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These are excerpts and elaborations from my book "The Nature of Consciousness"
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Synchronized Oscillators There is a way to look at
processes of self-organization that is alternative to the view based on phase
transitions: it is based on synchronized oscillators. Self-organization of a
system implies that every part of that system is somewhat
"synchronized" in realizing some kind of order. Clocks and cycles are
pervasive in our universe, ranging from the biological clocks of the tiniest
organisms to the cycles of human history, from the cycles of electrons around
the nucleus to the cycles of planets around their stars. The order of these
cycles emerges from the synchronized behavior of "coupled
oscillators". The tendency for members of a population to work in unison,
to get synchronized, is ubiquitous in nature, from flocks of birds to groups of
neurons. It is a general property of our universe as much as gravity and
electricity. The US mathematician Norbert
Wiener(the inventor of Cybernetics)
believed that the activity of the brain is synchronized by a clock that is
implemented by a group of neurons. Each neuron is a terrible clock, and is
highly vulnerable. A group of neurons, though, each of them a bad clock, that
influences each other, tends to converge towards a synchronized state that
constitutes a much more reliable clock. Wienerproved mathematically that a
population of interacting neurons (that adjust their frequency based on what
their neighbors are doing) yields over time a population of synchronized
neurons. He speculated that "frequency pulling" might be a universal
method of self-organization for any complex system. The US mathematician Charles
Peskin("Mathematical Aspects of
Heart Physiology", 1975) reached a similar conclusion when studying the
"clock" of the heart: its rhythm is set not by a specific cell but by
the collective behavior of a group of cells. In both cases the advantage of
having a population (rather than just one member) provide the clock is that the
process becomes fault tolerant: if one fails, the whole corrects it; if one
dies, the others are enough for the process to continue. The US biologists David
Welshand Steve Reppert("Individual Neurons Dissociated
From Rat Suprachiasmatic Nucleus Express Independently Phased Circadian Firing
Rhythms", 1995) discovered that the suprachiasmatic nucleus of the
mammalian hypothalamus contains a circadian clock. This "clock" is
actually made of a large population of independent, single-cell oscillators
that collectively provide an accurate time keeping. This "master"
clock is probably responsible for all the rhythms in the body of a mammal. Populations of synchronized
oscillators seem to be pervasive in nature. The Indian physicist Satyendra Bosediscovered in 1924 that at low
temperatures all bosons behave like one. Such a Bose-Einsteincondensate was first achieved
in a gas in 1995. This means that all their quantum waves are synchronized (or,
better, "phase coherent"). The British physicist Brian
Josephson("Coupled
Superconductors", 1963) discovered an odd quantum phenomenon called
"Johnson junction", which is a consequence of quantum tunneling effect:
an electric current arises between two weakly coupled superconductors (whose
waves overlap slightly but don't interfere with each other too much) that are
separated by a very thin non-conducting barrier. Richard Feynmanrealized that this was a
special case of a universal phenomenon: the Josephsoneffect will occur for any pair
of weakly coupled phase-coherent systems. It was later realized that the
equations for the electrical oscillations in a Josephson junction are identical
to the equations of the motion of a pendulum. The US physicist Arthur
Winfreestudied the nonlinear equations
of a population of coupled oscillators and verified that, if each oscillator
can influence the others, the population as a whole has a tendency to get
synchronized. The population does not need any leader in order to achieve this:
it's the interaction among the various oscillators of the population that
creates the order. Winfreerealized that synchronization of a population of oscillators is a
phenomenon similar to the phase transition of a substance (for example, water),
in which all the molecules of that substance have to "cooperate" in
order for the substance to change state (for example, to turn into ice).
Organizing a population of oscillators is similar to organizing a population of
molecules, except that the former gets organized in time and the latter gets
organized in space. The Japanese physicist
Yoshiki Kuramotoproved that a system of such equations always has one obvious
solution (the state of incoherence, in which the population is completely
disorganized, a state which can actually be implemented in a very large number
of ways) and sometimes also has another solution, one of complete
synchronization. The latter occurs only when the initial states are not too
chaotic. There is a threshold value for their chaos below which that solution
of complete synchronization exists and above which it does not exist. The
initial states have to be at least partially synchronized. Again, this
principle evokes the threshold above or below which a phase transition occurs
in a substance. The US mathematician Steven
Strogatzthen proved that the state of incoherence is a state of unstable
equilibrium, which means that it will sooner or later collapse into one of the
other possible states, the states that represent synchronous behavior. In other
words, Strogatzproved that synchronicity (and therefore self-organization)
"will" emerge at some point in any system that exhibits partial
synchronicity above the threshold. Strogatzalso figured out that, under
certain circumstances, a population of coupled Josephsonjunctions will behave like
Kuramoto's biological oscillators: the junctions will suddenly synchronize. Any
system made of many independent oscillators that are weakly coupled, and that
are coupled with the same intensity to all the others, will exhibit spontaneous
synchrony. The US physicist John
Hopfield("Neurons, Dynamics and
Computation", 1994), the man who had rescued neural networks from
oblivion, made the connection with self-organized systems: a system of
synchronized oscillator is a self-organized system of the kind studied by
Kauffmanand Bak. Self-organization can be achieved in time or in space. Some
interacting molecules, cells and atoms achieve self-organization in space
through spontaneous reorganization, whereas some coupled oscillators achieve
self-organization in time through spontaneous synchrony. Synchronized oscillators
exhibit mathematical properties that might explain natural phenomena. For
example, chemical reactions can oscillate spontaneously. During such
oscillations there is a point (the "phase singularity") that does not
oscillate like the rest, in which the cycle amplitude collapses down to zero
and its phase cannot be determined anymore. It turns out that this phase singularity
generates a spiral wave that cannot be destroyed for as long as the phase
singularity exists. The spiral is extremely resilient, almost invulnerable.
These spiral waves emerge in chemical, biological and physical systems under
the right conditions. Phase transitions occur
everywhere in nature. It is not only water that turns to ice or to steam. There
are mental phenomena that exhibit the behavior of phase transitions. Since the
time of Piaget, we have been studying how
children go through different stages of understanding. Each stage emerges
suddenly after a period of years during which no training and education would
make it emerge. Stages still occur in the daily lives of adults. Sometimes it
takes us time to understand a concept, especially a scientific one. We read the
same sentences again, apparently incapable of grasping the meaning. Then
suddenly we "get it". We understand what those sentences meant. From
that point onwards, we will always understand it and it will be much easier to
understand similar concepts. Something has happened in our brain that suddenly
made it easier to do something that one second earlier was difficult. The brain
has undergone a phase transition. And the functioning of the brain depends on
synchronized oscillations of neurons. Back to the beginning of the chapter "Self-organization and the Science of Emergence" | Back to the index of all chapters |
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