under the usual correspondence. We have in fact been investigating the utility of such schemes.

Question:

"The point is really about your last scheme, with the random
connection. I would like to hear more about what advantage
or virtue the randomness has over some equidistant spacing of
the possible connections." (Dr. S. Papert, National Physical
Laboratory)

Mr. Cowan: Let me put it this way. It should be clear that the aim of this
work, namely the construction of reliable automata from unreliable components,
is really a part of the general problem of obtaining reliability of function
(whether it be computation or transmission) in the presence of a variety of
disturbances. This in turn is within the domain of Information Theory and
of Statistical Mechanics. Two features of this problem are immediately
apparent. Firstly we would like to construct nets that are as rugged as
possible; i.e., nets that produce minimum distortion of function given max-
imum distortion of individual components, and of the structure of the net.
Clearly if we can construct nets whose function is little perturbed by small
variations of structure, then this is desirable. Hence we do not insist on
precise connectivity in our nets, but permit (local) variations of connec-
tion: and our nets don't function because of this variability, but in spite
of it. Secondly, we have to live with elemental chaos, as it were, and to
insist on such precise connectivity is to insist on a degree of order which
is scarcely credible, in those automata which we are trying to model, and
in fact smacks of physical demonology. It is thus of little use to postu-
late the existence of ideal noiseless components combined into a precisely
connected net. We have to put the chaos in at the beginning, and start from
there. Furthermore, if we consider the specification of such model neural
nets as we have considered, from a genetical standpoint, the selective in-
formation content of such precise schemes is incredibly high. By allowing
imprecise connectivity (within certain limits), and imprecisely functioning
components, the selective information content of such schemes is consider-
ably lowered. Finally, while we have stressed the point that we are only
interested in nets which perform simple logical functions, we would really
like to use them (eventually) to investigate more complex and interesting
phenomena such as learning: and for this purpose we would like to have,
initially at least, an imprecise connectivity in our model nets. We can
do no better to summarize these points, than to quote from a famous paper
by Dr. McCulloch and W. Pitts,* viz: "To demonstrate the existential con-
sequences of known characters of neurons, any theoretically conceivable net

*W. Pitts and W. S. McCulloch: "How we know Universals: The Perception of Auditory and Visual Forms" Bull. Math. Biophysics, Vol. 9, 1947.

embodying the possibility will serve. It is equally legitimate to have every net accompanied by anatomical directions as to where to record the action of its supposed components, for experiment will serve to eliminate those which do not fit the facts. But it is wise to construct even these nets so that their principle function is little perturbed by small perturbations in excitation, threshold, or detail of connection within the same neighborhood. Genes can only determine statistical order, and original chaos must reign over nets that learn, for learning builds new order according to a law of use."

STABILITY, OSCILLATIONS, AND NOISE IN THE
HUMAN PUPIL SERVOMECHANISM*

Lawrence Stark

Reprinted from the PROCEEDINGS OF THE IRE
Courtesy The Institute of Radio Engineer

INTRODUCTION

The pupil of the eye acts as a regulator of light impinging upon the retina. The transfer function and noise characteristics of this stable type zero servomechanism (fig. 1) will be presented in this paper. The normal behavior of the pupil system can be modified by changing the experimental conditions. Then such interesting phenomena as instability and oscillations can be demonstrated.

The pupil was chosen for study from a host of possible examples of biological servosystems for several reasons (ref. 1,2). First, its motor mechanism, the iris, lies exposed behind the transparent cornea for possible measurement without prior dissection. This had previously been exploited for scientific and clinical researches by using high-speed motion picture cameras. Further, by employing invisible infrared photographic techniques, measurements can be made without disturbing the system, because its sensitivity is limited (by definition) to the visible spectrum. Second, the system can be disturbed or driven by changes in intensity of visible light, a form of energy fairly easy to control, and painless in its administration to the subject. The first two advantages lead to still a third: the possibility of performing experiments on awake, unanesthetized animals whose nervous system is fully intact and functional. In fact, all of the experiments to be discussed below have been performed on human subjects. Lastly, the system responds with a movement having only one degree of freedom, a change in pupil area, which simplifies the system equation analysis.

Fig. 1--A simple servosystem.

FEEDBACK. PATH

FOR LC

This shows forward and feedback paths in the servoloop and different components therein. Symbols are explained in diagram and text. Dashed lines indicate where loop might be opened and a disturbance be introduced, and response around the loop measured.

The pupil is so widely observed an organ that most persons are already acquainted with certain basic facts of its anatomy and physiology. The pupil is the hole in the center of the iris muscle which enables light to enter the eye and impinge upon the retina, the sensitive layer of the back of the eye. The retina is comprised of primary sense cells containing photosensitive pigments which trap photons and subsequently stimulate nerve cells. The retina is part of the central nervous system and possesses a complex multineural integrative (i.e., information transforming) apparatus. The optic nerve leads mainly to the visual cortex of the cerebral hemispheres via a relaying station, the lateral geniculate body. However, some fibers, called the pupillomotor fibers, go directly to the brain stem and relay in the pretecal area and thence to the Edinger-Westphal nucleus. This nucleus contains the nerve cells, part of the parasympathetic system, whose fibers (after an external relay in the ciliary ganglion) control the powerful sphincter muscle of the iris. Fiber tracts also go to the sympathetic system in the spinal cord. Here, nerve cells send fibers back to the orbit, after relaying in the superior cervical ganglion. The dilator of the pupil is controlled by these sympathetic fibers and is responsible for the wide dilation of the pupils after the administration of adrenalin.

Excitation of the Edinger-Westphal nucleus produces constriction of the pupil and it is also probable that inhibition, i.e., decrease in the operating level, of this nucleus is also the most important mechanism for dilating the pupil.

Any further relevant and necessary details of neuroanatomy will be discussed in the main body of the paper. The reader is assumed to possess a knowledge of linear servomechanism as presented in a college text such as Schultheiss and Bower (ref. 3).

EXPERIMENTAL METHODS

In order to obtain careful, quantitative data from the human pupil system under a variety of experimental conditions we felt it would be impossible to use the older infrared photographic techniques (ref. 4,5) and developed a simpler modification of this technique. In figure 2 the essential nature of the experimental arrangement of our pupillometer is shown.

VISIBLE LIGHT
SOURCE AND MODULATOR

Fig. 2--Experimental arrangement. Optical portions of visible light stimulus path are not shown. Modulator consisted of polaroid filters in rotary oscillation with respect to each other. fixation point was provided, as well as a biteboard.

The pupil area was measured continuously by reflecting infrared light from the iris onto a photocell. The pupil is ordinarily black because most of the light passing through the pupil into the eye is absorbed by pigment layers behind the retina. Thus, when the pupil is large (and the iris small) less light is reflected from the front of the eye onto the photocell. When the pupil is small (and the iris large) more infrared light is reflected onto the photocell. In this manner we obtained a convenient and continuous measurement of the system response. At first an attempt was made to use specular reflection from the iris in order to improve linearity of the response, but retinal specular reflection was also obtained and this was not negligible. Therefore the use of scattered light reflection from the iris onto the infrared sensitive photocell was an important part of the experimental instrument design. Another way of increasing the signal-to-noise ratio was by the use of a relatively small area of infrared illumination of the iris. This was arranged to be only slightly larger in diameter than the largest diameter of the pupil. The use of a narrow spectral band of infrared light shaped to the infrared spectral sensitivity of the photocell also aided in this experimental approach. The elimination of the long wavelength infrared meant that most of the heat and discomfort to the subject was removed. The output of the photocell, a vacuum-type no. 917, was fed directly into the high impedance input of the recording amplifier. There was a small capacitance across it in order to remove high-frequency noise, and the tube and leads were shielded. The photocell housing could be shifted for studying the right or left eye. The infrared sensitive photocell was shielded with an infrared Wratten filter to eliminate the effects of stray visible light. Whenever beam splitters were placed in the path of the infrared light these were made dichroic to minimize attenuation of infrared light. The infrared light source was a 35-mm slide projector with a built-in fan for cooling, and it was supplied from a constant voltage transformer to obtain stability of light intensity.

In order to translate the photocell currents into pupil area measurement it was necessary to calibrate the instrument. Such a calibration is shown in figure 3. This was obtained by taking flash photographs of the pupil and at the same time noting the amount of photocell current. The flash of light naturally produced a pupillary response in the subject but the photographic measurements were over and completed before the pupil had a chance to respond. There has been found a fairly proportional relationship between pupil area and photocell current, but in the figure one can see that there is a diversion from linearity. However, this is small and not significant within the renge of most of the experiments, and was not corrected for. The calibration camera was a permanent part of the apparatus and was a single lens reflex camera with a built-in viewfinder. A dichroic beam splitter was placed so that most of the visible light reflecting from the iris was transmitted to the camera while interfering relatively little with the measuring infrared light. The electronic photoflash light was heavily filtered to permit only blue light to illuminate the iris, a practice which markedly reduced intensity and discomfort for the subject, as well as the effect on the infrared measuring photocell. An event marker automatically indicated on the recording graph the instant the photograph was taken. The camera viewfinder had excellent split-image focusing so that the subject could be accurately determined to be in the focal plane of the camera. Further details concerning positioning of the subject's head and eyes will be given in a later portion of this section.