> If it requires a significant investment to arrive at an algorithm you can do in your head, one which would others would want to use, isn't it in our best interest to offer a monopoly on use of the algorithm to the inventor?
As various studies have shown, it's not in our best interest to offer monopolies at all, even for things which *are* within the domain of patents.
However, to consider granting monopolies over certain patterns of thought... I'm having a hard time believing that you're serious. Among other things, it would be a very literal form of thoughtcrime, which implies not only an incredible infringement of the rights of the individual, but also that it would be impossible to enforce fairly.
Moreover, historically, algorithms have been researched because they were needed for a specific task, not because of the promise of a patent, and once used they are basically impossible to maintain as a trade secret. Consequently, no further incentives are required to encourage either the discovery of algorithms or their public disclosure. A monopoly in this case does not merely cost the public more than it benefits them, as with normal patents; it is a pure public cost which brings *no* public benefit.