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Dreaded_Anomaly comments on Rationality Quotes August 2011 - Less Wrong
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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.