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I serendipitously came cross this article today about how our brains are self-organized criticality or systems living on the edge of chaos. There are many interesting ideas and gold nuggets in that article, and I’ll briefly quote from it.

In reality, your brain operates on the edge of chaos. Though much of the time it runs in an orderly and stable way, every now and again it suddenly and unpredictably lurches into a blizzard of noise.

Neuroscientists have long suspected as much. Only recently, however, have they come up with proof that brains work this way. Now they are trying to work out why. Some believe that near-chaotic states may be crucial to memory, and could explain why some people are smarter than others.

In technical terms, systems on the edge of chaos are said to be in a state of “self-organised criticality”. These systems are right on the boundary between stable, orderly behaviour – such as a swinging pendulum – and the unpredictable world of chaos, as exemplified by turbulence.

The quintessential example of self-organised criticality is a growing sand pile. As grains build up, the pile grows in a predictable way until, suddenly and without warning, it hits a critical point and collapses. These “sand avalanches” occur spontaneously and are almost impossible to predict, so the system is said to be both critical and self-organising. Earthquakes, avalanches and wildfires are also thought to behave like this, with periods of stability followed by catastrophic periods of instability that rearrange the system into a new, temporarily stable state.

Self-organised criticality has another defining feature: even though individual sand avalanches are impossible to predict, their overall distribution is regular. The avalanches are “scale invariant”, which means that avalanches of all possible sizes occur. They also follow a “power law” distribution, which means bigger avalanches happen less often than smaller avalanches, according to a strict mathematical ratio. Earthquakes offer the best real-world example. Quakes of magnitude 5.0 on the Richter scale happen 10 times as often as quakes of magnitude 6.0, and 100 times as often as quakes of magnitude 7.0.

These are purely physical systems, but the brain has much in common with them. Networks of brain cells alternate between periods of calm and periods of instability – “avalanches” of electrical activity that cascade through the neurons. Like real avalanches, exactly how these cascades occur and the resulting state of the brain are unpredictable.

Two of the power laws that are found in human brains relate to the phase shift and phase lock periods of EEG/fMRI or human brain systems etc. As per this PLOS comp biology paper:

Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal “avalanches” previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain’s physiological bandwidth.

Further, as per research by Thatcher et al, the EEG phase shift is larger in people with high IQ, while phase lock is smaller in the people with high IQ.

Phase shift duration (40–90 ms) was positively related to intelligence (P < .00001) and the phase lock duration (100–800 ms) was negatively related to intelligence (P < .00001). Phase reset in short interelectrode distances (6 cm) was more highly correlated to I.Q. (P < .0001) than in long distances (> 12 cm).

Further, in this paper , thatcher eta look at autistics and conclude that the people with autism show some deficits in phase shift and phase lock.

Results: In both short (6 cm) and long (21 – 24 cm) inter-electrode distances phase shift duration in ASD subjects was significantly shorter in all frequency bands but especially in the alpha-1 frequency band (8 – 10 Hz) (P < .0001). Phase lock duration was significantly longer in the alpha-2 frequencyband (10 – 12 Hz) in ASD subjects (P < .0001). An anatomical gradient was present with the occipitalparietal regions the most significant.
Conclusions: The findings in this study support the hypothesis that neural resource recruitment occurs in the lower frequency bands and especially the alpha-1 frequency band while neural resource allocation occurs in the alpha-2 frequency band. The results are consistent with a general GABA inhibitory neurotransmitter deficiency resulting in reduced number and/or strength of thalamo-cortical connections in autistic subjects 

It is interesting that in the original new scientist article , thatcher speculates that the pattern in schizophrenia may be reverse of what is seen in autism (exactly my thoughts, though the confounding of low IQ with autism may explain his autism results to an extent):

He found that the length of time the children’s brains spent in both the stable phase-locked states and the unstable phase-shifting states correlated with their IQ scores. For example, phase shifts typically last 55 milliseconds, but an additional 1 millisecond seemed to add as many as 20 points to the child’s IQ. A shorter time in the stable phase-locked state also corresponded with greater intelligence – with a difference of 1 millisecond adding 4.6 IQ points to a child’s score (NeuroImage, vol 42, p 1639). Thatcher says this is because a longer phase shift allows the brain to recruit many more neurons for the problem at hand. “It’s like casting a net and capturing as many neurons as possible at any one time,” he says. The result is a greater overall processing power that contributes to higher intelligence. Hovering on the edge of chaos provides brains with their amazing capacity to process information and rapidly adapt to our ever-changing environment, but what happens if we stray either side of the boundary? The most obvious assumption would be that all of us are a short step away from mental illness. Meyer-Lindenberg suggests that schizophrenia may be caused by parts of the brain straying away from the critical point. However, for now that is purely speculative. Thatcher, meanwhile, has found that certain regions in the brains of people with autism spend less time than average in the unstable, phase-shifting states. These abnormalities reduce the capacity to process information and, suggestively, are found only in the regions associated with social behaviour. “These regions have shifted from chaos to more stable activity,” he says. The work might also help us understand epilepsy better: in an epileptic fit, the brain has a tendency to suddenly fire synchronously, and deviation from the critical point could explain this. “They say it’s a fine line between genius and madness,” says Liley. “Maybe we’re finally beginning to understand the wisdom of this statement.”

Thus, it seems Autism and Psychosis are just two ways in which self-organized criticality can cease to do what it was designed to do- live on the edge , without falling on either side of order or chaos.

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