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shminux comments on Dissolving the Question - Less Wrong
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That's a model along the lines of the one I was thinking of in response to the question; any number of simple algorithms for processing data, creating a worldview, determining the expected utility of a series of actions, and choosing the action which seems to have the greatest utility might believe it has 'free will', by the definition that its actions cannot be predicted, if it is not capable of understanding its own nature.
Humans are, of course, more complicated than this, but idea alone produces the question... is your mind the sort of algorithm which, if all of its processing details, utility functions, and available worldview data are fully known, will produce output which can be predicted in advance, given the information? That doesn't feel like an ending, but it is, perhaps, grounds to explore further.
Following up...
Having (almost) finished the Quantum Physics sequence since this last comment, and come to the point at which this particular assignment is referred to, I figured I'd post my final conclusion here before 'looking at the answer', as it were.
Given a basic understanding of QM, and further understanding that macroscopic phenomenon are an extension of those same principles... Knowing that nothing 'epiphenomenal' is relevant to the question of consciousness... And assuming that no previously unobserved micro-phenomenon is responsible for consciousness, by virtue of the fact that even if there were, there is, at present, no reason to privilege that particular hypothesis...
There's no question left. What we call consciousness is simply our view of the algorithm from the inside. I believe that I have free will because it seems like the choices I make change the future I find myself in... but there are a great many other factors implicit in my thinking before I even arrive at the point of making a choice, and the fact that the probabilities involved in defining that future are impossible to calculate under existing technology does not mean that such a feat will never be possible.
That said, even full knowledge of the state of a given brain would not allow you to predict it's output in advance, as even in isolation, that brain would divide into a very large number of possible states every instant, and QM proves that there is no way of determining, in advance, which state that brain will arrive at at any given time. This is not randomness, per se... given sufficient information, and isolation from contaminating entanglements, one could theoretically plot out a map of possible states, and assign probabilities to them, and have reasonable expectations of finding that mind in the predicted states after a determined time... but could never be certain of finding any given result after any amount of time.
That doesn't mean that I don't have control over my actions, or that my perception of consciousness is an illusion... what it does mean is that I run on the same laws of physics as anything else, and the algorithms that comprise my awareness are not specially privileged to ignore or supersede those laws. Realizing this fact is no reason to do anything drastic or strange... this is the way that things have been all along, and my acknowledgment of it doesn't detract from the reality of my experiences. I could believe that my actions are determined by chance instead of choice, but that would neither be useful, nor entirely true. Whatever the factors that go into the operation of my cognitive algorithms, they ultimately add up to me. Given this, I might still believe that I have free will... while at the same time knowing that the question itself does not have the meaning I thought it had before I seriously considered the question.
Do neurons operate at the quantum level? I thought they were large enough to have full decoherance throughout the brain, and thus no quantum uncertainty, meaning we could predict this particular version of your brain perfectly if we could account for the state and linkages of every neuron.
Or do neurons leverage quantum coherence in their operation?
I was once involved in a research of single ion channels, and here is my best understanding of the role of QM in biology.
There are no entanglement effects whatsoever, due to extremely fast decoherence, however, there are pervasive quantum tunneling effects involved in every biochemical process. The latter is enough to preclude exact prediction.
Recall that it is impossible to predict when a particular radioactive atom will decay. Similarly, it is impossible to predict exactly when a particular ion channel molecule will switch its state from open to closed and vice versa, as this involves tunneling through a potential barrier. Given that virtually every process in neurons is based on ion channels opening and closing, this is more than enough.
To summarize, tunneling is as effective in creating quantum uncertainty as decoherence, so you don't need decoherence to make precise modeling impossible.
Interesting! I hadn't thought about quantum tunneling as a source of uncertainty (mainly because I don't understand it very well - my understanding of QM is very tenuous).
Quantum uncertainty is decoherence. All decoherence is uncertainty. All uncertainty is decoherence. If it's impossible to predict the exact time of tunneling, that means amplitude is going to multiple branches, which, when they entangle with a larger system, decohere.
That is not quite the conventional meaning of decoherence, though. Of course, if I recall from your QM sequence, it is, indeed, yours. Let me explain what I think the difference is between the two phenomena: a spin measurement and the tuneling process.
During an interaction such as spin measurement, a factorized state of a quantum system becomes entangled with the (quantum) state of the classical system as some of the terms in the product state decay away (according to Zurek, anyhow). The remaining "pointer" states correspond to what is usually termed "different worlds" in the MWI model. I believe that this is your interpretation of the model, as well.
Now, consider radioactive decay, or, to simplify it, a similar process: relaxation process of an excited atom to its ground state, resulting in an emission of a photon. This particular problem (spontaneous emission) requires QFT, since the number of particles is conserved in QM (though Albert Einstein was the first to analyze it). Specifically, the product state of an excited atom and the ground (vacuum) state of the electromagnetic field evolves into a ground state of the atom and an excited state of the field (well, one of almost infinitely many excited states of the field, the "almost" part being due to the Planck-scale cutoff). There is virtually no chance of the original state to reappear, as it occupies almost zero volume in the phase space (this phase space includes space, momentum, position, spin, etc.). I believe even time is a part of it.
To call radioactive decay "decoherence", one would have to identify the ground state of the field (electromagnetic vacuum) with the classical system that "measures" the excited atom. Calling a vacuum state a classical system seems like a bit of a stretch.
An alternative approach is that the measurement happens when an emitted photon is actually detected by some (classical) external environment, or when the atom's state is measured directly by some other means.
I am not sure if there is a way to distinguish between the two experimentally. For example, Anton Zeilinger showed that hot fullerene molecules self-interfere less than cold ones, due to the emission of "soft photons" (i.e. radiating heat). His explanation is that the emitted radiation causes decoherence of the fullerene molecule's factorized state, due to the interaction with the (unspecified) environment, and hotter molecules emit shorter-wave radiation, thus constraining the molecule's position (sorry, I cannot find the relevant citation).
If you identify each of the branches in the MWI model with each possible excited state of the electromagnetic field, you would have to assume that the worlds keep splitting away forever, as all possible (measured) emission times must happen somewhere. This is even more of a stretch than calling the vacuum state a classical system.
Feel free to correct me if I misunderstood your point of view.