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R. Price

Marr, David (194580)

David Courtnay Marr was born on January 19, 1945in Essex, England. He attended Rugby, the Englishpublic school, on a scholarship, and went on to TrinityCollege, Cambridge. By 1966, he obtained his B.S. andM.S. in mathematics, and proceeded to work on hisdoctorate in theoretical neuroscience, under the super-vision of Giles Brindley. Having studied the literaturefor a year, Marr commenced writing his dissertation.The results, published in the form of three journalpapers between 1969 and 1971, amounted to a theoryof mammalian brain function, parts of which remainrelevant to the present day, despite vast advances inneurobiology in the past three decades. Marrs theorywas formulated in rigorous terms, yet was sufficientlyconcrete to be examined in view of the then availableanatomical and physiological data. Between 1971 and1972, Marrs attention shifted from general theory ofthe brain to the study of vision. In 1973, he joined theArtificialIntelligence Laboratory at the Massachusetts

Institute of Technology as a visiting scientist, takingon a faculty appointment in the Department ofPsychology in 1977, where he was made a tenured fullprofessor in 1980. In the winter of 1978 he wasdiagnosed with acute leukemia. David Marr died onNovember 17, 1980, in Cambridge, Massachusetts.His highly influential book, Vision: A ComputationalInestigation into the Human Representation and Pro-cessing of Visual Information, which has redefined andrevitalized the study of human and machine vision,was published posthumously, in 1982.

1. A Theory of the Brain

Marrs initial work in neuroscience combined high-level theoretical speculation with meticulous synthesisof the anatomical data available at the time. Thequestion he chose to address is the nec plus ultra ofneuroscience: what is it that the brain does? Marrproposed a definite answer to this question for each

of three major brain structures: archicortex (thephylogenetically older part of the cerebral cortex), cer-ebellum, and neocortex. The three answers com-plement each other, rallying around the idea that thebrains central function is statistical pattern recog-nition and association, carried out in a very high-dimensional space of elemental features. The basicbuilding block of all three theories is a codon, or asubset of features, with which there may be associated

a cell, wired so as to fire in the presence of thatparticular codon.

In the first paper, Marr proposed that the cerebel-lums task is to learn the motor skills involved inperforming actions and maintaining posture (Marr1969). The Purkinje cells in the cerebellar cortex,presumably implementing the codon representation,associate (through synaptic modification) a particularaction with the context in which it is performed.Subsequently, the context alone causes the Purkinjecell to fire, which in turn precipitates the next elementalmovement. Thirty years later, a significant proportionof researchers working on the cerebellum seem toconsider this model as generally correcta strikingexception in a field where the nihil nisi bonomaxim isnot known to be observed.

The next paper (Marr 1970) extended the codontheory to encompass a more general kind of statisticalconcept learning, which he assessed as capable ofserving many of the aspects of the brains function(the vagueness of this aspect of the theory would leadhim soon to abandon this approach, which, as herealized all along, was once removed from thedescription of any task the cerebrum might perform).How can a mere handful of techniques for organizinginformation (such as the codon representation) sup-port a general theory of the brain function? Marrsviews in this matter are profoundly realist, and arebased on a postulate of the prevalence in the world ofa particular kind of statistical redundancy, which ischaracterized by a Fundamental Hypothesis, statingthat Where instances of a particular collection ofintrinsic properties (i.e., properties already, diagnosedfrom sensory information) tend to be grouped suchthat if some are present, most are, then other usefulproperties arelikely to exist which generalize over suchinstances. Further, properties often are grouped in thisway (Marr 1970 pp. 15051). These ideas presagedmuch of the later work by others on neural networkmodels of brain function, which invoke the intuitionof learning as optimization (mountain climbing) inan underlying probabilistic representation space.

A model at whose core is the tallying of probabilitiesof events needs an extensive memory of a special kind,

allowing retrieval based on the content, rather thanthe location, of the items. Marrs third theoreticalpaper considers the hippocampus as a candidate forfulfilling this function (Marr, 1971). In analyzing thememory capacity and the recall characteristics of thehippocampus, Marr integrated abstract mathematical

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(combinatorial) constraints on the representationalcapabilities of codons with concrete data derived fromthe latest anatomical and electrophysiological studies.The paper postulated the involvement in learning ofsynaptic connections modifiable by experienceanotion originating with the work of Donald Hebb (seeHebb, Donald Olding (190485)) in the late 1940s anddiscussed by Marrs mentor Brindley in a 1969 paper.Marr provided a mathematical proof of efficient

partial content-based recall by his model, and offereda functional interpretation of many anatomical struc-tures in the hippocampus, along with concrete test-able predictions. Many of these (such as the existencein the hippocampus of experience-modifiable synap-ses) were subsequently corroborated (see the reviewsin Vaina 1990).

2. The MIT Period

A consummation of this three-prolonged effort todevelop an integrated mathematical-neurobiologicalunderstanding of the brain would in any case haveearned Marr a prominent place in a gallery, spanning

two and a half centuries (from John Locke (seeLocke,John (16321704)) to Kenneth Craik) of BritishEmpiricism, the epistemological stance invariablymost popular among neuroscientists. As it were,having abandoned the high-theory road soon after thepublication of the hippocampus paper, Marr went onto make his major contribution to the understandingof the brain by essentially inventing a field and a modeof study: computational neuroscience. By 1972, thefocus of his thinking in theoretical neurobiologyshifted away from abstract theories of entire brainsystems, following a realization that without anunderstanding of specific tasks and mechanismstheissues from which his earlier theories were onceremovedany general theory would be glaringlyincomplete.

Marr first expressed these views in public at aninformal workshop on brain theory, organized in 1972at the Boston University by Benjamin Kaminer. In hisopening remarks, he suggested an inverse square lawfor theoretical research, according to which the valueof a study varies inversely with the square of itsgeneralityan assessment that favors top-downreasoning anchored in functional (computational)understanding, along with bottom-up work groundedin an understanding of the mechanism, but nottheories derived from intuition, or models built onsecond-hand data.

The new methodological stance developed by Marr

following the shift in his views is summarized in aremarkably lucid and concise form in a two-page bookreview in Science, titled Approaches to BiologicalInformation Processing (Marr 1975). By that time,Marr came to believe firmly that the field of biologicalinformation processing had not yet accrued an em-

pirical basis sufficient for guiding and supporting aprincipled search for a general theory. Remarking thatthe brain may turn out to admit of no general theoriesexcept ones so unspecific as to have only descriptiveand not predictive powersa concern echoed in oneof his last papers (Marr 1981)he proceeded to mounta formidable critique of the most common of thetheories circulated in the early, 1970s, such as cata-strophe theory and neural nets (the current popu-

larity of dynamical systems and of connectionism,taken along with the integration of Marrs criticalviews into the mainstream theoretical neurobiology,should fascinate any student of the history of ideas).

The main grounds for his argument, which wasfurther shaped by an intensive and fruitful interactionwith Tomaso Poggio (Marr and Poggio 1977), wereprovided by an observation that subsequently grewinto a central legacy of Marrs career: the under-standing of any information processing system isincomplete without insight into the problems it faces,and without a notion of the form that possiblesolutions to these problems can take. Marr and Poggiotermed these two levels of understanding compu-tationalandalgorithmic, placing them above the third,

implementational, level, which, in the study of thebrain, refers to the neuroanatomy and neuro-physiology of the mechanisms of perception, cog-nition, and action.

Upon joining the MIT AI Lab, Marr embarked ona vigorous research program seeking computationalinsights into the working of the visual system, andputting them to the test of implementation as com-puter models. Marrsthinking in the transitionalstage,at which he treated computational results on par withneurobiological findings, is exemplified by the paperon the estimation of lightness in the primate retina(Marr 1974); subsequently, much more weight wasgiven in his work to top-down, computational-theoryconsiderations. This last period in Marrs work isepitomized by the theory of binocular stereopsis,developed in collaboration with Poggio, and presentedin a series of ground-breaking papers (Marr andPoggio 1976, Marr and Poggio 1979). At that time,Marr also worked on low-level image representation(Marr 1976, Marr and Hildreth 1980), and on shapeand action categorization (Marr and Nishihara 1978,Marr and Vaina 1982). Marrs book, Vision, writtenduringthe last months of his life, is as much a summaryof the views of what came to be known as the MITschool of computational neuroscience as it is apersonal credo and a list of achievements of thesecondpart of Marrs scientific endeavor, which lasted fromabout 1972 to 1980.

3. Legacy

The blend of insight, mathematical rigor, and deepknowledge of neurobiology that characterizes Marrs

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work is reminiscent of the style of such titans ofneuroscience as Warren McCullochexcept thatMcCullochs most lasting results were produced incollaboration with a mathematician (Walter Pitts),whereas Marr did his own mathematics. A decadeafter his quest was cut short, it has been claimed boththat Marr is cited more than he is understood(Willshaw and Buckingham 1990), and that his in-fluence permeates theoretical neurobiology more than

what one would guess from counting citations(McNaughton 1990). Still, contributors to the main-stream journals in neurobiology now routinely refer tothe computations carried out by the brain, and themost exciting developments are those prompted (or atleast accompanied) by computational theories.

In computer vision (a branch of artificial intel-ligence), the influence of Marrs ideas has beencomplicated by the dominance of the top-downinterpretation of his methodology: proceeding from anotion of what needs to be done towards the possiblesolutions. For some time, Marrs school was identifiedwith the adherents of a particular computationaltheory of vision, which claims that constructing aninternal model of the world is a prerequisite for

carrying out any visual task. The accumulation offindings to the contrary in neurobiology and in thebehavioral sciences gradually brought to the fore thepossibility that vision does not require geometricreconstruction. This encouraged researchers to seekalternative theories, some of which employ conceptsand techniques that did not exist in the 1970s, or werenot known to the scholars of vision at the time. Thesenew ideas, in turn, are making their way into neuro-science, as envisaged by Marr.

On a more general level, Marrs work provided asolid proof that a good theory in behavior and brainsciences need not have to trade off mathematical rigorfor faithfulness to specific findings. More importantly,it emphasized the role of explanation over and abovemere curve fitting, making it legitimate to ask why aparticular brain process is taking place, and not merelywhat differential equation can describe it.

See also: Cognitive Neuroscience; ComputationalNeuroscience; Concept Learning and Representation:Models; Feature Representations in Cognitive Psy-chology; Information Processing Architectures: Fun-damental Issues; Mental Representations, Psychologyof; Neural Plasticity in Visual Cortex; Neural Repre-sentations of Objects; Perception and Action; VisualPerception, Neural Basis of; Visual System in theBrain

Bibliography

Marr D 1969 A theoryof cerebellar cortex. Journal of PhysiologyLondon202: 43770

Marr D 1970 A theory for cerebral neocortex.Proceedings of theRoyal Society of London B176: 161234

Marr D 1971 Simple memory: a theory for archicortex.Philosophical Transactions of the Royal Society of London B262: 2381

Marr D 1974 The computation of lightness by the primateretina.Vision Research 14: 137788

Marr D 1975 Approaches to biological information processing.Science190: 8756

Marr D 1976 Early processing of visual information. Philo-

sophical Transactions of the Royal Society of London B275:483524

Marr D 1981 Artificial intelligence a personal view. In: Hauge-land J (ed.)Mind Design. MIT Press, Cambridge, MA, Chap.4, pp. 12942

Marr D 1982 Vision: A Computational Inestigation into theHuman Representation and Processing of Visual Information.W. H. Freeman, San Francisco, CA

Marr D, Hildreth E 1980 Theory of edge detection. Proceedingsof the Royal Society of London B207: 187217

Marr D, Nishihara H K 1978 Representation and recognition ofthe spatial organization of three dimensional structure.Proceedings of the Royal Society of London B200: 26994

Marr D C, Poggio T 1976 Cooperative computation of stereodisparity.Science194: 2837

Marr D C, Poggio T 1977 From understanding computation to

understanding neural circuitry. Neurosciences Research Pro-gram Bulletin 15: 47091

Marr D, PoggioT 1979 A computational theoryof human stereovision. Proceedings of the Royal Society of London B 204:30128

Marr D, Vaina L M 1982 Representation and recognition of themovements of shapes. Proceedings of the Royal Society ofLondon B214: 50124

McNaughton B L 1990 Commentary on simple memory: Atheory of the archicortex. In: Vaina L M (ed.)From the Retinato the Neocortex: Selected Papers of Daid Marr. Birkhauser,Boston, MA, pp. 1218

Vaina L M (ed.) 1990From the Retina to the Neocortex: SelectedPapers of Daid Marr. Birkhauser, Boston, MA

Willshaw D J, Buckingham J T 1990 An assessment of Marrstheory of the hippocampus as a temporary memory store.

Philosophical Transactions of the Royal Society of London B329: 20510

S. Edelman and L. M. Vaina

Marriage

1. The Definition of Marriage

Marriage has been a central area of study since thebeginnings of anthropology, as a main factor inexplaining the variety of kinship systems (Morgan1870, Rivers 1914). The institution of marriage,however, has not been easy to define as an anthro-pological concept.

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Copyright 2001 Elsevier Science Ltd. All rights reserved.International Encyclopedia of the Social & Behavioral Sciences ISBN: 0-08-043076-7