Thought is not property

"Patents and copyrights are the legal implementation of the base of all property rights: a man's right to the product of his mind."
So wrote Ayn Rand, a deity of libertarian thought.
Her cry has been taken up by "intellectual property" lobbyists the world over (example
here), but most particularly in America, where Rand is still considered to be a great philosophical thinker.
Rand was wrong, and it's important to understand why.
The sole "product of mind" is thought. Everything else made by humans needs "mind and muscle", so to speak: there is an action following thought which results in the expression of that thought.
The thought itself, however, is not property. The mind is mine, but the nature of property makes it inapplicable to mind.
I'm going to avoid the very abstract parts of this discussion. Much of the debate over intellectual property (from one side) focuses on "exhaustability" and "exclusivity". That is, that when I own this hammer, you can't use this hammer; and because there's a finite supply of hammers, my ownership changes your position. A debate focussing on these characteristics ends up in a quagmire, so I ignore it.
Instead, let's look at two other aspects of property: evidence, and enforcement. I can provide evidence that I bought the hammer and therefore I own it; and on its theft, I can appeal to an authority to enforce my ownership of the hammer.
Exclusivity and exhaustability are abstract economic concepts; evidence and enforcement are more concrete. More to the point, evidence and enforcement don't have to take economics into account. The bottom of the matter is that I own the hammer, not that there are plenty of other hammers around to own; and that the state agrees that I own it, and agrees that my right of ownership can be backed by the law.
Ownership of thought, divorced from effort, cannot be owned: ownership cannot be established by any reasonable evidence, and a claim of ownership is unenforceable.
Until someone sets pen to paper, or finger to keyboard, or tool to timber, the thought has no expression. I can be the first person to make a polished-maple space shuttle, but I cannot ever reasonably claim to be the only person to have thought of making a polished-maple space shuttle.
Copyright and patent protect not the thought, but the first expression of the thought. Until the thought has been published, it has no protection, for very good reason: there's no way to prove primacy (that you thought of it first), and there's no way to enforce exclusivity (to stop somebody else thinking of it).
Back to Ayn Rand. As I said, the product of the mind is thought. But what if, as Rand asserted, thought were to be treated as property?
The only body either enabled or empowered to enforce the evidentiary or enforceability basis of property is the state.
In other words, to make thought into property is to invite the state to police the contents of the mind.
As far as I can tell, only the most oppressive state mechanisms in history have ever attempted that: the policing of thought, for whatever reason, is the extreme end of totalitarian behaviour.
Thought is private, but not property.