Embodiments of Mind

Embodiments of Mind

Warren S. McCulloch

The MIT Press

Cambridge, Massachusetts

London, England

© 2016 Massachusetts Institute of Technology

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Library of Congress Cataloging-in-Publication Data

Names: McCulloch, Warren S. (Warren Sturgis), 1898–1969 author.

Title: Embodiments of mind / Warren S. McCulloch ; foreword by Michael A. Arbib, Jerome Y. Lettvin ; introduction by Seymour A. Papert.

Description: Cambridge, MA : The MIT Press, 2016. | Includes bibliographical references and index.

Identifiers: LCCN 2016010806 | ISBN 9780262529617 (pbk. : alk. paper)

eISBN 9780262340946

Subjects: LCSH: Cybernetics. | Knowledge, Theory of. | Psychophysiology.

Classification: LCC Q303 .M3 2016 | DDC 003.5—dc23 LC record available at https://lccn.loc.gov/2016010806

ePub Version 1.0

d_r0

Table of Contents

Title page

Copyright page

Foreword to the 2016 Reissue

Foreword to the 1988 Reissue

Preface

Acknowledgments

Introduction

1 What Is a Number, That a Man May Know It, and a Man, That He May Know a Number?

2 A Logical Calculus of the Ideas Immanent in Nervous Activity

3 A Heterarchy of Values Determined by the Topology of Nervous Nets

4 How We Know Universals: The Perception of Auditory and Visual Forms

5 Modes of Functional Organization of the Cerebral Cortex*

6 Why the Mind Is in the Head

7 Through the Den of the Metaphysician

8 Mysterium Iniquitatis of Sinful Man Aspiring into the Place of God

9 Effects of Strychnine with Special Reference to Spinal Afferent Fibres*

10 Reflex Inhibition by Dorsal Root Interaction*

11 Toward Some Circuitry of Ethical Robots or an Observational Science of the Genesis of Social Evaluation in the Mind-Like Behavior of Artifacts*

12 Agathe Tyche: Of Nervous Nets—the Lucky Reckoners

13 Where Is Fancy Bred?

14 What the Frog’s Eye Tells the Frog’s Brain*

15 Finality and Form in Nervous Activity

16 The Past of a Delusion

17 Machines That Think and Want

18 The Natural Fit

19 A Historical Introduction to the Postulational Foundations of Experimental Epistemology*

20 Physiological Processes Underlying Psychoneuroses

21 What’s in the Brain That Ink May Character?*

Afterword: Warren McCulloch’s Search for the Logic of the Nervous System

Index

List of Illustrations

Figure 2.1a 10937_e002_049.jpg

Figure 2.1b 10937_e002_050.jpg

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Figure 2.1e 10937_e002_053.jpg

Figure 2.1f

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Figure 2.1i

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 4.2 Impulses of some chord enter slantwise along the specific afferents, marked by plusses, and ascend until they reach the level ℳa in the columns of the receptive layer activated at the moment by the nonspecific afferents. These provide summation adequate to permit the impulses to enter that level but no other. From there the impulses descend along columns to the depth. The level in the column, facilitated by the nonspecific afferents, moves repetitively up and down, so that the excitement delivered to the depths moves uniformly back and forth as if the sounds moved up and down together in pitch, preserving intervals. In the deep columns various combinations are made of the excitation and are averaged during a cycle of scansion to produce results depending only on the chord.

Figure 4.1 Vertical section of the primary auditory cortex in the long axis of Heschl’s gyrus, stained by Nissl’s method which stains only cell bodies. Note that the columnar cortex, typical of primary receptive areas, shows two tiers of columns, the upper belonging to the receptive layer IV and the lower, lighter stained, to layer V.

Figure 4.3 Impulses relayed by the lateral geniculate from the eyes ascend in specific afferents to layer IV where they branch laterally, exciting small cells singly and larger cells only by summation. Large cells thus represent larger visual areas. From layer IV impulses impinge on higher layers where summation is required from nonspecific thalamic afferents or associative fibers. From there they converge on large cells of the third layer which relay impulses to the parastriate area 18 for addition. On their way down they contribute to summation on the large pyramids of layer V which relays them to the superior colliculus.

Figure 4.4a The following is the original caption. Kleine und mittelgrosse Pyramidenzellen der Sehrinde eines 20 tägigen Neugeborenen (Fissura calcarina). A, plexiforme Schicht; B, Schicht der kleinen Pyramiden; C, Schicht der mittelgrossen Pyramiden; α, absteigender Axencylinder; b, rückläufige Collateralen; c, Stiele von Riesenpyramiden.

Figure 4.4b The following is the original caption. Schichten der Sternzellen der Sehrinde des 20 tägigen Neugeborenen (Fissura calcarina). A, Schicht der grossen Sternzellen; a, halbmondförmige Zellen ; b, horizontale Spindelzelle; c, Zellen mit einem zarten radiären Fortsatz; e, Zelle mit gebogenem Axencylinder; B, Schicht der kleinen Sternzellen; f, horizontale Spindelzellen; g, dreieckige Zellen mit starken gebogenen Collateralen; h, Pyramiden mit gebogenem Axencylinder, an der Grenze der fünften Schicht; C, Schicht der kleinen Pyramiden mit gebogenem Axencylinder.

Figure 4.5a The following is the original caption. Coupe sagittale montrant l’ensemble des fibres optiques du tubercule quadrijumeau antérieur; souris âgée de 24 heures. Méthode de Golgi. A, écorce grise du tubercule antérieur; C, courant superficiel des fibres optiques; D, courant profond; E, région postérieure du corps genouille externe; b, foyer où se terminent des collatérales des fibres optiques; c, nids péricellulaires formés par les fibres optiques; d, fibres transversalea de la couche ganglionnaire.

Figure 4.5b The following is the original caption. Coupe transversale du tubercule quadrijumeau antérieur; lapin âgé de 8 jours. Méthode de Golgi. A, surface du tubercule tout près de la ligne médiane; B, couche grise superficlelle ou couche cendrée de Tartuferi comprenant les zones des cellules horizontales et des cellules fusiformes verticales; C, couche des fibres optiques; D, couche des fibres transversales ou zone blanc cendré profonde de Tartuferi; L, M, cellules de la couche ganglionnaire ou des fibres transversales; a, cellules marginales; b, cellules fusiformes transversales ou horizontales; c, autre cellule de même espèce, montrant bien son cylindre-axe; d, petites cellules à bouquet dendritique compliqué; e, cellules fusiformes verticales; f , g, differents types cellulaires de la couche grise superficielle; h, j, cellules fusiformes de la zone des fibres optiques; m, collatérale descendante allant à la substance grise centrale; n, arborisation terminale des fibres optiques.

Figure 4.6 A simplified diagram showing occular afferents to left superior colliculus, where they are integrated anteroposteriorly and laterally and relayed to the motor nuclei of the eyes. A figure of the right superior colliculus mapped for visual and motor response by Apter is inserted. An inhibiting synapse is indicated as a loop about the apical dendrite. The threshold of all cells is taken to be one.

Figure 6.1 Effect of a light flash upon alpha rhythm.

Figure 9.1 Each pair of traces shows (upper) the response traveling antidromically in the dorsal root and (lower) the response orthodromically in the ventral root. Two succeedingstimuli are given by a bipolar microelectrode in the ventral horn of the segment of the recording roots (L7). Upper pair: normal responses of the sensory afferent fibers and the motor horn cells. Center pair: responses after 0.2 cc IV strychnine. Lower pair: responses after a further 0.3 cc strychnine. Bottom: time in milliseconds. There is no change in the height of the volley evoked from the motor horn cells; there is a decrease in that from the terminal afferent arborizations.

Figure 9.2 The effect of strychnine on the early components of the dorsal root potential. a: Continuous line shows the shape of the first four components of the dorsal root potential as recorded in one preparation. The dotted line shows the effect on these potentials of a tetanus delivered to the recording root. b–d: The continuous line shows the shape before strychnine of the first four components. The dotted line shows the effect of (b) 0.2 cc, (c) 0.4 cc, and (d) 0.6 cc of intravenous strychnine on the shape of these components.

Figure 9.3 Top: strychnine was applied to nuclei cuneatus and gracilis. The trace shows a single spike being generated within the nucleus. Center: at the same time a recording is taken from the seventh lumbar dorsal, root 2 cm from the cord. An antidromically running spike is seen running out in the root. Bottom: time in 2 milliseconds and 10 milliseconds.

Figure 10.1 Tracing of cross section of cat spinal cord between L4 and L5 showing the 162 positions from which the potentials were recorded. Area analyzed is approximately 2.7 mm. by 1.8 mm.

Figure 10.2 Right: distribution of isopotentials within spinal cord 20 msec. after conditioning root L6, alone, had been stimulated. This time was found to be that at which stimulation of root L6 exerted its maximum inhibitory effect on reflex following stimulation of test root L5. Left: distribution of sources (diagonal lines) and sinks (dots) within spinal cord 20 msec. after stimulation of conditioning root. Each dot or line represents an equal amount of source-density. For interpretation see text.

Figure 10.3 Top left: distribution of sources (lines) and sinks (dots) 1.2 msec. after test root L5, alone, had been stimulated. This is pattern of earliest disturbance recorded in region after test stimulation. Bottom left: isopotential map 1.2 msec. after stimulation of L5 alone. Top right: source-sink map 1.2 msec. after stimulating test root but preceded 20 msec. by stimulation of inhibitory conditioning root L6. This shows that earliest sign of arriving volley in white matter is inhibited by preceding volley. Bottom right: isopotential map 1.2 msec. after stimulating test root but preceded 20 msec. earlier by conditioning volley.

Figure 10.5 Arranged as in Figures 10.3 and 10.4; top left, source-sink distribution, and bottom left, isopotential map, 2.8 msec. after stimulation of test root alone. Top right, source-sink distribution, and bottom right, isopotential map, at the same time after test root volley but preceded 20 msec. by conditioning volley.

Figure 10.4 Arranged as in Figure 10.3; top left, source-sink distribution, and bottom left, isopotential distribution, 1.6 msec. after stimulation of test root L5. Top right, source-sink map, and bottom right, isopotential map, at the same time after test volley but preceded 20 msec. by inhibitory conditioning volley.

Figure 10.6 See text.

Figure 10.7 See text.

Figure 10.8 See text.

Figure 12.1 Venn figures with spaces for all intersections of δ classes. S is the number of spaces; F, the number of functions.

Figure 12.2 Synaptic diagrams for 10937_012_fig_0052.jpg appearing before 10937_012_fig_0053.jpg .

Figure 12.3 A logically stable net for 10937_012_fig_0054.jpg .

Figure 12.4 A best stable net for 10937_012_fig_0055.jpg .

Figure 12.5 A best unstable net for 10937_012_fig_0056.jpg .

Figure 12.6 Unstable improvement net for 10937_012_fig_0057.jpg .

Figure 12.7 Alternating improvement net for ×.

Figure 12.8 Input δ = 3, output degenerate δ = 3 neuron for 10937_012_fig_0058.jpg .

Figure 12.9 Input δ = 2, output degenerate δ = 3 neuron for 10937_012_fig_0059.jpg .

Figure 12.10 Flexible net, always unstable.

Figure 12.11 Flexible net, logically stable for 10937_012_fig_0060.jpg .

Figure 14.1a (a) This is a diagram of the frog retina done by Ramón y Cajal over 50 years ago [9]. The rods and cones are the group of elements in the upper left quarter of the picture. To their bushy bottom ends are connected the bipolar cells of the intermediate layer, for example, f, g, and h. Lateral connecting neurons, called horizontal and amacrine cells, also occur in this layer, for example, i, j, and m. The bipolars send their axons down to arborize in the inner plexiform layer, roughly the region bounded by cell m above and the bodies of the ganglion cells, o, p and q, below. In this sketch, Ramón has the axons of the bipolar cells emitting bushes at all levels in the plexiform layer; in fact, many of them branch at only one or two levels. Compare the dendrites of the different ganglion cells. Not only do they spread out at different levels in the plexiform layer, but the patterns of branching are different. Other ganglion cells, not shown here, have multiple arbors spreading out like a plane tree at two or three levels. If the terminals of the bipolar cells are systematically arranged in depth, making a laminar operational map of the rods and cones in terms of very local contrast, color, ON, OFF, etc., then the different shapes of the ganglion cells would correspond to different combinations of the local operations done by the bipolars. Thus would arise the more complex operations of the ganglion cells as described in the text.

Figure 14.1b (b) This is Ramόn y Cajal’s diagram of the total decussation or crossing of the optic nerve fibers in the frog [9]. He made this picture to explain the value of the crossing as preserving continuity in the map of the visual world. O is the optic nerve and C is the superior colliculus or optic tectum (the names are synonymous).

Figure 14.1c (c) This is Ariens-Kapper’s picture of the cross section of the brain of a frog through the colliculus, which is the upper or dorsal part above the enclosed space.

Figure 14.1d (d) This is Pedro Ramón Cajal’s diagram of the nervous organization of the tectum of a frog. The terminal bushes of the optic nerve fibers are labeled a, b, and c. In this diagram A, B, C, D, and E are tectal cells receiving from the optic nerve fibers. Note that the axons of these cells come off the dendrites in stratum 7, which we call the palisade layer. The endings discussed in this paper lie between the surface and that stratum.

Figure 14.2 Operation 1—contrast detectors. The records were all taken directly with a Polaroid camera. The spikes are clipped at the lower end just above the noise and brightened on the screen. Occasional spikes have been intensified by hand for purposes of reproduction. The resolution is not good, but we think that the responses are not ambiguous. Our alternate recording method is by means of a device that displays the logarithm of pulse interval of signals through a pulse height pick-off. However, such records would take too much explanation and would not add much to the substance of the present paper. (a) This record is from a single fiber in the optic nerve. The base line is the output of a photocell watching a somewhat larger area than the receptive field of the fiber. Darkening is given by downward deflection. The response is seen with the noise clipped off. The fiber discharge to movement of the edge of a 3° black disk passed in one direction but not to the reverse movement. (Time marks, 20 per second.) (b) The same fiber shown here giving a continued response when the edge stops in the field. The response disappears if the illumination is turned off and reappears when it is turned on. Below is shown again the asymmetry of the response to a faster movement. (Time marks, 20 per second.) (c) The same fiber is stimulated here to show asymmetrical response to the 3° black object moved in one direction, then the reverse, and the stimuli are repeated under a little less than a 3-decade change of illumination in two steps. The bottom record is in extremely dim light, the top in very bright light. (Time marks, 20 per second.) (d) In the bottom line, a group of endings from such fibers is shown recorded from the first layer in the tectum. A black disk 1° in diameter is moved first through the field and then into the field and stopped. In the top line, the receptive field is watched by a photomultiplier (see text), and darkening is given by upward deflection. (Time marks, 5 per second for all tectal records.) (e) OFF and ON of general illumination has no effect on these fibers. (f) A 3° black disk is moved into the field and stopped. The response continues until the lights are turned OFF but reappears when the lights are turned ON. These fibers are nonerasable. (g) A very large black square is moved into the field and stopped. The response to the edge continues so long as the edge is in the field. (h) The 3° disk is again moved into the field and stopped. When it leaves, there is a slight after-discharge. (i) A l° object is moved into the field, stopped, the light is then turned off, then on, and the response comes back. The light is, however, a little less than 300× dimmer than in the next frame. Full ON and OFF are given in the rectangular calibration on the right. (j) The same procedure as in Fig. 14.2i is done under very bright light. The return of response after reintroducing the light seems more prolonged—but this is due only to the fact that, in Fig. 14.2i, the edge was not stopped in optimal position.

Figure 14.3 Operation 2—convexity detectors. The photomultiplier is used, and darkening is an upward deflection. (a) These records are all from the second layer of endings in the tectum. In the first picture, a 1° black disk is imported into the receptive field and left there. (b) The same event occurs as in Fig. 14.3a, but now the light is turned off, then on again. The response is much diminished and in the longer record vanishes. These fibers are erasable. (c) The 1° disk is passed through the field first somewhat rapidly, then slowly, then rapidly. The light is very bright. (d) The same procedure occurs as in Fig. 14.3c, but now the light has been dimmed about 300×. The vertical line shows the range of the photomultiplier, which has been adjusted for about 3½ decades of logarithmic response. (e) A 1° black disk is passed through the field at three speeds. (f) A 15° black strip is passed through at two speeds, edge leading. (g) A 15° black strip is passed through in various ways with corner leading. (h) The same strip as in Fig. 14.3g is passed through, edge leading.

Figure 14.4 Operation 3—moving-edge detectors. The first two pictures are taken from a single fiber in the optic nerve. (a) Shows a 7° black disk moving through the receptive field (the photocell was not in registration with the field). There is a response to the front and back of the disk independent of illumination. There is about a 300:1 shift of illumination between top and bottom of the record. Darkening is a downward deflection with the photocell record. (Time marks, 5 per second.) (b) OFF and ON of general lighting. (Time marks, 50 per second.) Note double responses and spacing. (c) This and succeeding records are in the third layer of endings in the tectum. Several endings are recorded but not resolved. Darkening is an upward deflection of the photomultiplier record. The response is shown to the edge of a 15° square moved into and out of the field by jerks in bright light. (d) The same procedure occurs as in Fig. 14.4c, but in dim light. Calibration figure is at the right. (e) The response is shown to a 7° black disk passed through the receptive fields under bright light. The sweep is faster, but the time marks are the same. (f) The same procedure as for Fig. 14.4e, but under dim light. The OFF and ON of the photomultiplier record was superimposed for calibration. (g) OFF and ON response with about half a second between ON and OFF. (h) Same as Fig. 14.4g, but with 2 seconds between OFF and ON.

Figure 14.5 Operation 4—dimming detectors. (a) This and the next frame are taken from a single fiber in the optic nerve. Here we see the response to a 7° black disk passing through the receptive field. The three records are taken at three illumination levels over a 300:1 range. In the phototube record, darkening is a downward deflection. (Time marks, 5 per second.) (b) OFF and ON of light. The OFF was done shortly after one sweep began, the ON occurred a little earlier on the next sweep. The fiber is silenced completely by the ON. (Time marks, 5 per second.) (c) In this and the three next frames, we are recording from the fourth layer of endings in the tectum. This frame shows the response to turning OFF the general illumination. (d) OFF and ON of light at regular intervals. (e) OFF then ON of the light to a lesser brightness. (f) OFF, then ON, of the light to a still lesser brightness. The level to which the ON must come to abolish activity decreases steadily with time. (g) The synchrony of the dimming detectors as described in the text. At the top are three or four fibers recorded together in the optic nerve when the light is suddenly turned off. The fibers come from diverse areas on the retina. In the second line are the oscillations recorded from the freshly cut retinal stump of the optic nerve when the light is suddenly turned off. In the third line are the oscillations recorded on the surface of the tectum, the visual brain, before the nerve was cut. Again the light is suddenly turned off. The last line is 20 cps. These records of synchrony were obviously not all made at the same time, so that comparing them in detail is not profitable.

Figure 17.1

Figure 17.2

Figure 17.3

Figure 17.4 A simplified diagram showing occular afferents to left superior colliculus, where they are integrated anteroposteriorly and laterally and relayed to the motor nuclei of the eyes. A figure of the right superior colliculus mapped for visual and motor response by Apter is inserted. An inhibiting synapse is indicated as a loop about the apical dendrite. The threshold of all cells is taken to be one. This diagram is used through the courtesy of the Bulletin of Mathematical Biophysics.

Figure 17.5

Figure 20.1 Gasser’s diagram

Foreword to the 2016 Reissue

Michael A. Arbib

Nineteen forty-three was the year that Warren McCulloch (1898–1969), then Professor of Neurology at the University of Illinois in Chicago, turned forty-five and Walter H. Pitts (1923–1969), a protégé of McCulloch and the mathematical logician Rudolf Carnap, turned twenty. And 1943 was the year that McCulloch and Pitts published a paper, A Logical Calculus of the Ideas Immanent in Nervous Activity, that helped change the world—three times. In the 1940s, it linked the computability of Turing machines to a controller that could be implemented by a network of highly formalized neurons (now known as McCulloch-Pitts neurons); in the late 1950s/early 1960s, it helped foster the emergence of artificial intelligence; and in the 1980s, it formed a jumping off point for the rise of an adaptive distributed computing technology, connectionism/artificial neural networks.

In 1965, McCulloch selected twenty-one of his papers, and these were published by the MIT Press as Embodiments of Mind with a short preface by McCulloch and an introduction by Seymour Papert. In 1988, Embodiments was reprinted with the addition of a foreword by Jerry Lettvin. And now, in 2016, a new reprinting adds this foreword plus my biographical sketch Warren McCulloch’s Search for the Logic of the Nervous System as afterword—two slices of bread for the McCulloch sandwich. For some readers, the afterword may be the best way to frame a reading of McCulloch’s selection of papers, but the purpose of this foreword is to offer a brief guide to his selection. And here I must confess that I have not decoded the logic whereby McCulloch chose to order his papers—they are neither ordered chronologically nor grouped by theme. But let me frame McCulloch’s world view by introducing the earlier front matter.

McCulloch’s introduction is brief but makes two crucial points:

The book presents an attempt to found what he refers to as a physiological theory of knowledge and as experimental epistemology. Although trained as a neurologist, McCulloch was (as the afterword makes clear) always motivated by the quest to understand the human mind, and it is thus fitting that, in a selection of papers ranging from 1943 to 1964, he chose to place What Is a Number, That a Man May Know It, and a Man, That He May Know a Number? (1961 [1]—i.e., originally published in 1961 and reprinted in this volume as chapter 1) first in this selection, for its title states the fundamental question of his career.

He acknowledges that his indebtedness to Walter Pitts is, of course, much greater than appears from our joint publications. However, Google Scholar (as sampled in mid-April of 2016) suggests that in the 40 years since McCulloch acknowledged this debt, the world has come to fully recognize it. In the Google Scholar search, McCulloch’s three most cited papers were A Logical Calculus of the Ideas Immanent in Nervous Activity by McCulloch and Pitts (1943 [2]; cited by over 12,000), What the Frog’s Eye Tells the Frog’s Brain by Lettvin, Maturana, McCulloch, and Pitts (1959 [14]; cited by over 1,800), and How We Know Universals: The Perception of Auditory and Visual Forms by Pitts and McCulloch (1947 [4]; cited by over 800).

Strangely, McCulloch asserts that "Except for three papers that were published in the Journal of Mathematical Biophysics, the articles were lectures, written over some twenty years for dissimilar audiences." But the book contains a number of other journal articles as well. However, the lectures have the special value that they can be read as timeless attempts by McCulloch to think his way toward the expression of an experimental epistemology.

Walter Pitts taught himself logic and mathematics. A correspondence with Bertrand Russell when he was twelve led him to attend Russell’s lectures at the University of Chicago in the fall of 1938. He stayed there without registering as a student. Russell led him to the logician Rudolf Carnap and his book The Logical Syntax of Language. Pitts was homeless. In 1938 he met Jerry Lettvin, then a pre-medical student, and they became firm friends. Later, McCulloch also arrived in Chicago, and in early 1942 invited Pitts and Lettvin to live with his family. Evening discussions led to the 1943 classic and in due course to the 1947 paper. In 1951 Norbert Wiener (author of the 1948 book Cybernetics: or Control and Communication in the Animal and the Machine that provided a key impetus to linking applied mathematics to biology) convinced Jerome Wiesner to bring Pitts, Lettvin, McCulloch, and Pat Wall to MIT in 1952, with funding in the Research Laboratory of Electronics. (The tragic story of the impact on Pitts of the later break between Wiener and McCulloch, presented in the afterword, is told at more length by Neil Smalheiser (2000): Walter Pitts, Perspectives in Biology and Medicine. 43(2): 217–226.)

In his foreword to the 1988 reprint of Embodiments, Jerry Lettvin (1920–2011) draws on his long friendship with McCulloch and Pitts to give an eyewitness account of the influence of Leibnitz on the development of A Logical Calculus of the Ideas Immanent in Nervous Activity (1943 [2]) and How We Know Universals: The Perception of Auditory and Visual Forms (1947 [4]). He also discusses how his collaboration, as the neurophysiologist, with the Chilean neuroanatomist Humberto Maturana was influenced by his own interest in giving the Kantian a priori a biological twist. However, I want to emphasize two points that add to our perspective on McCulloch’s work:

McCulloch published his collection in the infancy of Artificial Intelligence (AI) when it was being nurtured by Allen Newell and Herb Simon at Carnegie-Mellon University and by Marvin Minsky and John McCarthy at MIT and under a very different rubric in England. Only in 1961 had Minsky published his classic review paper, Steps Towards Artificial Intelligence (Proceedings of the IRE, 49: 8–30), and it is only in two papers from that same year that McCulloch mentions AI, and with the emphasis on artificial neural networks: in What Is a Number … (1961 [1]) and Where Is Fancy Bred? (1961 [13]). In 1969, Minsky and Seymour Papert (of whom more below) published Perceptrons, An Introduction to Computational Geometry with MIT Press, and many read this as proof that artificial neural networks could make no contribution to AI. (Perceptrons provided one example of McCulloch-Pitts neurons with a learning rule added to modify the weights of synaptic connections.) But what the book really showed was that if you restrict the networks to be simple, they can’t do much, and in 1986 David Rumelhart and Jay McClelland published the edited collection Parallel Distributed Processing (PDP; MIT Press), which included significant papers of their own, and acted as a catalyst (in association with a range of work by other authors) for the emergence of a new form of AI in which adaptive artificial neural networks, and machine learning more generally, would provide the crucial role, as is very much the case in 2016 where deep learning has met big data. Thus, Lettvin could write in 1988: We can observe the results of processing in the behavior of animals and in records taken from individual neurons, but we cannot account for either by mechanism. This is where a prior art is needed, some understanding of process design. And that is where AI, [and] PDP … enter in. … Enthusiasts in AI have long maintained that it is easier to build a human than to analyze one already in operation. That is essentially how Warren McCulloch thought, and it explains how he helped to lay the foundations of AI.

McCulloch published many papers in empirical neuroscience—see, for example, his work with Dusser de Barenne outlined in the afterword. These papers and many more can be found in the four-volume Collected Works of Warren S. McCulloch (Intersystems Publications, 1989), edited by Warren’s widow Rook McCulloch, with a preface by Heinz von Foerster and contributions (reminiscences, and commentaries on papers) by twenty former colleagues of McCulloch. But perhaps the more important point made by Lettvin was that, in developing experimental epistemology, McCulloch was less concerned with models that could be tested against the current data of empirical neuroscience than with charting plausible mechanisms that the brain might employ. Despite fifty years of new publications in empirical neuroscience (including imaging data on the human brain), much that we would want to know about how interacting neural networks support cognition remains outside the realm of what neurophysiology can currently measure. My chapter Evolving the Language-Ready Brain in the textbook From Neuron to Cognition via Computational Neuroscience (M. A. Arbib and J. J. Bonaiuto, eds., MIT Press, 2016) offers a sample of the pleasures and perils of seeking to bridge from computational models rooted in empirical data on the neurophysiology of the behaving macaque to the McCullochian attempt to develop an experimental epistemology that charts areas where we can only point to "this is how the brain might work," in the hope that this will stimulate experimentalists to conduct the experiments which can help us test and build upon these more speculative models. The afterword recounts Pat Wall’s hypothesis that it was Wiener’s inability to understand this distinction between current data and plausible but speculative mechanisms that led to the unfortunate break with McCulloch that hit Pitts so hard.

The preface to the original 1965 printing of Embodiments was written by Seymour Papert (b. 1928) who, unlike Lettvin, was a newcomer to the McCulloch group. Born in South Africa, Papert worked as a researcher in a variety of places, but especially with Jean Piaget (who styled himself a genetic epistemologist, focusing on the emerging construction of reality in the mind of the child; an interesting counterpoint to McCulloch’s experimental epistemology) at the University of Geneva from 1958 to 1963. At that time, Papert had lost his citizenship, due in part to his outspoken opposition to apartheid in South Africa, and was stateless. In 1962, McCulloch established a position for him at MIT, initiated the paperwork to get him travel papers and a US visa, and hired Rachel Fuchs as a secretary to help Papert once he arrived. Rachel left a year later, and it was only some time after that that Papert reached MIT in 1963. There he established a great rapport with Marvin Minsky as well as developing a theory of learning called constructionism, building upon his work with Piaget.

In the beginning of his introduction to the 1965 Embodiments, Papert remarks on McCulloch’s somewhat complex style of writing (he claimed to have been influenced by Robert Burton’s Anatomy of Melancholy) and is then at pains to distance McCulloch’s approach to experimental epistemology from the linguistic turn in then-current discussions of the mind-brain problem. He emphasizes that philosophy, neurology, and psychology each had settled modes of tackling problems, to none of which McCulloch conformed. Indeed, it is in part thanks to McCulloch and his network of colleagues that the methods of these disciplines have changed, with an increasing flow of ideas and data between them. Papert offers Kenneth Craik, Julian Bigelow, Arturo Rosenblueth, Norbert Wiener, and Jean Piaget as those whose work combined with that of McCulloch and Pitts in effecting this transformation. Complementing the biological a priori charted in What the Frog’s Eye Tells the Frog’s Brain, Piaget showed, according to Papert, that Kant’s schemas must be seen not as innate and unchangeable but can themselves be explained in terms of more fundamental processes … guided by his observation of children to formulate more precise theoretical tools for the conceptualization of the mechanisms of knowing. … Throughout, Papert’s guiding principle is that the common feature of the relevant proposals is their recognition that the laws governing the embodiment of mind should be sought among the laws governing information rather than energy or matter.

Of course, there is much worth reading in Lettvin and Papert’s pieces that is not summarized here, but with this it is time to offer a brief reading guide to the papers that follow. Here I simply group the papers included in Embodiments by theme (with the chapter number noted in brackets), and order them chronologically within each theme:

Papers from the Bulletin of Mathematical Biophysics

[2] W. S. McCulloch and Walter H. Pitts, A Logical Calculus of the Ideas Immanent in Nervous Activity, 1943.

[3] W. S. McCulloch, A Heterarchy of Values Determined by the Topology of Nervous Nets, 1945.

[4] Walter Pitts and W. S. McCulloch, How We Know Universals: The Perception of Auditory and Visual Forms, 1947.

Papers Focused on Empirical Studies of the Brain

[5] W. S. McCulloch, Modes of Functional Organization of the Cerebral Cortex, 1947.

[20] W. S. McCulloch, Physiological Processes Underlying Psychoneuroses, 1949.

[9] P. D. Wall, W. S. McCulloch, J. Y. Lettvin, and W. H. Pitts, Effects of Strychnine with Special Reference to Spinal Afferent Fibres, 1955.

[10] B. Howland, J. Y. Lettvin, W. S. McCulloch, W. Pitts, and P. D. Wall, Reflex Inhibition by Dorsal Root Interaction, 1955.

[14] J. Y. Lettvin, H. R. Maturana, W. S. McCulloch, and W. H. Pitts, What the Frog’s Eye Tells the Frog’s Brain, 1959.

Towards Reliable Networks from Unreliable Neurons

[12] W. S. McCulloch, Agathe Tyche: Of Nervous Nets—the Lucky Reckoners, 1958.

A Dig at Freud’s Future of an Illusion

[16] W. S. McCulloch, The Past of a Delusion, 1953.

Poetry

[18] W. S. McCulloch, The Natural Fit, 1959

Papers Exploring the Development of Experimental Epistemology

[7] W. S. McCulloch, Through the Den of the Metaphysician, 1948.

[17] W. S. McCulloch, Machines That Think and Want, 1950.

[6] W. S. McCulloch, Why the Mind Is in the Head, 1951.

[15] W. S. McCulloch, Finality and Form in Nervous Activity, 1952.

[8] W. S. McCulloch, "Mysterium Iniquitatis of Sinful Man Aspiring into the Place of God," 1955.

[11] W. S. McCulloch, Toward Some Circuitry of Ethical Robots or an Observational Science of the Genesis of Social Evaluation in the Mind-Like Behavior of Artifacts, 1956.

[1] W. S. McCulloch, What Is a Number, That a Man May Know It, and a Man, That He May Know a Number?, 1961.

[13] W. S. McCulloch, Where Is Fancy Bred?, 1961.

[19] W. S. McCulloch, A Historical Introduction to the Postulational Foundations of Experimental Epistemology, 1964.

[21] W. S. McCulloch, What’s in the Brain That Ink May Character?, 1964.

And with this summary to guide your choices, it is time to turn to the writings of W. S. McCulloch.

Foreword to the 1988 Reissue

Jerome Lettvin

There are two kinds of goals directing the current arts of artificial intelligence (AI), parallel distributed processing (PDP), and the hard-wired nets that process images or sounds. The first are products that are useful to industry and the military. This pays for the research. The second are ideas that play back into the study of brain. These ideas are most important because, while controversial, they represent the only successful notions so far in the study of brain as information processor.

The literature in neuroscience and psychology is now so large and growing so fast that no one can master what has been written or keep up with current work. That is because it is composed of endless empirics. There is no theory to give coherence to this mountain of data in terms of how the brain functions as a mechanism that sustains mental process. Since, in the end, that is the goal of neuroscience—to account for how such process can occur—the absence of working models points out how undeveloped is the discipline.

Some of the trouble comes from the physical intractability of nervous tissue. Signal-to-noise relations limit considerably the observations that can be made on a living system. What samples may be had are not enough, even in the simplest cases, to found a notion of the circuitry. But, even if ideally one could record from any element or part of an element in situ, it is not in the least obvious how the records could be interpreted. To a greater degree than in any other current science, we must know what to look for in order to recognize it. Precisely here is the deficit in neuroscience. We can observe the results of processing in the behavior of animals and in records taken from individual neurons, but we cannot account for either by mechanism.

This is where a prior art is needed, some understanding of process design. And that is where AI, PDP, and the whole investment in building [neurocomputational models of intelligence] enter in. Critics carp that the current golems do not resemble our friends Tom, Dick, or Harry. But the brute point is that a working golem is not only preferable to total ignorance, it also shows how processes can be designed analogous to those we are frustrated in explaining in terms of nervous action. It suggests what to look for. After all, golems now are capable of doing contingent tasks, of changing adaptively, and of showing processes that resemble induction and learning in a vague way.

Enthusiasts in AI have long maintained that it is easier to build a human than to analyze one already in operation. That is essentially how Warren McCulloch thought, and it explains how he helped to lay the foundations of Al. But it is a more remarkable position than appears at first.

McCulloch knew very well that single neurons are not gates but rather that each is a complex analog processor of analog data. In the brain any neuron receives as input a variety of different concurrent messages from other neurons. As output it expresses the running state history of its input by a running time series of pulses that in a way is much like language. It is almost as if an observer on a complex scene sends what he sees expressed in a code that uses continuous variability of pulse interval. The pulses do not signify clocked logical operations but simply define the important variable, the time between pulses. This sort of device is hard to think about in ensembles of neurons that are massively interconnected. It is no surprise that there are few interesting models of real nerve nets.

Knowing this, McCulloch nevertheless felt that much could be learned simply from considering pulse generators of any description under broad interconnection. Accordingly he subverted the notion of a neuron in a way that I will describe shortly.

Neuroscience, as I remarked earlier, has long been in the doldrums with respect to understanding the mechanisms used for information processing in nervous tissue. The main progress in neuroscience is in the fine anatomy and chemistry of the brain—the material substrate for the machine. Thus AI and related fields have grown almost independent of biology. But recently, with the revival of the perceptron in layered form (PDP), there are signs of a new liaison. For now there is the image of self-organizing neural nets which modify themselves according to the sort of instruction that is little more than the remarking of error. This development has had a great impact on neuroscience, cognitive science, and related fields. From the biological view the products of PDP are not related to actual living systems any more than those that have issued from AI. But the idea that distributed processing has important properties has struck a loud chord, and McCulloch would have loved to have heard it.

Real nervous systems are characterized by widely distributed many-to-many connections between neurons. Such connectivity is the rule rather than the exception. One neuron in the brain receives its input from thousands of others and distributes its output to yet thousands of others. This massive connectivity accounts for the despair of those who sought to model real nervous nets and for the sudden enthusiasm with which PDP has been greeted. In a sense there are properties of such connected systems that are more or less independent of the intrinsic nature of the nonlinear elements used, whether gates or neurons.

By now it is clear that the immediate future of study in the modeling of the brain lies with the synthesis of gadgets more than with the analysis of data. Sooner or later the modelers will have to winnow the empirics of neuroscience and psychology. But as it stands today, they are the avant-garde and are rolling.

It is only natural that students in this burgeoning art should be curious about its origins and about what the originators thought. That is why this book has been reissued. And students can dream of how to rewrite How We Perceive Universals had Warren McCulloch known of PDP.

Warren McCulloch chose the writings in this collection. It is a sampler rather than an omnibus; many important works are not included. And that is as it should be since Warren preferred gesture and allusion to a full picture with everything spelled out. This made him a most enjoyable teacher, somewhat cryptic, but in a way that enhanced his ideas rather than obscured them. He wrote, talked, and comported himself as a cavalier. I do not think any of his friends would have been surprised had he shown with a rapier slung at his side and wearing a plumed hat askew.

But his ideas rather than his person are the substance of this book. Some of them call for a perspective rather than a commentary, and that may be the best service for a preface.

Two essays with Walter Pitts (one on the logical calculus possible with neuronal arrays, the other on perceiving universals) were, as best I know, the first attempt at a theory of how the mechanism of the brain can sustain mental process. These two papers are at the foundation of what later became known as artificial intelligence. Because Walter and I were living with Warren at the time the papers were spawned, I can provide some background.

The drive behind Warren’s and Walter’s approach came from Leibnitz, who was Walter’s favorite philosopher and whom Warren much admired. Leibnitz had shown that all logic could be reduced to an arithmetic and the arithmetic expressed in binary notation. Indeed he had done much of what was later issued independently by Boole. He conceived a logic engine that could compute any computable number by carrying out a chosen series of algebraic operations—what we now call algorithms. And he spent a fortune trying to realize it. At the same time, Leibnitz was sharply aware that the very notion of such a machine raises some basic questions in epistemology. Some of his ideas are in part given in the Monadology, wherein he contrasts the principle of contradiction with the principle of sufficient reason, and the eternal truths of logic with the contingent truths of observation on the world. Such a dual approach to the nature of brain as meat machine (to use Minsky’s epithet) begins in the seventeenth century with Descartes and Leibnitz, among others.

Once it was realized in the nineteenth century that nerve fibers conduct electrical pulses and that the pulse trains on these fibers carry meaningful messages, the problem was to account for how such information was processed by the brain as nerve net. Both excitation and inhibition had been shown as nervous actions before 1900, but it was not until David Lloyd’s work in 1939–41 that the direct monosynaptic inhibitory and excitatory actions of nervous pulses were demonstrated. This finding, more than anything else, led Warren and Walter to conceive of single neurons as doing logical operations (à la Leibnitz and Boole) and acting as gates. Their concept was the first and most inspired attempt at a theory of nervous action that transcended Sherrington’s earlier town-meeting model of central excitatory and inhibitory states, as if the strength of a proposed action could be measured by a simple continuous tally of yea and nay votes. Once this idea of neurons as logical gates was clear, Warren and Walter had to lay out the designing of them and then the ways of connecting them for specific operations; and this they did in engineering style with great verve. It doesn’t matter that the rigor was not perfect—and the neurons very different from real ones—they were concerned more with the notion of working devices than with formal completeness of the system.

That ambition—to show how mental process is sustainable by nervous mechanism—comes to its height in the paper on how universals might be perceived. Here they took what was known of the architecture of the brain cortex to show how relations between the parts of a form could survive changes of scale of the form. It is a remarkable venture, as ingenious in its marriage of anatomy and function as it is purposely naive. Having devised the logical calculus [of] nervous activity, Walter and Warren were obliged to show how it could be used. And with gleeful hubris they chose as example not some simple reflex mediated by a system of not too great fine structure but rather what can be called a higher function processed by an unutterably complicated system. It doesn’t matter whether the mechanism they describe actually occurs. That is beside the point. What matters is that such an engine can be designed using the methods they had laid down. They would rather have been clearly wrong than maunderingly vague, as was the accepted style. No point is served by elaborating further on this work. Other more extended appreciations and criticisms are well known.

Once this model of nervous function appeared, so apposite to the notions of digital computers already in the planning stage, great excitement spread among students of the emerging information sciences. But there was relatively little impact on nervous physiology. Warren and Walter were certainly alive to the kind of reservations that von Neumann later voiced in his essay The Natural and Logical Theory of Automata (thereby restating the duality in Leibnitz’s thought). This important double view is usually caricatured in learned discussions of the mind-body problem. It is relevant here because Warren, who began as a gifted naturalist and remained so to the end, became entranced with alternative logics—three-valued logic, probabilistic logic, etc. At the same time Walter, who early in life dreamed of conquering the whole of natural science by logic, became ardently involved in empirics. In a sense they converted each other.

When Warren, Walter, Pat Wall, and I came to MIT, it was with the aim of marrying physiological data to advanced speculation on how a nervous system works. Norbert Wiener had already had an encounter with the problem. He had challenged Arturo Rosenblueth, saying that a few weeks of work would suffice to give an analytic expression to the input-output relations of a simple reflex. Whereupon Arturo mischievously invited him to design the experiments and to watch them being done in Mexico City. Wiener’s letter at the end of three weeks was a lively diatribe on noisy nonlinear systems that were clearly designed to frustrate right-thinking analysts.

After some initial work on spinal cord mechanisms, I shifted to the study of the frog’s eye and then entrained Humberto Maturana from Harvard. When we collected the data put forth in one of the papers of this sampler, Warren, Walter, Humberto, and I gathered with Oliver Selfridge to hammer out the account. In line with our own perceptual experience we couched what we found in terms of universals of perception in the frog. The experiments had been done with that in mind. I remember well Walter’s delighted despair at the results and Warren’s almost bland acceptance of them as to have been expected. Warren never much shared Walter’s and my enjoyment of Kant, and yet he admired Otto Magnus for the notion of the physiological a priori. So Walter, Oliver, Humberto, and I pushed strongly to couch the paper as the physiological demonstration of the synthetic a priori. Warren, with wry humor, gave in.

In this way Warren and Walter conspired to what seemed the idealistic obverse of their logical calculus. The universals are clear but hard to define, and the proper descriptions of them are fairly long even in precis because of the multiple contingencies. Now the challenge was to account for these distinct and dear but endlessly described universals or invariances in terms of a logical circuitry compatible with the retinal anatomy as then known.

As Warren pointed out, he accepted the synthetic a priori—he was not going to pretend to any tabula rasa notions like those of Locke or Bertrand Russell. But he still held that in the end there would be an algorithmic description of the processes that engendered what perceptual operations we found. There is no magic. And of course he is quite right. The retina is a machine, meaty and miraculous, but still a machine. Bit by bit the mechanism is coming to light, so to speak. The nervous engine is not had from neurons as logical gates but more as complex analog processors. Yet this does not contradict the spirit of the original essays on the logical calculus. It complements and augments those earliest notions.

Reminiscences may not be proper to a preface that ought to deal with the text in a dispassionate and thoughtful way. But Warren took such care with words and sculpted his essays with so loving a hand that I could not rival his prose nor pretend disinterested judgment of it. On rereading his essays and poems, I find them as delightful as when I first read them fresh from his pen. Only one confession is due and it is my defect. He wrote many of his essays to be read aloud, but I always found them much harder to audit than to read—and that is because his allusions, which are transparent on paper, go by too quickly, as does his wordplay. He has an enviable style and is marvelously the cavalier that I remember.

Preface

This book presents our attempt to found a physiological theory of knowledge. It is gratefully dedicated to all my collaborators.

Except for three papers that were published in the Journal of Mathematical Biophysics, the articles were lectures, written over some twenty years for dissimilar audiences. Each can be read by itself.

It is in the interest of science to expose the formation of hypotheses to the criticism of fellow scientists in the hope of experimental contradiction. Facts have often compelled me to change my mind; but, to keep the record straight, no sins of commission or of omission have been corrected in these texts. You may hold me responsible, as principal author of all but one of these.

I have had about one hundred collaborators whom I must thank collectively without catalogue of their names or their contributions. My indebtedness to Walter Pitts is, of course, much greater than appears from our joint publications.

Jerome Lettvin, with Humberto Maturana, wrote What the Frog’s Eye Tells the Frog’s Brain. I am delighted to have it included, for it is our first major step in experimental epistemology.

Warren S. McCulloch

Cambridge, Massachusetts

January 1965

Acknowledgments

The following have been reprinted with permission of the authors and publishers:

1. Warren S. McCulloch, What Is a Number, That a Man May Know It, and a Man, That He May Know a Number? (the Ninth Alfred Korzybski Memorial Lecture), General Semantics Bulletin, Nos. 26 and 27 (Lakeville, Conn.: Institute of General Semantics, 1961), pp. 7–18.

2. Warren S. McCulloch and Walter H. Pitts, A Logical Calculus of the Ideas Immanent in Nervous Activity, Bulletin of Mathematical Biophysics, Vol. 5 (Chicago: University of Chicago Press, 1943), pp. 115–133.

3. Warren S. McCulloch, A Heterarchy of Values Determined by the Topology of Nervous Nets, Bulletin of Mathematical Biophysics, Vol. 7 (Chicago: University of Chicago Press, 1945), pp. 89–93.

4. Walter Pitts and Warren S. McCulloch, How We Know Universals: The Perception of Auditory and Visual Forms, Bulletin of Mathematical Biophysics, Vol. 9 (Chicago: University of Chicago Press, 1947), pp. 127–147.

5. Warren S. McCulloch, Modes of Functional Organization of the Cerebral Cortex, Federation Proceedings, Vol. 6 (Washington, D.C.: Federation of American Societies for Experimental Biology, 1947), pp. 448–452.

6. Warren