It's hard to figure out what you really want to know, after many commenters have tried to explain why replacement mining technology doesn't reduce overall energ

It's hard to figure out what you really want to know, after many commenters have tried to explain why replacement mining technology doesn't reduce overall energy consumption, which was your broader line of questoning. So I will focus on this one part: > Where is the required energy use here? Fundamentally, the hash calculation is designed so that energy consumption is proportional to required hashrate - regardless of hashing technology. The required hashrate is reactive. It's governed by the difficulty adjustment algorithm which reacts to economic competition on the blockchain as well as economic competition among miners, so as to create two decoupled markets with money nonetheless flowing between them, which incentivises miners to spend most of the fees offered by blockchain users on energy, regardless of how efficient the mining technology is per hash. So the required hashrate always adjusts until most of the mining fees offered by blockchain users gets spent on energy. If your question is, essentially, "why any energy at all", the answer is that calculating things using zero energy isn't possible. If your question is "why can't we come up with a way to calculate these numbers that's so efficient the system won't increase the difficulty to fully compensate", that might be possible, but it would require the brute-force algorithm assumption to be broken. That is a type of breaking cryptography. The cryptography is designed so that it uses energy proportional to the hashrate on any type of computer. There is no known way around that. People try, of course; the incentives are very high for them to succeed. Merely building a faster computer won't do it. A photonic computer, for example, doesn't challenge this assumption at all. A computer a trillion times more energy efficient would not challenge this assumption either. My limited understanding tells me even a quantum computer doesn't challenge this assumption, because SHA256 hashing is not amenable to Shor's algorithm, and Grover's algorithm only divides the bit-difficulty in half, which the difficulty threshold adjustment would automatically compensate for. However, switching away from proof-of-work does change this assumption, and that's how to reduce the energy consumption. > this is a sort of economic framing, but also, not the question You cannot ignore the economic framing - it is a key technical part of the proof-of-work design. It is such an important and powerful effect, it has a technical name, cryptoeconomic incentive, and it's treated as a critical technical factor in all major blockchain designs. Although you can see it as a statistical or human effect, it is a strong and predictable effect. It is almost analogous to statistical mechanics, where we can calculate the properties of physical substances from underlying "random" individual behaviours, because the statistical ensemble behaves in a predictable way.