In the fractal world I suggested, that is a world constructed from scratch using a basic algorithm, if you looked at the world from outside, you would see people and other things in it. They might appear to have free will, but all their actions would be determined by the algorithm. We might see the demon within the same world, and we might see that he's appeared to discover the algorithm and has started running his own algorithms - but again all his actions would be the result of the original algorithm, which would be giving an illusion of free will and purpose. The demon might be seen, in his part of the fractal, building a world from scratch using the same rules as the fractal does, but, because his actions and their speed are actually all actions of the basic algorithm, he can't outpace it and, therefore, can't do the predicting.
There's another problem for the demon: if he wants to build a complete model of the world, it has to include his model, which also needs to include that model and so on. It's like building a model village inside the village itself. The model has to contain a model, which has to contain a model and so on indefinitely. The model then has to have infinite parts which is impossible.
So, as part of the fractal he can't have complete knowledge. However, if somehow, with his demon like nature, he wasn't part of the original fractal, i.e., he wasn't under control of the basic algorithm, he could then build his own fractal, and if it was identical to the original but just ran faster, he could predict exactly everything that the original would do in the future.
Thanks again for a lovely essay.
P.S. Thanks also for taking the time and effort to read my essay. What you said really made me think. I've posted a reply which I hope you will also find interesting.