Interesting topic and thought experiment. But this theory is not very fleshed out and not at all convincing (especially the part regarding using an existing efficient market to perform computation for anything other than price of the underlying instrument, i.e. what the computation is intended for). The following quote sums up how the author makes very open ended assumptions:
> So what should the market do? If it is truly efficient, and there exists some way to execute all of those separate OCO orders in such a way that an overall profit is guaranteed, including taking into account the larger transactions costs from executing more orders, then the market, by its assumed efficiency, ought to be able to find a way to do so. In other words, the market allows us to compute in polynomial time the solution to an arbitrary 3-SAT problem.
In reality, most financial markets are pretty efficient but none are perfectly efficient -- if they were perfectly efficient, it would imply not only perfectly efficient trading systems and an inability to get an 'edge' on the market, but also perfectly efficient market systems, which are limited by technology, conventions, and regulations (for example, significant inefficiencies arise in US securities from not being open all the time, with very little liquidity still available in the 'after hours' markets). To achieve even 'pretty good' efficiency requires significant energy, and I'm not sure I understand how the author can imply that the energy used in the past to calculate the current price is equivalent to the energy to verify the current price. As a trader, I can tell you that most market participants do not care to verify past calculations of the current price; they only care about the future price, and will generate an action from the differential between the predicted price and the current price.