pnrjulius comments on Rationality Quotes June 2012 - Less Wrong

4 Post author: OpenThreadGuy 02 June 2012 05:14PM

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Comment author: TheOtherDave 01 June 2012 03:12:50PM 36 points [-]

I recall a math teacher in high school explaining that often, in the course of doing a proof, one simply gets stuck and doesn't know where to go next, and a good thing to do at that point is to switch to working backwards from the conclusion in the general direction of the premise; sometimes the two paths can be made to meet in the middle. Usually this results in a step the two paths join involving doing something completely mystifying, like dividing both sides of an equation by the square root of .78pi.

"Of course, someone is bound to ask why you did that," he continued. "So you look at them completely deadpan and reply 'Isn't it obvious?'"

I have forgotten everything I learned in that class. I remember that anecdote, though.

Comment author: pnrjulius 09 June 2012 01:18:54AM 1 point [-]

The standard proof of the Product Rule in calculus has this form. You add and subtract the same quantity, and then this allows you to regroup some things. But who would have thought to do that?

Comment author: gwern 09 June 2012 01:33:37AM 10 points [-]

One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can't, almost surely you are not going to. Courage is one of the things that Shannon had supremely. You have only to think of his major theorem. He wants to create a method of coding, but he doesn't know what to do so he makes a random code. Then he is stuck. And then he asks the impossible question, ``What would the average random code do?'' He then proves that the average code is arbitrarily good, and that therefore there must be at least one good code. Who but a man of infinite courage could have dared to think those thoughts? That is the characteristic of great scientists; they have courage. They will go forward under incredible circumstances; they think and continue to think.

--Richard Hamming

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