Energy Waste Fallacy

There is a theory that proof-of-work (PoW) wastes energy. This implies that the level of security provided is greater than necessary or the same level of security can be provided by another externalized proof at a lower energy cost. An internalized proof, specifically proof-of-stake (PoS), is an entirely different security model which is not considered here.

Total hash power is a function of reward, which is a function of fees, which are determined by the confirmation market. If a person considers current hash power insufficient to secure trade at a given value against double spend then the depth requirement increases. As shown in Utility Threshold Property, transactions with insufficient value for even single confirmation security are priced out of the chain.

These upper and lower security bounds depend on confirmation cost and are therefore independent of the proof technique. There is no necessary level of security, just a subjective confirmation depth and minimum utility.

Confirmation security increases with the cost of generating each block. The double spend of a transaction requires that its branch be superseded by another with a probabilistically greater cost. So the only way energy cost can be reduced is by expending the same average per-block cost with a lower energy component.

PoW incurs cost in several forms, including labor, hardware, services, land, etc. Any other externalized proof consumes these same resources, though potentially in different proportion. The question of energy cost reduction is therefore reduced to whether an energy component of the cost of a proof can be replaced by another resource with the same cost.

It has been proposed that a proof-of-memory (PoM) can replace some fraction of the PoW energy cost with hardware, even relying on existing memory devices. Since a constant level of security requires a constant ongoing expenditure, such a system would require a comparable level of hardware (and/or labor, etc.) consumption to offset any reduction in energy cost.

In other words total energy consumption cannot be reduced, it can only be transferred in full to hardware manufacture, operation and disposal. The hardware acts as a proof battery, representing energy provably consumed in its manufacture. The theory is therefore invalid.

It is worth considering the economic behavior of a theoretical system in which PoM is determined by an existing (free) fixed pool of memory with no expiration or operational costs. As the cost of mining is zero, rewards flow at no expense in proportion to memory (assuming no pooling pressures). Any increase in average fee increases this reward for memory. Capital invested is zero and therefore rate of return is perpetually infinite. Despite unbounded incentive, the assumption of zero expansion precludes competition. But since the proof is externalized, competition cannot actually be restricted. In an actual system hardware expands perpetually for a given fee level, and this rate of expansion grows with fee level increases.