Mind is Motion
Whilst you are alive, your brain is continuously active. Every second of every day, your neurons are firing and signals are being passed along perhaps the most complex communication network in the universe. Your brain is continuously processing, even in the absence of any obvious stimulus (e.g. when you are asleep or in a coma). This continuous activity or ‘motion’ appears to be fundamental to all our conscious cognitive activities (e.g. perception, reasoning, motor control, speech etc). Some neuroscientists believe that this activity is driven by what is described in mathematical circles as ‘Chaos’, the properties of which endow the brain with some jaw-dropping capabilities. I gave a brief introduction to Chaos in Part 1 of this mini series. In this second article, we will dig a little deeper into how the properties of chaos have the potential to super-charge the information processing capabilities of the human brain.
Super-charged Neurons
Back in the 1990’s I became fascinated by the possibility that human cognition and intelligence is facilitated by the presence of chaos in the neural circuits of the mammalian brain. I embarked on a scientific quest to explore how chaos may arise in these neural circuits and understand the advantages that this brings the brain as it processes and stores sensory experiences and forms memories.
As a Computer Scientist my approach was to build computer models of networks of neurons that were endowed with Chaotic properties and observe how this affected their capacity to process information.
I created one such model which I called the Nonlinear Dynamic State (NDS) neuron. The NDS neuron model has a dynamic internal state that is modelled by three time-dependent variables: u, which represents the degree of electrical activation of the neuron, and x and y that represent other time dependent internal conditions of the neuron. The time-varying values of these three variables are driven by a chaotic attractor.
Whenever the activation (u) reaches a particular threshold value (‘0’), the neuron fires, sending an action potential to the other neurons to which it is connected. This firing behaviour is illustrated in Fig 1, which shows the animation of a short sample of the time series of the activation (lower part of the plot, below zero) and firing (upper part of the plot, above zero) of the neuron.
My Latest Book
“For anyone interested in where questions of robotics ultimately take us, I highly recommend this book.”
DR. SHARON DIRCKX
SPEAKER, FORMER NEUROSCIENTIST
AND AUTHOR OF ‘AM I JUST MY BRAIN?’
Available now on Amazon (Click here)
You will see that in this sample the neuron fires three times. Fig 2 shows the animation of the corresponding phase plot (see Part 1), with the neuron’s activation u plotted against internal state variable x.
One of the primary advantages that chaos offers the brain is the potential for a rich set of dynamics to support its information processing requirements. What I mean by ‘rich set of dynamics’ is that chaos makes available a wide range of dynamical features for the brain to draw upon as it represents and processes information. Let’s take a look at one such feature: the Unstable Periodic Orbit (UPO).
Unstable Periodic Orbits
One of the surprising features of many chaotic systems is the ease with which they can be controlled. Due to its sensitivity to initial conditions, small instantaneous changes (‘nudges’) to the state of a chaotic system can cause it to repeat a dynamic path within phase space. Remember that by definition chaos is a non-repeating pattern of activity. But small, repeated and well timed ‘nudges’ can push the trajectory of the dynamical system in phase space back to where it had previously been so that the systems repeats the trajectory it had just completed. These repeated trajectories are called Unstable Periodic Orbits; they are unstable because, without the appropriately timed nudges, the system would move away from the periodic orbit towards a different area of the attractor.
This control of chaos is one of the features of the NDS neuron model. Fig 3(c) shows the time series of an extended run of the model. During the first 1000 time steps of the run, the model is free to follow its internal chaotic dynamics. You will note that the activation (u) and the firing patterns of the neuron during this phase are irregular. Then between time steps 1000 and 2000, an external influence is applied to the model in the form of a repeated pattern of two ‘nudges’. It is important to note that in between these nudges, the model is free to follow its chaotic dynamics. Note that part way through this first external influence stage, the model falls into a repeated pattern or UPO in which it fires twice. Plot (a) in Fig 3 shows this UPO superimposed onto the NDS neuron attractor.
Following the removal of external influence 1, the neuron returns to its chaotic activity until a second external influence is introduced at time step 3000, this time subjecting the model to a repeated pattern of three nudges. Once again, this nudging leads the neuron to fall into another UPO, which is shown in Fig 3(b).
We ran experiments on the NDS neuron model and discovered that it could fall into over 6,000 different UPOs, each with its own unique spiking pattern of action potentials. In other words, the neuron could be in any one of these dynamic states, and it could communicate to other neighbouring neurons which dynamic state it was in though the associated unique spike train. This is like giving the neuron a vocabulary of upwards of 6,000 words with which it could ‘talk’ to other neurons.
Although, through experimental runs, we discovered over 6,000 UPOs, it is likely that the model has significantly more, as yet undiscovered UPOs. In fact, a feature of chaotic attractors in general is that they embed a theoretically infinite number of UPOs. These are the rich dynamics that I mentioned earlier. Imagine for a moment that the mammalian brain is chaotic, and imagine also that each UPO in the brain’s chaotic attractor corresponds to a thought (this is a gross over-simplification, but let’s run with the idea for now). This would mean that the brain has a limitless capacity in terms of the number of different thoughts it could potentially entertain, which is an awesome possibility!
2 responses to “Chaos in the Brain – Part 2”
Wow! Limitless number of different thoughts! The late John Fox was v. interested in cognitive aspects, we miss his input, like yours… We are careful with use of “AI” and sometimes add “transparent AI” or “machine executable documents (thoughts) – I hope our paths cross again soon, thanks Nigel
Many thanks Peter. Looking forward to seeing you again.