der to be meaningful to n — Gnomon
Well, this of course assumes we narrow down the discussion of computed answers or solutions our hypothetical computer is capable of to machines that rely on a programmer right?
But is that really any longer the case? Computers that are hardcoded are no different than a classical cash register with mechanical key in many respects and need the human input PLUS their machinery to work. Programs ARE confining for solutions and that's why machine learning was a good idea. It removes the programmer from the equation and also the program, it removes the programming language, and replaces it all with pretty much an optimisation process.
Its limited still I suppose to the capacity of the processors (although obviously the faster or more parallel the processor the faster the model can be trained) , and all that really governs is the 'speed' at which computations are done, not the capacity for computations themselves.
Now is the machine 'free' to make decisions on its own without its origin, or programmers, or other physical baggage getting in the way? Well no, its a physical object in the physical world, governed by the laws of nature... So its not free to do any computation it wants, just the ones confined to the universe we live in. That might seem like no restriction, but it IS a restriction.
So this argument of our hypothetical programmer holds up until around 2008 and then it doesn't any more. It didn't before obviously but you'd need to understand how technology that would arrive in the future was going to work to argue anything else. Add if we top this with quantum computation and no programmers where are we? Its still a 'machine' and likely now freer in scope than a human brain. As far as we know we do not use quantum computation as a primary source of thought. The latest from neuroscience is that the brain is simply a machine where the combined output and system of the agents within it is greater than the sum of those agents. (A complex adaptive system CAS, as opposed to an MAS or multi agent system, like umm... a car or bicycle)
But then where are we...? Well a machine is STILL confined by things a machine can do and the limitations of computation, which are not infinite. Machines do have an absolute top speed of computation and a lowest possible use of energy to carry out a compute. (see Landauer's principle)... and those are fundamental laws of nature we have either discovered or calculated as being so. So this top speed of computation (or rather lowest energy a binary calculation can be performed at) is a limit, if, and only if, the universe itself is not infinite.
However a machine that was maxed out even a few decades from now would be operating many times faster with much higher capacity than any human brain, or likely our entire population and then some. It might not be infinitely free in terms of compute.... but it would be freer than any human is.
And the programmer now, who built this system, has a lower compute capacity, lower knowledge, lower everything than the fruits of his/her labour. It wouldn't matter now how they determined anything or their capacity for doing so.... such a machine would beat them every time and operate at greater levels of freedom. But unless the universe is infinite it can not operate at infinite degrees of freedom. So says the math.... there will always be a limit in a finite universe... hence the word 'finite'.