Imagine a computation-intensive crypto-coin-mining activity somehow linked to a real-world, practical use, say, curing cancer (say, by digging through vast amounts of genetic data). Instead of paying for the computation time directly, people could work on chuncks of the problem as they wish and be rewarded with CCCs (Cancer Cure Coins) for defined partial results.

Then we could say the computing ressources are not wasted.

This is a frequent point that comes up from people who haven't really thought through all the details of how PoW based cryptocurrencies work.

A good proof of work function needs two things (among other desirable properties I will elide):

1) For some difficulty factor D, you should be able to generate an instance of the problem that takes time proportional to D to solve

2) The solution should be verifiable in time much less than D (preferably constant time)

So until you can show me a foolproof way to generate protein folding problems, genetics problems, or SETI problems, etc. that have these properties (I haven't found one myself), it seems quite difficult to make a "useful" PoW.

Now, theoretically, if you found a "useful" problem that had property 1, but not property 2, you could convert it into a viable PoW using efficient zero knowledge proof techniques [0], but at the moment that isn't really viable.

[0] - https://eprint.iacr.org/2013/507.pdf

It was just an example to clarify the criticism of "cryptocurrencies waste energy". It would be up to the cryptocurrency advocates to show such a function.

On the plus side, the problem does not necessarily be "proportional to D", in fact, finding a better function would be incentivized. Since the computer cycles would produce a "real" value (curing cancer), the upper limit for these coins would be the amount of money society would spend on a cancer treatment.

/speculation

I heard talk of some math that said, in effect, "if the work is useful, proof of work breaks down." Not finding a link...