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A system where it's not profitable to solve problems won't do much problem solving.

This is just taking the rational consumer model, forgetting it's just a model and treating it as a fact of life, and then inventing corollaries from it. Plenty of people find intrinsic value in solving problems without there needing to be a profit. See, e.g. Open Source Software, The Apollo Program, Academia, the BBC.

And that only works for problems that are cheap to solve. Most aren't.

You are replying to a post that references exceptionally expensive efforts. The inflation adjusted cost of the Apollo Program was hundreds of billions of dollars[1]. By what measure is that cheap? Maybe I'm missing intended sarcasm?

[1] https://www.planetary.org/space-policy/cost-of-apollo

The Apollo Program, Academia, and the BBC all pay their workers, which makes it profitable for them to do the work.

I get your point: These are not for profit enterprises and they still get important work done.

I'm making a different point: People don't work for the benefit of others without being rewarded.

Open Source Software is not a bad counter example. I think there are rewards in the joy of programming, making a name for yourself, and a few other things, but I'll concede that there is some nuance there.

Spoken like a true Ferengi.

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