This is kind of my point, I can do something a computer cannot do because I am conscious. I'm skeptical that a computer could transcend its programming into consciousness to solve a problem that mathematically it should not be able to solve.
I don’t think it’s your point, since that would contradict what you’re saying. I don’t believe you can do what you think you can do. And you literally can’t convince me unless you can invent a non-algorithmic way of describing how you would tell if an arbitrary program will terminate.
A computer cannot tell you that this program will not terminate, short of memorizing this specific set of instructions as a "non-terminating" program.
I can read it and know it will not terminate, but I could not define to you how I know that algorithmically. Despite that, I know it will not terminate, and so does any programmer. Just because it cannot be expressed algorithmically doesn't mean we don't possess that capability.
This is my point about consciousness: there is some aspect to it which cannot be articulated, hence my skepticism that computers will ever become conscious.
