OliveMarmot
Thank you for the engagingly accessible essay on decision-making, free will and moral responsibility in a quantum world, whether deterministic or indeterministic.
The analogy you draw between stochastic rounding and human decision-making is very interesting (to me at least!) especially as you link it to control theory where past experience (memory) tunes a control parameter governing the impact of noise on rounding (rather than always “max pros minus cons”) and thus shapes reasoning and choice.
The “Hitler dilemma” is also fine by me, it's not simply provocative as you use it to motivate why free will and moral responsibility matter! I do, however, have some reservations on how you define the term 'free will':
3a Counterfactuality
For now, let us define free will in the way it is often defined in abstract philosophical discussions - in terms of an ability to have done otherwise (Kane, 2002). Later we will consider free will in more physical terms.
This definition is precisely what compatibilists (e.g., Dennett, Frankfurt-style cases, reasons-responsiveness accounts) contest: free will does not necessarily entail 'an ability to have done otherwise'. One probably oversimplified example is negative feedback preventing a certain action from being completed so the agent freely chooses the only available alternative. They 'could not have done otherwise' even though they may have wanted to, so they freely chose the path of least resistance, so to speak. On the compatibilist view, agents can act freely under constraints, exercising reasoning and responsive control at the agent level regardless of whether the quantum microphysics is deterministic or indeterministic (Everett, collapse, etc.).
I think the essay's thesis hangs on just this anticompatibilist or libertarian notion of 'free will', and framing it as 'free will vs determinism' risks a straw man argument without taking compatibilism into account.
But if we just go with the anticompatibilist and/or libertarian definition of free will grounded in stochastic rounding, you aim to base it in quantum rather than classical processes, which makes sense given the competition's theme. WRT the essay's quantum speculation re stochastic probability and credence, is it a necessary condition for its argument that I simply assume with you that:
"In quantum physics we should think of Y_n as a free variable. If Y_n is a free variable, it could have been otherwise at times earlier than tn when its value was set. Hence our decisions could also have been otherwise for times earlier than t_n."
I get that from a libertarian 'could have done otherwise' perspective on free will that you need a degree of freedom in your stochastic rounding process, but rebranding a local noise term Y_n as “quantum” or a Bell-style “free variable” doesn't yield any operational advantage over classical stochasticity, does it? I can't see as how there's any necessity here to count Y_n as a quantum rather than classical term.
And, correct me if I'm wrong, your physical basis for this quantum over classical argument is 'quantum energy efficiency' in ion transport:
"The primary reason the brain operates on the principles of quantum physics may have nothing to do with free will, but rather that quantum processes in the brain can be much more energy efficient that [sic] corresponding classical processes. An example is the transport of ions across ion channels in the membrane of a neuron Summhammer et al (2018) where quantum tunelling [sic] makes for a much more energy efficient transport process. In so far as free will emerged from such primitive energetic considerations, it was clearly evolutionarily advantageous for it to do so."
I would say that this is, for me, the weakest link in the essay's logic, given its emphasis on quantum over classical processes for its decision-theoretic stochastic take on free will. It’s reasonable to note that biology exploits quantum effects (as most of the essays here argue) but your specific claim that neural ion transport is “much more energy efficient” due to tunnelling is AFAIK highly speculative. And if this quantum advantage is the primary reason for your argument that the brain “operates on the principles of quantum physics,” then it remains as yet unsubstantiated.
Then on this physical ground you draw your long bow: In what sense can you claim that "free will emerged from such primitive energetic considerations"? Tying the necessity of quantum processes in neural decision-making to a quantum energy-efficiency claim about ion transport is I think under-motivated, especially where you then attempt to relate 'vestigial quantum parallelism' in neuronal states with the 'fleeting gut feeling' of doubt vis-à-vis 'could have done otherwise' which is an extremely long bow to draw! Equating neuronal 'fleeting' times (milliseconds) with decoherence times (femtoseconds) is the usual critical failing of most of these sort of quantum–neuronal models, including of course the well known Penrose–Hameroff ORCH-OR:
if decision making draws on quantum physics, and quantum parallelism in particular, then we will have a cognitive awareness of the counterfactual worlds associated with making different decisions, not through signals from our sensory organs, nor from approximate 'pro minus con' calculations that we may or may not do, but from the direct projection of the quantum state onto the neuronal state of the brain.
I really can't see how this IF–THEN proposition linking decision-making to 'quantum-parallelism' is 'speculative' rather than just simply unmotivated. I get the quantum computing analogy, but not how that maps to neuronal networks, control theory and higher level (emergent) agent reasoning/decision-making. Quite apart from the fact the 'counterfactual worlds' are (if I follow you) orthogonal components and thus unobservable (FAPP) due to the rapid decoherence – I think the essay's emergence story is underdeveloped. In attempting to link emergent phenomenal experiences (gut feelings, moral responsibility, freedom of choice) with microphysical quantum coherence/decoherence or fundamentally deterministic or indeterministic physics, you risk conflating two very different realms, the phenomenal and its external physical reality. The structural relation between them is not simple and directly mapped, and I think equating introspective feeling with decohered superpositions is a category error. Moving on:
3c Moral Responsibility and AI
As discussed in the Introduction, it is impossible to attribute a sense of moral responsibility to decisions if they are predestined by cosmological initial conditions or equally if they are the result of unfettered (i.e., uncontrolled) randomness.
As already stated, I'm not sure this 'impossibility' is an established fact, as determinism and responsibility can coexist via compatibilism. And I think the possibility for a free moral responsibility depends on the structural relation between physical reality – as say a (deterministic) universal wave function on Hilbert space or (indeterministic) objective collapse in a classical world – and its decoherently emergent quasi-classical everyday phenomenal experience within which we humans assume moral responsibility. Our practices of praise, blame and guidance operate at the macroscopic, decohered control and prediction level. We track stable (real) patterns of agency (intentions, understanding, control), not a microphysical global quantum state. And that holds whether your preferred recipe for quantum microphysics is single-outcome collapse, stochastic or unitary Everettian.
Finally:
- Conclusions
We have devoloped [sic] a model of free will based on ideas from classical numerical analysis, but where quantum physics was shown to necessarily play a vital role.
This concluding claim regarding quantum necessity appears to me to be false. Your stochastic-rounding model of decision-making, free will and moral responsibility is I think an excellent standalone account that is actually well founded on classical stochastic grounds. You don't need the quantum addition for it to work, and the effort to shoehorn it in just conflates quantum, neuronal and phenomenal levels, treating phenomenal and normative properties (gut feelings, responsibility, freedom) as if they should directly map to quantum coherence/decoherence or determinism/indeterminism – with no real bridge model to speak of.
All that said, I'd like to reiterate my genuine thanks for such a stimulating line of reasoning tackling such an interesting problem as the observer's free will in a quantum world!
