophical contemporaries of Feynman, would probably tell you that there are relatively few Problems, and that through solving problems can you really develop your understanding [and then maybe solve a 'new' problem, and illuminate a new facet of a Problem]. Your biblical quote is not even wrong.

steve hsu said...

Because the distribution from +3 to +5 is filled out uniformly, they don't stand out that much *from each other* -- in the same way that top WRs in the NFL aren't that different from each other, but many of them today are bigger, stronger, faster than, say, Jerry Rice was.

Re: Elon Musk, I don't find what he is doing nearly as impressive as the work of the nameless, faceless teams of engineers and applied physicists who keep Moore's Law and its equivalents in storage, bandwidth, DNA sequencing, etc. going year after year. The actual underlying technologies for, e.g., chip fabrication or DNA sequencing, change on roughly 5 year timescales, so whole new fields have to be invented with regularity to keep these cost-capacity curves going decade after decade. See, for example, "spintronics".

http://www.technologyreview.com/sites/default/files/legacy/costs_plummeting_x900%5B1%5D.jpg

Bobdisqus said...

I don’t expect to see it’s not nano-lithography, or it’s not next-gen sequencing enter the lexicon any time soon but that is not to belittle their accomplishments.

Tractal, here is the thing though, that is not my experience. Plus 2 are the norm where I work and +3 are not uncommon on the ground, yet among them Charles (Shenhou) who is a +4 stands out clearly even to my limited sight. We all ride on his shoulders. I certainly would grant some truth to the old saw about communication across more than 2σ, yet I do not need to know what he knows to see the result.

steve hsu said...

Here are bios of some of the "minor figures" in the early development of the computer (minor relative to, say, von Neumann or Turing). I'd guess these guys are +(3-4) at least, with vN and Turing way beyond. Every new hard technology has to have people like this around to make progress (Schwinger and similar types made very important contributions to waveguides and radar, etc., etc.). Multiple directions are investigated (each by competing teams or companies) for every one that succeeds. Only a few superstar (or highly memorable) figures make it into the popular histories, but you can be sure there are lots of guys like these around as well who remain relatively unknown.

http://infoproc.blogspot.com/2011/07/creators.html

Guess how many +2,3,4's are involved in this:

https://www.google.com/search?q=atlas+detector&hl=en&safe=off&tbo=d&source=lnms&tbm=isch&sa=X&ei=u3cGUamXJMKsyAHYmYHIAw&ved=0CAoQ_AUoAA&biw=822&bih=416

or this:

http://www.nanoporetech.com/



Is your question "Why don't +4,5s stand out among +2,3s?" (they do) or "Where are all the +4,5s?" (100k of them spread around the world, but concentrated in certain places ...)

Stephen Hsu said...

Because luck plays such a huge role in discovery (and life!), even most +5s will not be remembered by history. The most accomplished and the smartest are usually not the same individual: accomplishment and smartness, while correlated, are only imperfectly so. Drive / ambition is another quasi-independent variable.

http://infoproc.blogspot.com/2006/03/success-vs-ability.html

vN was "smarter" than Einstein, but the latter made larger contributions to science.

http://infoproc.blogspot.com/2010/10/wigner-recollections.html

David Coughlin said...

Endeavor is a team game.

gide07 said...

I have no idea what a post-structuralists is. I know fro Sokal's book Fashionable nonsense that late 20th c. French "philosophy" is all bs. The quote isn't from "The Bible", Dave. It's from Ecclesiastes. It's over your head, apparently. Read A Mathematicians Apology.

gide07 said...

"Every new hard technology has to have people like this around..." The cleverest cavemen came from all around the world and solved the hard problem of the bow and arrow. Steve, dear, you're suffering from "bounded cognition".

gide07 said...

+1s, -1s, 0s, +4s, +5s, ..... betas, deltas, gammas, plus alphas, double plus alphas....why bother defining your terms... and when you try you find these double plus alphas like Feynman are really only beta plusses and Bobby Fischer is a +6. There is big diff between being smart and being a nerd, but nerds will never learn it.

James Lizenby said...

I think a more interesting question might be: What percentage of the capable 22+ are just lost and lacking guidance?

Bobdisqus said...

These guys say they can see them, and put their money where their mouth is:



http://www.forbes.com/sites/matthewherper/2013/02/20/billionaires-anoint-biogeeks/

Mike McCarthy said...

I am no longer surprised at your knowing only six
accomplished women. I rather wonder
now at your knowing any.

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