I have no cogent argument with your first situation (there are some subtleties there that you omit, but it's basically correct modulo other uses for the energy)

I have no cogent argument with your first situation (there are some subtleties there that you omit, but it's basically correct modulo other uses for the energy). The second, however, is fundamentally inaccurate: > Heat production for buildings and water. Most space and water heaters produce heat directly from their energy source (electricity or gas) without producing anything else of value. The primary byproduct of Bitcoin mining is heat, so it’s relatively straightforward to use mining hardware to produce, or at least augment, traditional heating elements. A company called Wisemining has a product called the Sato Boiler that does this now. This is incorrect because a mining-based heater will be new and use electricity as its fuel source. You can't compare with an old electric heater because a replacement will obviously be new. You can't compare with hydrocarbon heaters, because you need to convert to electricity to run a computer. That means meaning we need to compare with a new electric heater. That comparison is unfavorable, however, because it will probably be based on a heat pump. Heat pumps have efficiency much greater than 100% (usually around 200%) by takng heat from the outside air or ground. A better example would be something like an electric oven, which typically does just use resistive heating. However, this sort of undermines the argument, since the energy spent on heating food isn't that much compared to things like residential and commercial heating.