3 ms·
I wouldn't be entirely surprised if the idea for Ricci flow or PageRank was generated with a dinner napkin. Quite literally, I once used a napkin to explain th
by michael_nielsen 16y ago
I wouldn't be entirely surprised if the idea for Ricci flow or PageRank was generated with a dinner napkin. Quite literally, I once used a napkin to explain the Ricci flow to a mathematician, and I've seen dozens of papers start that way, including a few of my own. Such ideas gain value from their scarcity, not from some immense complexity.
- jacobolus 16y agoOkay, but you wouldn’t come up with PageRank until you’d thought about searching and sorting big quantities of data for some time. If you were just trying to sort 10 numbers, you wouldn’t come up with PageRank. It took a “search the whole web” scale problem for the ideas about how to accomplish it to start bubbling up to the surface. (Probably a bit of an oversimplification, but you get the idea.) Ricci flow isn’t even meaningful until you’ve developed up differential geometry – not exactly an afternoon stroll for a layman.
- michael_nielsen 16y agoI completely agree. My original point was that valuable ideas are very difficult to have, and thus scarce. That's why Ricci flow and PageRank are valuable, while "let's build a social network to do X", for some choice of X, is not. Difficult-to-have and can-write-on-a-napkin are not mutually exclusive, of course!
- jacobolus 16y agoYou’re right. The difference is just one of definitions. What you call “valuable ideas” are what I call “solutions to really hard problems, developed after years, decades, or sometimes centuries of dedicated work.” What Adams calls “ideas” (e.g. for movie plots) are a completely different animal.