Chaos, Meaning, and Rabbits: Remembering Walter J. Freeman III

The nostrils of a rabbit may seem like an unusual path to studying the nature of meaning and chaos.  But Walter J. Freeman III was not a usual man.  His father, Walter J. Freeman II, helped to popularize the frontal lobotomy in America, a procedure unthinkable by today’s ethical sensibilities.  While continuing in the medical profession, Walter III transcended his father’s reputation and forged a unique identity for himself.  Ever the polymath, he studied topics as varied as physics, philosophy, electronics, mathematics, and medicine, each discipline leaving a distinct mark on his work.  The ideas Freeman synthesized from these diverse fields were often paradigm-shifting yet esoteric, as many of his papers are dense with idiosyncratic language and heavy equations.  Freeman died last April at the age 89, leaving the world an immense corpus of work including almost 500 papers, several books, and many big ideas.

wfreeman750

How do brains create meaning from stimuli?  This was the question that summarized Freeman’s career.  To address this question, Freeman trained rabbits to respond to odors and recorded spatial patterns of electrical activity from the olfactory bulb, a part of the brain that responds to odor stimuli. Because the spatially distributed pattern was important in perception of the odor, Freeman was among the first to realize that perception requires the “mass action” of thousands to millions of neurons.  Beginning his career during a time when most neuroscientists either studied isolated action potentials from single neurons or clinical EEGElectroencephalogram, a technique that places electrodes on ... More recordings reflecting global brain activity, Freeman bridged a gap between the two extremes by studying the brain at the intermediate or “mesoscopic” scale with small electrodePart of a circuit that conducts electricity and contacts a n... More arrays.  Even today, a disconnect still exists between cellular neurobiologists–many of whom view EEG recordings as noise — and neuroimagingTechniques for viewing the brain and its activity, especiall... More specialists — many of whom view single cell recordings as myopic.  Freeman emphasized the scale invariant, self-organized properties of the brain by describing cell assemblies called “K-sets” that vary in size from small networks of neurons to the entire neocortex.

NSRW_Brain_1
A rabbit brain (left) compared to that of a dog (right). The olfactory bulb, studied by Freeman, is circled in blue. Note that the rabbit cortex is smoother with less surface area compared to that of the dog.

To analyze the dynamic patterns observed in the olfactory bulb, Freeman founded the field of neurodynamics, merging physics and biology to create a new framework for studying the brain.  Neurodynamics falls under the broader umbrella of computational neuroscience, the discipline of understanding brain function through mathematical models. Although the tradition of computational neuroscience began with Hodgkin and Huxley’s model of the squid giant axonThe long process that carries an action potential from the c... More, Freeman instilled neuroscience with a new level of mathematical rigor.  To understand the context in which Freeman studied dynamic patterns of brain activity, we first need to take a detour into the world of chaos theory.

In an earlier Knowing Neurons piece, we explored neural oscillations.  If you’ve ever seen an oscilloscope, you know the appearance of a glowing, green beautiful sine wave, the kind that Bill Nye uses to demonstrate sound waves.  When neuroscientists talk about neural oscillations, they sometimes conjure up an image of such an idealized sine wave, straight out of high school trigonometry class.  This is because the mathematics often used to describe neural oscillations treats them as sine waves.  In this sense, oscillations are perfect, regular cycles.  Geometrically, a perfect cycle can be represented as a circle. Imagine, for instance, the regular cycle of a pendulum.  If we plot the position of the pendulum against its velocity, the resulting graph will show a circle.  This particular graph is called a phase portrait.  Start the pendulum from any combination of position and velocity — in other words, from any coordinate point around the phase portrait — and the system is inevitably drawn into the orbit of the circle.  For this reason, the orbit is known as an attractor.

Simple Pendulum

Now imagine that you mischievously hang a second pendulum from the bottom of the first one.  If you give the double pendulum a push, it wildly dances every which way, sometimes completely flipping over its pivot point.  Although the double pendulum’s motion still obeys simple equations, its behavior is wild and difficult to predict, a phenomenon called deterministic chaos.  Drawing a phase portrait, you see a chaotic mess of lines never tracing the same path twice, yet following a recognizable pattern.  This tangled pattern is a chaotic attractor.  Unlike the simple pendulum, the double pendulum shows different behavior when we start its swing from different points, a hallmark of deterministic chaos.  You can play around with an interactive chaotic pendulum simulation here!

ChaosPend_small

Phase portraits are not limited to pendulums. An economist might draw a phase portrait to visualize the simultaneous behavior of inflation rate and unemployment rate.  Similarly, a neuroscientist might draw a phase portrait to visualize the simultaneous activity of two brain recordings.  Doing just that, Walter Freeman discovered that in the absence of a familiar odor, the olfactory system of the rabbit followed a chaotic attractor, hardly what one would expect from an idealize image of neural oscillations!  However, following the presentation of a familiar odor, the phase portrait became more ordered, like the orbital attractor of the simple pendulum.  Freeman concluded that learned odors popped the system from one attractor to another, much like the Hopfield network that settles into stable patterns of activation from learned stimuli.  In fact, Freeman believed that these patterns were the actual meaning that brains construct from stimuli.  Our experience of the world lies in these patterns, with the raw, physical properties of the stimulus being discarded by the brain almost immediately.  The experience of seeing a familiar face is possible because we went to school with that person or have memories of holidays and dinners with her.  The actual photons of light reflected off her face hold no meaning without a brain to generate it.

But why is chaos important to the mind’s ability for perception and experience?  Unfortunately, the term chaos is something of a misnomer.  Chaos is not chaos in the traditional sense.  Rather, it is a level of complexity so great as to appear random without careful inspection.  Chaos in the brain, as described by Freeman, may lend the brain vital flexibility while allowing it to visit many states — thoughts, feelings, precepts–in quick succession.  In the case of the chaotic pendulum, the extra pivot point gives the pendulum greater flexibility, allowing it to visit many more states in the phase portrait.  In fact, Freeman discovered that the brain is constantly switching between attractors.  This switching manifests itself as an interruption in the EEG signal that Freeman referred to as a “null spike” or “phase reset.”  Freeman described stable periods between such interruptions as perceptual frames that make up our conscious experience, like the cinematographic frames in a movie.

KN_chaotic_attractor
The Lorenz Attractor (shown in yellow), one of the first chaotic attractors discovered, appears in many physical systems, including models of the atmosphere. Its phase portrait resembles the wings of a butterfly, perhaps leading to the popular term “the butterfly effect” used to describe small causes (e.g., a butterfly flapping its wings) with large effects (e.g., the path of a hurricane).

The ability of complex systems to rapidly switch between different states — known as self-organized criticality — may allow the brain to escape the snare of disease.  Following in Freeman’s footsteps, physicist and neuroscientist Mikhail Rabinovich has explored ways in which dynamical flexibility may be compromised in disorders such as OCD and bipolar disorder, in which the brain seems “stuck” in a particular cognitive or emotional state.  In fact, Freeman’s work has provided inspiration for generations of neuroscientists, including myself. In my own research, I have developed a measure that reflects the phase resets described by Freeman in EEG signals.  Because this measure is negatively correlated with age in young children, it may reflect changes in brain dynamics occurring with development, helping clinicians to detect disorders like autism.

Can chaos explain mental illness?  Can meaning be revealed through spatial patterns of voltageThe potential energy between two points in space felt by an ... More?  Can rabbits offer insight into human consciousness?  The greater implications of Freeman’s work are still unclear.  Yet we can all agree that Walter thought big, offering inspiration and innovation for the neuroscientists of yesterday, today, and tomorrow.

The nostrils of a rabbit may seem like an unusual path to studying the nature of meaning and chaos. But Walter J. Freeman III was not a usual man. His father, Walter J. Freeman II, helped to popularize the frontal lobotomy in America, a procedure unthinkable by today's ethical sensibilities. While continuing in the medical profession, Walter III transcended his father's reputation and forged a unique identity for himself. Ever the polymath, he studied topics as varied as physics, philosophy, electronics, mathematics, and medicine, each discipline leaving a distinct mark on his work. The ideas Freeman synthesized from these diverse fields were often paradigm-shifting yet esoteric, as many of his papers are dense with idiosyncratic language and heavy equations. Freeman died last April at the age 89, leaving the world an immense corpus of work including almost 500 papers, several books, and many big ideas. [Image: file:///-/blob/GNZAAAle6u3/ZTNYfuuFpL3m3UrrnRQ4uQ] *How do brains create meaning from stimuli? *This was the question that summarized Freeman's career. To address this question, Freeman trained rabbits to respond to odors and recorded spatial patterns of electrical activity from the **olfactory bulb**, a part of the brain that responds to odor stimuli. Because the spatially distributed pattern was important in perception of the odor, Freeman was among the first to realize that perception requires the "mass action" of thousands to millions of neurons. Beginning his career during a time when most neuroscientists either studied isolated action potentials from single neurons or clinical EEG recordings reflecting global brain activity, Freeman bridged a gap between the two extremes by studying the brain at the intermediate or "mesoscopic" scale with small electrode arrays. Even today, a disconnect still exists between cellular neurobiologists--many of whom view EEG recordings as noise--and neuroimaging specialists--many of whom view single cell recordings as myopic. Freeman emphasized the scale invariant, self-organized properties of the brain by describing cell assemblies called "K-sets" that vary in size from small networks of neurons to the entire neocortex. [Image: file:///-/blob/GNZAAAle6u3/sY7HZBHOXLC6wg6j2JpquA] To analyze the dynamic patterns observed in the olfactory bulb, Freeman founded the field of **neurodynamics**, merging physics and biology to create a new framework for studying the brain. Neurodynamics falls under the broader umbrella of **computational neuroscience**, the discipline of understanding brain function through mathematical models. Although the tradition of computational neuroscience began with Hodgkin and Huxley's model of the squid giant axon, Freeman instilled neuroscience with a new level of mathematical rigor. To understand the context in which Freeman studied dynamic patterns of brain activity, we first need to take a detour into the world of chaos theory. In an earlier Knowing Neurons piece, we explored neural oscillations. If you've ever seen an oscilloscope, you know the appearance of a glowing, green beautiful sine wave, the kind that Bill Nye uses to demonstrate sound waves. When neuroscientists talk about neural oscillations, they sometimes conjure up an image of such an idealized sine wave, straight out of high school trigonometry class. This is because the mathematics often used to describe neural oscillations treats them as sine waves. In this sense, oscillations are perfect, regular cycles. Geometrically, a perfect cycle can be represented as a circle. Imagine, for instance, the regular cycle of a pendulum. If we plot the position of the pendulum against its velocity, the resulting graph will show a circle. This particular graph is called a *phase portrait. *Start the pendulum from any combination of position and velocity--in other words, from any coordinate point around the phase portrait--and the system is inevitably drawn into the orbit of the circle. For this reason, the orbit is known as an *attractor*. [Image: file:///-/blob/GNZAAAle6u3/iXWvf92HbktIJVZH-lKVjQ] Now imagine that you mischievously hang a second pendulum from the bottom of the first one. If you give the double pendulum a push, it wildly dances every which way, sometimes completely flipping over its pivot point. Although the double pendulum's motion still obeys simple equations, its behavior is wild and difficult to predict, a phenomenon called *deterministic chaos*. Drawing a phase portrait, you see a chaotic mess of lines never tracing the same path twice, yet following a recognizable pattern. This tangled pattern is a *chaotic attractor*. Unlike the simple pendulum, the double pendulum shows different behavior when we start its swing from different points, a hallmark of deterministic chaos. You can play around with an interactive chaotic pendulum simulation here! [Image: file:///-/blob/GNZAAAle6u3/MXSNJYJ5N6v1D6aIBx7IeQ] Phase portraits are not limited to pendulums. An economist might draw a phase portrait to visualize the simultaneous behavior of inflation rate and unemployment rate. Similarly, a neuroscientist might draw a phase portrait to visualize the simultaneous activity of two brain recordings. Doing just that, Walter Freeman discovered that in the absence of a familiar odor, the olfactory system of the rabbit followed a chaotic attractor, hardly what one would expect from an idealize image of neural oscillations! However, following the presentation of a familiar odor, the phase portrait became more ordered, like the orbital attractor of the simple pendulum. Freeman concluded that learned odors popped the system from one attractor to another, much like the Hopfield network that settles into stable patterns of activation from learned stimuli. In fact, Freeman believed that these patterns were the actual *meaning* that brains construct from stimuli. Our experience of the world lies in these patterns, with the raw, physical properties of the stimulus being discarded by the brain almost immediately. The experience of seeing a familiar face is possible because we went to school with that person or have memories of holidays and dinners with her. The actual photons of light reflected off her face hold no meaning without a brain to generate it. But why is chaos important to the mind's ability for perception and experience? Unfortunately, the term chaos is something of a misnomer. Chaos is *not* chaos in the traditional sense. Rather, it is a level of complexity so great as to appear random without careful inspection. Chaos in the brain, as described by Freeman, may lend the brain vital flexibility while allowing it to visit many states--thoughts, feelings, precepts--in quick succession. In the case of the chaotic pendulum, the extra pivot point gives the pendulum greater flexibility, allowing it to visit many more states in the phase portrait. In fact, Freeman discovered that the brain is *constantly *switching between attractors. This switching manifests itself as an interruption in the EEG signal that Freeman referred to as a "null spike" or "phase reset." Freeman described stable periods between such interruptions as perceptual frames that make up our conscious experience, like the cinematographic frames in a movie. [Image: file:///-/blob/GNZAAAle6u3/UXRTbHQ5btpTtn1r0pUnfg] The ability of complex systems to rapidly switch between different states--known as self-organized criticality--may allow the brain to escape the snare of disease. Following in Freeman's footsteps, physicist and neuroscientist Mikhail Rabinovich has explored ways in which dynamical flexibility may be compromised in disorders such as OCD and bipolar disorder, in which the brain seems "stuck" in a particular cognitive or emotional state. In fact, Freeman's work has provided inspiration for generations of neuroscientists, including myself. In my own research, I have developed a measure that reflects the phase resets described by Freeman in EEG signals. Because this measure is negatively correlated with age in young children, it may reflect changes in brain dynamics occurring with development, helping clinicians to detect disorders like autism. Can chaos explain mental illness? Can meaning be revealed through spatial patterns of voltage? Can rabbits offer insight into human consciousness? The greater implications of Freeman’s work are still unclear. Yet we can all agree that Walter thought big, offering inspiration and innovation for the neuroscientists of yesterday, today, and tomorrow. [Image: file:///-/blob/GNZAAAle6u3/5KUElFYNNlVXlM177LPo5A]References Solé, Ricard, and Brian Goodwin. *Signs Of Life How Complexity Pervades Biology: How Complexity Pervades Biology*. Basic books, 2008. Freeman, Walter. *Neurodynamics: an exploration in mesoscopic brain dynamics*. Springer Science & Business Media, 2012. Bystritsky, A., et al. "Computational non-linear dynamical psychiatry: a new methodological paradigm for diagnosis and course of illness." *Journal of psychiatric research* 46.4 (2012): 428-435. Frohlich, Joel, Andrei Irimia, and Shafali S. Jeste. "Trajectory of frequency stability in typical development." *Brain imaging and behavior* 9.1 (2015): 5-18.

~

References:

Walter J. Freeman photo by Bruce Cook/UC Berkeley.

Other images by Joel Frohlich and Jooyeun Lee.

Solé, Ricard, and Brian Goodwin. Signs Of Life How Complexity Pervades Biology: How Complexity Pervades Biology. Basic books, 2008.

Freeman, Walter. Neurodynamics: an exploration in mesoscopic brain dynamics. Springer Science & Business Media, 2012.

Bystritsky, A., et al. “Computational non-linear dynamical psychiatry: a new methodological paradigm for diagnosis and course of illness.” Journal of psychiatric research 46.4 (2012): 428-435.

Frohlich, Joel, Andrei Irimia, and Shafali S. Jeste. “Trajectory of frequency stability in typical development.” Brain imaging and behavior 9.1 (2015): 5-18.

Joel Frohlich

Joel Frohlich graduated from the College of William and Mary in 2012 with a BS in neuroscience. He is currently working towards his PhD in the lab of Shafali Jeste at UCLA, examining EEG biomarkers of neurodevelopmental disorders. His recent research has focused specifically on autism and duplication 15q11.2-13.1 (Dup15q) syndrome. He is also a student intern at F. Hoffmann-La Roche in Basel, Switzerland and an expert blogger for Psychology Today. When he is not engaged in neuroscience, Joel's other hobbies include exploring national parks and reading about other fields of science such as astronomy and space exploration.

Joel Frohlich

Joel Frohlich graduated from the College of William and Mary in 2012 with a BS in neuroscience. He is currently working towards his PhD in the lab of Shafali Jeste at UCLA, examining EEG biomarkers of neurodevelopmental disorders. His recent research has focused specifically on autism and duplication 15q11.2-13.1 (Dup15q) syndrome. He is also a student intern at F. Hoffmann-La Roche in Basel, Switzerland and an expert blogger for Psychology Today. When he is not engaged in neuroscience, Joel's other hobbies include exploring national parks and reading about other fields of science such as astronomy and space exploration.

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