Man walking in a tunnel.

It takes a long walk to get to responsible free will. (steve p2008/via flickr)

By Stuart Kauffman

In this blog I will attempt to formulate a conceivable, if scientifically still improbable, theory of a responsible free will. The problem is formidable so any potential progress is to be welcomed, if also taken with scientific skepticism, as we may try to formulate testable hypotheses. I will attempt just such hypotheses below.

Here is the problem: However we conceive of the mind-brain system, if it is deterministic, as is, for example, Newtonian classical physics, then we can have no free will at all.

So if I kill the old man in the wheel chair, it is not my responsibility. Conversely, if quantum events such as the purely chance radioactive decay of a nucleus yields a non-deterministic, hence "free will", and I happen, by chance to kill the old man in the wheel chair, I can hardly be responsible for the chance event that lead to the death of the old man.

We seem ineluctably caught on the horns of a dilemma. My co-blogger, Ursula has discussed approaches to this problem, in her blog, My I Self, as has Tom Clark. Please see their efforts. Also, Daniel Dennett's "Freedom Evolves" is well worth reading.

I think I do not agree with either Ursula nor Tom, for despite their nuanced efforts, I feel they remain in a stance in which mind is an epiphenomenon of a deterministic brain. I disagree with Dennett, because his mind remains algorithmic, and, as I argued in my blog, "Is The Mind Algorithmic?," I do not think the mind is algorithmic.

The two stances I am taking place me on a track in which I hope to show that it is possible, as in my last blog, "How Can Mind Act On Matter?," that it is indeed possible for a mind-brain system that is quantum coherent, decohering to classicity and back partially or totally to coherence. Then mind has consequences for the classical matter of the brain by acausal decoherence to classicity, not by acting classically causally on the classical matter of the brain.

The above arguments rest on plausible physics, but remain very much to be proven. To do so requires some hypothesis about where and when my hoped for quantum decoherence and recoherence may take place in the brain. I will suggest in this blog that candidate loci include the neurotransmitters in the synaptic vesicles, their post synaptic receptors, and transmembrane channels in the dendrites and axons of nerves. This is an extremely tentative hypothesis, but conceivably open to empirical test.

There are two central parts to my effort here to find a conceivable grounds for a morally responsible free will: 1) The mind-brain system of 10 to the 11th neurons can perform a partially random walk among ontologically possible alternative patterns of neural activities which is both somewhat random at each step, but intensely correlated as a specific historical random walk over a long time, even perhaps a life time, of a single brain. There is, then no law for this walk, yet taken as a whole it is not random. 2) I propose that the poised mind-brain system as a whole can tune how quantum and how classical it is in the Poised Realm between quantum coherent and decoherence to classicity, in specific regions of the brain. I will hypothesize that approaching classicity allows the poised mind-brain system, hovering between quantum and classical, to "decide" and can result in a specific classical event, such as the firing of a specific neuron or set of neurons.

In order for an approach to classicity to constitute a "decision" with specific classical conseqeuences, I must claim that recoherence and decoherence can tune the absence or presence of such a decision and its acausal consequences via acausal decoherence. Thus the responsible free will I seek "acts" acausally, hence is not subject to the horns of the dilemma stated above, which is stated in terms of classical physics, without recourse to quantum mechanics. Yet both quantum and classical are true of the real world. (Some physicists would say that even the classical world retains a residue of quantum behavior.)

I begin a long step removed from the brain. Consider a familiar random walk of a classical particle on a two dimensional lattice. At each discrete time moment, the particle moves one step to the right, and randomly moves one step up or down on the lattice. Over a period of time moments, the particle carries out the familiar random walk, so well studied in stochastic processes. Now the first thing we know is that this walk is random at each step, but the walk over hundreds of steps or more, is very strongly correlated. Thus, if the walk drifts below the starting position on the lattice, it will remain below that starting position for a long time, a law called the arcsin law. Thus, while each step is random, the entire walk, taken as a correlated whole, is not random.

The immediate connection to the quantum horn of the responsible free will dilemma is that, in this horn of the dilemma, one considers only a single random quantum event, say the radioactive decay of one nucleus. But similarly, if one considers only one step of a random walk, it is, indeed, entirely random. There is no long term history which can become correlated along the walk, as shown by the arcsin law.

I now take a second step on my way to the real human brain by reconsidering a "vast" chemical reaction graph with 600,000 molecules, 100,000 each of carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur, CHNOPS, the atoms of organic chemistry. As I discussed in my blog, "Can A Changing Adjacent Possible Change History?", the reaction graph among all possible molecules these 600,000 atoms could form is indeed vast. Consider all possible small proteins, length 200 amino acids. Each has about ten atoms, hence only 2000 atoms compared to 600,000 atoms. Even for such small proteins, as I've discussed, at the Planck time scale of 10 to the -43 seconds, if the 10 to the 80th particles in the universe were doing nothing but making these proteins it would take 10 to the 39th times the history of our universe to make all proteins length 200 once. The time scale to make all possible molecules up to 600,000 atoms of CHNOPS is vastly longer, so even in a closed thermodynamic system, the time to equilibrium is vastly longer than the lifetime of our universe and the "hypopopulated" reaction system will, in effect, take a random walk on this vast reaction graph where I am quite confident that fluctuations will not damp out.
The intuition that fluctuations will not damp out is readily testable using what is called chemical master equations, simulated by what is known as the "Gillespie Algorithm", so can be studied now.

For my conceptual purposes, imagine a region on this reaction graph in which molecules that are adjacent to one another by legal reactions form a coherent "blob" on the graph, with each molecule present in only a single copy. At the edge of the blob lies the Adjacent Possible on this vast graph. Consider a specific reaction, A + B, present on the graph at the frontier of the blob, can react to form C + D in the Adjacent Possible. This reaction is "shifted to the left", that is the substrates exist, a single copy each, the products do not exist. So A + B in the next short time, by an acausal quantum process may, or may not form C + D. But C + D do not exist classically, so cannot form A + B.

The consequence is that, in due course, C + D will virtually certainly be formed by a quantum event.

The next critical step, completely implausible for the reaction system I discuss, but to make a conceptual point, is to imagine that the classical B molecule can recohere partially (or completely) to a quantum state, as Hans Briegel of the Physics Department at the University of Innsbruck says is possible. (I do not think such recoherence is physically possible in the case above for phase information that is lost cannot easily be recovered, but will argue that it may well be possible in the mind-brain system below.) All I need for the point I want to make in this hypothetical example is that if B can recohere sufficiently such that it cannot participate in the reaction in which A + B form C + D, then that reaction is blocked by the hoped for recoherence of B.

Notice that I am supposing a new means to allow or disallow a chemical reaction, or ligand binding event: if one of the partners can recohere such that the event can no longer occur, it is blocked. This is a new idea as far as I know, and may be testable.
Before we ask if it is testable, let's ask if, given known physics, it is possible? A quantum chemist would treat B as a quantum object and solve the time dependent Schrodinger equation for the molecule. But to do so, the quantum chemist typically idealizes the locations and number, N, of the nuclei as fixed in space, and solves for the behavior of the electron cloud. In other words, the quantum chemist assumes the nuclei of the B molecule and worries about the electron cloud and the formation of bonds among N nuclei to form the B molecule. But is that idealization realistic? Well, perhaps not. First, the nuclei move in three dimensional space. More deeply, my physicist friends inform me that in quantum field theory, even the number of nuclei in a spatial region is indeterminate.

If even the number of nuclei is indeterminate in quantum field theory, part of a hoped for wave equation of the universe, and if recoherence can reach back to quantum field theory, then the "existence" of the classical B molecule is "gone". The A + B reaction to C + D may, in fact, be blocked by the recoherence process. Ultimately, this should be testable experimentally.

As noted above, it seems virtually impossible for such recoherence to happen on my vast reaction graph. Lost phase information cannot be recovered easily. But it may not be impossible for the mind-brain system. Recall that the chlorophyll molecule is surrounded by an evolved antenna protein and is quantum coherent for at least 7000 femtoseconds at 77K, when decoherence within 1 femtosecond, 10 to the - 15 seconds, is a typical decoherence time. It is thought that the antenna protein either prevents decoherence, or, in analogy with Shor's quantum error correction theorem, where injection of phase and amplitude information can yield recoherence in decohering degrees of freedom, the antenna protein may interact with the quantum coherent but decohering chlorophyll molecule to yield recoherence to some degree with respect to phase and amplitude information.

Now let's turn to the human brain with its 10 to the 11th power number of nerve cells. As an underestimate, assume that only 10% of these are in the cortex, hence 10 to the 10th power number of neurons. Assume for consideration that we can idealize any neuron to be firing, 1, or not firing, 0. Then the possible states of the cortex are 2 raised to the 10 to the 10th power! This is hyper-astronomical. There are only 10 to the 80th particles in the known universe, infinitesimal compared to the possible states of the binarized cortex.

Now consider neural processes over a lifetime in this cortex. Before we enter quantum considerations, let this process be classical but a familiar noise driven stochastic process. Then, like the random walk above which may be random at each step, we can anticipate that over a long history the walk in the vast state space of the neural system is non-random yet lawless.

I now add the quantum decoherence recoherence ingredients to this conceptual and neural model. The neuroanatomy of the brain has axons of neurons ending in synaptic junctions. In the presynaptic region of the incoming neuron are vesicles filled with different numbers of specific neurotransmitter molecules. The axon synapses on the dendrites of the post-synaptic neuron. Transmission of activity from the upstream neuron to the downstream neuron is achieved by release of the neurotransmitter molecules which diffuse across the synaptic cleft and are bound by receptors on the postsynaptic membrane of the downstream neuron. In turn, this binding induces a small voltage change in the post synaptic membane. The summation of these "depolarizations", achieved via transmembrane channel proteins allowing ion passage through the membrane, is accumulated at the axon hillock of the nerve cell and, if above a "threshold" the nerve initiates an action potential which propagates down the axon of the neuron.

Now let me suppose that the recoherence of neurotransmitter molecules in the presynaptic vesicles can render them incapable of binding to the post synaptic receptor molelecues, and/or that recoherence of the post synaptic receptor can render it incapable of binding the neurotransmitter, and/or that recoherence of the protein ion transmembrane channels can render them incapable of allowing ion flux. In the above hypothesized case, recoherence has blocked or tended to block activation of the specific downstream neuron.

Conversely, decoherence of these molecules to classicity has permitted activation of specific down stream neurons.

Then we can conceive of "deciding" by the mind-brain system as a controlled acausal decoherence at specific loci in the brain that enable specific classical events to happen.

In the hypothesized quantum-decohering-recohering - brain system we are considering, we have at our disposal for a responsible free will only the above. But it seems that may well suffice. The now quantum random walk in the vast state space of neural activities may be random at any single step, but it is both true that the walk as a whole is highly correlated, non-random but non-lawful, and that decoherence at specific sites for one or more neurons and dendrites can acausally yield specific neural activities in the brain. The mind-brain system thereby acausally decides and acts to make specific classical events happen. Therefore, and critically, the "walk" in the space of neural activities is no longer merely random and correlated. Our decisions change specific neural activities in specific ways and change the walk.

I think we have here a conceptual and hopefully a physical foundation for a responsible free will, no longer bound by the familiar, purely classical, conception of the mind-brain system, nor the specter of mere quantum chance.

12:33 - March 26, 2010