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Holography. holonomy and brain function 899

Holography, holonomy and brain functionKarl H ribmmThe re is considerable controversy as to whether holography canserve as a good rnodel for certain aspe cts of brain function. Theroots of this controversy are often to be found in misunderstand-ings of what holography is and what the proponents of a holo-graphic hypothesis are claiming. Furthermore. a feature detectormodel is often seen as a more viable altern,I t ~ v e .Holograp hy wa s invented in 1949 by Dennis Gabor, amathematician. Primarily, holography is a set of mathematicalpropositions based on ~no difica tions f the Fourier theorem. Inshort, the holographic hypothesis of brain function proposes an~athematicalmodel. Criticisms levied against the hv~othesisthat rely on optical holography as an analogy are misguided.The Fourier theorem states that any pattern can be analyzedinto components, each of which is represented by a regularwaveform of specified amplitude and frequency. The phaserelations alnong wavefortns are also critical since both thesine and cosine properties of the wave (i.e., its quadriture) areencoded. Furthermore, in holography, the waveforms becomedistributed over the entire surface of the recording medium.With distribution, the information encoded in the hologram isenfolded into each portion.An initial general criticism of the holographic hypothesis ofbrain function c oncerned the F ourier transform. Experiments inpsychophysics and neurophysiology have shown that channelsof limited band width encode Fourier components. However,the resultant fails to become distributed over the entire surfaceof the brain. Prior to his inventing holography, Gabor haddeveloped a model of telecommunication based on what wenow call a Gabor function. This function places a Gaussianenvelope over the Fourier waveforms, thus constraining theirotherwise infinite extent. Such constraints on colnputationalspaces are called holono~nic(Hertz. 1956: Pribram , 199 1).Ho log ra~ ns made of patches of Gabor functions have allthe essentials attributes of more globally tsansformed Fourierholograms (Bracewell, 1989).A second general criticism of the holographic hypothesis ofbrain function devolves on the use of waveform representationsin the model. Much of this criticism ca me from investigators inthe field of artificial intelligence who use digital computers tomodel brain and psychological processes. In the brain, however,most cornputations are performed by interactions am ong gradedfluctuating e lect roch e~n ical polarizations, often with the aidof local circuit neurons, most of which do not possess theaxon hi llocks and axons in which digi tal nerve i~ n p ~ ~ l s e sregenerated and propagated. Whether one wishes to rnodel theselocal graded interactions in wave mechanical. statistical orvector matrix terms depends on the data being modelled. Themathematics often turns out to be equivalent with regard tothe operations of the neural substrate (much as H eisenberg smatrices and S chroedinge r s wave equations are equivalent inquantum physics).The advantage of a Gabor-based approach is that it is essen-tially linear and invertible. Thus holonomic image processingallows easy access to the original form of the images beingprocessed in the transform domain by simply applying the in-verse transform. In brainlbehavioral systems, this inverse ap-pears to be carried out by movement (Pribram and Carlton,1986; Pribram, 1991). The advanta ge of processing in the holo-nomic domain is co~nputationalpower, especially the compu-tation of coherencelcorrelation, and the enormous capacity ofreadily retrievable storage. Thus the hypothesis is worth pur-suing. Much evidence in its support has accrued over the pastthree decades.

The neuroscience comnlunity has become Inore and moreaware of the importance of local dendritic field potentials inthe processing of signals in the sensory input systems throughthe work of George Bishop, W. Rall, Walter Freeman, GordonShepherd, Pasko Rakic, and Francis Schmitt. Observationsthat early stages of retinal processing (as well as those inmost other receptor systems) are devoid of nerve i~npulseshave provided convincing evidence that interactions alnonggraded polarizations can play a critical role in sensory signalprocessing. Additionally. these observations have providedmini-models of some aspects of the functional organizationof more central stations (especially of the cortical sheets thatso closely resemble the layered retinal mosaic). The questionthat arises is whether the transfer functions that are being~neticulouslydescribed by mapping receptive (i.e., dendritic)f ield proper ties for each stage of s ~ ~ c hrocessing can togetheraccount for neural image processing.

Two views of the neural process in vision have emerged:That pioneered by David Hubel and Torsten Wiesel emphasizesthe convergence of signals onto neurons that, at successivelevels of processing, progressively extract features encodedin the signals. The other, represented in the work of FergusCambell, Daniel Pollen, Vadim Glezer and Russell DeValois,among others, emphasizes what is called a harmonic analysis.Harmonic analysis emphasizes a parallel process that by virtueof lateral inhibition functions linearly to encode signals in thespectral domain. In the auditory mode. the idea that the sensorysystem may function as a harmonic analyzer goes back to thework of Ohm and Helmholtz over a cen tury ago. In 1967 vonBekesy dem onstrated with an elegant series of experiments thatsomatosensory experience is processed according to more orless identical rules. Experimental results in our laboratory haveshown that neurons in the somatosensory and somatomotorcortex respond to limited bandwidths of the frequency ofwhisker stimulation and of m ovement of a foreleg.More recently Daniel Pollen and S. Ronner have demon-strated the presence in the same cortical co lu ~ nn f cells re-sponding to complementary phases of an input, i.e., to thesine and cosine components. Vadi~n Glazer, Frane Marcela,John Daugman, among others, have evidence that it is the Ga-bor transform (or closely related Hermitians) that most accu-rately describes the process. Russell and Karen DeValois andtheir group have demonstrated the anatomical distribution ofspectrally-tuned analyzers and have thoroughly and criticallyreviewed their own and others psychophysical and neurophys-iological investigations on the topic of spectral encoding inthe visual system. They also have reported experiments thatmake implausible a Euclidian, hielarchical approach to imageprocessing based on the detection of lines.A feature analytic (as opposed to a feature detector) processis not ruled out, however. Each cortical receptive field displaysselectivities to several features including a limited band of spa-tial frequency, orientation. direction a nd velocity of mo vemen t,change in luminance and color. Under current investigation isthe nature of the output code that recognizes these featuressingly or in combination. There is already considerable evi-dence that ensembles of neurons are involved to form a ma-tial code. This would function much as the pattern formed in aclassroom when all students who are wearing glasses are askedto raise their hand. When. alternatively. all students wearinggrey sweatshirts are asked to raise their hand, the result wouldbe a different pattern.

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900 Homeobox and nervous system developmentThe two views of the sensory processing mechanism - hatof a hierarchical nonlinear feature extraction process and thatof parallel processing linear harmonic analyzer are thus notmutually exclusive. Feature extraction can lead to informationprocessing and harmonic analysis to image processing.A final critique of the holographic hypothesis of brainfunction has been that it is counterintuitive. If. however. oneimagines the sensory receptor surface to be something like apiano keyboard and the topologically corresponding corticaldendritic ensem ble to function like a sounding boarcl, a feel forthe mechanism can be obtained. Input patterns to the receptorsare transduced into neural patterns that are transmitted to thecortical sounding board where each receptive field resonates toa limited bandwidth of frequency. Patterns of the complexity ofsonatas can be processed in this manner.The counterintuitive aspects of holography and liolononiycan also be grasped by analogy to the patterns of radio andtelevision programs simultaneously present in the broadcastspace. Each program is in fact broadcast, i.e., distributed, castbroadly over that space, and each portion of spa ce has enfoldedin it all the programs that are being transmitted at that mo men t.In order to make sense of any of the programs transrnitted in a

frequency code, we must tune in selected bandwidths that actas carriers for oarticular Drocrams and re-transform them intoauditory and v iklal im ages. In order to make sense of the neuralholographic process, the sense organs must tune in on selectedbandwidths of environmental energv Datterns and re-transform2 them into images, probably by virtue of the motor processes ofthe brain (Pribram and Carlton, 1986).The neural holorraohic model has become refined in itsz applications to understanding memory as well as perception.Here, two forms of the model were initially pitted againstone another: a matrix versus a convolutional approach. In thematrix model remembering is triggered when successive inputsare related to one another by taking the outer products ofvectors representing features; while in the convolutional modelcorrelations are achieved by superposition and by taking theinner products of these vectors.Matrix models, such as those of James Anderson have beenshown to be superior in explain ing categorical mem ory; convo-lutional models, such as those of Ben Murdoch, in explainingserial position memory effects. Work from our laboratory hasshown that receptive fields in the lateral geniculate n ucleus andthe visual cortex can be altered (probably by influencing lat-eral inhibition) by electrical stirnulations of the posterior andfrontal association cortex (and the subjace nt basal gang lia).Posterior stirnulation enhances inhibitory surrounds thus pro-clucing a separation of excitatory centers. Such separate recep-tive fields are best represented by Gabor functions and matrixoperations. Frontal stimulation disinhibits the surrounds with

the result that excitatory receptive fielcls tenel to merge into amore continuous processing mode which is best representedby a convolutional motlel. Further, the systems of the poste-rior cerebral convexity have been shown important to estab-lishing prototypes necessary for categorizing: the frontolimbicsystems, to processing serial position of events occurring in anepisode.The holographic and holonomic models of brain function inperception and memory have t l i ~ ~ seceived support from neu-ropsychological evidence which is consonant with the evidenceobtained in experimental psychology and in neurop hysiology.ReferencesBracewell R N (198 9): The Fourier transform. Sci Arrr 86-95,Hertz H (1956): Tlrc l ritrcil11e.s of Meclr crr~ics Jrz..s~rrreclrr rr Newf i n r r . (Transl. by DE Joncs and JT Willcy with prelhcc by H vonHelmholtz and introduction by Robert S Co hen .) New York: DoverPribrwm KH (199 : H,rrirr crrrtl I ercept iorr: Holorrorrr?; crrrrl Strrrctrrle irrfigrrrol Pn)cessirr,q. Hillsdale. NJ: Lawrence Erlb;ulm Associates.Inc.Pribram KH, Cnrlton EH (198 6): Holonomic brain theory in imagingand ob.ject perception. Acro IJ.s?;chol63: 175-2 10

urther readingBracewell R N (1965): Tlre Forrri er Trcrrr.yfi)rrrr trrrcl it.s Al) l~l ico rio rrs.New York: McGraw-HillDeValois RL. DeValois K K (198 8): Spatial vision. Arrrrlr Re11 P.sy lro l3 :309-34 1Daugman JG (1 984 ): Spatial vision chan nels i n the Fouricr plan. VisiorrRe.s 24: 89 1-9 10Glczer VD (1 985 ): Spatial ;uid spatial frequency characteristics ofreceptive tieltls of the visual concx ant1 piecewise Fourier analysis.In: Moc1el.s of tlre Visrrcrl Corto.~,Rose D. Dohson VG. eds. NewYork: Wiley. pp. 265-272King J. Xie M. Zhcng B, Pribram KH (1994): Spectral dens ity maps ofreceptive fields i n the rat's somatosensory cortex. I n 0ri~irr.s: rrrincirrtl Sclf Or~crrrizcrtiorr.Pribrurn KH, cd. Hillsdale, NJ: Lawrence

Erlhaum Associates, Inc.Marcel.ja S 1 980) : Matlie~naticnllescription o fthc responses of simplecortical cells. J Opticcrl Soc 70: 1297-1 300Prihram KH (19 66): Some tlimensions of remembering: Step s towarda ncuropsychologic;~lmodel of memory. I n Mrronrrrolecr11e.s crrrclBe lrn~~ior .aito J. ed. New York: Academic Press. pp. 165-187Pribram KH, Lassonde MC, Ptito M (198 1): Classilication of receptivefield properties. Brrrirr Rex 43: 1 19-1 30Priblxm KH. Shnral'a( A. Bcekmwn GJ (1984): Frcqucncy encotlingi n motor systems. In Hrrrrrcrtr M o ior Acriorr: Uerrrsteir r Kecr.s.se.s.sec1,Whiting HTA. ed. Am sterdam : Elsevier. pp. 13 1-156Schmitt FO, Dev P. Smith BH (19 76): Electronic processing ofinformation by brain cells. Scierrce 193: 114-120

See also Mcrnory. distributed

Homeobox and nervous system developmentCahir J O KuneThe honieobox is a conserved DNA sequence of 180 base The homeodomnin is a DNA-binding domain that is partpairs, which codes for a protein dornain of 6 amino acids, of a larger protein. or homeoprotcin. Homeoproteins bindthe horneodomain. It was discovered in 1 984 as sequence specifically to DNA sequcnces adjaccnt to other genes andho~ nolo gy etween several genes that specify segment identity thus regulatc their transcription. They have evolvcd two distinctin the fruitfly I l roso / ~ l ~ i l r i .ince then, hundreds of horneobox- roles in animal development. First. they can determine thecontaining genes have been found throughout the eukaryotic identity and biological p roperties of piu-ticular cells, includingkingdom, in animals. fungi and plants. neural cells, by regulating w hich other proteins ar e expressed in