In this book, I discovered one of the most inspiring (fore)words in the area of BRAIN SCIENCE that swiftly explain consciousness as if it never represented much of a problem. I am sure you will enjoy.

"Modeling Phase Transitions in the Brain"
Editors: D. Alistair Steyn-Ross · Moira Steyn-Ross

Early in the 19th century debates on Darwinian theory of evolution, William James
asked the question whether consciousness had biological survival value, such that
it might be subject to natural selection. The alternatives he considered were widely
held notions that consciousness was either an epiphenomenon or a celestial gift of
the capacity to conceive and know a Creator. He answered in fluid Victorian prose:
A priori analysis of both brain and conscious action shows us that if the latter were efficacious
it would, by its selective emphasis, make amends for the indeterminacy of the former;
whilst the study `a posteriori of the distribution of consciousness shows it to be exactly such
as we might expect in an organ added for the sake of steering a nervous system grown too
complex to regulate itself.1
In raising and answering the question this way, James penetrated to the essential
role of the brain in behavior. The brain simplifies. We and other animals cannot
fully know the world, Kant’s Ding an sich, as it is in its infinite complexity. Instead,
we make finite educated guesses about the world that Kant called “categories” and
that we now call “representations” or “world models”. We test these hypotheses by
taking action into the world and refining our guesses into formal theories. We learn
to know our world by accommodating and adapting to the sensory consequences of
our own and others’ actions through trial-and-error reinforcement learning [Freeman
(2001)].2 Thereby we achieve the simplicity that makes it possible for each of us,
immersed in a sea of uncertainty, to take effective action lit by flashes of insight.
Neurodynamicists model this self-organized, self-educating process by constructing
mathematical descriptions of the motor systems that thrust the body into
and through the world. They postulate that the sensory systems maintain attractor
landscapes that are constructed by Hebbian and other forms of synaptic modification
in cortical networks, which are the structural repository of experience. Each act of
observation is a test of the world, and the multiple attractors are predictions of possible
outcomes of the test, giving evidence for sustenance, companionship, danger,
nothing new, or something novel. The basins of attraction are generalization gradients
from prior receptions of stimuli. A stimulus places cortical dynamics in one of
the basins of attraction. Convergence to an attractor is an inductive generalization by
which the stimulus is categorized. The attractor manifests a spatiotemporal pattern
of neural activity to which the cortical trajectory converges [see Chaps 1, 2, 7 of this
book; also Freeman (2001)], and which the sensory cortex transmits to its targets by
well-known networks and pathways [Chap. 5 of this book].
Here is the crux of perception. The sensory input is a representation of the stimulus;
the cortical output is not. Based on the memories of the stimulus, the output
is the mobilized knowledge about the meaning of the stimulus [Freeman (2001)].
The experience is familiar to everyone; a whiff of perfume, a few notes of a tune,
or a glimpse of a face can trigger a cascade of recollection and emotion. Whereas
the pattern of the sensory-driven cortical activity is defined by the parameters of
the physical world, and by the neural operations of the sensory systems, the selforganized
pattern of cortical activity is defined by the modified synapses that store
the accumulated experience of the perceiver [Chap. 11]. Hence the critical event
in each act of perception is the reorganization of a stimulus-driven activity pattern
in cortex, which embodies the unique and unknowable impact from the world into
an endogenous pattern of self-organized activity. The neurons are the same; their
anatomical connections are the same; even their level of energy may be the same;
what differs is the spatiotemporal organization of their interactions.
The process of sudden reorganization of neural masses in the brain is the subject
matter of this book. It is the phase transition [Freeman (1999)]3 that is modeled
by use of differential equations [Chap. 8; Freeman and Vitiello (2006)]4 or random
graph theory [Chap. 5; neuropercolation, Kozma et al. (2005)].5 In its simplest form
it is the succinct, localized transition in the state of a sensory cortex from a receiving
state to a transmitting state. Cortex transforms a recept into a percept by constructing
knowledge from information. That is the first step in the transition by the brain from
an expectant state to a knowing state, the elusive “Aha!” experience. It is also the
transition from body into mind, from a pattern determined by the physics of matter
in the world to a self-organized pattern that exists only in the perceiver as a mental
state. Abrupt global reorganizations by phase transitions in larger brain systems
implement a wide variety of intellectual and intentional brain functions, ranging
from simple go/no-go choices, switching from rest to action and back [Chap. 4],
from prodrome to epilepsy [Chaps 2, 5], from sleep to wake or REM [Chap. 9], and,
far beyond our current reach, from Heidegger’s thrownness in childhood through
adolescence to mid-life crises, military, religious or political conversions, and all
other forms of social bonding.
Physicists and engineers are familiar with state changes, charting them as discontinuities
in trajectories of state variables through state space. Neurologists and
psychiatrists well understand states of mind and altered states of consciousness.
What is to be gained by calling brain states “phases”, which gives the title of this
book?
On its face the usage appears to be no more than a treacherous analogy. On the
one hand the classical thermodynamic definition holds for closed systems at equilibrium,
whereas brains are open, dissipative systems operating far from equilibrium.
The classical phases and their boundaries are unequivocally defined in terms
of temperature and pressure, whereas brains homeostatically regulate temperature,
pressure, volume, and mass. Conventional phase transitions involve latent heat, so
that the Ehrenfest classification by discontinuities of derivatives has been largely
discarded by physicists, but as yet no comparable transition energies have been seen
or postulated in cortical phase transitions, so discontinuities must suffice for neurodynamicists.
On the other hand, the several fields of condensed-matter physics have evolved
in diverse directions such as nonequilibrium thermodynamics, ferromagnetics, optics,
and computational fluid dynamics, but with commonality in important aspects
[Schroeder (1991)].6 Phase now is defined as a state of aggregation of particles
[Schwabl (2006)],7 whether they are atoms, molecules or neurons. In each complex
system there are multiple types of state. In the brain, families of attractor landscapes
in sensory cortical dynamics define the phase space [Freeman and Vitiello (2006)].
In each aggregate there are certain conditions that specify a critical point in the phase
space at which the system is particularly susceptible to transit from one phase to another
phase [Chap. 1]. The transition involves a change in the degree of order, as
when the neurons in sensory cortex transit from a disorganized state of expectancy
to an organized state of categorization, from noise to signal, from the symmetry of
uniformity of the background activity at rest to the asymmetry of spatiotemporal
structure in action. This is symmetry breaking, which is described using bifurcation
theory [Chaps 1, 10, 11].
Most importantly, the order emerges by spontaneous symmetry breaking within
and among populations of cortical neurons. Order in the form of gamma synchrony
[Chaps 7, 8, 11, 12] is not imposed by sensory receptors or pacemaker neurons. It
is constructed by broadly distributed synaptic interactions by which neurons constrain
or “enslave” themselves and each other in circular causality [Haken (1983)].8
Modeling symmetry breaking requires the introduction of an extra variable, an order
parameter [Chap. 3], which serves to evaluate the strength of interaction by which
the order is achieved [Sethna (2009)].9 The variable must be evaluated by measuring
the summed activity of the aggregate, minimally from practical experience on
the order of 10,000 neurons [Freeman, (2001)]. The mesoscopic order [Chap. 7]
is undefined in microscopic activity, in much the way that molecules do not have
pressure and temperature. Furthermore, it is undetectable in microelectrode recordings
of action potentials except by prolonged time-averaging in histograms, which
precludes measuring rapid changes in the degrees of freedom or patterns of order.
Herein lies the value of the dendritic potentials recorded from cortex extracellularly
and referentially in various forms of electroencephalogram (EEG) and local
field potentials [Chaps 1, 6, 8, 11], which are averages of potential fields from local
neighborhoods of neural populations. The EEG order parameter (derived from
field potential measurements) is not the order, nor is it the agency of the order; it is
an index of the distributed, self-organized and self-organizing interaction strength
among the neurons.
The perceptual phase transition is many-to-one by convergence to an attractor,
so it is irreversible, non-Abelian and non-commutative with no inverse. Unlike the
holographic transformation, which is information-preserving and non-categorizing,
the phase transition destroys information in categorizing as the prelude to decisionmaking.
To these properties are added the characteristic amplification and slowing
of fluctuations as criticality is approached [Chaps 1, 8]; the emergence of powerlaw
distributions of spectral energy and functional connectivity [Chaps 1, 3, 4, 8];
long correlation lengths reflecting emergence of truly immense domains [Freeman
(2003)]10 of coherent gamma oscillations; and reorganization/resynchronization of
phase and amplitude modulations of the transmission frequencies at rates in the theta
and alpha ranges [Freeman (2009)].11
Perhaps the most compelling reason to model the dynamics of perception as a
phase transition is the reduction in degrees of freedom owing to augmented interaction
[Freeman and Vitiello (2006)],12 which resembles the increase in density as
gas condenses to liquid. The condensation of neural activity is manifested in the
long-range spatiotemporal coherence of gamma oscillations (Chaps 1, 4, 12), and
the conic phase gradients resembling vortices that accompany the EEG amplitude
patterns that are correlated with behavior [Freeman (2001)]. The phase transition
begins at a singularity (Chaps 1, 8), which in cortex is demarcated spatially by the
apex of the cone. It is marked temporally by a downward spike in power in the pass
band of the transmission frequency [Freeman (2009)].
Given these properties in brain dynamics, the analogy is exceedingly attractive
and likely to persist and grow, because it provides matrices of educated guesses by
which further progress can be made in making sense of diverse data. The phase
transition establishes a link between energy and order. Brains are profligate in the
dissipation of metabolic energy, yet by their own feedback controls they keep constant
a vast reservoir of electrochemical energy in the ionic concentration gradients
that empower the neural activity of the brain. The major thermodynamic variables
are in steady state, owing to provision by arterial blood flow of free energy and the
disposal by the venous blood flow of waste heat, except one: there is a continual
decrease in entropy [Chap. 4], which is paid for by the throughput of energy. Initially
the patterns are solely functional, the creation of chaotic dynamics. Owing to
the plasticity of cortical connectivity [Chaps 2, 4, 7, 9, 11] the functional patterns
guide the structural connectivity into more or less permanent brain patterns, which
constitute the neural foundation for long-term memory.
Despite these properties and the powerful tools used to derive and describe them,
the hypothesis that phase transitions underlie perception and other brain functions
remains unproven. Asserting it is like signing a promissory note. There are immediate
intellectual gains from access to the capital of others’ ideas, but they bring
unsolved problems, salient among them defining the relation between metabolic
brain energy and neural activity, in which both excitation and inhibition dissipate
energy. The debt will not be paid until a detailed theory of nonlinear neurodynamics
is constructed that can stand on its own, in company with other major branches of
physics devoted to the study of condensed matter. Considering the saliency of its
subject matter, a successful theory of neurodynamics is likely to outshine all others.

University of California at Berkeley
Walter J. Freeman
August 2009


1 See p. 18 of James, W: Are we automata? Mind 4, 1–21 (1879)
2 Freeman,W.J.: How BrainsMake Up Their Minds. Columbia University Press, New York (2001)
3 Freeman, W.J.: Noise-induced first-order phase transitions in chaotic brain activity. Internat. J.
Bifur. Chaos 9(11), 2215–2218 (1999)
4 Freeman, W.J., Vitiello, G.: Nonlinear brain dynamics as macroscopic manifestation of underlying
many-body field dynamics. Physics of Life Reviews 3, 93–118 (2006),
doi:10.1016/j.plrev.2006.02.001,http://repositories.cdlib.org/postprints/1515
5 Kozma, R., Puljic, M., Balister, P., Bollab´as, B., Freeman, W.J.: Phase transitions in the neuropercolation
model of neural populations with mixed local and non-local interactions. Biol. Cybern.
92, 367–379 (2005),http://repositories.cdlib.org/postprints/999
6 Schroeder, M.R.: Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise.W.H. Freeman,
New York (1991)
7 Schwabl, F.: Statistical Mechanics, 2nd ed. Ch. 7. Phase transitions, scale invariance, renormalization
group theory, and percolation. 331–333, Springer (2006)
8 Haken, H.: Synergetics: An Introduction. Springer, Berlin (1983)
9 Sethna, J.P.: Statistical Mechanics. Entropy, Order Parameters, and Complexity. Clarendon Press,
Oxford (2009),
http://pages.physics.cornell.edu/sethna/StatMech/EntropyOrderParametersComplexity.pdf
10 Freeman, W.J., Burke, B.C., Holmes, M.D.: Aperiodic phase re-setting in scalp EEG of betagamma
oscillations by state transitions at alpha–theta rates. Hum. Brain Mapp. 19(4), 248–272
(2003),http://repositories.cdlib.org/postprints/3347
11 Freeman, W.J.: Deep analysis of perception through dynamic structures that emerge in cortical
activity from self-regulated noise. Cognit. Neurodynamics 3(1), 105–116 (2009),
http://www.springerlink.com/content/v375t5l4t065m48q/
12 Freeman, W.J., Vitiello, G. Dissipative neurodynamics in perception forms cortical patterns that
are stabilized by vortices. J. Physics Conf. Series 174, 012011 (2009),
 http://www.iop.org/EJ/toc/1742-6596/174/1,  href="http://repositories.cdlib.org/postprints/3379" target="blank">http://repositories.cdlib.org/postprints/3379