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Comment by ericand | Hacker News Reader

"He guessed that the problem might take him a few weeks. Instead, it took him five years"

Perhaps the key to their success was typically programming work estimations ;)

More seriously, I think that if you think something is easy for you, or that you are almost there, you may be more willing to put in the necessary time, than if you knew it would take 5 years from the outset.

"Spielman realized that he himself might be in the perfect position to solve it. “It seemed so natural, so central to the kinds of things I think about,” he said. “I thought, ‘I’ve got to be able to prove that.’”"

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Related but different advice: build the habit of learning things by trying to figure it out yourself. Richard Feynman did this when learning quantum mechanics, and invented the Feynman diagram as a result. While not a different model or theory per se, the diagram made apparent the connection to functional integrals and a different method for solving that made previously intractable problems (relatively) simple.

Funny story is he “invented” this technique in his school days and only found out that it wasn’t standard during he Manhattan project when a colleague complained a problem was t tractable and Feynman went to the black board to illustrate the “obvious” solution.

Sometimes optimal solutions aren’t found because nobody bothered to look, assuming if they think about it at all that any remaining work must be more complex than the already known suboptimal solution.

> Related but different advice: build the habit of learning things by trying to figure it out yourself.

This can be a wonderful habit, or it can create cranks. As you mention, Feynman used it to great success, but he was Feynman. I had a few classmates in graduate school—I nearly was one, until my advisor set me straight—who couldn't make any progress because they couldn't take any results for granted; they wouldn't do anything until they could prove everything. This is intellectually admirable, but a sure recipe for stagnation (at least for me and these classmates).

I think we can generalize the last two comments to: when you look at a problem, learn about it, it's structure, until you think you can resolve part of it. Keep repeating that until you get there. Assume that what everyone knows is good until your next steps push you to reexamine assumptions, and don't be reluctant to do so.

Happy ground between 'must build stack myself' and 'too orthodox to ever question the masters'.

> Assume that what everyone knows is good until your next steps push you to reexamine assumptions, and don't be reluctant to do so.

This is a fantastic summary. I like it a lot, and may steal it for future use.

What I took from Feynman's biography is that he would periodically attempt to rebuild his understanding of all of physics from first principles i.e. basic arithmetic, through algebra to calculus, mechanics etc. Looking for new insights and simplifications, he would apply new tools to reformulate and solve older problems. His seminal work in Quantum Electrodynamics used the Principle of Least Action to great effect. Despite initial scepticism, he came to appreciate the power of LA after seeing that it could be used to elegantly reformulate Classical Mechanics.

Doing this even after becoming a world famous physicist led to the Feynman Lectures in Physics - written as much for his own benefit as for his students. However, I am not sure he used this strategy when learning entirely new concepts the very first time.

It makes sense to do this as practice. To build new theoretical structures, building new constructions of the stuff we already know is a great way to sharpen a toolbox of problem-solving techniques and reveal potential shaky theoretical foundations.

> "He guessed that the problem might take him a few weeks. Instead, it took him five years"

>> Perhaps the key to their success was typically programming work estimations ;)

No, you should always normalize programmer estimates by increasing both the unit and the measure by one. So "a few weeks", say 4 weeks, will actually take: 5 months! So he still took 12 times longer than the properly normalized estimate! :-)

Y'know, if you take "a few" to mean 3 instead of 4, then do that same transformation twice, it lands right on 5 years...

Yes, great catch! Perhaps Tom said "3 weeks" to Dick, Dick said "4 months" to Harry, and Harry said "5 years" to Jane! :-)

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