What is the Mantra of Polya?

by Mark_Eichenlaub 1 min read31st Jul 201215 comments

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The other day at dinner, someone showed me this video of a slinky dropping. It shoes that the bottom of the slinky stays perfectly stationary for a while after it's been dropped. (The link goes to the 10-second interesting part).

I spent some time trying to figure out why that happens, but didn't get it. The next day, I spent half an hour writing down the differential equations that describe the slinky's motion and staring at them, with no idea how to proceed. Eventually, I watched the video again with sound, and learned the simple answer, which is that the speed of waves traveling in a slinky is very slow - a few meters per second - and the bottom half sits still until a wave can travel down and inform it that the slinky's been dropped.

The strange thing is that I already knew this, or at least the idea was familiar to me. Also, while at dinner, someone mentioned the "pole-in-the-barn" paradox from special relativity, and mentioned the same speed-of-information-in-materials idea in resolving the paradox, but I still didn't make the connection to the problem I was considering.

I want a simple phrase, similar to "check consequentialism", "take the outside view", or "worth it?" that applies to checking your own thought process while solving problems to stop you from revving your engine in the wrong direction for too long. I realized I've read a book about what to do in such situations. It's George Polya's How to Solve It. (Amazon Wikipedia Google Books) I don't have a copy of the book anymore, and I would like to crowdsource creating a short phrase that captures the general mindset endorsed by it. Some questions I remember the book suggesting are

  • Have you seen a similar problem before?
  • What are the unknowns?
  • What information do you have?
  • Is it obvious that the unknowns are enough information?
There are more of these listed in the Wikipedia article.

Also, "Mantra of Polya" doesn't roll off the tongue well (at least I think it doesn't, since I'm not sure how to pronounce "Polya"), so a better name for this mnemonic would be good, too.

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