The New School represents the deterministic universe of Newton, the one that we intuitively inhabit. Theoretically, if you can know all factors influencing an event, you can predict that event. Planetary orbits are the outcomes of several complex factors, but they're regular enough that we can predict them. The Game Master might not have already determined what's on the other side of the hill, but if he hasn't, he will do so using the most logical outcome based on the other factors of the campaign. Frequently, though, the story dictates what's on the other side of the hill, and that's probably been determined.
The Old School represents the probabilistic universe of modern physics (the domain of Schrödinger,
Heisenberg, et al.), the universe we inhabit that seems counterintuitive to a bunch of uplifted hunter-gatherer apes. There are limits to what we can know, simply because the universe isn't already determined, it's a morass of uncertainty that is only realized when it is observed. An unobserved area has the possibility of being anything, but there is a sliding scale of probability that it is occupied by any one thing. The Game Master probably hasn't worried about what's on the other side of the hill, and when you go to explore it, he randomly rolls on a chart that gives a list of things likely to exist there. This chart doesn't represent everything that could be in the area, only those things most likely to be in the area.
Once again, that's a highly simplified metaphor, but it's one I share with you.
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