Can this shed light on determinism v free will ?
In a sense, "Indeterminism" implied by probabilities at the quantum level can be said to give rise to "Free Will" as the strict chain of cause and effect is broken at the fundamental level. Since there are multiple possible outcomes from the same starting conditions, "Consciousness" may be the causal agent (Observer?) which selects one of the possible outcomes i.e. "choice due to free will". Think of it as Physics leaving all options open for an event (within bounds) and Consciousness selecting one among the set. Since the probabilities must add up to one, at the aggregate macro level it is predictable and deterministic while being unpredictable and indeterministic at the quantum micro level.
You also imply (I think) that there is a finite space (bounded) for a variable to range in. Analogous to an LLM spanning and recombining its training materials. But what of the infinite - the unknown ? Of course one might say that we as hoominz are similarly bounded - that we are a variety of wetware LLM, limited by our own training materials (i.e. genes + sensory inputs + generated mental experiences).
But being of a spiritual bent myself, I ask: Where is the foot in the door for the divine ? Knocking at the door of fundamental unknowability - as you say, "unpredictable and indeterministic at the quantum micro level". If there is an intangible, immaterial element to our existence - call it a "soul" - then we might have identified the interface where "the rubber meets the road".
Obv others have considered this question at great length and in great depth.
By "aggregate macro level" I mean the averaging out of aggregate probabilities of multitudes of random events. This is what gives rise to an emergent predictability and determinism which we perceive as certainty. One way to understand this is; For any one event its aggregate probabilities must sum to one thus making it certain within its outcome space. This is carried forward when you consider (as you put it) "a combinatorial explosion" of multitudes of random events.
> You also imply (I think) that there is a finite space (bounded) for a variable to range in. Analogous to an LLM spanning and recombining its training materials. But what of the infinite - the unknown ?
Your comparison of random variables in quantum theory with random variables in LLMs is a bit far-fetched but there certainly are some parallels in the usage of probability distributions in a information-theoretic sense (including infinity).
> Of course one might say that we as hoominz are similarly bounded - that we are a variety of wetware LLM, limited by our own training materials (i.e. genes + sensory inputs + generated mental experiences).
W.r.t. Humans vs. LLMs one needs to bring together; a) A study of Language as being indistinguishable from the "Reality" it describes. b) A study of psychological theories like "Self-Determination Theory" (SDT), "Operant Conditioning", "Behaviourism" and finally, c) Neurobiology which gives rise to what we call "emergent Consciousness". Humans are not just a variety of "wetware LLM".
> But being of a spiritual bent myself, I ask: Where is the foot in the door for the divine ? Knocking at the door of fundamental unknowability - as you say, "unpredictable and indeterministic at the quantum micro level". If there is an intangible, immaterial element to our existence - call it a "soul" - then we might have identified the interface where "the rubber meets the road".
Now we are in the philosophical realm. At the human level we have the various schools of philosophy of which the dualistic Hindu school of "Samkhya" is a good model to study and seek mappings from. According to this school, there is a constant/unchanging/attributeless "Consciousness" (which in materialistic science we can map to an "Emergent Property" of a complex system that is the total Human Organism) and no "divinity" outside of you. Complementing it is the "External Reality" which includes everything else both material(matter etc.)/immaterial(your thoughts/feelings etc.) and which is constantly changing/evolving dynamically over time. It is said that "Consciousness Observes/Witnesses Reality".
This directly parallels quantum theory where the Observer and the Object are entangled into one system during the act of Observation/Measurement though they are separate. This entanglement is what you could call (roughly) "The Mind" where you build Reality i.e. collapse of the possibilities into a single result.
The above is one of the reasons that most Quantum Physicists were quite enamoured of and studied the various Hindu schools of philosophy since there were many parallels here.
Finally, at the Physics level see the excellent "Physics and Philosophy by Werner Heisenberg" for a nice exploration.
One explanation that I heard of free will is that it depends on the complexity of a system. A simpler being might think it had free will while it is predictable to us because we see how it works. A much more complex being might be able to predict what we will do.