From Scholarpedia

Figure 1:

The Holonomic Brain Theory describes a type of process that occurs in fine fibered neural webs. The process is composed of patches of local field potentials described mathematically as windowed Fourier transforms or wavelets. The Fourier approach to sensory perception is the basis for the holonomic theory of brain function. Holonomy, as its name implies, is related to the unconstrained Fourier co-ordinate system described by holography. The Fourier transformation changes a space-time coordinate system into a spectral coordinate system within which the properties of our ordinary images are spread throughout the system. Fourier transformations are routinely performed on electrical recordings from the brain such as EEG and local field potentials. The term “holonomy” to describe a constrained, windowed, Fourier process, was borrowed from Hertz who used it to express in more generally applicable co-ordinates a specific co-ordinate system. Holonomic processes have more recently been called “Quantum Holography” by Walter Schempp (1993) in their application to image processing in tomography as in PET scans and functional Magnetic Resonance (fMRI) -- and even more recently for processing images in digital cameras. Dennis Gabor (1946) had pioneered the use of windowed Fourier processes for use in communication theory and noted its similarity to its use in describing quantum processes in subatomic physics. Gabor therefore called his units of communication “quanta of information”. Karl Pribram's holonomic theory is based on evidence that the dendritic receptive fields in sensory cortexes are described mathematically by Gabor functions.

Taking the visual system as an example, the form of an optical image is transformed by the retina into a quantum process that is transmitted to the visual cortex. Each dendritic receptive field thus represents the "spread" of the properties of that form originating from the entire retina. Taken together, cortical receptive fields form patches of dendritic local field potentials described mathematically by Gabor functions. Note that the spread of properties occurs within each patch; there is no spread of the Fourier process over the large extent of the entire cortex. In order to serve the perceptual process the patches must become assembled by the operation of nerve impulses in axonal circuits. Processing the vibratory sensory inputs in audition and in tactile sensation proceeds somewhat similarly.

But Gabor and similar wavelet functions, though useful in communication and computations, fail to serve as the properties of images and objects that guide us in the space-time world we navigate. In order to attain such properties an inverse Fourier transformation has to occur. Fortunately the Fourier process is readily invertible; the same transformation that begets the holographic domain, gets us back into space-time. The inverse Fourier transformation is accomplished by movement. In vision, nystagmoid movements define pixels, points which are mathematically defined by "Point Attractors". Larger eye and head movements define groupings of points which can readily be recognized as moving space-time figures. Such groupings are mathematically defined as "Symmetry Groups". The brain processes involved are organized by a motor cortex immediately adjacent to the primary visual cortex. Similar motor strips are located adjacent to other sensory input systems. The details of the evidence for how these processes work are described in Lectures 3, 4, and 5 of Pribram, Brain and Perception.





Roots of the Holonomic Theory

The holonomic theory of brain function has two roots:

the experimental evidence accrued during the 1960s and 1970s that mapped certain brain processes as local field potentials as well as bursts of electrical discharges traversing circuits, and the mathematical insights of Dennis Gabor in the 1940s as realized in optical imaging by Emmett Leith in the early 1960s.

The experimental mapping procedure originated with Stephen Kuffler. Kuffler (1953), working with the visual system took the common clinical procedure of mapping visual fields into the microelectrode laboratory. A visual field is described as the part of the environment that a person can see with one eye without moving that eye. Maps of this field are routinely recorded by means of the verbal response of the person to a spot of light on an appropriate medium such as graph paper.

For the verbal response of the human, Kuffler substituted the response of a single neuron recorded from a microelectrode implanted in the visual system of an animal. Because the record was made from the domain of a single neuron rather than the whole visual system, the map portrayed what was going on in the dendritic arbor of that neuron. The map was no longer a map of what was “seen” by the whole visual system but only that part, the receptive dendritic field, “viewed” by the particular neuron.

The dendritic arbor ( Figure 1) is made up of fibers for the most part too fine to support propagated action potentials, spikes. Rather the local field potential changes oscillate between moderate excitation (postsynaptic depolarization) and inhibition (post-synaptic hyper-polarization). The maps therefore represent a distribution of oscillations of electrical potentials within a particular dendritic arbor.

Hubel and Wiesel, (1959) working in Kufler’s laboratory discovered that the visual cortex responded more effectively to an elongated line or bar presented at a specific orientation rather than to a spot of light. However, a decade later many laboratories -- especially those of Fergus Campbell (1974) at The University of Cambridge, England; and Russel and Karen DeValois (1988) at The University of California at Berkeley -- found that oriented gratings composed of lines at different spacing, rather than single lines were the effective stimulus to engage a neuron in the visual cortex. These gratings were characterized by their spatial frequency: scanning the grating produces an alternation between light and dark, the frequency of alternation depending on the spacing of the grating. An example in the somatosensory cortex of three receptive fields and their contour maps produced by a tactile grating is presented in Figure 2.

Figure 2: An example of the three dimensional representation of the surface distribution and associated contour map of the electrical response to buccal nerve stimulation.

Theories of visual perception built on the finding of oriented lines gave rise to what may be called a two dimensional “stick figure” view of how we come to perceive images of objects based on Euclidian Geometry. Theories of perception based on frequencies gave rise to a transformational view of the processing of visual signals.

Mathematically, this transformational view is based on the Fourier theorem. This theorem states that any space-time pattern can be transformed into a spectrum based on waveforms that encode amplitudes, frequencies and the relationships among their phases. Usefully, we can invert the process to regain the space-time pattern from the spectrum.

A fast Fourier procedure (FFT) is commonly used in statistics to make correlations. The Fourier procedure is also routinely found useful in electroencephalography (EEG) to distinguish individual frequencies and frequency bands among the recorded electrical waveforms.

Russ and Karen DeValois in their 1998 book “Spatial Vision” expressed what Fergus Campbell at Cambridge University, Vadim Glezer at the Pavlov Institute at Leningrad and many others of us were experiencing: “Linear systems analysis originated in a striking mathematical discovery by a French physicist, Baron Jean Fourier, in 1822 … [which] has found a wide application in physics and engineering for a century and a half. It has also served as a principle basis for understanding hearing ever since its application by Ohm (1843) and Helmholtz (1877). The successful application of these procedures to the study of visual processes has come only in the last two decades.

The Fourier approach to sensory perception is the basis for the holonomic theory of brain function . The term “holonomy” was borrowed from Hertz who used it to express in more generally applicable co-ordinates a specified co-ordinate system. Holonomic processes have more recently been called “Quantum Holography” by Walter Schempp (1993) in their application to image processing in tomography as in PET scans and functional Magnetic Resonance (fMRI). Holonomy, as its name implies, is related to the less constrained co-ordinate system described by holography. Quantum holography, holonomy, uses windowed Fourier transformations, often called "wavelets". Gabor (1946) had pioneered this use in communication theory and noted its similarity to its use in describing quantum processes in subatomic physics. Gabor therefore called his units of communication “quanta of information”.

Figure 3: Satial decay of a synaptic potential initiated by an input onto a dendrite.

Misconceptions

There are four common misconception about the application of holographic and holonomic theories – that is, holonomic procedures -- to brain function. The first and most important of these is that, contrary to what is shown in Figure 3, the processing that occurs in the dendritic arbor, in the receptive field, is performed by propagated nerve impulses. Finding that impulses do occur in certain dendrites readily produces such a misconception. An excellent example appears in Eric Kandell’s 2006 biographical “In Search of Memory.” Kandell found such impulses in the dendrites of the hippocampus early in his career:

“By applying the powerful methodologies of cell biology, Alden and I easily picked some low hanging intellectual fruit. … We found that action potentials [nerve impulses] in the pyramidal cells of the hippocampus originated at more that one site within the cell. … We had good evidence to suggest that action potentials in pyramidal cells of the hippocampus can also begin in the dendrites … .

This proved to be an important discovery. Up to that time most scientists including Dominick Purpura and Harry Grundfest, thought that dendrites could not be excited and therefore could not generate action potentials.

Willifred Rall, a major theorist and model builder at NIH, had developed a mathematical model showing how dendrites of motor neurons function. This model was based on the fundamental assumption that the cell membrane of dendrites is passive: it does not contain voltage-gated sodium channels and therefore cannot support an action potential. The intracellular signals we recorded were the first evidence to the contrary, and our finding later proved to be a general principle of neuronal function.”



The problem that Kandell’s finding poses can be called “The tyranny of names”. Those of us who have been concerned with processes occurring in fine-fibered webs have been too prone to focus on dendrites per se. Kandell’s finding has been repeatedly confirmed as has his conclusion which has been restated in his (as well as other) otherwise excellent neuroscience texts. Dendrites, defined as afferents to neural cell bodies, come in all sizes. The biggest of them all are the afferent peripheral nerves entering the spinal cord. Such large fibers readily support the propagation of nerve impulses. Large diameter fibers occur both as afferent (dendritic) and efferent (axonal) fibers in neural circuits.The hippocampal dendrites, though not as large as peripheral nerves, have sizable diameters. The very fact that Kandell and others can make intracellular recordings from these hippocampal dendrites attests to their considerable size. The webs wherein holonomic processes occur (in the hippocampus and elsewhere) are made up of pre- and postsynaptic slim branches of larger fibers. Fine fibered webs occur in the brain, both at the ends of branching axons and within dendritic arbors. The holonomic brain theory is founded in the processing that occurs in fine fiber webs wherever they occur. ( Figure 4).

[The tyranny of names was called to my attention when, in the early 1950s I found responses in the precentral motor cortex of the brain evoked by sciatic stimulation. It took much subsequent research and weeks of phone conversations and visits by neuroscience friends Clint Woolsey and Wade Marshall to witness demonstrations in my laboratory to convince them – and me – that the precentral cortex is actually a sensory cortex for intentional action, not just an efferent path to muscles from the brain.]



Contrast Kandell's statement with another, made repeatedly over the decades by Ted Bullock (1981):

“In 1957 it was possible to say ‘These considerations also lead us to the suggestion that much of normal nervous function occurs without impulses [emphasis in the original] but mediated by graded activity, not only as response but also as stimulus’ (Bullock 1957). The notion had appealed to me for some time (Bullock 1945) and in 1947 I wrote in a review: ’The far-reaching implications of the assumption that neurons can affect each other by means distinct from classical impulses in synaptic pathways are obvious’. I referred to Bremer (1944) and Gerard (1941) who influenced me most in this view, which remained for a long time ignored in the conventional orthodoxy. [Currently therefore,] I propose that a ‘circuit’ in our context of nervous tissue is an oversimplified abstraction involving a limited subset of communicated signals …. That, in fact, there are many parallel types of signals and forms of response, often skipping over neighbors [that are] indirect contact and acting upon more or less specified classes of nearby or even remote elements. Thus the true picture of what is going on could not be drawn as a familiar circuit; and specified influence would not be properly called connectivity, except for a very limited subset of neighbors. Instead of the usual terms ‘neural net’ or ‘local circuit’ I would suggest we think of a ‘neural throng’, that is a form of densely packed social gathering with more structure and goals than a mob.”

Hopefully, things are changing in the current century.

Figure 4: Diagram of microstructure of synaptic domains in cortex. The ensemble of overlapping circles represents the junctions between branches of input axons and cortical dendrites.

Or take author’s statements in 1991 “Brain and Perception.” In Chap. 4, Pribram describes one example of properties of the manner in which some cortical dendrites interact:

“Receptive fields in the sensory cortex are composed of … polarizations occurring in dendritic arbors of cortical neurons. According to the holonomic brain theory these polarizations collectively interact to produce the receptive field properties mapped during single neuron recording ( Figure 4). [The recording electrode, that is, the relevant the axon, samples that interaction.] Dendrites are fitted with spines that resemble little cilia, or hairs, protruding perpendicularly from the dendritic fiber. These spines have bulbs at their endings, knob-like heads that make contact with branches of axons and other dendrites to form synapses. Activity in axons and in other dendrites such as those stemming from reciprocal synapses produce depolarizations and hyperpolarizations in the dendritic spines. …

Shepherd, Rall, Perkel and their colleagues modeled the process whereby these postsynaptic events occurring in the spine heads interact. The issue is this: The stalks of the spines are narrow and therefore impose a high resistance to conduction (active or passive) toward the dendritic branch. Spine head depolarizations (as well as hyperpolarizations) must therefore interact with one another if they are to influence the action potentials generated at the axon hillock of the parent cell of the dendrite. The interactions (dromic and antidromic) among dendritic potentials (by means of which the signal becomes effective at the next stage of processing) thus depend on the simultaneous activation of both pre and postsynaptic sites.”

According to Shepherd ---

“the relative efficacy of distal dendritic inputs would [in this manner] be greatly enhanced --- information might thus be processed through precise timing of specific inputs to different neighboring spines … These precise interactions would greatly increase the complexity of information processing that can take place in distal dendrites”.





Holonomy is Patch Holography

Another common misconception is that the Fourier transformation is globally spread across the entire brain cortex. This has led to misleading statements such as “The brain is a hologram.” Only one particular brain process is holonomic, the one taking place in the transactions occurring in its fine fibered web. From the outset in the early 1960s when Pribram proposed the theory, he noted that the spread function (as it is appropriately called) is limited to a receptive field of an individual neuron in a cortical sensory system – and he actually thought that this was a serious problem for the theory until it was shown by radio-astronomers that such limited regions could be patched together to encompass large regions of observations.

Despite these precise early descriptions, psychophysicists and others in the scientific community spent much time and effort to show that a global Fourier transformation would not work to explain sensory function. Few paid heed to patch holography -- which Pribram had dubbed holonomy and which engineers and mathematicians call a “windowed Fourier Transformation”.

Interference Patterns

The third common misconception regarding holography and holonomy is that these processes deal with waves. Waves occur in space and in time. The Fourier transformation deals with the intersections among waves, their interference patterns created by differences among their phases. The amplitudes of these intersections are Fourier coefficients, discrete numbers that are used for computation. These numbers are useful in statistical calculations. The statistical and the spectral computations are readily convertible into one another: successive terms in the Fourier series correspond to “orders” in statistics and thus can serve as vectors in graphs. [For instance it takes 4th order statistics to adequately analyze the waveforms of an EEG by Independent Component Analysis (ICA)]. (See Pribram,Xie,Zheng,Santa Maria,Hovis Shan and King).

Convertibility raises the question of the value of having multiple mathematical representations of data. In author’s experience, which reflects earlier discussions in quantum physics, the spectral representation displays a more nuanced (“Anschaulichkeit” in German) representation while the statistical/vector representation is more computationally friendly.

Deep and Surface Structures of Memory

A final common misconception that needs to be dealt with, is that all memory storage is holonomic (holographic). This misconception stems from juxtaposing memory storage to memory retrieval. However, in order for retrieval to occur, the memory must be stored in such a way that it can become retrieved. In other words, retrieval is dependent on storing a code. The retrieval process, the encoding, is stored in the brain's circuitry. We can, therefore, distinguish a deep holonomic store (which can be content addressable) from a surface pattern (such as naming) of stored circuitry. Thus the deep dis-membered holonomic store can be re-membered.





Conclusion

Holographic and holonomic processes are “holistic” as their names imply. This attribute has endeared the concept to humanists and some philosophers and scientists. However, many of these proponents of a holistic view conflate two very different forms of holism. In biology and psychology a well known form which I like to call “wholism” is captured in the saying that “the whole is more than and different from the sum of its parts.” Reductionist and materialist scientists and philosophers like this form of wholism because they can discern emergent properties as they investigate higher orders and can try to reduce the higher order to the lower ones either as to their properties or the theoretical terms that describe their relations.

By contrast, holographic and holonomic processes are truly “holistic” in that they spread patterns everywhere and everywhen to entangle the parts with one another. In this domain, space and time no longer exist and therefore neither does “causality” in Aristotle’s sense of “efficient causation”. This relation between cause and effect has served well as the coin of much of current science and the philosophy of science. However, Aristotle’s more comprehensive formal or formative causation is more appropriate to descriptions of more complex orders such as language and those composed by holographic and holonomic brain processes. Holism in this form is related to “holy” and “healthy”. My hope has been that as scientists begin to understand and accept the validity of holonomic processes as truly scientific, this understanding will help resolve the current estrangement between the sciences and the humanities, and between sophisticated pursuits of science and sophisticated pursuits of religion.

References

Bullock T.H. (1981) Spikeless neurons: where do we go from here? In B.M.H. Bush & A. Roberts (Eds) Neurons without impulses (pp 269-284) Cambridge University Press

DeValois R. L. and K.K. DeValois (1988) Spatial Vision. Oxford University Press, NY

Fourier J. (1807) Sine and Cosine Series for an Arbitrary Function in Joseph Fourier 1768-1830 Ed. and annotated by I. Grattan-Guinness The MIT Press, Cambridge, MA

Gabor, D. (1946) Theory of communication: Journal of the Institute of Electrical Engineers, 93, 429-441

Gabor, D. (1948) A new microscopic principle: Nature, 161, 777-778

Helmholtz, H. (1954) The Sensations of Tone. Dover, N.Y.

Hubel D.H. (1959) Receptive fields of single neurons in the cat’s striate cortex. Journal of Physiology 148 574-591

Kandel, E.R. (2006) In Search of Memory: The Emergence of a New Science of Mind: W.W. Norton and Co. N.Y.

Kuffler, S.W. (1953) Discharge patterns and functional organization of the mammalian retina. Jl. Neurophysiology 16 37-69

Perkel, D.H., & Perkel, D.J. (1985) Dendritic spines – role of active membrane in modulating synaptic efficacy. Brain Research, 525, 331-335

Prideaux, J (2000) Comparison between Karl Pribram's "Holographic Brain Theory" and more conventional models of neuronal computation. http://www.acsa2000.net/bcngroup/jponkp/

Pribram, K.H. (1971) Languages of the Brain: Experimental Paradoxes and Principles in Neuropsychology: Prentice Hall/Brandon House, N.Y.

Pribram, K.H. (1991) Brain and Perception: Holonomy and Structure in Figural Processing

Pribram, K.H. Min Xie, Bibo Zheng, Michael SantaMaria Shannon Hovis Peijun Shan and Joseph King (2004) Representation of Cortical Unit Response to Texture and Orientation of Tactile Gratings in the Rat: Forma, 19, 3-12.

Rall, W., & Rinzel, J. (1973) Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model. Biophysics Journal, 13, 648-688.

Schempp, W. (1993) Cortical Linking Neural Network Models and Quantum Holographic Neural Technology. In Pribram, K.H. (ed.) Rethinking Neural Networks: Quantum Fields and Biological Data

Shepherd, G.M., Brayton R.K., Miller, J.P., Segey, I., & Rall, W. (1985) Signal enhancement in distal cortical dendrites by means of interactions between active dendritic spines: Proceedings of the National Academy of Science, 82, 2192-2195

Internal references

See Also

Brain, Fourier Analysis, Neurons