Free Thinking/Willing
Much simpler systems than the brain may also satisfy the criteria for free thought and volition.
We are not into metaphysical intricacies but asking whether Nature imposes any restrictions on our thoughts. Also, we are not concerned with stimuli coming from outside but with the brain’s intrinsic functioning. It can be argued that Nature sets no constraints, but then it seems that systems much simpler than the brain also satisfy the same criteria that are needed for free thought and volition.
Thinking is associated with brain activity. Any activity can be thought of as time evolution of a system’s states, in our case, the brain. It is relatively straightforward that for free thinking to exist, an earlier state of the brain should not deterministically control a later state of the brain. The question is then: is it possible, at least in principle, to predict how the states of an isolated brain evolve? If no, the brain’s later states develop without constraints from its past, and thoughts and volition emerge freely; if yes, there is no such thing as free will because we are executing only a preexisting blueprint.
Generally, to predict any system’s future state, two things are needed: one, full knowledge of the present state, and two, knowledge of the physical laws governing the system’s time evolution. The brain, of course, is the most complex system that we know of, but why could one not know with sufficient precision, at least in principle, its state at one point? And we know the physical laws relevant to the brain’s functioning. These laws come from electrodynamics and quantum theory, with possibly some added mechanics, all fields we know well. (Chemistry is encompassed within these fields of physics.) Then, is free will in danger, not from the omnipotence of a supernatural being, but simply from the unyielding laws of Nature? Not to worry, but before continuing with the brain, it is quite interesting to take a look first at a much simpler system.
A system with illustrative value and possibly intriguing implications would be three masses, for instance, three planets, interacting through their mutual gravitational attraction. Such a system is commonly known as the three-body system or problem. It should not be difficult to determine its present state, and the laws of its time evolution are simple mechanics, the oldest branch of physics. Consequently, one might think that predicting the behavior of three masses for an arbitrarily long time is fairly easy, but it is not so. It turns out that notwithstanding the simplicity of this system, its state for an indefinite future can’t be known even in principle. The fundamental reason for this is in the equations governing its time evolution. While those equations are straightforward — discovered centuries ago by Newton — their solution leads to a time evolution that is characterized as being chaotic. The defining attribute of a chaotic system is that any uncertainty regarding the system increases exponentially with time. (The popular name of such behavior is the “butterfly effect.”) One can think of a chaotic process as being surrounded by fog. The further one looks, either backward or forward, the less visible the path becomes. As time goes on, eventually, the system has no information whatsoever about its past and looking far enough ahead about toward what state it is heading for. The growing uncertainties are washing out everything. Thus, the only way a chaotic system’s future could be deterministically known is if at one time-instance its state could be determined with zero uncertainty. And, such infinite precision is not possible even in principle. So the inability to predict the future of a three-body system is not due to a lack of our capabilities; no, the laws governing its evolution are such that the information regarding its future state simply does not exist in its present state. Thus, with time, the states of a chaotic system somehow emerge as if by themselves.
Now that we illustrated chaos with the three-body system let’s return to the brain. Obviously, given its complexity and the laws governing it, the brain must be an extreme case of a chaotic system. We can’t show this simply with calculations as we can for the three-body system, the brain as a whole is way too complex for that. But we know that some of its functioning, like the firing of neurons, involves extreme non-linearities. Non-linearity and chaotic outcome go hand in hand. Since, for us, the brain’s evolution in time manifests itself as thoughts, this means that the common natural phenomenon of chaos is the one that affords the freedom of our thinking and volition!
Considering the three-body system again, is there a fundamental difference between its behavior and that of the brain? The brain is more complicated, but they are both chaotic; thus, the future emerges on its own accord for both. Could one aver that the three-body system also has free will? In fact, almost all phenomena in Nature are chaotic, is free will then universal?
The big difference between the brain and simpler systems lies in how long it takes for this freedom under the aegis of chaos to manifest itself. In the brain, a rough guess could link such freedom to the rate neurons communicate with each other. With each neuron typically connecting to more than 1000 others and firing on average every few milliseconds, the brains’ time to freedom might be sub-microsecond. From the point of view of what we are sensing: instantaneous. While in the three-body system, the same time scale might be that of thousands of its revolutions. Suppose, however, that one normalizes times with a measure of the system’s complexity, something like multiplying the time to freedom with the number of states that the system at any moment can enter into. Maybe such normalized times to freedom are more or less the same independently from any given system’s peculiarities. This would mean that all chaotic systems are free to the same degree after having traveled through roughly the same amount of phase space. Accordingly, the difference between the brain and a three-body system is in their complexity and not inherently in their capacity to act free. The brain has no exclusivity; the differences are in quantity, not in quality.
Of course, one presumes that although a three-body system seems to have the ability to behave according to its own choice, it is not self-conscious. The interesting question is, then, how complex a system has to be for sentience to emerge? Will Artificial Intelligence (AI), or in general anything we humans are capable of creating, ever reach a complexity to become sentient? One could not be faulted for wagering against such an outcome.
An aside, pure quantum systems, even complicated ones, evolve predictably. However, in Nature, pure quantum systems fall prey to what is called decoherence. The time for a macroscopic system like the brain, or parts of the brain, to stay in a pure quantum state is exceedingly short. Thus the predictability of a quantum state does not stand in the way of classical physics’ chaotic behavior. The only exception may be the whole universe’s quantum state, which by definition has no outside disturbance to cause its decoherence. Do we seem to be then in the paradox that while the universe itself is strictly deterministic, minor parts of it, like our brain, or the Milky Way, have free will? Maybe all these little freedoms are somehow correlated to add up to determinism on the largest of scales?
An earlier version published at http://www.infinitetime.org.
