holonomic-theory

Course Handout - Pribram's Holonomic Theory of Memory

Copyright Notice: This material was written and published in Wales by Derek J. Smith (Chartered Engineer). It forms part of a multifile e-learning resource, and subject only to acknowledging Derek J. Smith's rights under international copyright law to be identified as author may be freely downloaded and printed off in single complete copies solely for the purposes of private study and/or review. Commercial exploitation rights are reserved. The remote hyperlinks have been selected for the academic appropriacy of their contents; they were free of offensive and litigious content when selected, and will be periodically checked to have remained so. Copyright © 2003-2018, Derek J. Smith.

First published online 13:12 GMT 27th February 2003, Copyright Derek J. Smith (Chartered Engineer). This version [2.0 - copyright] 09:00 BST 4th July 2018.

Earlier versions of this material appeared in Smith (1996; Chapter 6). It is repeated here with minor amendments and supported with hyperlinks.

The Neural Hologram

One highly original and extremely promising explanation of physiological memory borrows the concept of the hologram from physics. Holography was first discovered as a photographic technique by Dennis Gabor in 1947, but it received comparatively little attention until the early 'sixties, when Emmett Leith and co-workers at the University of Michigan rediscovered it (eg. Leith and Upatnieks, 1965). The essence of the technique is the interference of light, the principle that two separate but converging wave patterns can produce a third pattern - an interference pattern - which bears no obvious resemblance to either of the originals [experiment with].

Wave interference is actually extremely easy to demonstrate: there are many simple shape which, when overlaid, produce a whorled and shimmering visual impression of some sort. Such patterns are sometimes called moire patterns [picture], after moire - or watered - silk, a fabric which has a characteristic shimmering appearance (Oster and Nishijima, 1963). The simplest demonstration of all is to create two sets of ripples on the surface of a pond. Where the resulting wavepeaks coincide they make a single peak twice as high, but where they are half a wavelength "out of phase" they interfere, and the trough of one wave simply cancels out the peak of the other.

Exercise - Wave Interference in the Bathtub

1 Run two inches of water into your bathtub.

2 Place the tips of your index fingers about 1 meter apart in the water, and gently create two ripple sources. (No other part of your anatomy need get wet.)

3 Study the shadows cast by the ripples onto the bottom of the bath.

NB: To get the best effects from step 3, the water - not to mention the fingers - should be unsoiled.

Much the same thing happens with light, save that the wavelengths involved are very much shorter. The wavelength of the visible light spectrum runs from 7 x 10-5 cm for red light to 4 x 10-5 cm for violet, so the interference patterns are correspondingly small. Moreover, with white light you get interference simultaneously for every different wavelength in the spectrum, giving rise to the sort of rainbow effects you see when you drop a film of oil onto water. As a result, the best interference patterns are obtained using laser light, because this has a single very precisely known wavelength. What you need to do is split the source beam into two half beams using a prism system, and then bring the two half beams back together again using mirrors [picture]. This then produces an interference pattern just as would two converging water waves, and a photographic plate placed at the point of convergence will store this pattern. The pattern thus stored is called a hologram.

What makes holography powerful as a photographic medium is when one of the two beams has in the meantime been "bounced off" the object to be holographed. In this case, the interference pattern "contains" (albeit in complex light-encoded form) an image of that object. And, just as with a conventional photograph, that image can subsequently be viewed as often as you want to. The processes of "taking" and subsequently "viewing" a hologram are shown in Figures 1 and 2 respectively.

Two very curious properties then emerge. On the one hand, holographic images can be viewed three dimensionally, that is to say, they have - or at least appear to have - depth. As you move your head from side to side, previously hidden surfaces and details come into view. On the other hand, the entire image can be recreated from any one portion of the plate. That is to say, if a hologram is broken in half each half can still be used, on its own, to reproduce the whole image. And if each half is broken into quarters, all four quarters can still be used, on their own, to reproduce the whole image. And so on with practically no theoretical limit. All that happens is that every fragmentation simply reduces the clarity of the image. A hologram, in other words, obeys its own version of the Law of Mass Action. This is shown in Figure 3.

Figure 1 - "Taking" a Hologram: The reference beam arrives at the holographic plate via the mirror at top left. The reflected beam, on the other hand, has been bounced off the target scene on the way, and thus "contains" details of that target. The holographic plate is placed where the two beams converge, and captures the resulting interference pattern.

If this diagram fails to load automatically, it may be accessed separately at

http://www.smithsrisca.co.uk/PICholonomic-fig1.gif

Figure 2 - Viewing a Hologram: The holographic plate is now re-illuminated from behind by the laser beam, and further interference takes place between the stored image and the incident light. This results in a diverging beam of light emerging at a slight angle and appearing to come from a point in space on the laser side of the plate. If this diverging beam is then focussed, it can be viewed by an observer at the point shown as though emanating from a virtual recreation of the original scene.

If this diagram fails to load automatically, it may be accessed separately at

http://www.smithsrisca.co.uk/PICholonomic-fig2.gif

Figure 3 - The Advantage of Partial Holograms over Partial Photographs: Half a hologram shows the entire image at half clarity. Half a photograph, on the other hand, shows half the image at full clarity. Therefore for some purposes biological memory needs to be "photographic", whilst for other purposes it needs to be "holographic".

If this diagram fails to load automatically, it may be accessed separately at

http://www.smithsrisca.co.uk/PICholonomic-fig3.gif

So what we have in laser holography is a mechanism capable of (a) storing information about a three dimensional target scene in two-dimensional physically distributed form, (b) getting it back again in three-dimensional form, (c) doing this even if only part of a retrieval cue is available, and (d) functioning proportionately even when damaged. And these are precisely the most mysterious properties of biological memory systems. So could some sort of neural holography be responsible for biological memory? After all, nervous tissue has been known to demonstrate wavelike properties ever since Berger's development of electroencephalography in the 'twenties. Nor is the ripple metaphor itself new to memory theory, because Karl Lashley himself used it as long ago as 1942:

"Briefly, the characteristics of the nervous network are such that, when it is subject to any pattern of excitation, it may develop a spread of activity, reduplicated throughout an entire functional area by spread of excitations, much as the surface of a liquid develops an interference pattern of spreading waves when it is disturbed at several points." (Lashley, 1950, pp479; emphasis added. At this point Lashley was citing a 1942 paper of his own.)

But in 1942, of course, the laser hologram had not yet been discovered, and the explicit parallel was not drawn until the mid-'sixties when the neuropsychologist Karl H. Pribram - chancing upon the then-recently-discovered fact that the entire holographic image was stored on every fragment of the holographic plate - concluded that this might explain how the biological engram seemed to be in one place one moment and all over the place a moment later (Pribram, 1966, 1969). What Pribram therefore suggested was that engrams were neural interference patterns:

"One can imagine that when nerve impulses arrive at synapses [they] produce electrical events on the other side of the synapse that take the form of momentary standing wave fronts. Typically the junctions made by a nerve fibre number in the dozens, if not hundreds. The pattern set up by arriving nerve impulses presumably form a microstructure of wave forms that can interact with similar microstructures arising in overlapping junctional circuits. [..... These wave fronts] set up interference patterns [] producing in their totality something resembling a hologram." (Pribram, 1969, p77;86; emphasis added.)

The resulting engram would not just be widely distributed .....:

"The attractive feature of the hypothesis is that the information is distributed throughout the stored hologram and is thus resistant to insult. If even a small corner of a hologram is illuminated by the appropriate input, the entire original scene reappears. Moreover, holograms can be layered one on top of the other and yet be separately reconstructed." (Pribram, 1969, p86; emphasis added.)

More recently, the Pribram school (particularly Pribram, 1991, 1993) has coined the name the holonomic theory of brain function to describe this approach, and has been developing the mathematics of analysing and modelling neural wave activity. One adherent to the Pribram tradition, Bruce MacLennan of the University of Tennessee, explains some of the beliefs underlying the equations:

* It is important to distinguish between axonal and dendritic aspects of neural interconnection. Axonal anatomy is actually quite anatomically discrete, and there are well-defined projections from one brain area to another. Dendritic anatomy, on the other hand is "randomly and densely connected" (MacLennan, 1993, p168).

* The function of the axons is for communication, whilst the function of the dendrites is for computation; in particular, the structure of a dendritic net is biologically suited to processing linear wave interactions.

* Neural network models are therefore inherently better suited to simulating what happens at the dendritic level than at the axonal level.

To put it another way, it is what happens at the axonal level which really determines the performance of a memory system.

Where to Next?

For a recent discussion on the status of holonomic theory, click here.

References

Lashley, K.S. (1942). The problem of cerebral organisation in vision. Biological Symposia, 7:301-322.

Lashley, K.S. (1950). In search of the engram. Symposia of the Society for Experimental Biology, 4:454-482. [Page numbering from reprint in Physiological mechanisms in animal behaviour. Danielli JF & Brown R (Eds). Cambridge: Cambridge University Press.]

Leith, E.N. and Upatnieks, J. (1965). Photography by laser. Scientific American, 212(6):24-35.

MacLennan, B. (1993). Information processing in the dendritic net. In Pribram, K.H. (Ed.). Rethinking neural networks. Hillsdale, NJ: Erlbaum.

Oster, G. and Nishijima, Y. (1963). Moire patterns. Scientific American, 208:54-63.

Pribram, K.H. (1966). Some dimensions of remembering: Steps toward a neuropsychological model of memory. In Gaito, J. (Ed.), Macromolecules and Behaviour. Academic Press. [Excerpt in Pribram, K.H. (Ed.) (1969), Brain and Behaviour 2 - Perception and Action. Harmondsworth: Penguin.]

Pribram, K.H. (1969). The neurophysiology of remembering. Scientific American, 220:73-86.

Pribram, K.H. (1991). Brain and perception: Holonomy and structure in figural processing. Hillsdale, NJ: Erlbaum.

Pribram, K.H. (Ed) (1993). Rethinking neural networks. Hillsdale, NJ: Erlbaum.

Smith, D.J. (1996). Memory, Amnesia, and Modern Cognitive Theory. Cardiff: UWIC. [ISBN: 1900666006]

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