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Nic_Smith comments on Rationality Quotes August 2011 - Less Wrong
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I think another category would be "What few other people can or do learn" (rare foreign languages, chess, obscure trivia about a favorite subject). Knowing something that others don't is good for getting status, at least in the subcultures with which I have experience.
My sample is biased (geeks), but it seems to be mising "What makes them go 'Ooh, shiny!'"
Is that not "What has value that is easy to appreciate"?
Not really. I have a reaction like that to non-Euclidean geometry, but I don't know many things it can be used for.
Despite the fact that "non-Euclidean geometry" may sound like something that only concerns people in ivory towers, we all know of lots of things that aren't straight and flat, but instead are curved, bent, or distorted.
Non-Euclidean geometry is essential to the theory of general relativity, which is of immense use in astronomy and also allows the GPS system to function accurately.
What is astronomy used for?
General relativity does. Non-Euclidean geometry does not. I'm pretty certain you can approximate it well enough with Euclidean geometry. Gravitational time dilation is just a function of hight.
Also, GPSs already work. There's no need for me to use non-Euclidean geometry.
Finally, that was just an example. If someone is interested in pure mathematics, and there's an application for it, it's just a coincidence. I've heard some mathematicians actually go as far as disliking it when people find applications for there work.
Studying the territory improves the map.
No, that is not the case. The spacetime geometry near the Earth is non-Euclidean, and using a Euclidean approximation does not produce the required accuracy.
You are conflating "value" with "applications." Different people see value in different things for different reasons.
Polar coordinates
Admittedly this comes up in my life about as often as Euclidean geometry does, which is to say basically never.
I meant to say, is that feeling of "ooh, shiny!" not easily appreciable value in itself?