My understanding of Bit coin is well represented bythis comic
But as I understand it bit coin mining is done by identifying a solution to a computationally intensive problem, whose only value is that it is computationally intensive and so limits the number of bit coins.
Currently mining operations are taking 73 TW of power per year, or somewhat more than the energy consumption than the state of New Jersey, all to solve problems that have no practical use.
Meanwhile there are a lot of other projects that also are highly computationally intensive but which may actually advance scientific understanding.
Would it be possible to generate a bitcoin like entity that relied on these calculations? Or better yet, but probably impossible, alter the current bitcoin market to use useful problems instead?