Magic is the fundamental manipulation of the four basic forces of the universe -- Water, Fire, Shadow, and Light. This is the only definition. Since Zeal found so many wondrous applications and uses for magic, and since time is kind of what we're dealing with here, I'm going to leave it at that.
I also submit that if you program and oversee the creation of a computer, knowing beforehand its buried ambitions (since this was an improved Mother Brain), you're going to have some idea of what it's going to do, neh? Man, Belthasar is a Guru of Zeal, and the Guru of Reason at that. He can use advanced temporal magic and has the clout to establish a veritable time research instituion complete with a computer able to not only officiate and maintain the building but conduct rigorous simulations and oversee the going ons of an entire chain of islands, down to the last bug. The methods are there.