DISCUSSION

W.S. McCulloch

Being now in my second century and knowing that nerve cells die daily and none are replaced, I can calculate that I have lost some 9 to 10% of my original equipment--yet I work. I am also an unsuccessful farmer concerning pigs. In Connecticut we have a saying worthy of all men to be remembered, that pigs would live longer if they didn't make hogs of themselves. The danger became explicit when my very good friend described biophysics.

Biophysics is not all science. It is a very important branch of science, but the biologist and the engineer differ crucially from the physicist or the physical chemist or the chemist and it is for this reason that you will find me at the Research Laboratory of Electronics.

I am a psychiatrist. My whole interest centers on one simple question: "What is a number, so conceived that a man may know it, and a man, that he may know a number?" That has kept me working since 1917. I think I know a little bit about the numbers but my Itinerary To Man is still incomplete. I suspect that it always will be.

Now Sam Clemens once enunciated a great law. He happened to have been talking about pigs and Sam Clemens' law is this--or Mark Twain's-"You have to have the facts before you can pervert them." The great difficulty was clearly specified first by C. H. Prescott, formerly with the Bell Laboratories, now unfortunately deceased. He described the farmer's difficulty when his hog had grown so great that he could no longer pick So he doesn't know what it weighs and so he doesn't know what he has to get for the hog. He places a plank across a log. He trusses the pig and places it on one end of the plank and then he picks up a stone and puts it on the other end of the plank until it balances the pig. Then he measures the distance from the pig to the log and from the log to the stone and then he guesses the weight of the stone to find out what he should get for the pig.

it up.

There never was and there never will be a way of avoiding that ultimate guess. It is much less important when one guesses the weight of the stone than when one makes a guess as to the nature of logic necessary for the task. Now biology suffers from one great difficulty, which again I will give you in the words of C. H. Prescott. He was describing a farmer who is feeding a pig and he carries out a swill pail full to the brim and he bangs on it and the pig comes and starts eating and he stands there and he reckons as to how he will plow his field, this way this year and that way the next year and when he gets through reckoning he bends over to pick up the swill pail and it is so heavy he can't pick it up so he looks and finds out that the pig has crawled into the pail so he reckons that the pig is bigger on the inside than it is on the out.

That is the great difficulty with all of us in biology. The complexities at the lower levels are always so much greater than the complexities which we are ready to handle, understanding that intellectually the pig is bigger on the inside than on the out.

Now let me come back and explain wherein the field in which we labor is more inclusive than physics and chemistry, because I think this is where the biologist and the engineer necessarily go hand in hand. You will remember that Carnot was an engineer and he had to distinguish between work and energy • The electronic engineer is equally impelled--I mean the man working with weak currents--he is necessarily compelled to distinguish between signal and noise. The engineer and the biologist both live in a world in which there are utilities in the world about which he is speaking. It is not merely that his speech is useful or useless. It is that the things themselves are compelled to succeed or disappear. Consequently, one has to talk about signals which are true or else false, perfectly good physically in either case. The value is there in the thing about which we speak. That is not so for the physicist. Things merely happen or they don't, so you will find us natural allies at all times. Unnaturally we are thrown against each other.

The first reason we are thrown against each other is that biology has by and large selected men who were good at observing, good at recording and mathematically incompetent, unusually unable to think. There are exceptions such as Aristotle. In the team play between the biologist and the engineer we always encounter our greatest difficulty with the Gentlemen of my qualities, the physician.

Again and again a youngster working in an Army Camp built for himself a computing machine made out of bird watcher's cards, things with holes punched in them and an old clothes hanger opened to spear them. These Emmas are continually built and every time they appear in public the medical profession comes out in horror against them. It takes about 350 cases in an ordinary army camp, for Emma to be a better diagnostician than the man who created her. One cannot remember that many things. This hostility you will encounter always among the echt biologists. You cannot expect them to give you ordinary team play. There are exceptions. I see in the back of the room a psychiatrist--Braitenberg, the Head of Cybernetics in Naples. I have just come back from England where I was very happy talking with Ross Ashby, a psychiatrist, the author of "Design for a Brain." He will be coming to this country to work in Illinois in the Department of Electrical Engineering, I believe. I have been in France where I have seen another one of the ventures that our Air Force has been supporting. He is a physician, Tony Remond, who has done the best job that I have seen anywhere in the whole field of recording and computing the proper parameters of the electrical activities of the brain. The support is still inadequate, but it is a superb job.

What I would like to make very clear to you is this: We have in general a tendency to make models. This tendency appears first in building what we call theories. They are only verbal models. Kline, some years ago

proved past per adventure that if all one wants is to preserve the logic
of the system in question then the only hardware he needs are the natural
numbers. This is the simplest form of model. It lacks similitude. When
Pitts and McCullock produced the Pitts and McCulloch neuron they did it
for the following reason: They wanted to find out what is the absolute
minimum that one has to attribute to the components of a brain in order
that that brain shall be an adequate Turing machine. What we did in the
paper in question was to show that a neuron of such an oversimplified
kind was still an adequate component out of which, with proper circuitry,
to build a machine which can compute any computable number.

The history of that paper is very funny, it was picked up by John Von Neuman and used in the teaching of the theory of computing machines and it is referred to everywhere for that reason. That neuron is hopelessly below par for a real neuron.

I'm

In the first place, for the sake of simplicity, that inhibition was absolute. We know it is not. We did not suppose there were any spontaneous active neurons, we know that there are. We treated the whole business as oversimplifiedly as possible and even so it worked. Now the real neuron is best described by an eighth order nonlinear differential equation. sorry, such an affair is fairly opaque even to a good mathematician and there occurs a delightful battle--I'll tell you no names--between people who thought that they had destroyed the Hodgkin-Huxley Neuron and the people who thought they had defended it. In each case their argument defected. Their experiments were 0.K. There happens to exist in that differential equation the possibility of a prolonged state between the state of not firing and the state of firing. It can be found experimentally, but I assure you it took Walter Pitts about three months of work to find it mathematically. That is to say we do have a mathematics which does describe the actual behavior of a real component but the mathematics is usually so difficult that to a superb mathematician it is extremely difficult. But worst of all the reason we do not use mathematics in biology the way we should is generally that the mathematics does not exist. The mathematics were built in such a form as to handle those things which the physicist could manipulate--there it works, but given an ordinary thing like a neuron with a shape that no mathematician can describe, how are we going to handle the situation? We have to invent our mathematics as we go along. So I have to invent probabilistic logistic and you have seen the kind of mathematical treatment which the youngsters in my group have presented you with. That kind of mathematical treatment did not exist until very recently. It is at the front in its own field. Models then we will make, people like like Baitenburg, like Ross Ashby, like Schutzenberger. As psychiatrists, we are confronted with the toughest of all medical problems and are thoroughly convinced of our incapacity to handle them. We will do all that we can do to understand the working of the brain, but we know still that the logic that we need for psychology and for psychiatry is beyond our grasp.

When we speak of these things we almost always talk nonsense. We do this because there does not exist, even for diadic relations, a proper calculus. The minimum number of things related in all problems of consciousness, belief, the common donative relations of law, and so on are triadic relations. For these there is as yet no calculus.

M..

FURTHER DISCUSSION

(SOME BIOLOGICAL IDEAS)

Peter H. Greene
University of Chicago

The subtitle of this Bionics Symposium is "Living Prototypes-The Key to New Technology." We have had sessions entitled "The Life Sciences in Bionics," "Analysis of Biological Principles," and "Mechanical Realization of the Higher Functions of Living Systems." But I believe that some of the most characteristically biological features have not been mentioned. Although I concede that we do not yet know enough to recreate these features, or even to describe them in adequate detail, I feel that unless we view this lack with regret and keep these features in view as part of our goal, we shall be much the poorer.

If the Russians knew how to build truly biological machines, we would spare no pains to learn their secrets. We would gladly master their foreign language and interpret their difficult phraseology in our terms so that we might take advantage of their knowledge. But I believe that engineers are not taking these pains in regard to much of the knowledge gained by modern psychology. I'd like to list in barest outline a few of the biological features which differ from present machine design. Since these exist at a prelogical stage of thought development, for which we do not have an adequately descriptive language, the full force of these points can be felt only by reference to numerous biological examples*.

Present designs for perceptual machines subject inputs to a number of transformations to obtain a useful result. Real biological systems largely fabricate their experience out of their own constructions. The elemental behavior scheme seems to be largely one in which stimuli act by switching the organism from one of its existing modes of behavior to another. These modes are inherent or derived through processes that obviously use processed inputs like the machines, but the direction of emphasis is from inside to outside in biology, outside to inside in most machine design.

In present design one program or function may be added onto another, or may be included in it, while in typical biological patterns of thought and action one schema may thoroughly permeate another in a way which may be

*A few of the relevant references may be found in the bibliographies of my papers in the Proceedings of the 1959 Western Joint Computer Conference and the Univ. of Ill. Symposium on the Principles of Self-Organization (1960) (in press), and some discussion in the Proc. 1960 W.J.C.C.