Contains reports on four research projects.National Institutes of Health (Grant B-1865-(C3), Grant MH-04737-02)United States Air Force, Aeronautical Systems Division (Contract AF33(616)-7783)Teagle Foundation, IncorporatedBell Telephone Laboratories, Incorporate

Cowan, J. D.

Goodall, M. C.

Howland, Bradford H.

Howland, Howard C.

Lettvin, Jerome Y.

Winograd, S.

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XVI. NEUROPHYSIOLOGYW. S. McCulloch Herta von Dechend Diane MajorJ. A. Aldrich Rachel G. Fuchs L. M. MendellM. A. Arbib R. C. Gesteland N. M. OnestoF. S. Axelrod M. C. Goodall W. H. PittsM. Blum K. Kornacker J. A. RojasJ. E. Brown J. Y. Lettvin A. TaubJ. D. Cowan P. D. WallA. RELIABLE COMPUTATION IN THE PRESENCE OF NOISEThis report is essentially an abstract of a paper that has been submitted for publi-cation to the Philosophical Transactions of the Royal Society of London.A theoretical study of the problem of constructing reliable automata from componentsof low reliability has been made. It is shown that information theory can be applied tothis problem so that a computation capacity may be defined for modules computing prob-abilistic logical functions, which corresponds to the capacity of a noisy communicationchannel.It is proved that definite events may be realized with arbitrarily high reliability, bynetworks assembled from modules and connections of low reliability, provided that theresulting networks are sufficiently redundant. If the assumptions are made that modulesare sufficiently complex, and that modular malfunctions are independent of modular com-plexity, then the module redundancy of such networks need only be greater than a certainminimum whose value is determined by the computation capacity of modules comprisingthese networks.A further result is a proof concerning errors in the pattern of modular interconnec-tion. It is shown that if the frequency of errors of interconnection is less than a certainfunction of computation capacity and module redundancy, then with high probability, sucherrors may be corrected, and automata may be constructed, to function with arbitrarilyhigh reliability despite errors in their interconnection patterns.The functional organization of these automata is shown to be diffuse. Any one functioncomputed by an automaton is computed by many modules, and any one module computesa diverse mixture of many of these functions. The resultant multiple diversity of functionis closely connected with the high reliability exhibited by such automata.J. D. Cowan, S. Winograd(Mr. S. Winograd is now at the IBM Thomas J. Watson Research Center, YorktownHeights, New York.)*This work was supported in part by Bell Telephone Laboratories, Inc.; the NationalInstitutes of Health (Grant B-1865-(C3), Grant MH-04737-02); The Teagle Foundation,Inc.; and in part by the U. S. Air Force (Aeronautical Systems Division) under ContractAF33(616)-7783.QPR No. 67 195(XVI. NEUROPHYSIOLOGY)B. COGNITIVE SYSTEMSWork on inductive logic has been summarized and written up in mimeographed notesentitled "Cognitive Systems and Logical Induction. " It is shown how the limitations ofBayesian induction can be overcome by going to a universal logic (formalized languageor associative system) and handling the axioms and rules probabilistically. This ideais worked out in terms of Post I normal systems on binary symbols employing an analogywith many-particle quantum mechanics. Shannon communication is then the special(Bayesian) case of such a theory when the Post system is a Boolian algebra.Realizability of this theory is considered in terms of a quasilinear threshold (Pitts-McCulloch) net with three values and probabilistic thresholds.A complimentary principle arising in the general theory has been published. 2 Itanswers partly, at any rate, a celebrated paradox of Hume's Treatise of Human Nature(1739).The author believes that this theory will have applications to the problem of epigene-sis in biology.M. C. GoodallReferences1. E. L. Post, Recursively enumerable sets of positive integers, Bull. Am. Math.Soc. 50, 284 (1944).2. M. C. Goodall, Nature 194, 998 (1962).C. STATUS OF OTHER RESEARCH1. Rat VisionJ. E. Brown has succeeded in recording from single fibers in the optic nerve of rat.This is a resumption of work begun three years ago by R. Burde and then dropped.Mr. Brown has now found at least one fiber that is concerned with moving boundariesbut indifferent to changing average flux in its receptive field. He reports what Burdealso saw, that the description of what a fiber sees in its receptive field seems to be inpart a function of the state of consciousness of the rat, and, perhaps, the state of atten-tion. Certainly, barbiturates seem to have a profound action on the activity found inn. opticus, but whether from general suppression of population groups or general changein function cannot yet be told.2. OlfactionR. C. Gesteland and J. A. Rojas have prepared a paper on crude groups of olfactoryfibers. A new finding has recommended the possibility of an additional mode of study.QPR No. 67 196(XVI. NEUROPHYSIOLOGY)Butyric acid - and some related chemicals - have the property of giving a completelypositive, or initially positive, but diphasic Ottoson potential. This suggests a groupingof some odors not only by chemical similarity but by site of action. The question willbe studied in detail. It is now possible to distinguish olfactory and NV fibers in themucosa by the shape of the transient. Furthermore, recording from NV fibers in thenerve bundle itself is rather easy and confirms the functional separation observed inthe mucosa. In general, we suspect that, at least in the frog, Beidler's view of thefunction of N V fibers is not applicable.3. Dorsal RootsIn the course of playing with dorsal rootlets in cat to record from certain myelinatedfibers, and using our platinum-plated probes, Dr. Henneman, Rojas, Brown, and I noteddischarging units showing triphasic action potentials, 5-10 msec long. These respondedto peripheral stimulation of skin and/or muscle, and we believe them to be the unmye-linated fibers of the dorsal root. If this proves to be the case (we shall know in a fewweeks), it will become possible for the first time to study these fibers easily. Thereis an enormous number of them and our knowledge about what they do and where theygo is very limited.4. CerebellumF. S. Axelrod has been recording from various kinds of cerebellar cells in the frog.There is a complex projection system from the limbs into cerebellum and it is hard todecide what function of limb movement and position and skin sensation is taken by thecells. The preparation is quite stable and permits of long recording from the sameneurons.5. History of ScienceSome of our work has been in the history of science, concerned, in particular, withthe reasons behind the divorce of psychology and physics in the latter half of the nine-teenth century. This material will be presented elsewhere as part of an introductionto our new approach to nervous physiology.J. Y. LettvinD. PHOTOGRAPHIC METHOD FOR THE STUDY OF VISION FROM A DISTANCEWe describe in this report an instrumental method for the measurement of the stateof refraction of an animal (or human) eye from a distance. This technique, which makesuse of flash photography, has an important advantage over other methods of measuringQPR No. 67 197(XVI. NEUROPHYSIOLOGY)accomodation in that it does not require that the eye under study be carefully positionedwith relation to the optic axis of an instrument. It is only necessary that the eye belocated within a volume determined by the depth of field and the field of view of a camera.In some situations we may also require that the eye fixate on a point near or coincidentwith the camera.In Fig. XVI-1 we show an arrangement by which light from a point source is causedto appear to emanate from the central region of a camera lens of wide aperture. Thislight is assumed to be imaged by an eye of unknown refractive state located a few metersaway. Since the retina is an imperfect absorber, a reflection or "light reflex" will passback through the lens of the eye, returning in the general direction of the camera (dottedlines of Fig. XVI-1). If the eye is within a few diopters of the best focal adjustment, wemay reasonably expect that all or most of the light reflex will pass back through theaperture of the camera lens to expose the film or plate when the shutter of the camerais opened. If the camera is adjusted to focus sharply objects that are in a plane con-taining the eye, we record an image of the pupillary aperture, that is, the eye will appearto be illuminated from within (see Fig. XVI-2).The interesting effect occurs when, in the arrangement of Fig. XVI-1, the cameraSUPPLEMENTARYLENSCAMERAFig. XVI-1.HALF - SILVE REDMIRRORPOINTSOURCEFLASHTUBEEYE (DEFOCUSED)Arrangement for illumination by point source of light centrallypositioned with respect to a wide-aperture camera lens.QPR No. 67 198(XVI. NEUROPHYSIOLOGY)Fig. XVI-2. Light reflexes from goldfish eyes.is purposely defocused, for example, by the addition of a supplementary lens of one-tenth the dioptral power of the camera lens. Ordinarily, we expect the image of a defo-cused point source of light to be an extended blur of uniform intensity. In outline, thisblur will exhibit congruence with the aperture stop, the scale of proportionality beingdetermined by the extent of defocus. Figure XVI-3 illustrates this effect; this picturewas taken with a lens having a hexagonal aperture stop. In the present instance, how-ever, the greatest part of the light reflex passes through the camera lens entirely withinthe confines of the aperture stop, that is, as if occluded by a stop of smaller size. Theblurred image resulting from the reflex will therefore be more concentrated than thedefocused image of a diffuse reflector similarly positioned in the plane of the eye. Thisblur is, in fact, a reproduction in miniature of the cross section of the light reflex asit enters the camera lens. Measurements of the size and shape of the blur image thusenable us to determine the angular divergence of the light reflex as it leaves the eye;these data, together with knowledge of the size of the eye, the pupillary aperture, andthe reflective properties of the retinal surface, should suffice to determine the refractiveQPR No. 67 199(XVI. NEUROPHYSIOLOGY)Fig. XVI-3. Photograph illustrating blur images of defocused lightsources. (The lens used to take this picture has ahexagonal aperature stop.)state of the eye.There are at least three different ways in which we can defocus the camera to obtainuseful information about the state of refraction of the eye. (i) We may alter either thepower or the focal adjustment of the camera lens from that which would sharply focusthe light reflex. This simple method has the advantage of yielding information concerningastigmatic, as well as spherical, focal errors of the eye, but has the disadvantage thatthe intensity of the spot will vary greatly with the refractive error of the eye. (ii) Wemay defocus the camera by means of a circular or astigmatic supplementary lens withthe advantage that the blur is concentrated into a line image of variable extension; thevariation of exposure with the refractive state of the eye is thereby greatly reduced.These data are better suited to microdensitometer analysis. Furthermore, a smallerQPR No. 67 zo200(XVI. NEUROPHYSIOLOGY)area of film is exposed by each individual eye within the field of view of the camera. Adisadvantage of this method is the difficulty of determining a spherical refractive errorin the presence of appreciable astigmatism. (iii) The camera may be defocused by usinga conical supplementary lens (an "axiconic"). The resulting blur will be in the shape ofthe circumference of a circle. The angular distribution of intensities about this circum-ference will give an indication of the axis and the degree of astigmatism relative to thespherical error. Since the size of the circle is invariant, the photographic exposurewill be little affected by the refractive errors under study. A disadvantage of this methodis that is does not give complete information, since it gives no indication of the absolutemagnitude of the refractive errors.For preliminary experiments we have concentrated our attention on method (ii). Forthis purpose, we have employed an untrimmed 2-diopter ophthalmic-quality cylindricallens; this is placed in front of the 58-mm (17.2 diopter) f 1.4 lens of a 35-mm single-lens reflex camera. This combination produces good quality line images of pointsources of light as long as their images are located within 10 mm of the center of the24 mm X 36 mm film plane. A refinement of some importance which we have employedis the use of a symmetrical occluding wedge, carefully centered and axially positionedto lie in the same plane as the virtual image of the point light source. The function ofthis wedge is to block those rays that diverge in directions that are orthogonal, or nearlyso, to the axis of the cylindrical lens; these would otherwise register falsely on the filmas weakly diverged rays. A subsidiary effect of this occluding wedge is to alter the formof the linear blur image, which now exhibits two maxima, as illustrated by the sequenceof photographs of an artificial eye, shown in Fig. XVI-4. The spacing of these maximaprovides indication of the divergence of the light reflex. Figure XVI-4a shows the blurimage corresponding to the best focal adjustment of this "eye," a 13-mm f 1.5 movie-camera lens set at f 2. (A piece of white paper attached to the end of a micrometerbarrel comprised the retina.) For Fig. XVI-4b we moved the micrometer 0. 1 mm frombest focus; in Fig. XVI-4c, 0.55 mm.Using the same apparatus, we photographed a young adult male human subject withgood vision and not requiring glasses, in various states of accomodation. Figure XVI-5ashows this subject looking at the camera (and light source); Fig. XVI-5b shows the samesubject concentrating his gaze on the tip of a pencil approximately 8 inches in front ofhis eyes. The difference in the focal adjustments, as indicated by the separation of themaxima in light intensities of the two cases, is evident. A third photograph (not shown),taken with the subject fixating on a point behind the camera, indicated an intermediatedegree of dispersion.In its present form the instrument described in this report has two possible applica-tions to physiology. (i) The study of animal vision. The possibility of studying the ani-mals in their natural state (that is, fish swimming freely, etc.) should be of greatQPR No. 67 201bCFig. XVI-4. Photographs of artificial eye with various focal adjustments. (a) Bestfocus. (b) 0.10-mm defocus. (c) 0.55-mm defocus. Camera waspurposely defocused with a 2-diopter cylindrical lens.QPR No. 67 202(a) (b)Fig. XVI-5. Photographs of human subject. (a) Subject fixating on camera,1. 3 meters distant. (b) Subject fixating on pencil, 0.2 meterdistant. Camera was defocused with 2-diopter cylindricalsupplementary lens.(XVI. NEUROPHYSIOLOGY)importance. Our first animal experiments will be with fish because there exists littlereliable experimental data, either from behavioral experiments or from direct retino-scopic observation, concerning their visual capabilities.l (ii) As an instrument of massretinoscopy, as for example, for the rapid determination of defects of far-vision ingroups of children. Simple modification of the present apparatus, utilizing the knownchromatic aberration of the human eye, should also enable one to determine the sign ofthe refractive errors.B. Howland, H. C. Howland(Mr. Bradford Howland is a staff member of Lincoln Laboratory, M.I. T. Mr. HowardC. Howland is from the State University of New York on Long Island, Oyster Bay, NewYork.)Referencesi. R. J. Pumphrey, Concerning vision, The Cell and the Organism, Essays pre-sented to Sir James Gray (Cambridge University Press, London, 1961), pp. 193-208.QPR No. 67 204

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