[moonchrome]

>But sometimes the connection between "beautiful art project" and "practical tools" is totally unexpected. We often invest time in projects that seem simply like "beautiful art", and then much later stumble upon something practical.

That's like saying that we should randomly start drilling holes in the ground because sometimes we will strike oil.

people arguing for it usually ignore the silent evidence of research that lead nowhere and also, more importantly, the potential research accomplishments those people could have acheived if guided to work on different problems.

[zardo]

>That's like saying that we should randomly start drilling holes in the ground because sometimes we will strike oil.

Unless you have better tools for locating the oil, that's not a bad strategy.

[moonchrome]

I would argue that if you didn't have better tools for locating oil or determining viable research areas you shouldn't be digging/funding it in the first place because unless you have a high probability of finding something (and we've left the times of early science when there was a bunch of low hanging fruit) the cost of failed attempts will outweigh the benefits of the success stories.

[dllthomas]

Your broader point - that we're a lot more likely to find useful things using some guidance as to where useful things are likely to be than in proceeding randomly - is important.

A crucial difference between digging for oil and doing math, however, is the nature of the externalities. In either case, you're burning some work that could be spent somewhere better, but with oil you're left with a hole that you probably want not to be there and there's no good way to put it back. In both drilling and math, "drilling" helps us refine our methods. In the case of math exploring more of the ramifications of our axioms also helps raise our confidence that they're not subtly inconsistent.

And of course, math is generally less expensive than an oil well.

I don't know where the cost-benefit analysis puts work on math when we don't yet see practical application. And I think that's often over-romanticized. However, I do think there are a lot of reasons we should expect the analysis to come out more favorably than for drilling random holes.