To this I would add, as I understand it of course, that the math bitcoin wants you to solve isn’t related to productivity.
It would be an entirely different thing if the currency was related to solving parts of massively distributed software, which could be used productively and processor time rented out for actual currencies ... but it’s seemingly not.
Unless, of course, it is and what it’s about is the sort of espionage or counter espionage that one might expect or something rooted in the NSA. Distopian sci-fi novel version: they’re really trying to steal all the money from all the banks so that their’s is the only available money. Make a great Bond movie. Probably isn’t happening in real life though.
You are describing the Etherium network.
About $700 each.
It’s backed by a hamster on a wheel that doesn’t generate electricity, it uses electricity.