I don't think learning makes a difference. Learning is just changing the system around. At any one point in time, the system is what the system is, and does what it can do; and then the argument above applies.

Note that the system in my argument is not necessarily simple. The first appendix alone may have to be very complex. We are yet to create a program which understands how addition works, and to be able to itself write a program that performs addition. The only computer we know capable of doing this currently is the human brain.