Mar 20 2009

The Brain and Chaos

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Comments: 17

The brain is not a computer, as anyone reasonably familiar with both should know. There are many similarities – both store and process information. But the fundamental architecture and function of the silicon on your desktop and the meat inside your skull are very different. That is why computers which are merely scaled up in power and speed will not spontaneously become conscious.The computational paradigm offers some insights into how the brain works, but it is not enough. Neuroscientists are searching for deeper understanding of brain function, particularly how it relates to consciousness. For example, it is known that the brain is organized as a massively parallel processor. There is also the neural network model of brain organization which tries to understand the brain as a collection of overlapping patterns of connectedness (networks).

At the same time there is a modular model of the brain which tries to understand brain function as a collection of anatomically identifiable modules that each have a specific function and interact interact to create the net effect of both consciousness and subconscious processing. I think that the network model and modular model are not mutually exlusive but are each part of the picture.

Now a newly published paper in PLOS Computational Biology argues that the brain operates at a critical point between organization and chaos – a state previously described as self-organized criticality. This is more of a description of the dynamic function of the brain, rather than its organization, and again is complementary to the modular and network models.

Self-Organized Criticality

The concept of self-organized criticality (SOC) emerged out of physics, mathematics, and efforts to understand complexity in nature. SOC explains how complexity can spontaneously emerge from simple interactions, such as individual cells interacting with each other. Such complexity would have various features. These include the property of being scale invariant – meaning that the overall structure of the complexity does not change significantly at different scales.

If that sounds familiar it’s because that is the defining feature of fractals described by Benoît Mandelbrot. As you scale up and down through a fractal pattern the amount of complexity remains the same.

Another feature of SOC is that it occurs at the critical point between ordered and random behavior, such as might exist between different phases of matter.

And a very important feature was described in 1987 by Bak, Tang and Wiesenfeld – that complexity in an SOC system emerges in a robust manner, which means it is not sensitively dependent on conditions. Therefore, the system can maintain its complexity even through great changes in the parameters of the system – the system does not have to be “finely tuned” in order for complexity to emerge.

What all this means is that a dynamic system, even one made of relatively simple parts with individual interactions that are also simple, can spontaneously generate complexity in a robust way – and exactly the kind of complexity we see in nature.

SOC and the Brain

Manfred Kitzbichler and his coauthors decided to look at brain function to see if it also has the features of self-organized criticality. They thought that SOC would be a good model for brain function because it optimizes information transfer, memory capacity, and sensitivity to external stimuli.

They looked specifically to see if brain complexity exhibits the feature of scale invariant complexity – if patterns in the brain are similar across scales of space and time. They examined a phenomenon known as phase coupling – essentially different parts of the brain firing in synchrony, presumably because they are part of a functional network – and measured how this coupling changed over time.

What they found is that this feature of brain activity does indeed have the signature features of self-organizing criticality.

Of course, this is an extremely complex topic and no one study such as this will be the final word. But they do appear to have provided the first direct evidence of SOC in the overall dynamic function of the brain.

If further investigations support this conclusion then this new way of looking at brain function is likely to deepen our understanding of what is perhaps the most complex system studied by science. This might also help us one day design computers that are more like human brains. Perhaps what this means is that such computers will have to be “grown” not built – they will also have to have complexity emerging out of self-organization, functioning at the edge of chaos.

17 responses so far

17 Responses to “The Brain and Chaos”

  1. Benjamin Lobatoon 20 Mar 2009 at 4:03 pm

    My brain does not understand this post.

    I don’t understand what SOC is, how it relates to brain function, or how the researchers were able to find evidence for SOC in the brain. Any good books on the subjects you could recommend?

  2. tmac57on 20 Mar 2009 at 5:02 pm

    Were the researchers focusing their study on the human brain or brains in general? It would interesting to know if their findings hold true for the brain structure of a fruit fly for example.

  3. MarkMarijnissenon 20 Mar 2009 at 5:28 pm

    Interresting concept. In Good Old-Fashioned AI, and also in early robotics, you see that researchers tried to determine, plan and organize everything beforehand. Everything was rational, and sought out. This only worked to a certain level: you can’t figure out everything, and, with robots like Shakey: they became very slow because the had to plan and calculate everything.

    Then Rodney Brooks introduced the reactive paradigm in robotics. It looked at biology, and saw that when layering relatively simple reflexes on each other, more complex intelligent behavior emerges. And since reflexes are simple and computationally inexpensive, faster robots became possible – often insect like robots. From this, a notion of autopoiesis or self-organization evolved. Why were these robots acting intelligent? It could not be the reflexes, for they are simple and “stupid”. It was through interaction with its environment, it became smart.

    Through interaction with the environment, multiple simple reflexes can give rise to an emergent intelligence. This evolved later in embedded embodied cognition. Which essentially states intelligence arises from having a body and acting in an environment. If a robot is truly embodied, it can be considered autonomous – because it “sets its own law” in its environment. And to do this, the robot must be self-organizing.

    In a way, the paradigm shift in robotics from compute everything to reactive to a embodied approach with self-organizing properties also resembles the way researchers investigate the brain. First, everyone looks at a functional level and says: if we know all the functions, we know how the brain works. Then, with discoverys of paralell processing and (artificial) neural networks, people are saying: well, you can explain everything with functions, because things get rather mixed up if you have massive parallel processing.

    And now it seems that even parallel processing is not enough, you have also to consider the organisation.

    What constraint is next? Must we also look at the goals of the system of the brain? Are these also essential to the brain? Should it be biological – or be build up from down to simple molecules? (well, SOC essentially states not, if I understand this correctly)

    Also, like Benjamin, some further literature about SOC would be nice, Steve.

  4. artfulDon 20 Mar 2009 at 5:47 pm

    Evolution is an SOC system which directs mutations in ways we don’t yet fully understand. But part of that understanding requires this recognition – that evolution IS a self-organizing process that forms its own purposes.

  5. daedalus2uon 20 Mar 2009 at 9:27 pm

    This is very interesting. It isn’t the first demonstration of near critical behavior in the brain, it is the first with magnetic imaging. Not to take anything away from their work, it is quite interesting and shows near critical behavior at much wider frequency scales than has earlier work.

    There has been a lot of work in the anatomic nervous system in heart rate variability, gastric motility variability, essentially every neural system that has been looked at shows near critical behavior (when it is working well). When neural systems become pathologic they become more regular and less chaotic. Reduced heart rate variability is observed in virtually all disorders characterized by low NO.

    Near critical systems are a subject that is near and dear to me. I have worked in that area for more than 30 years. Mostly in the thermodynamics of near critical fluids for separation, and lately in near critical effects in neuronal networks.

    An important part of my low NO hypothesis of autism is that the brain self-regulates in the near percolation threshold. In discussing that with Gene Stanley (of BU) (one of the experts on critical phenomena), he said that all natural neural networks self-regulate in the near percolation threshold.

    I don’t like the use of the terms “ordered” and “chaotic” to describe the near critical state. They can be confusing unless one has a good understanding of what the terms mean in the sense that they are being used. In the cited paper the term chaotic was used both in the sense of “disordered” and also in the sense of mathematical chaos, a system where different discrete states (often called strange attractors) are linked via differential paths. Using the terms order/disorder is better because it reduces the possibility of confusion with chaotic systems. It is optimal for a neural network to operate at the order/disorder transition because in the chaotic system that results the cost to transition from one state to another is minimized.

    The percolation threshold is a true critical point, the sensitivity of the properties of the neural network to change increase exponentially as the critical point is approached (from both directions). The critical percolation threshold is where the network first becomes completely connected. In a mathematical sense, as you increase from no connections between nodes in a network to all nodes connected, the percolation threshold is where the first infinite cluster forms.

    In a magnetic critical system the two states are magnetized (the magnetic fields of the individual magnetic elements aligned such that there is a macroscopic external magnetization) and unmagnetized where the magnetic elements are randomly oriented such that there is no external macroscopic magnetization. In a near critical fluid the two states are liquid (with short range order and surface tension) and a gas, with no short range order and no surface tension. The derivatives actually diverge, that is they become infinite. In thermodynamic critical systems the compressibility diverges, in magnetic critical systems the susceptibility diverges.

    My conceptualization is that NO is the neurotransmitter that mediates the functional connectivity. That is, it is NO that regulates the connectivity of the neural network and that the “proper” levels of NO are necessary to keep the brain in the near critical percolation threshold. The fMRI BOLD signal is due to the decreased magnetic susceptibility of a brain volume due to a decreased level of deoxyhemoglobin (paramagnetic) and an increased level of oxyhemoglobin (diamagnetic). This is caused by vasodilation which increases local blood flow. This vasodilation is caused by NO activating soluble guanylyl cyclase and producing cGMP which relaxes the smooth muscle in the vessels causing them to dilate. In a very real sense, what the fMRI BOLD technique is measuring is where the NO levels are high enough to cause vasodilation.

    When the brain self-regulates in the near critical percolation threshold, it does so by modulating the functional connectivity around that critical percolation threshold. When the neurogenic NO signal is low, the vessels are undilated and the functional connectivity is low, presumably below the critical percolation level. When neurogenic NO adds to the basal NO level, the NO level gets high enough that the vessels become dilated and the fMRI BOLD signal is observed. The increased oxyhemoglobin then takes up that NO and sweeps it away (oxyhemoglobin is the sink for NO in the body).

    The basal NO level is a very delicate balance between NO production (by multiple sources) and NO destruction (mostly by superoxide, hemoglobin and take up by lipid). If the superoxide level gets too high, the NO level gets too low, and the neurogenic NO production isn’t enough to get that region up to the critical percolation threshold. This is what neuroinflammation does. In autism this is what is called a melt-down. In neurosyphilis this inflammation is what causes the reduced cognitive function. To the extent that cognition difficulties are due to the inability to generate sufficient NO to reach the critical percolation threshold, those symptoms are reversible with either more NO, or with less superoxide. In Alzheimer’s disease, perispinal injection of Etanercept (a TNF-alpha blocker) has greatly reduced the symptoms of Alzheimer’s in minutes. My hypothesis is that this is due to restoring a higher basal NO level by reducing superoxide produced through the TNF-alpha signaling cascade. Similarly in autism, acute fever increases the basal NO level due to NO from iNOS. I have an extensive blog about the physiology behind that.

    People with autism exhibit increased neuronal functionality during fever because increasing their NO level brings them closer to the critical percolation threshold. People who are NT exhibit decreased neuronal functionality during a fever because increasing their NO level moves them away from the critical percolation threshold.

    Low NO can also show up as white matter hyperintensities. NO also regulates the ATP level, also through sGC, and a major ATP consuming pathway in the brain is axonal transport. When axonal transport is blocked (by ATP reduction as in ischemia), there is an acute reduction in apparent water diffusion as observed by MRI. What MRI observes is not necessarily “diffusion”, but rather water movement. Cytoplasm is entrained by cargo being moved in axons. When that stops there is less water “diffusion” as observed by MRI.

  6. HHCon 21 Mar 2009 at 12:09 am

    At first reading of the British psychiatric article, it appears they are measuring brains at rest or stimulaion. Is the dynamic flux measured in the fMRI an artifact of cell dehydration?

  7. HHCon 21 Mar 2009 at 12:18 am

    Also, the authors are calculating the slow speeds of electrical impulses which are narrow or broadband. Where is the chaos in a healthy study subject?

  8. titmouseon 21 Mar 2009 at 10:06 am

    I wonder if I understand the concept of self-organized criticality.

    Analogy: Your C hard drive is nearly full. You get another drive D to back stuff up. But some files on C are locked by the operating system. So you boot up on a third drive E and now can muck about with C as you please.

    When representational systems have sufficient redundancy to allow a degree of self-representation, self-monitoring becomes possible. Some redundant, proto-intelligent systems may spontaneously develop servo-mechanisms for self-correction. Some of these servo-mechanisms may decay or otherwise be transient. Some may serve their own self-correction in such a way as to insure their own survival against a background of procedures competing for processing resources. Once that happens, the system may become self-organizing.

  9. DevilsAdvocateon 21 Mar 2009 at 12:13 pm

    “…complexity emerging out of self-organization, functioning at the edge of chaos.”

    Also an apt description of American politics and of my home life.

  10. daedalus2uon 21 Mar 2009 at 2:17 pm

    titmouse, I am not sure I understand your analogy well enough to comment on it.

    The classic example of self-organized criticality is a sand pile. One way to conceptualize that is a pile of sand, with single grains slowly added one by one in a gravitational field. The sand reaches a certain “angle of repose” and then an avalanche occurs. The dynamic angle of repose is less than the static angle of repose, so that once the sand starts flowing, it overshoots and continues to flow beyond the static angle of repose.

    The size and frequency of the avalanches becomes correlated as 1/f, that is the size goes inversely with the frequency, there are half as many avalanches that are twice as big.

    The size of the avalanche does not depend on the stimulus because the stimulus is always a single grain of sand. That single grain can trigger an avalanche of 1, 100, or 10^6 grains of sand.

    In a neural network, the critical state is the state where a single firing neuron could trigger an avalanche of 10, 100, or 10^6 downstream neurons to fire. The “average” number of neurons that fire after a single neuron stimulus is one. That is the number of neurons that are in a state of firing stays about the same, if it was more than one it would increase until they all were firing, a seizure, if it was fewer, eventually the firing would extinguish and the brain activity would stop.

    The critical nature of the system means that the response (how many nerves fire) is not proportional to the stimulus (the single firing nerve that triggered it). The response is inherently non-linear.

    The term “chaos” has multiple meanings. The response of a critical system is “chaotic” in that differential inputs can produce macroscopic and different out puts. Those chaotic outputs may be completely deterministic. Randomness or disorder is not implied by the use of the term chaos in that sense.

  11. artfulDon 21 Mar 2009 at 3:35 pm

    Neural networks serve their own purposes. Sand piles do not.

  12. geoff394on 21 Mar 2009 at 7:01 pm

    Great post. Thanks Steve!

    I have a somewhat unrelated question I was hoping you could answer:

    This news piece on the ‘schizophrenia’ gene seems to have drummed up some old news on the subject.

    I thought the link between intelligence and schizophrenia was already established. (?)

    Are these new or are these replications of older studies with new information about the enzyme that can control symptoms.

    In any event, I think it’s very exciting science and hopefully will lead to new drugs.

    It’s my hope that you blog about schizophrenia more because it’s one disease that is so misunderstood and I have lost a couple of good friends to it.

    Keep up the great work. Thanks,


  13. HHCon 21 Mar 2009 at 11:39 pm

    geoff394, Interesting study using lithium and mice. However, lithium washes out of the system and can be hard to properly regulate. Schizophrenia, was not a category designed with mice in mind. The category was a military diagnostic term during wartime which categorized indiviudals who were a threat to themselves and other persons. Schizophrenia is descriptive of a disorganized mind, chaotic verbalizations, aberrant action including assault and battery, untimely hallucinations and delusions.

    In America, there have been televised documentaries which illustrated that Haight Ashbury styled hippies and their children manifested similar types of psychotic behaviors and hallucinatory experiences, specifically when the parents and children consumed LSD ritually.

    Genes studies are interesting in mice. But the researchers are creating a definition of schizophrenia in rodents. Far from the military classification for the enemy within.

  14. artfulDon 22 Mar 2009 at 5:11 pm

    Here’s a little something about SOC, chaos and purpose that comes from somewhat of an authority:

    From Dorion Sagan’s Amazon Blog at:

    The truth is that we, and other animals, and indeed even plants and microbes, exhibit purposeful behavior: finding food, avoiding predators, and looking for mates if not always tax planning or protecting the environment for future generations. What is strange, however, is that even inanimate systems exhibit a form of purposeful behavior: they come to equilibrium, using up energy as they settle into a quiescent state. Such behavior is famously described by the second law of thermodynamics and seems, at first glance, to be the antithesis of living behavior. Indeed, the second law of thermodynamics has been a favorite trumpet of creationists and intelligent design theorists who want to claim that, even if life has evolved, it must have originated by a divine act. But, as Benedict de Spinoza pointed out several centuries ago, a God who needs to intervene in His creation is less miraculous than one who does not. But if everything is heading toward the atomic chaos of entropy, how can complexity–let alone the high-fidelity complexity of life–accrue? In fact the second law states that
    energy will always spread out/disperse throughout a sealed-off system: the organization shown by life, an open system, does not violate the second law because systems become more complex by feeding off energy and order from the outside. Scientists have long known this. But what is new is that the relationship between evolution and entropy is not just compatible–it is intimate. Complex systems are not just compatible with the second law, they produce entropy more effectively than mere random arrangements of matter. Or, if we dispense with the term entropy, natural complex systems disperse energy (energy dispersal is the essence of the second law) more effectively than their unorganized brethren.

    This is related to purpose. For natural complex systems act with purpose to bring organized systems to equilibrium. Take a very simple example, a tornado. Feeding off an energetic difference in air pressure, a tornado forms. Spinning into existence, it would never be predicted on the basis of random particle movements. Tornados are like life in this respect, that they cycle matter and feed on energy. Fascinatingly, tornados also show a very mundane but obvious function or purpose: to get rid of the barometric pressure difference. When this difference, or gradient, is eliminated, the tornado itself vanishes. One may say that the natural purpose of the tornado is to reduce the previous organization and energetic potential represented by the pressure gradient. In the same way life reduces the electromagnetic gradient between the hot sun and cold space. This is not just theory, but measurable and measured by thermal sensing satellites and thermometer-like devices on low-flying planes. Indeed, the biggest gradient reducers are the most complex ecosystems–areas like the Amazon and the Borneo rain forest. It would seem that not only humans, but life itself, is not so special in its relationship to purpose as we like to think. This is important for several reasons. One is that science has long attempted to deny that life is deeply purposeful because of the association of purpose or teleology with religion. A further irony is that Aristotle’s teaching on the subject, which was explicitly not religious, was absorbed into Church learning so that Aristotle himself is often considered to be a religious thinker on this subject. In fact, Aristotle said, in The Physics, that it was folly to think that, just because life exhibited purpose, it required a “conscious deliberator.”

    Now consider this intriguing example. Imagine a heated but slightly leaky cabin on a snowy mountain top: wherever there is a leak in the cabin, the hot air will try to escape. No one would say that the hot air is conscious and yet it seems in many ways to exhibit purpose–a sort of will to get out of the hotter house. Hot air can even be seen to be “calculating” its escape route: insulators who add fine powder to see leaks have reported cases of streamers of colored (hotter) air moving through an electric outlet, up a wall, halfway across a ceiling, and then turning around to go through the same outlet whence they came. Again, the streamer of air does not change its mind, but it sure looks like it is doing something purposeful. The question arises, If simple inanimate systems can exhibit such mind-like behavior on the way to equilibrium, is our own purposeful behavior based on this process? Considering the building evidence that life is another naturally complex energy system that rectifies imbalances in the environment, the chances are increasing that our mindful, purposeful activity is part of a larger tendency for systems to temporarily grow and become more complex as they bring their environments to equilibrium. While this may not be the basis of a new religion, it is exciting in that it explains the natural purpose of life.

  15. TheBlackCaton 23 Mar 2009 at 11:59 pm

    Interesting article. I agree with your assesment of the nervous sytem, it certainly has discrete components with specific functions but is also highly parallelized (both within components and between components).

    I am not that familiar with SOC (err…yes I am, that acronym is really going to mess me up). However, the way you describe it makes it sounds like it is good for increasing the sensitivity of a system. If I recall correctly, generally speaking if you want a system to be as sensitive to inputs as possible you want it just at the edge of chaotic behavior. That is where the system is most sensitive to small changes in input. Is that at all related to what they are talking about in this article?

    One thing I do take issue with:

    SOC explains how complexity can spontaneously emerge from simple interactions, such as individual cells interacting with each other.

    If I had to pick a word to describe the interactions between neurons, “simple” would most definitely not be it. Even the seemingly simplest type of neuronal interaction, the calyx of Held, appears to considerably more complicated than we originally thought.

  16. NeuroLogica Blog » Brain on a Chipon 26 Mar 2009 at 11:33 am

    […] continues to develop computers which more closely simulate brain activity. As I recently discussed, the brain is not a computer, and computers are not brains. But since brains operate by physical […]

  17. Mjhavokon 30 Mar 2009 at 12:53 pm

    “complexity emerging out of self-organization, functioning at the edge of chaos.”

    That sounds cool. 😀

    Interesting article.

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