Do you believe in free will or determinism? Either way, imagine you are creating a life form, and that you want it to have free will. You figure out that you need to design an organ that would be responsible for this. You decide to call it the "free willer".
What would this organ do? You realize that it must make decisions, as that is what "will" allows you to do. But how will it do so? You realize that learning is involved — that this organ needs to take into consideration past events. Oops, you have just created the deterministic willer!
Ok ok, let's back up a minute. If we don't take into consideration past events... well then the decisions it would make would have to be random. Is that what we want? Not really, random decisions won't get this new life form very far!
What other decision mechanisms could we come up with for this organ? Well it could be influenced by some predetermined set of rules or genes that get better over time, but that's just another determinism!
Ideally what we want is something that is influenced by past events (learning). Something that can improve its programming over generations (genes). And finally something that can decide to do OTHER than its deterministic inputs dictate (the free part).
Turns out that the brain marries randomness with learning and genes in a perfect way to achieve just this! We already have an organ that will purposefully introduce randomness into our thinking process so that we can come up with unique solutions and choices that are not predetermined by the universe or by our genes and past experiences (at least not exclusively).
Here's a paper I wrote about this that goes into this in more detail. The brain is sooo cool.
The field of computer artificial intelligence often finds algorithms that use randomness extremely useful. Simulated annealing, genetic algorithms, random walk, stochastic algorithms and neural networks, cryptography, random constraint satisfaction, and even the common quicksort all employ randomness to some degree or another (Russel, S. J., Norvig, P., 2003). Randomness is often used to get an algorithm unstuck or to allow an algorithm to find an approximate solution much quicker than it would take to find an optimal one (finding the optimal solution in large state spaces is very often simply not computationally feasible).
For instance, in simulated annealing a local search algorithm will randomly choose among nearby solutions in an effort to prevent getting stuck at a local optimum (ibid., pg 120). A local search algorithm is an algorithm that changes the current state (or states) based on information it knows about surrounding states rather than exhaustively searching down paths from a start state. A simple example of this is the hill climbing algorithm (ibid., pg.122). The algorithm simply examines positions in the search space adjacent to it's current position and picks the better one. When nothing adjacent is better it stops. However, stopping at this point does not necessarily imply the best solution: this might be the top of a small hill that is next to a big mountain. To make this algorithm not get stuck at local maxima, whenever it gets to the top (since we are talking about climbing), instead of claiming victory it should attempt a random jump to another location, but remember the last highest peak. This way after some number of maximum random jumps the algorithm will either find the global optimal or the best it could find in the given time. The physics annealing analog is repeatedly heating a metal (to progressively less high temperatures) and allowing to cool in between cycles to align the crystalline structure into continually smaller-finer crystals. Thus instead of simply randomly jumping the algorithm could assign a lowering probability for each step as it jumps to avoid jumping too far as it narrows in on the actual optimum (ibid., pg 124).
Genetic algorithms (and stochastic beam search on which they are based) can be explained in terms of evolution. In stochastic beam search a greedy local search such as hillclimbing is run some n number of times in parallel. At each step, n of the best possible successors are chosen at random with a decreasing probability assigned to each given its value (provided by some heuristic value function) and the current time step. The biological analogy to this is natural selection. Each successor state is an offspring of a parent state organism and the successors are selected based on their fitness. Genetic algorithms take this a step further by combining two parent states analogously to sexual reproduction. They are similar to stochastic beam search except with the addition of a few steps that deal with crossing the 'genes' of the parent states. States are usually stored as sequences of characters or numbers and after being crossed are also randomly mutated.
These are just a few examples of randomness in AI computing. These are fairly simple examples however, a larger problem for AI is what to do when the world is complex and uncertain. Simulated annealing and stochastic beam search are part of the Monte Carlo family of algorithms that use randomness to help deal with uncertainty in large numbers of inputs. Any large scale modeling with uncertain inputs requires probabilistic reasoning which often requires randomness to deal with any sort of large connected network (ibid., 530).
In these algorithms, randomness plays a part, however the other essential part is probability. Without probabilistic reasoning, no complex modeling, learning or planning given uncertain inputs could be possible (ibid., 480). Bayesian networks are perhaps the most famous of probabilistic tools used to compute the probabilities of unknown variables using networks of connected probabilities. At the neuronal level in the physical brain probability plays a big role. The research areas most clearly connecting AI to the human brain are artificial neural networks.
Artificial neural networks can have a fairly simple mathematical model. A neural network is composed of units connected to each other. Each connection has a weight which not only carries the 'strength' of the connection but also whether it is excitatory or inhibitory (the numerical weight is signed). Each node has inputs (which are summed), an activation function (either a hard threshold or a sigmoid) and output links to other nodes (ibid., 728). After training, an artificial neural network can not only encode complex boolean operations but also can function as short term memory (if connected as a recurrent network with reafferent loops). The significance of this model is that although it is quite simplified, it shows a probabilistic network analogous to the neural network of the cortex.
Since the brain's neuronal circuitry is the basis for artificial neural networks, there are clear parallels even though the actual system is much more complicated than the computational model. The weights can be conveyed not only by width of the synaptic gap (usually around one forty-thousandth of a millimeter (Penrose, R., 1989)) but more importantly by the timing of the axonal pulses (Freeman, W. J., 2000, pg. 41). The presynaptic electrical axonal pulse has a constant current height and so the strength of the signal is conveyed by the rate of the pulses. The dendrite of the postsynaptic neuron (via the action of neurotransmitters in the synaptic cleft) integrates these pulses into a amplitude modulated wave input for the postsynaptic neuron. The various currents from the dendrites on the postsynaptic neuron are summed up in the trigger zone near the nucleus of the neuron. That current is what triggers the neuron and is capable of being measured as potential in an electroencephalogram (EEG) (ibid., pg. 42). If the current reaches the action potential then the neuron will trigger it's own axonal pulses. The axonal pulses take some time to travel but there is no attenuation of the signal — this is essential to be able to transmit values over long distances without losing energy. Dendrite current modulation is different — it is able to integrate with currents from other dendrites in the cell body current loop. This enables the summing of potentials (ibid., pg. 46). One thing to note about the pulse-width conversion (ibid, pg. 46) is that it is not stepped or linear but rather sigmoid (leaning s) shaped. Slow at low and high activation but increasing linearly in the middle. By this action the neuron reacts differently to incoming pulses given its current state.
Some neurons have leaky terminal membranes allowing a slow change in potential (Burns, B.D, 1968, pg. 23) . This causes them to fire at random intervals. Taken alone this periodic random firing does not amount to much, however given the density of neuronal connections, it is useful to also consider the action of groups of neurons rather than single individuals. A noticeable group effect that occurs is subthreshold oscillation. For each neuron to stay alive it needs to periodically activate (Freeman, W. J., 2000, pg. 41). There appear to be synchronization waves that result in periodic rises in subthreshold membrane neuron potential. These result from a collective pattern of recurrent excitation and inhibition from interneurons (shorter local reach neurons (ibid., pg 39) (Buzsaki, G., 2006). Not every neuron fires every time but collectively there is an oscillation pattern. This oscillation constrains the times during which neurons may fire and thus produces a synchronizing effect (Buzsaki, G., 2006, pg. 76). Neuronal firing often needs to be synchronized to produce the desired effect — if two neurons fire and if, because of the oscillation, the probability that they will fire simultaneously is increased, they are more likely to push a third neuron over it's activation threshold. If the neural process is widely distributed and complex then the synchronicity becomes even more important in it's constraint of timing differences because of distance (ibid., pg. 115). There are several different oscillation frequencies ranging from multiple seconds to 600hz. Since they temporally constrain neural firing the different frequencies have different purposes/ranges. Fast oscillation is more appropriate for local, small distance neural patterns whereas slower clock speeds allow neurons further apart to cooperate. Additionally the oscillations are not constant, they are perpetually attracting and repelling each other as they do not have any stable phase relationship. Thus, they interfere with each other, but that chaos and fluctuation may be a necessary part of the temporal organization of the brain as a whole. All of this oscillation can be seen as noise, not only because the neurons are firing without any external stimuli but also because the relationship between all the different oscillation frequencies is e (2.71), the natural logarithm — this results in a chaotic pattern that appears like "pink" noise on an EEG (ibid., pg. 113). "Pink" noise is also known as complex noise — this is because its power ratio is 1/f, meaning that the amplitude of the waves decreases as the frequency increases. Although to a physicist this would simply suggest that it is a noisy system, what appears as noise is also a chaotic yet functional synchronizer and organizer of neuron systems (ibid., 119). The same neurons participate in multiple rhythms, and the oscillating groups can change and influence each other.
The brain not only gives rise to large-scale, long-term patterns, but these self-organized collective patterns also govern the behavior of its constituent neurons. The firing patterns of single cells depend not only on their instantaneous external inputs but also on the history of their firing patterns and the state of the network into which they are embedded (Buzsaki, G., 2006, pg 122).
However, these collective patterns are transient, they fluctuate around different brain areas, organizing temporal information where needed on specific time-scales depending on how large of a neuronal pattern is needed. "Transient order emerges from halfway between order and disorder from the territory of complexity" (ibid., pg 135).
It turns out that the power ratio of the pink noise also happens to fit the data for other time-related brain tasks: forgetting, habituation, music and speech. The brain is not competing with its own noise, it is in essence harnessing the noise as multiple dynamic timing devices synchronizing particular groups of neurons for specific tasks at specific clock rates. Indeed because of this very action, and the fact that neurons are strongly interconnected (some pyramidal cells can have thousands of dendrite connections sites (Buzsaki, G., 2006, pg. 32)), even small local perturbations can become amplified and spread throughout the network.
This amplification is of great importance. Consider a neuron that is almost ready to fire, but does not quite have enough current to reach it's action potential. A noise input could cause it to fire when it otherwise would not have. Because the noise is stochastic, the neuron's firing is not deterministic. It may or may not fire depending on the noise in the system around it. Small weak local signals can become noticeable when the noise bumps it up. Additionally small periodic signals can act as attractors to the noise oscillation and can in effect draw attention to themselves by pulling the oscillation frequency toward their own.
Given these mechanisms it is evident that neuronal firing is probabilistic. Even sensory neurons such as the ganglion cells in the retina have been shown to have unpredictable responses (Burns, B.D, 1968, pg 28). This behavior is of interest because it allows for a break with deterministic, simple input-output machine operation and allows a greater uncertainty to exist.
Another source of uncertainty in the brain could be brownian motion. Brownian motion is the basis for brownian noise. Brownian noise is also called random walk noise and has a power density ratio of 1/f 2 (Buzsaki, G., 2006, pg. 121). It gets its name from brownian motion. Brownian motion was originally discovered by Robert Brown, a biologist, who noticed that particles of pollen on the surface of water will move around erratically (Nelson, E., 1967, pg. 11). The concept was later further worked on by Einstein who in part used it to prove the existence of atoms. The basic idea is that a larger particle surrounded by a myriad of smaller particles suspended in a liquid or gas that all have their own movement will be pushed around by the motion of the smaller particles in a random fashion. Brownian motion over longer periods/distances is random, but can be predicted at short intervals by the average velocity and density of the molecules in the suspension (Buzsaki, G., 2006, pg. 121). It has been shown that brownian motion applies to all biological systems, "as a result of thermal agitation processes, molecules are constantly on the move, colliding with each other and bouncing back and forth" (Marguet, D., Lenne, PF., Rigneault, H., He, HT., 2006, pg. 288). On a macroscopic level however brownian motion is a diffusion process.
Diffusion processes have the following main features: (1) the diffusion rates are temperature-depen- dent, (2) as collisions with other molecules slow down diffusion processes, the higher the molecular density of a medium is, the lower the diffusion rate will be and most importantly, (3) as the random forces generated by collisions have no preferred direction, diffusion will cause a tendency towards homogeneity. (ibid., pg. 288)
Marguet et al suggest that any variability in activation of the postsynaptic neuron would be due purely to "stochastic variations in basic presynaptic elements, such as the vesicle volume, the vesicle docking position, and the vesicle neurotransmitter concentration" (ibid., pg. 298) rather than any variability due to brownian motion. So although brownian motion is used as a diffusion process and is certainly harnessed by the brain to effect homogenous dispersal of neurotransmitters in the synaptic cleft, it is not responsible directly for any variability in actual neuronal firing.
There are many theories involving consciousness and quantum theory. The problems with these theories is that the brain is too hot to be susceptible to any currently known quantum effects. There is too much classical noise and complexity for a single quanta to have any effect at all. A single cell in the retina may react to a single photon (which would be a quantum event) however our brains need at least seven neurons to react to actually perceive it (Penrose, R, 1989, pg. 516). Additionally, most neurons in the brain require many neurotransmitters to trigger many sodium or chloride channels to open which in turn could trigger the neuron to fire. This would require too many quanta to be useful. However, theories abound of either undiscovered cells that respond to single quanta or computational complexity that can only be solved by quantum computation. Additionally there are dualist theories that a mental energy influences the physical brain through quantum effects. These theories attempt to escape from determinism and provide a explanation why free will is non-determined. Christoff Koch (2006) provides an eloquent rebuttal of quantum theories, for now at least:
The content of consciousness is rich and highly differentiated. It is associated with the firing activity of a very large number of neurons spread all over the cortex and associated satellites, such as the thalamus. Thus, any one conscious percept or thought must be expressed in a wide- flung coalition of neurons firing together. Even if quantum gates exist within the confines of neurons, it remains totally nebulous how information of relevance to the organism would get to these quantum gates. Moreover, how would it be kept coherent across the milli- and centimeters separating individual neurons when synaptic and spiking processes, the primary means of neuronal communication on the perceptual timescale, destroy quantum information?
It is far more likely that the material basis of consciousness can be understood within a purely neurobiological framework, without invoking any quantum-mechanical deus ex machina. (Koch, C., 2006).
How do these various theories relate to consciousness? Randomness can be, at least partially, an escape from determinism. If every neuron firing were physically determined then there is no way that we as as 'free agent' could have chosen differently from how we did choose. This breaks a mandate of 'free will': we are free to have chosen differently from how we did choose. However, going too far toward randomness would break the other mandate of 'free will': our actions belong to us and reflect who we are (and that our actions are not simply random). A middle ground would surprisingly satisfy both of these criteria and allow a free will that is both based on our past experiences but is not tied down to them deterministically. If the system is probabilistic, then at any point we can say both, "I could have done differently," and "I chose that way based on my past experiences, based on who I am." At least semantically this fulfills the requirements of free will. Additionally, it is hard to imagine what third rule would invalidate this solution and would at the same time define the concept of free will in such a way as to keep the common intuition of what it is. Wegner in "The Illusion of Conscious Will" poses a thought experiment of inventing a Free Willer — an organ that makes free will choices. Such an instrument cannot ignore past experiences as that would be meaningless, and it cannot be purely random as that is equally meaningless. How do the various sources and types of randomness affect the free will problem?
AI randomness is an example of how randomness is useful purely computationally. AI algorithms attempt, at least in part, to make sense of a complex uncertain world and to make internal models of it and for this they need randomness. This does not imply that the human brain requires randomness in the same way however.
The probabilistic nature of neuronal firing and the noise of oscillation appears very promising however. Not only is a neuron not guaranteed to fire when presented with some stimuli, but it may also fire randomly when presented with stimuli that should be too weak. This creates an instability in the system allowing alternative solutions and unpredictable effects. Rodolfo Llinas (2003) goes even further to claim that conscious experience is created by the temporal organization provided by oscillatory synchronization.
Quantum effects could provide a very interesting source of uncertainty in the brain, but unfortunately there is no current reason to think that that it does.
It appears from this summary of some of the primary randomness theories that indeed there are some sources of randomness in the brain. However, not all of these sources are useful for a discussion of consciousness. For instance, no solid proof exists for quantum effects in the brain. Brownian motion in the synapse is useful for diffusion but not specifically for volition or free will. However oscillation and pink noise provide an interesting systemic effect that should not be overlooked. If this noise is truly stochastic and unpredictable enough it provides a middle ground between the two opposites of randomness and determinism and allow us to feel that our decisions are our own.
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