more conventional models of neuronal computation
By Jeff Prideaux
Virginia Commonwealth University
The Hologram Relationship
Other Aspects of the holonomic theory
The Uncertainty Principle
One of the problems facing neural science is how to explain evidence
that local lesions in the brain do not selectively impair one
or another memory trace. Note that in a hologram, restrictive
damage does not disrupt the stored information because it has
become distributed. The information has become blurred over the
entire extent of the holographic film, but in a precise fashion
that it can be deblurred by performing the inverse procedure.
This paper will discuss in detail the concept of a holograph and
the evidence Karl Pribram uses to support the idea that the brain
implements holonomic transformations that distribute episodic
information over regions of the brain (and later "refocuses"
them into a form in which we re-member). Particular emphasis will
be placed on the visual system since its the best characterized
in the neurosciences. Evidence will be examined that bears on
the validity of Pribram's theory and the more conventional ideas
that images are directly stored in the brain in the form of points
and edges (without any transformation that distributes the information
over large regions). Where possible, the same evidence (for the
visual system) will be used to evaluate both theories.
1. Holonomic theory where Fourier-like transformations store information of the sensory modalities in the spectral (or frequency) domain. The sensory stimulus is spread out (or distributed) over a region of the brain. A particular example (in the case of vision) would be that particular cortical cells respond to the spatial frequencies of the visual stimulus.
2. The more conventional theory that particular features of the
untransformed sensory stimulus is stored in separate places in
the brain. A particular example (in vision) would be that particular
visual cortical cells respond to edges or bar widths in the visual
It will be necessary in this report to first explain the concepts
of a hologram and Fourier transforms before the physiological
experiments can be understood. Bear in mind that the discursion
into these other fields serves a purpose for later in the report.
Karl Pribram's holonomic theory reviews evidence that the dendritic
processes function to take a "spectral" transformation
of the "episodes of perception". This transformed "spectral"
information is stored distributed over large numbers of neurons.
When the episode is remembered, an inverse transformation occurs
that is also a result of dendritic processes. It is the process
of transformation that gives us conscious awareness.
Chapter 2 will outline the basic concept of a hologram and start
to introduce Pribram's holonomic brain theory.
Chapter 3 will briefly describe the conventional accepted view
of the pathway of neural processing (with particular emphasis
on the visual system). The main computational event in this view
is the generation of the action potential.
Chapter 4 will review the evidence for the alternative holonomic
view. The holonomic theory is based on evidence that the main
computational event of neurons is the polarizations and hyper
polarizations at the dendritic membranes of neurons. The evidence
will be reviewed that supports the notion that these dendritic
processes effectively take something close to a Fourier transform.
What is holography?
The word "holography" is derived from Greek roots meaning
"complete writing". The idea is that every part of "the
writing" contains information about the whole. A hologram
(the material manifestation of a holograph) is a photographic
emulsion in which information about a scene is recorded in a very
special way. When the hologram is illuminated, you see a realistic,
three-dimensional representation of the scene. If you cut the
holographic photographic plate up into small pieces, the whole
image can still be extracted from any of them (although with some
loss of clarity). Pribram uses the term holonomy to refer to a
dynamic (or changing) hologram.
The Hologram Relationship
The basic idea of a hologram can be understood without even considering
the holograms found in novelty stores. The idea is simply that
each part contains some information of the whole. Or stated another
way, the information (or features) are not localized, but distributed.
To clarify this concept, consider the following thought experiments
(demonstrations). As will be demonstrated, light is in the holographic
domain before it gets transformed (focused) by a lens.
Demonstration #1. Remove the converging lens in a slide projector
that forms the image. Place a slide in the projector and project
the light onto a screen. No image will form. Technically, the
light incident on the screen is in a holographic form. Each point
on the screen is receiving information from every point from the
slide. If a converging lens is placed at a location between the
screen and the slide projector an image can be formed on the screen.
The lens can now be moved to new locations in a plane cutting
through the light path to the screen and in each case a complete
image is formed (Taylor, 1978).
Demonstration #2. The above principle can be demonstrated with using a camera. Consider taking pictures of an object (for example, a far-away mountain). You take a picture, then move over a few feet and take another one. You move over a few more feet and take another one. Upon getting the pictures developed, they all look about the same. This demonstrates the idea that the information necessary to form the image was present at each of the locations that you took the pictures. Additionally, if you look at an object very far away, then tilt your head to the side, you can still see the object. The light incident on your eye in both positions was sufficient to form the whole image.
Demonstration #3. Take a pair of binoculars. Just look through
one side focusing at a distant object. Now place your fingers
in front of the lens so that only light coming from in-between
your fingers enters the monocular. You will still see the whole
image. If you bring your fingers together so that the light enters
only through tiny slits, the whole image will still be present,
only dimmer (and there will be some loss of resolution) . If you
rotate your hand, exposing the light to different parts of the
lens, the whole image can still be formed. This is another representation
that the light incident at the surface of the lens at any point
is in a holographic form.
Demonstration #4. A pinhole camera represents a special case where
an image can be formed without using a lens (without taking a
transformation). Note that if the pinhole is moved over a bit,
the image still forms. This demonstrates the rudimentary idea
of the whole being included in a part (the part being the area
of the pinhole). All of the information necessary to produce the
image is contained in the area of the pinhole. A lens functions
to allow the light incident on a larger area to all be transformed
(focused) to form an image. This will improve both image resolution
and light gathering capability.
It is perhaps unfortunate that most physiology textbooks use a
figure something like the following (figure 1) to describe the
operation of the eye.
The above figure doesn't express the transform-taking aspect of
a lens. The above figure is really more indicative of a pinhole
camera. Figure 4 (shown later in the report) gives a better depiction
of what happens at the lens of the eye.
Mathematically (in one implementation), a Fourier transform converts
a function of time f(t) into a function of frequency F(jw) where
the j indicates that it is a complex function of frequency. In
other words, a Fourier transform can convert a signal from the
time domain to the frequency domain. A Fourier transform could
also be used to convert something from a spatial locational domain
(the coordinates in space) to a frequency domain (more about this
The idea (the mathematics) of the Fourier transform is independent
of what the data sets represent. It will be argued that if the
brain performs a Fourier transform for visual stimuli, then it
is possible that it also performs a Fourier transform for the
other senses also (hearing, taste, smell, touch).
The same principle can be shown with optics. Consider, for example,
that a large telescope lens (or mirror) can resolve two distinct
images (for example two stars that only have a small angle separating
them in respect to us). A smaller telescope lens (or mirror) will
not be able to resolve (separate) those two stars. Likewise, small
parts of a hologram, although they have information of the whole,
will suffer some resolution deficit.
As seen above in figure 2, the holographic plate records an interference
pattern between the diverged laser light and the scattered laser
light bouncing off the object. The pattern recorded on the holographic
plate is in the holographic domain. All parts of the holographic
plate contain information of the whole. Light bouncing off each
point on the object is distributed (spread out) to every location
on the holographic plate) . Alternatively, the pattern recorded
on the photograph is an image (non-holographic). The image features
are located at particular locations on the photographic plate.
Light scattered off the object (now in the holographic domain)
is transformed to the non-holographic (image) domain by the lens
of the camera (which does an effective inverse Fourier transform)
by focusing the image on the photographic film. For the photograph,
there is a one-to-one mapping between the two-dimensional projection
of points on the object to locations on the photographic plate.
Correspondingly, there is a one-to-all mapping for the holographic
In the case of the photograph (see figure 3), light is scattered off the photograph (which is now in the holographic domain) and becomes incident on the eye which does a transformation (focuses) which forms an image on the retina. For the holograph, laser light is shined through the holographic plate (picking up the holographic information from the plate) and becomes incident on the eye which does a transformation (focuses) which forms an image on the retina. The holographic nature of the light incident on the lens is shown in figure 4.
The discussion so far has just taken us to the image formed at
the retina. The interesting part of the holonomic brain theory
is what happens next. The focal point of the above discussion
is that a lens does an effective (inverse) Fourier transform on
the light incident to it. The Fourier transform (and inverse Fourier
transform) consists of convolution integrals which mathematically
smear or de-smear the information. For continuous functions, the
Fourier transform and inverse Fourier transform are as follows
(for transforms between the time and frequency domain):
The Fourier transform also has meaning between a spatial domain
(for instance the position in two dimensional space) and spatial
frequency. Mathematically, the two-dimensional spatial Fourier
and the inverse transform is
where x and y are spatial coordinates and a and b are horizontal
and vertical frequencies.
One realization of the Fourier transform is the principle of diffraction.
If you shine coherent light through one point there will just
appear a large white blob on a screen. If coherent light is shined
through two separated points, though, a diffraction pattern will
appear (see figure 5). The orientation of the (sine-wave) grating
is caused by the relative orientation of the two points.
Mathematically, the diffraction patterns seen are explained by
taking (two-dimensional) Fourier transform of the points. The
right-hand side of each figure pair is the Fourier transform of
the left-hand side (and visa versa).
If coherent light (or light from a point source) is shined through
two slits, a diffraction pattern can be demonstrated as seen in
figure 6. Note a large blob in the middle and smaller blobs tapering
off to either side. The separation and angular position of the
spectral blobs is dependent on the separation and orientation
of the slits.
Figure 7 shows the mathematical Fourier transform of three different
patterns (square-wave grating, checkerboard, and plaid) into their
respective spatial frequency domains. The spectrum of the square-wave
grating has odd numbered harmonics that taper off in amplitude
to each side. Note that the plaid shape is made up of the addition
of vertically and horizontally oriented square-wave gratings.
Similarly, the spectral representation of the plaid is the superposition
of the spectral representation of the vertical square-wave grating
and what the spectrum would be (not shown) for a horizontal square-wave
grating. Pay particular attention to the dominate four components
to the plaid spectrum (the heaviest four dots towards the center.
Now compare those dominate dots to the corresponding ones in the
spectrum of the checkerboard. Note that there is a 45° rotation.
This can be intuitively understood because you can perceive rows
of white and black squares running at the 45 degree orientation
for the case of the checkerboard. This fact will become very important
in the physiological experiment to be described later in the report.
Before proceeding, a couple of examples will be shown of the effect
of not using the entire spectral domain in performing the inverse
Fourier transform. This demonstrates the holographic idea of the
"whole" being stored in all the parts. It also shows
that fairly good images can be achieved without taking the full
theoretical transforms. This is important because neural processing
isn't infinite in extent. The brain (because of its finite nature)
would only be able to take a truncated Fourier transform.
When an inverse Fourier transform is taken of smaller and smaller
areas of the spectral domain. the "whole" is always
captured, but the resolution deteriorates. See figure 8.
The conventional theory is that the main computational event in neurons is the generation of the action potential. The firing of the action potential (for a single cell or a network of cells) indicates the triggering of a particular perception. In the extreme case (the "grandfather cell") the firing of a single cell can trigger a certain memory or perception. More typically, though, it would be the near simultaneous firing of a whole collection of cells in a network that triggers the perception. The perception would then be mediated by the action potential's propagation (through the axon) to other parts of the brain. It would be the integrative emergent response of "the other parts of the brain" (including parallel coupling to other sensory modalities) that yields the sensation of the perception.
For visual perception, there is the following information flow
(Kendel, Principles of Neural Science, page 438)
Retina: cells respond to small circular stimuli
Lateral geniculate nucleus: cells also respond to small circular stimuli
Primary visual cortex: transforms the concentric receptive field in at least three ways.
1. Visual field decomposed into short line segments of different orientation, through orientation columns. Early discrimination of form and movement.
2. Information about color is processed through "blobs" which lack orientation selectivity
3. Input from the two eyes is combined through the ocular dominance
columns (one of the steps necessary in depth perception.
Central connections of the visual system are remarkably specific.
Separate regions of the retina project to the lateral geniculate
nucleus in the thalamus in such a way that a complete visual field
for each eye is represented in the nucleus. Different cell types
in the retina project to different targets in the brain stem.
Each geniculate axon terminates in the visual cortex, primarily
in layer 4. The cells in each layer have their own patterns of
connections with other subcortical regions.
Cells in the visual cortex are arranged in into orientation-specific
columns, ocular dominance columns, and blobs. Some of these neurons
have horizontal connections. Information flows both between the
layers and horizontally through each layer. The columnar units
seem to function as elementary computational modules. Each group
of cells acts as a dedicated circuit to process an input and send
Hubel and Wiesel (1959, 1962) described and classified simple
and complex cortical cells. They concluded that both simple and
complex cells responded optimally to bars and edges of a certain
orientation. An alternative view was that each cortical cell might
be selective for a particular portion of the two-dimensional Fourier
spectrum (a certain frequency component at a particular orientation)
of the visual stimulus (Robson, 1975; De Valois, Albrecht &
Thorell, 1977). The issue was raised that a true edge detector
would need non-linear dynamics and it was unclear whether the
cortical cells exhibited the necessary nonlinear dynamics.
The two different views were (1) that the cortical cells function
as non-linear edge detectors or (2) as linear spatial frequency
filters. These two views each have different predictions about
how the cortical cells would respond to a visual stimulus. By
making use of gratings and checkerboards as the visual stimuli,
De Valois et. al., 1979, were able to distinguish between these
Figure 7 (from earlier in the report) shows different patterns
(that can be presented as visual stimuli) and the corresponding
frequency spectrum. Each spectrum here is plotted in polar form
where the distance from center represents the spatial frequency
of the stimulus and the angle (from 0°) represents the phase
information or the orientation of the spatial frequency of the
stimulus. The size of the dots represents amplitude. In rectangular
coordinates the spectrum would be interpreted as frequency components
in the vertical and horizontal directions.
For example, a square-wave grating with vertical bars (see figure
7) would manifest a frequency (repeating pattern) in the horizontal
direction. The spectral depiction of this image would be decomposed
into various frequency components all in the horizontal direction.
This would be plotted (in the representation used here) as dots
along the horizontal axis. A spectral plot of a square-wave grating
with horizontal bars would consist of dots along the vertical
When an animal is presented with the spatial visual field (the
left-hand side of each figure pair) the question can be asked
"are the cortical cells responding to information in the
original spatial domain or information in the frequency (spectral)
domain?". In what representation is the information getting
to the cortical cells? Can an experiment be devised to distinguish
between these two possibilities? For example, is a particular
cortical cell responding to the presence of a line in the visual
field or to the fundamental Fourier component (at a certain orientation)
of the spectrum? This issue was resolved by comparing the response
of the same cortical cell to different visual fields (De Valois
et. al., 1979).
A series of experiments were performed in both cats and monkeys
(De Valois et. al., 1979) to see if the cortical cells responded
to differences in the Fourier spectrums. The first experiment
was designed around the observation that spectral Fourier fundamentals
for the checkerboard were rotated at 45 degrees relative to the
Fourier fundamentals of either the square-wave grating or the
plaid (see figure 7). Vertical square-wave gratings, plaids, and
checker-boards each have vertical edges in the same orientation.
Therefor, if a cortical cell was functioning as an edge detector,
the cell should respond optimally (most number of spikes or action
potentials per sec) to square-wave gratings, plaids, and checkerboards
all in the same orientation. If, however, the cortical cells were
responding to the spectral fundamentals, the cortical cell should
respond optimally to a checkerboard pattern that is rotated 45
degrees relative to either a square-wave grating or a plaid pattern
that was oriented to produce the optimal response.
In both cats and monkeys, the procedure would be as follows. A
micro-electrode would be inserted into a visual cortical cell
to measure the number of action potentials (spikes) per second.
The optimal stimulus parameters were first determined for the
cell. The receptive field was located and the animal was positioned
so that the receptive field was centered on the scope display.
Then by experimenting with different sine-wave gratings, the optimum
orientation and the optimum spatial frequency for the cell was
determined. The optimum temporal frequency was determined by drifting
the best grating pattern across the respective field at different
rates. If the cortical cell was functioning as a true edge detector,
one would expect the square-wave grating, the checkerboard, and
the plaid to all induce maximal spikes/sec in the cell at the
same orientation. The cortical response to the square-wave grating
was determined with various angular rotations. Then the cortical
response (# spikes/sec) was determined from the checkerboard at
various angular rotations. The visual cortical cells responded
optimally to the checkerboard pattern which was rotated 45 degrees
relative to the square-wave grating that was rotated to produce
the optimal response (see figure 9). This was evidence that the
visual cortical cell was responding to the Fourier fundamentals,
not as an edge detector.
In another experiment, checkerboards stimuli of different check dimensions (1/1, 2/1. 0.5/1) were presented (to the animals) for comparison with the square-wave grating visual stimulus. The altered (orthogonal) dimension of the checkerboard checks should not matter if the visual cortical cells are responding to the unaltered edges. If, on the other hand, the visual cortical cells are responding to the fundamental Fourier frequency, the different checkerboard patterns would have to be rotated some to get the maximal spikes/sec from the cells. Note how the Fourier fundamentals (the biggest dots) are at a different angle from the center in comparing figure 7B to 7C). It was indeed found that the different checkerboard patterns had to be rotated an amount that matched exactly to what would be predicted from the mathematics of the Fourier transform (the location of the Fourier fundamentals). When the data was re-plotted with the points rotated according to the mathematically predicted position of the Fourier fundamentals, it was found that a very good match existed. This was further evidence that the visual cortical cell was responding to the angular location of the Fourier fundamentals and not the edge of the squares (or grating) seen in the untransformed pattern.
In another experiment, plaid checkerboard patterns with the same
dimensions were presented (with various rotations) as the visual
stimulus to the experimental animals. Again, if the cortical cell
was functioning as an edge detector, it would be predicted that
the cell would respond optimally to the two patters at the same
orientation (when the edges are at the same orientation). It was
found, though, that the cortical cell responded optimally to a
checkerboard pattern that was rotated 45 degrees relative to the
orientation of the plaid pattern (that had been oriented to give
an optimal response).
The next batch of experiments were centered around the observation
that the Fourier fundamentals for the checkerboard (with squares
of the same width as the bars of the square-wave grating) were
located farther out (from center) than the Fourier fundamentals
for the square-wave grating. Thus, a test could be done to see
whether the cortical cells were responding to the width (separation
between lines) or to the spatial frequency of the optimally presented
pattern. If the cortical cell was responding to the separation
between edges, then the best match should be for a checkerboard
with squares of the same width as the bars in the square-wave
grating. If the cortical cell was responding to the Fourier fundamentals,
then a checkerboard with a different sized check (or bar width)
would induce the optimal response. The "contrast sensitivity"
was defined as that contrast of the pattern that was necessary
to yield a particular number of spikes/sec for the cortical cell.
The control was the square-wave grating with a bar width (and
orientation) that produced the maximal cortical cell response.
The experimental bar width (yielding the best response for the
optimal orientation) for the checkerboard matched what was predicted
from the Fourier mathematics (De Valois et. al., 1979). This provided
more evidence that the visual cortical cell was responding to
the Fourier fundamental and not the edges ( or distance between
the edges) of the visual stimuli.
In another experiment, the relative check dimensions were changed
for the checkerboard patterns (2/1, 1.1, 0.5/1 ratios). Note from
figure 7 that as one dimension of the check is changed, the distance
(from center) of the Fourier fundamentals changes. It could then
be determined what width (given a certain ratio) produced the
best result (when oriented optimally). If the visual cortical
cells were responding to the check width, then the different height/width
ratios shouldn't influence the cell's response. If, the cell was
responding to the Fourier fundamentals, then it should respond
optimally to different check widths when the height/width ratio
changes. It was found that the cortical cell responded optimally
to checkerboard patterns of different widths and that these widths
matched what was predicted from the Fourier mathematics De Valois
et. al., 1979). When the data was plotted according to the theoretical
prediction, the cortical cell was shown to be responding to the
spatial frequency (the distance from center of the Fourier fundamental)
for the various optimally oriented patterns. This was further
evidence that the cortical cells were responding to the Fourier
transform of the presented visual stimuli.
All of these experiments were repeated for multiple visual cortical
cells in both the cat and monkey yielding similar results (data
not shown in this report).
The next set of experiments examined whether cortical cells could
be found that were sensitive to higher harmonic components of
the Fourier spectrum. If so, then this would be powerful evidence
that these cortical cells are acting like spatial-frequency filters
(and not as edge and bar detectors). The higher spectral harmonics
of the square-wave grating are at the same orientation as the
fundamental frequency but the higher harmonics of the checkerboard
are at other orientations (see figure 7). If a cortical cell exhibits
sufficiently narrow spatial tuning, it could potentially respond
separately to the fundamental and the third harmonics of patterns.
For instance, imagine a square-wave grating with more narrow bars
such that the fundamental frequency falls on what was the third
harmonic for a square-wave grating with wider bars. A cortical
cell sensitive to this spectral position, would respond to either
stimulus (and the stimuli would be presented at the same orientation).
For the checkerboard, the situation would be a little different.
A smaller sized checkerboard pattern sufficient to produce a Fourier
fundamental at the same frequency location as the third harmonic
(that a larger sized checkerboard pattern would produce) would
have to be rotated some for the optimal response (to get the angle
of the fundamental to fall on where the third harmonic would be
for the other pattern).
It was demonstrated that a cortical cell (responding to a square-wave
grating of a certain frequency and orientation) would also respond
optimally to a square-wave grating with bar widths three times
the size (which would be one third the spatial frequency) with
the same orientation. The Fourier fundamental of the grating with
the more narrow bars fell on the third harmonic of the grating
with the wider bars. It was also demonstrated that the same cortical
cell responding to a sine-wave grating (optimally at a certain
frequency and orientation) would not respond to a sine-wave grating
of 1/3 that frequency at the same orientation (remember that there
are no harmonics for a sine wave).
In order for the cortical cell to optimally respond, a checkerboard
pattern with check size of a certain size had to be rotated relative
to the optimal rotational orientation of a checkerboard with checks
that were three times larger producing the optimal response for
the same cortical cell. This observed rotation matched the theoretical
predicted rotation from the Fourier mathematics (De Valois et.
Similar experiments have been performed with the rat somatosensory
system (Pribram, 1994) where the cortical cells were also found
to respond to spectral information.
Other Aspects of the holonomic theory
Pribram says that both time and spectral information are simultaneously
stored in the brain. He also draws attention to a limit with which
both spectral and time values can be concurrently determined in
any measurement (Pribram, 1991). This uncertainty describes a
fundamental minimum defined by Gabor in 1946 (the inventor of
the hologram) as a quantum of information. Dendritic microprocessing
is conceived (by Pribram) to take advantage of this uncertainty
relation to achieve optimal information processing. Pribram then
says that the brain operates as a "dissipative structure"
where the brain continually self-organizes to minimize this uncertainty.
The next few sections will attempt to explain the concept of the
"uncertainty principle" and the concept of "dissipative
structures" that self-organize.
The Uncertainty Principle
In quantum physics, the uncertainty principle can be described
in the following way (paraphrased from Pagels, 1982): Consider
that you have a device that can simultaneously measure the position
and momentum of a single electron. Every time you push a button,
the device displays numerical values for the position and momentum.
Although, each time you press the button, you will get slightly
different measurements for the momentum and position. If enough
measurements are taken, then a statistical analysis can be performed.
Heisenberg defined the term delta q as indicating the spread or
uncertainty of the position measurements around some average value
and delta p as indicating the spread or uncertainty of the momentum
measurements around some average value (for the series of measurements).
He then found that (delta q)x(delta p)>=h where h is Plank's
constant. For a series of measurements, the positions can be expressed
as an average +/- some uncertainty. Likewise for the momentum.
No matter how good one makes a quantum measuring device, the products
of the uncertainties can never be less than Planks constant. For
example, if you could build a measuring device that exactly determined
the position (where delta q = 0) then you would not be able to
determine anything about the momentum (delta p = infinity). There
is a similar uncertainty relation for the energy of a particle
and the elapsed time. For a series of measurements, the product
of the uncertainty of the energy (delta E) and the uncertainty
of the elapsed time is always greater or equal to Planks constant.
(delta E)x(delta t)>=h.
In communication theory, a variation on the uncertainty principle
also holds (Gabor, 1946). The measurement of the frequency can
be made with arbitrary precision. Likewise, the measurement of
the time of occurrence can be made with arbitrary precision. But
there is a limit to the precision when these measurements are
taken simultaneously. One can exactly measure either the frequency
(of for example a tone) or the time (of occurrence) but not both
at the same time. For instance, if the time of occurrence were
known (indicating an impulse function) there would be frequency
components all up and down the spectrum. If, on the other hand,
the frequency information was exactly known, one would not know
any information about when it occurred. A single peak (or peak
pair if you consider the corresponding negative frequency) in
the spectrum implies that the tone has infinite extent in the
time domain. Analogously to the quantum uncertainty principle,
when frequency and temporal measurements are made simultaneously,
there is a limit to the precision possible. Pribram claims that
the brain functions as a dissipative structure to seek to decrease
this uncertainty in the direction of its theoretical limit.
The second law of thermodynamics holds that the entropy always
increases in any isolated system (figure 10). This simply means
that if something is left to itself, it will move towards equilibrium...it
will move towards maximal disorder...its internal energy state
will tend to be minimized. There has not been, to date, any confirmed
observation that this law is invalid.
An isolated system can itself be divided into a subsystem that is open to energy flow and the subsystem's environment (see figure 11). As such, the whole combined isolated system still obeys the second law of thermodynamics, but it is possible that the subsystem can experience a decrease in entropy at the expense of its environment.
The entropy increase in the "sub-system environment"
is guaranteed (by the second law) to more than offset the entropy
decrease in the subsystem. Also note that the sub-system can only
be maintained away from equilibrium as long as there is usable
energy in its environment. When the environmental entropy is maximized
(no usable energy), the subsystem is guaranteed to itself proceed
There is a special class of such subsystems (as described above)
where the subsystem's organization comes exclusively from processes
that occur within the sub-system's boundaries. This class of subsystems
was labeled "dissipative structures" by I. Prigogine,
1984 (who won the Nobel price for his work). Pribram believes
the brain to be such a "dissipative structure".
One way of modeling a structure that goes to equilibrium is to
minimize a mathematical expression for the internal energy (which
is the same as maximizing an expression for the entropy). This
is called the lest action principle. This would not be appropriate,
though, for a "dissipative structure" since it is not
going towards equilibrium. "Dissipative structures"
self-organize around a different "least action principle".
In the holonomic brain theory, Pribram has the entropy being minimized
(which maximizes the amount of information possible to store)
as the "least action principle". Thus, the system (the
brain) self-organizes such that more and more information can
In Hopfield networks and the Boltzmann engine (which are computer
models of neural processing), computations proceed in terms of
attaining energy minima. In the holonomic brain theory, computations
proceed in terms of attaining a minimum amount of entropy and
therefor a maximum amount of information. In the Boltzmann formulation
the principle of least action leads to a space-time equilibrium
state of least energy. In the holonomic brain theory, Pribram
describes the principle of least action as leading to maximizing
the amount of information (minimizing the entropy).
Independently, (in unrelated work) Schneider and Kay (1994) have
proposed a variation on the second law of thermodynamics which
may be applicable to Pribram's holonomic theory.
"The thermodynamic principle which governs systems is that
as they are moved away from equilibrium, they will utilize all
avenues available to counter the applied gradient. As the applied
gradients increase, so does the system's ability to oppose movement
It would be interesting to see if there is a connection between
the work of Schneider and Kay and Pribram.
The holonomic brain theory maintains that the brain is continuously
engaged in correlation processes. This is how we make associations
(how the senses are integrated). There is an obvious computational
advantage for the brain storing sensory information (and perceptions)
in the spectral (or holographic) domain as opposed to the brain
directly storing individual features and characteristics.
The holonomic brain theory claims that the act of "re-membering"
or thinking is concurrent with the taking of the inverse of something
like the Fourier transform. The action of the inverse transform
(like in the laser shining on the optical hologram) allows us
to re-experience to some degree a previous perception. This is
what constitutes a memory.
The medium of the optical holography, the silver grains on the
photographic film, encodes the Fourier coefficients. In the holonomic
brain theory, the Fourier coefficients are stored as the micro
process of polarizations and depolarizations occurring in the
Both Pribram's theory and the more conventional theory have the
brain divided up into various functioning communicating modules.
One main difference is in how the information is stored in these
brain modules. For example, in the case of vision, the conventional
theory has specific features stored in certain dedicated cells.
These different sub-modules then have parallel pathways to other
modules that produce the combined visual experience. This would
be somewhat analogous to a computer performing signal processing
directly on an image. For example, dedicated circuitry for edge
detection would interface with other circuitry for other features
like color. Every feature of the image gets stored (or processed)
in different dedicated "circuitry". These "circuits"
then have parallel pathways to other brain regions in which the
collective subjective experience of the perception is formed.
The holonomic theory (for the example of vision) summarizes evidence
that the image formed on the retina is transformed to a holographic
(or spectral) domain. The information in this spectral "holographic"
domain is distributed over an area of the brain (a certain collection
of cells) by the polarization of the various synaptic junctions
in the dendritic structures. At this point, there is no longer
a localized image stored in the brain. Correlations and associations
can then be achieved by other parts of the brain projecting to
these same cells. Conscious awareness (and memory) is the byproduct
of the transformation back again from the spectral holonomic domain
back to the "image" domain. Possibly the most radical
part of the holonomic theory is Pribram's claim that a "receiver"
is not necessary to "view" the result of the transformation
(from spectral holographic to "image"). He claims that
the process of transformation is what we "experience".
Memory is a form of re-experiencing or re-constructing the initial
Conventional neuro-physiology effectively pushes back the line
between observer and what is observed (between subject and object).
In signal processing, there always needs to be an end-user to
view the processed or transformed signal. At best, conventional
neuro-science leaves until later the ultimate explanation of the
observer. Who would bet their grant money (career) on being able
to answer this question in a couple of years? Aspects of Pribram's
holonomic brain theory attempts to address this question.
The conventional view is that the brain is a computational device.
There is a growing body of literature, though, that shows that
there are severe limitations to computation (Penrose, 1994; Rosen,
1991; Kampis, 1991; Pattee, 1995). For instance, Penrose uses
a variation of the "halting problem" to show that the
mind cannot be an algorithmic process. Rosen argues that computation
(or simulation) is an inaccurate representation of the natural
causes that are in place in nature. Kampis shows that the informational
content of an algorithmic process is fixed at the beginning and
no "new" information can be brought forward. Pattee
argues that the complete separation of initial conditions and
equations of motion necessary in a computation may only be a special
case in nature. Pattee argues that systems that can make their
own measuring devices can affect what they see and have "semantic
It is possible that the brain transcends computational behavior.
If this is the case, then it will be very interesting to see what
aspects of Pribram's holonomic theory are in collaboration with
these non-computable ideas.
Karl Pribram's holonomic brain theory weaves several concepts together in forming the holonomic brain theory. A partial list is the following:
1. The apparent spectral frequency filtering aspect of cortical cells
2. The relationship between Fourier transforms and holograms
3. The fact that selective brain damage doesn't necessarily erase specific memories
4. The computational advantage to performing correlations in the spectral domain.
5. His idea of conscious experience being concurrent with the brain performing these Fourier-like transformations (which simultaneously correlate a perception with other previously stored perceptions). He believes that conscious experience is the act of correlation itself and this correlation occurs in the dendritic structures by the summation of the polarizations (and depolarizations) through the processes in the dendritic networks.
6. The brain is a "dissipative structure" and self-organizes
around a least-action principle of minimizing a certain uncertainty
Most conventional experimental neurophysiologists are content
just to gather neurological data independent from any global theory
of the brain/mind and leave a theory of the brain to future generations.
As such, Karl Pribram is not referenced in many of the major neuro
physiology textbooks (such as Principles of neural science by
Kandel, Schwartz, and Jessell, 1991). This is unfortunate because
it helps to have a theory in asking important experimental questions.
With a different theory comes different questions which can lead
to new and different experiments that can bring forth novel information.
Hopefully, Pribram's ideas (or variations on them) will eventually
find their way into the consciousness of the conventional neurophysiologist
(and appear in most textbooks) once the current fascination with
molecular biology runs its course. Then the attention of physiologists
may again be directed back toward a system's organization and
away from simply analyzing its parts.
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