- The total mining income is determined by how much blockchain users are willing to pay for blockchain services. It's determined by market demand for transactions on the blockchain, in a grand auction competing with other users.

- There are two markets - competition between blockchain users offering fees in their grand auction, and competition between miners. These are strongly decoupled from each other by the difficulty threshold update algorithm. So the total mining income, offered by users and paid to miners, is independent of hashrate, number of miners, or mining technology. Miners don't change the total mining income, they can just compete to get a share of it.

- Finding the hash number requires a brute force algorithm. There are shortcuts to do it significantly faster, but it is assumed there is no mathematical shortcut which avoids the brute force property. (Brute force means a particular mathematical property of the search algorithm, it does not say how fast or what kind of technology.)

- No matter what technology is used to find the number, it requires some energy, and in proof-of-work, due to the brute force property, the rate of energy consumed is proportional to the hashrate.

- The required total hashrate automatically adjusts, via the difficulty threshold, so that a miner with X% of the total hashrate gets X% of the total network mining fees, no matter what technology they use.

- A miner with X% of the total hashrate can spend anywhere from 0% to X% of the total network mining fees and remain profitable, depending on how energy efficient their rigs are. No more than X%; that would make a loss, so they would stop.

- A miner with access to more energy efficient mining technology (lower rate of energy consumed per hash) will seek to maximise their profit by obtaining more mining rigs, if they can get them. When that technology is widely available, everyone will want it. The effect is to push up the total hashrate for everyone.

- When the total network hashrate goes up, miners without the new technology cease to be profitable (they are spending the same but their X% has reduced due to the total hashrate increase, so they receive insufficient payment), and those have to stop mining unless they can get the new technology. Only miners with the new technology can afford to participate.

- Therefore the network rapidly converges on the new technology.

- The total spent on mining costs must be between 0 and the total mining income.

- When the total spend on mining costs is much below the total mining income, and the new technology is widely available, someone sees a market opportunity and buys a mining rig. It works this way because the network has converged on the new technology, so it's a roughly level playing field to join.

- This raises the hashrate, and pushes up the total mining costs, without changing the total mining income. This keeps happening and converges towards an equilibrium where the total costs are close to the total mining income. As long as there's someone seeing an opportunity to get a little for themselves.

- Because much of mining costs is energy cost, the miner equilibrium is eventually reached when the total spend on energy is close to the total mining income.

- Therefore, total energy consumption is roughly determined by the amount of energy that can be purchased for the total mining income.

- As mentioned at the start, total mining income (before costs) is decoupled from all this mining business. So rolling out new mining technology doesn't change how much total income is available to spent on the whole blockchain mining network, and competitive self-interest among miners means most of that spend goes to energy.