In our current understanding of the world (quantum mechanics), the world is inherently probabilistic ("random", not deterministic) in the microscopic realm. There are differing opinions among physicists whether or not there could be a more fundamental layer of reality beyond this, and if so, whether it would be deterministic. Notably it could be said the mainstream view is that reality is not deterministic.
If you were shown a screen, told it consists of individual pixels, but no matter what microscope you grab you can't discern those pixels, does that screen consist of pixels or is it a continuous canvas?
That's kind of where physics is at, no? Until you succeed in building an apparatus that lets you see individual pixels, it's a continuous canvas for all intents & purposes.
Some discrete & deterministic layer underneath it all is a more elegant possibility imho. Might suit people who prefer "nature at its deepest level is math" worldview. But why would reality 'bother' to fit into that shoe? It just is. Whatever that is. Discrete or continuous, deterministic or probabilistic.
I think there are good epistemological reasons to at least consider the fact that this is not what quantum mechanics is about. There seem to be ways you could kind of try to make what you are talking about work, but they are incomplete and pretty incondite and have, at any rate and to the extent that I understand them, some pretty unappealing philosophical characteristics.
The real meaning of the commutation relation is not that there is a fundamental _relation_ between sets of observables but, I would argue, that at a deep level pairs of non-commuting observables like x and p, share a single ontological substance which we can view partially as either position or velocity depending on how we arrange our measuring apparatus.
The second most popular view is that the universe branches deterministically, which means there will be some observers in a very small percentage of branches who observe seemingly miraculous events (very low probability). Their notion of probability would be different from ours.
