Just a little bit before my graduation from computer science, I attended a course about computational intelligence, and my professor then challenged us to debate on whether the world/universe follows a deterministic model or a stochastic model. I have never read a single book about those topics and only until recently I started reading philosophical books but since then I have been thinking over it on my own, like ancient greek philosophers would do with all the parameters and consequences involved in each aspect. I have also talked a lot with ordinary people about the subject. For example a murderer is not in fault for his crime in determinism model, in stochastic modeling there is such thing as a free will etc. Personally, as an engineer I incline towards the deterministic approach and I would also love to hear other people's opinion, debate on the subject and provoke people that support Stochasticism to take a step and present their arguments on why they believe there is randomness in the world, and not just the human's inability to comprehend all the available chaotic finite non-measurable parameters of the system called universe. Although, lately, with quantum mechanics and the new quantum computer from Google, my firm beliefs took a blow because although computers follow determinism in their functions and systems, Google's PC had a 0.1% error based on indeterminism. I am digging into the issue and may form another question in the stackexchange, but my intuition about this uncertainty leads me to the principal of uncertainty from Heisenberg where you cannot predict precisely both the position and momentum
So, there are three models of quantum mechanics which maintain determinism: non-local hidden variables; superdeterminism; and determinism across many worlds. These are constrained by the Bell Inequality having being violated.
This is because, sensitivity to unitial conditions, the underlying characterustic of chaotic systems (such as whenever more than two oscillators interact), mean any quantum measurement could in principle be enough for a different outcome from otherwise the same initial conditions.
So. Non-local hidden variables are problematic because they violate Occam's forbidding of multiplying entities, a hidden invisible layer of order is required that seems to be unfalsifiable. Superdeterminism is problematic because from inside the system it would be unpredictable, and the implication has to be, for it to be verfiable, that you could step outside the system to view how it is deterministic, violating that determinism - so again it's unfalsifiable. Many world's (also called relative state interpretatiin) is probably the most popular interpretation of quantum mechanics among physicists, it allocates the randomness to which branch of the system we find ourselves in, and the system evolves down all posdible branches in a higher dimensional Hilbert space. It seems possible there is a fundamental limit to the information per unit of space-time, linked to the Planck length & time, which would help explain black hole behaviour. This would seem to place a constraint on the total number of paths a system could go in, but it's an extremely high number.
There is another option. The interpretations of quantum mechanics hinge on observer and observed, many worlds pictures states as relative, one quantum system observing another. The It From Bit doctrine suggests matter is not fundamental, information is. Emergent properties are self-stabilising systems, like life, and minds. I see these pieces as pointing towards a materialst-physicalist pan psychism, that the universe is on a deep level the result of it's own enquiry into itself, exploiting it's own lack of knowledge about itself to determine how to be, by amplifying those indeterminisms in a way that is self stabilising, like a mind. Like Indra's Net. Just a hunch though really.
I was talking about free will recently, and this may make the idea clearer: Free will from a self-conscious being's perspective; unfree will from the universe's perspective. Only, the universe has no perspective, there is in fact only intersubjectivity, no universal transcendental perspective, only relative local ones. Mind then wouod be the fundamental strata of being, and world and physicality arises from that, but is prevented from being arbitrary and purely subjective by arising with and in a shared intersubjective mental space. Arising at the 'door' (sense-gate) between mind and world. It's a logical continuation of the private language argument's intersubjectivity. To boil it down, we have freewill for the same reason we have identity, 'I' ness, or that fiat currency exists: we have a convention and act as if it's real, creating a world in which it is. You can say money isn't real, and I point to observables in the world which say it is - but the way in which it's real is not like atoms, it's like the category 'things you can sit on'. Relative, but social. See also peer-to-peer simulation hypothesis
In a deterministic universe nothing ever happens at random nor at will. A deterministic universe could not be intentionally created nor could it have evolved unintentionally through random fluctuations or probabilistic indeterminacy.
A deterministic universe is a logical impossibility. Determinism precludes both methods for determining the contents of a universe.