Electrical and Computer Engineering

Electrical and Computer Engineering

Thinking with the Teachable Machine

by John H Andreae. Academic Press, 1977.

Publisher's Word

This book introduces a system, called PURR-PUSS, which can be programmed into a computer to produce a teachable machine. It is both a new theory and a working model. Learning starts from scratch, with nothing in PURR-PUSS's memory, and it can be accomplished either on her own or with the aid of a human teacher. PURR-PUSS experiences, and remembers her experiences, as several streams of context -- such as sound, vision and touch. Based on new concepts of prediction, multiple context and novelty, PURR-PUSS can be connected to any real or simulated environment. As Brian Gaines writes in his Foreword, the "book represents an in-depth study of the possibility of learning complex behaviour through remarkably simple and general mechanisms."

Contents of Book

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Preface

I: PURR-PUSS is my contribution to the future sanity of mankind.
R Eh?!

I: You know, violence, crime and all that. No one knows what to do about it because no one has a working model of the brain.

R: Oh! Is that what PURR-PUSS is?

I: Well, as a paper dart is a working model of the flight of a bird. PURR-PUSS is a computer program that can learn.

R: Ah! You're one of those psychologists --- learning theory and all that. I suppose PURR-PUSS is a model of a rat!

I: Not likely! You know, psychologists really haven't got a decent theory of how the brain works. George Miller suggested in 1974 that the lack of a good theory accounts for why computers have had so little impact on psychology. PURR-PUSS is both a new theory and a working model.

R: Sort of artificial intelligence? Wasn't there a program called GPS that solved problems and modelled how people think?

I: Yes, but Newell and Simon's General Problem Solver (1972) had to be given everything. They never managed to work out a way in which it could learn about problems. The same is true of other famous programs in artificial intelligence. Even Samuel's Checkers Playing Program (1959) didn't learn how to play checkers, only how to win! Winograd's English understanding program (1972) was fully primed. These and others are very clever programs indeed. PURR-PUSS isn't clever at all. She starts with no knowledge about anything.

R: I've got it! You're a nerve net man. You think the brain is a big nerve net. The connections in the net couldn't have been predetermined, so you make them randomly and then see what happens. Hebb's 1949 classic "The Organization of Behaviour" started a real craze for nerve net simulations, didn't it? I thought that they had all fizzled out.

I: Yes, but PURR-PUSS is very different from that hit-and-miss game. One can only sympathize with the neuropsychologist, Luria (1973), complaining of the uselessness of computer models of the brain. The neurophysiologist has been carrying out painstaking studies of the detailed structure of the brain (Shepherd, 1974), while others spew out untested and untestable schemes. We have tentative ideas for a nerve net too, but we have yet to establish that it will work just like the digital computer program of PURR-PUSS.
R How does PURR-PUSS work?

I: The main idea is multiple context. PURR-PUSS experiences, and remembers her experience, as several streams of context --- like sound, vision and touch. She recalls her remembered experiences by predicting from contexts. Each event is seen in context.

R: Like a conditioned reflex?

I: Yes, but we do not talk about stimulus conditions in the vague way used for the conditioned reflex (McGuigan and Lumsden, 1973). In PURR-PUSS, the sequential nature of events is brought right out into the open.
The second main idea in PURR-PUSS is novelty --- and there is nothing new about that! (Berlyne, 1960) However, in PURR-PUSS novelty is something precise and meaningful; and PURR-PUSS doesn't have to search her memory, however large, to find out if an event is novel. This is why her memory could be as large in capacity as that of the human brain --- if we could pay for it!

R: There's not much point in an enormous memory unless PURR-PUSS can learn really interesting things. What can you teach PURR-PUSS?
I We haven't been teaching her for long and we haven't been able to give her a good body yet, but ...

R: Body? Ah! Robots! Didn't Sir James Lighthill (1973) suggest that robot builders were men without babies, or something?!

I: Actually, PURR-PUSS is probably the computer program most like a baby because she does have to start right from the beginning to learn about her body and world. At least she can be taught in any language!

R: Are you suggesting that PURR-PUSS will have to be taken through all the stages of baby and child learning before doing anything significant?

I: I fear so. The stages of development described by Piaget (1972) for the child seem quite unavoidable for a system that learns from scratch. The education of PURR-PUSS is likely to be a long job and we cannot count on finding short-cuts. This is why it is so important to discover any fundamental limitations in PURR-PUSS before embarking on a long teaching programme.

R: Well, what have you taught PURR-PUSS so far?

I: Small tasks like remembering nursery rhymes, counting objects and drawing simple pictures. We have shown that she can learn cumulatively, using earlier experience in later tasks; that she can do appropriate and original things; You really ought to come along and have a go at interacting with her. It is quite an experience getting used to an ignorant machine that responds to one's teaching, usually in a way that you didn't expect but which doesn't look unreasonable after it has happened. You soon give up trying to work out why she does something. Instead, one learns to guess what she knows from what she does and how she responds. Would you like to try? ... Dash! I've lost him.... Hi! ... Where are you?

Foreword

You and I, dear Reader, have been talking while tramping in the Southern Alps on a warm summer's day. In crossing a small valley, you became separated from me without my noticing it and, when I came out of the bush on the far side, you were still invisible in the bush below. I have just heard you call back. From the movement of branches I can tell where you are and I can see quite clearly which way you should go to get out. When I start to direct you I shall soon find that you are not seeing things down there in the way that I see them up here. My directions will have to be carefully worded so that they are meaningful to you where you are, rather than where I am.

Everyone knows how difficult it is to communicate a new idea to someone else --- and how difficult it is, afterwards, to see why something was difficult.

This book is about a teachable machine, called PURR-PUSS, that is much simpler than most present-day "intelligent" machines. When telling my friends about PURR-PUSS, however, I find that they are down in the bush of unfamiliarity and that they want a multitude of extraneous questions answered before going ahead with my explanation. From my vantage point, most of their questions are irrelevant and distracting (Can you see the Kowhai tree from where you are? Will I come out near the waterfall?). If only they would do exactly what I prescribed and follow my thought-path precisely, they would come out into the open and then be able to see clearly all that they wished. But that is not the way that people behave. Thinking is an active process and I must answer their distracting questions before they will do what I want.

In writing a book, there seems to be no way of providing the reader with these extra facts and fancies just when he or she wants them. The best that I have been able to do is to ensure that all the answers are there and that they are accessible to the reader who is prepared to look around using the Contents and Index. If a question comes to your mind and it is not answered in the next sentence, please look farther on! If you are not interested in the bit that I have put next, please skip on! Tables and Figures are provided for reference. All of the details have been meticulously checked so that a reader experienced in programming can easily program his or her own computer to behave like PURR-PUSS.

Just as the printed word prevents me from answering your questions as they come into your mind, so also does it prevent me from showing you in a real live way the conversational interaction between me, as Teacher, and PURR-PUSS the learning machine. The best that I can do is to list what did happen and hope that you will read through the list of happenings with your imagination filling in all the details of clicking keys, flashing lights, gasps of surprise and frustration, and patient watching while the minutes and hours of real time pass. But, if you have access to a computer and can write the programs for PURR-PUSS, you will find that there is nothing quite as convincing as interacting with her yourself.

Engineers build bridges, even though philosophers cannot define the word "bridge". Ordinary people, like you and me, know what "free-will" and "creativity" are without having definitions. When an orange squirts us in the eye, we do not exclaim "What free-will!" or "How creative!", but when a small boy squirts us in the eye, we acknowledge his will, his originality and his impertinence! When, in Chapter 7, PURR-PUSS suddenly dashes off after some cake, much to my surprise, we see something in between the orange and the small boy. The differences in free-will and creativity between orange and PURR-PUSS, or between PURR-PUSS and small boy, are not so obvious that we should be dogmatic about them. Such philosophical conundrums are best left to the philosophers and that is just what I shall do in this book.
The field of Artificial Intelligence has lost some of the sparkle it had in the fifties and early sixties, when all was new and exciting. The early enthusiasm and optism has given way to criticism and disappointment. The intelligence of man has failed to prescribe his own intelligence.

In this book, we go back to the beginning with a new approach, a simpler approach. PURR-PUSS is not a clever machine crammed with theorem-provers, language-parsers, problem-solvers, scene analysers and heuristics. She starts quite empty and ignorant --- but is very teachable.

PURR-PUSS learns in a paradigmatic way (that is, by example), using a multiple context. Her built-in goal is to repeat novel events that she has experienced only once. She selects actions according to her remembered experience and the current context. There are no obvious limitations to what a system like PURR-PUSS can do, but here you will be shown what PURR-PUSS has actually done. This is not a book about what machines might do, should do or can't do. It is a complete description of a working system that seems to have some of the qualities that people have said machines could not have

Prologue

The Waimakariri River winds down from the Southern Alps across the Canterbury Plain to the Pacific Ocean. On a hill above the river stands a small man-made house with a water system comprising an arrangement of pipes and tanks.

The water system of the house, like so many human designs, sets out to prescribe precisely each twist and turn that the water in the house must take. The mistakes of the designer are revealed by airlocks and blockages, by overflows and leakages.

The water in the river obeys the universal rule of gravity and flows downhill. It is not stopped by dams and other obstacles --- only delayed.

The general trend in artificial intelligence research today is to design systems that are more and more complex. In my analogy, the typical system is a house with a multitude of pipes and tanks.

In designing PURR-PUSS, I have had the river in mind. Fifteen years of research with the one aim of designing a system that can learn anything "from scratch" has taken me from simple ideas to simpler ones. Like the river, PURR-PUSS operates according to simple universal rules: "seek novelty" and "predict events from their contexts". The concepts of novelty, prediction and context are familiar to psychologists, but in PURR-PUSS they are stripped down to the bare essentials.

With the modest "body" that we have been able to give PURR-PUSS, she has been found capable of choice, of original actions, of counting, of substitution and recursion, of setting her own goals and of having them set for her. PURR-PUSS can be taught in any language, can be given any size of memory and can interact with the real world. She has no known fundamental limitation. She becomes her experience. There are still a few "pipes" in PURR-PUSS (as in the man-made house), but our research is directed to their removal.

We can expect quick spectacular results from the "pipe" programs of artificial intelligence, but, in my view, their achievements will be superseded and surpassed by "river" programs, like PURR-PUSS.

Chapter 1. Thinking with PURR-PUSS

Intelligence
Art is not to be found in a piece of canvas or in a pot of paint. Pots of the same paint may produce very different results from the brushes of different painters.

A computer is not intelligent --- nor is its set of basic instructions. Like a piece of canvas without a picture of paint, a computer is inert without a program of instructions. Using the same basic instructions, different programmers can produce quite different results in the same computer.

To ask if a programmed computer is intelligent is like asking if a painted canvas is beautiful. Intelligence, like beauty, seems to be "in the eye of the beholder", since what one calls beautiful or intelligent another scorns.

PURR-PUSS is an experimental "brain", in the form of a computer program, for exploring the processes of learning, teaching and problem-solving. In writing a computer program all assumptions have to be made explicit and precise. We cannot gloss over the difficult bits.

Everything must be defined down to the last detail. However, we can attempt to teach PURR-PUSS different tasks and we can alter the computer program which defines her structure. We can advance by small changes. This process of interaction and change is what I mean by "thinking with PURR-PUSS'. It reveals new abilities, new structures and new teaching methods. PURR-PUSS is an aid to thinking about systems which learn.

Both the structure and the behaviour of PURR-PUSS have philosophical, psychological, biological and educational implications, but I shall avoid stressing these beyond what is necessary to explain some of the things which I have done. My personal view is that many of the most controversial arguments about intelligence, purpose, values, free-will and so on melt away in the light of a real system, be it as primitive as PURR-PUSS.

Body and World
To call PURR-PUSS a "brain" is to use the word loosely. But, just as a real brain cannot function in isolation, so PURR-PUSS must be connected to a "body" and the body must be put in a "world". The body and world together are the environment of PURR-PUSS. The interaction of the brain with its body and world provide it with "experience".

In a general way, the body is that part of the environment which is more or less under the direct control of PURR-PUSS, while the world is the remainder. The boundary between body and world is indefinite, even though all parts of the environment are well defined. In a similar manner, the roots of a tree merge smoothly into the trunk and no precise boundary is definable even though the trunk and root exist in precise form. The boundary between PURR-PUSS and her body is also somewhat arbitrary but we shall define it for our convenience (Chapter 5). Just as a real brain and its body are intimately connected in a physical way, so is the PURR-PUSS program intimately connected with the programs and laboratory robots that provide the body of PURR-PUSS. (See Fig 1.1 [Fig 1.1 is a sketch of two laboratory robots connected to the computer and to a teacher.]).

Our experience of PURR-PUSS with many different bodies and worlds shows that better bodies and worlds permit richer behaviour. Body and world can be provided by simulation programs or by building robots in the real world. Although the PURR-PUSS program is simple, programs to simulate body and world have to be complicated in order to provide reasonably complex problem situations. Even the primitive laboratory robots (CAESAR and ESAW) that we have built for PURR-PUSS avoid elaborate simulation programs and enable her to act in the real world. It is hoped that researchers with larger resources than ours will give PURR-PUSS more effective bodies.

An important part of the environment is the human Teacher. Teacher can be the whole environment of PURR-PUSS, if he wishes. Teacher decides what body and world PURR-PUSS will have and he may provide every response to PURR-PUSS's actions, if he wishes. Usually Teacher instructs an auxiliary program called MEDEATOR to simulate some of the body and world so that he can concentrate on the difficult task of teaching PURR-PUSS. MEDEATOR carries out the chores for Teacher in a completely mechanical fashion.

Context
PUSS is a mechanism for remembering events and for recalling them. PURR is a decision strategy for choosing actions. When a number of PUSSes are combined with one PURR, then we have a PURR-PUSS.

PURR is less satisfactory than PUSS because it is still rather contrived and tentative. The primary message of this book is the simple mechanism of PUSS.

PUSS is a mechanism for storing events "in context". We would all accept that an event has to be seen in its context to be understood, perceived or recognized. Different events seem to need different amounts of context for their identification. Sometimes we recognize a face, place or picture "at a glance"; on other occasions it takes time. We have to learn to look for the appropriate clues. How can we design a system to associate an event with the appropriate context when the amount of context needed can vary so much?

The context used by a single PUSS in storing an event in memory is small and fixed, being the last "N" events where N is usually 3, 4 or 5.

To enable PURR-PUSS to find and use appropriate contexts, she is given several PUSSes, each contributing a different small and fixed context. The result is a "multiple fixed context" which turns out to be flexible and powerful. It may be likened to 4-wheel drive on a vehicle: when one pair of wheels cannot get a grip on the situation, the other pair may still manage.

The essence of PURR-PUSS is this multiple fixed context provided by several PUSSes. Imagine different people looking out through different windows from different directions on to the same scene. Each has a fixed field of view and each sees a different succession of contexts. The windows may be of different size. Now, each PUSS has a "window" which shows the last 3, 4 or 5 events, according to its size. Each PUSS receives a different sequence of events from the interaction of PURR-PUSS with her environment. The decision strategy of PURR uses the evidence of all these PUSSes to choose an action.

Novelty
In early experiments, PURR-PUSS was taught by reward and punishment. Simple individual tasks were taught successfully but Teacher had always to remember to give the reward and punishments at the appropriate times or PURR-PUSS would become confused. To "unteach" behaviour learned from inconsistent reward and punishment is difficult and slow.

When Teacher had decided to give reward and punishment in a consistent way and in clearly defined situations, he could instruct the auxiliary program, MEDEATOR, to perform the rewarding and punishing for him. This was satisfactory for simple individual tasks, but was no help for more complex tasks. Often Teacher is unclear at the start as to how he will teach a complex task. For his own convenience he may attempt to teach a complex task in sections. Unfortunately, but inevitably, a good deal of confusion is generated when reward for the first section is withheld so that it can be given at the end of the next section. Similar difficulties would arise whenever Teacher changed his rewarding schedule. The giving of reward does not seem to be an appropriate method for the teaching of tasks in a cumulative fashion. Punishment becomes an equally inflexible process if it becomes strongly linked to particular events. It may be necessary for Teacher to stop PURR-PUSS from doing something during the early learning of a task, even when he is going to require her to do the same thing later on when other contexts have been established.

For these reasons, Teacher will not use reward and punishment in any of the teaching reported in this book. Instead, PURR-PUSS will set her own "novelty goals" and Teacher will employ a mild form of punishment called "disapproval". Like most of the important features of PURR-PUSS, novelty-seeking was discovered by accident!

Brain Model
It is impossible to work in the field of artificial intelligence without wondering from time to time whether one's artefacts bear any resemblance to the human brain. We do not know how the brain works and, in my view, we shall be unable to unravel the physiology and psychology of the brain (its structure and behaviour) until we have made some good guesses as to how it might work. PURR-PUSS is not a model of the brain, but it may suggest how the brain works.

My design strategy over the past 15 years has forbidden the inclusion of features just for psychological or biological reasons. Each addition to PURR-PUSS is made in order to enable her to tackle an additional class of problems. Problems to do with survival in a harsh and competitive world have not been considered, as yet. This is probably why I have found no good reason for instincts or emotions. Even though reward and pain centres have been identified in the human brain, reward and pain have been omitted from PURR-PUSS. It seems that reward and pain are needed for survival (protection, provision and propagation), but not for problem-solving.

In problem-solving, the performance of the human brain stands before us as the ultimate and only challenge. In seeking ways to improve the scope of PURR-PUSS, every hint and tip fom psychology, neurophysiology and education has been gratefully received and often assimilated. With these influences, some similarity may be inevitable between the mechanisms in PURR-PUSS and those which will eventually be identified in the brain. After all, there may not be many simple mechanisms that would do the job ... and, surely, evolution found a simple mechanism?

PURR-PUSS starts with no knowledge of her body and world at all. Everything she learns is learned from her experience. She can be connected to any body and world. She can be given the largest memory we can afford and she is not made slower by a larger memory. The following chapters will illustrate how she learns and how she can be taught. As we attempt to teach more complex tasks, it becomes more difficult to tell whether failure is due to her or Teacher. The assessment of her performance is a major difficulty. I do not know of any other artificial system with which PURR-PUSS can be meaningfully compared. Nevertheless, many people have pointed to the need for a system like PURR-PUSS.

The Cage of Paradox
In designing PURR-PUSS, I have taken a different road from that followed by other researchers in artificial intelligence; but it is a road that many people have pointed to. There are signs that the popular road cannot lead to a machine intelligence comparable with human intelligence.

In 1931 the philosopher Gödel proved an important theorem. Quoting the later philosopher Lucas (1961): "Gödel's theorem states that in any consistent system which is strong enough to produce a simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true." Every formal system strong enough to be interesting is subject to paradox. A formal system operates within a "cage". We, humans, can see the paradoxes because our cages are wide open, but the formal system cannot. Now, every machine, robot or computer on its own (isolated from its surroundings) is a formal system and will never be able to do some of the things that we can do. If we try to remove the deficiencies of a machine by giving it extra cleverness, we may make the cage larger, but it will still be closed. The machine will be doomed to a lesser intelligence than man.

Sometimes people think of their bodies as cages within which they live, but bodies are quite the opposite of cages. My body connects me to the world around me in such an intimate and interactive way that I become part of that world. I can participate in the dynamic society and culture of humanity. My cage is wide open. Only if we enable our machines to interact freely with the world around them can we release them from the cage of paradox.

It is not possible at the present time to give PURR-PUSS an adequate body for intimate interaction with the world around her, so Teacher has to provide the missing link. By giving PURR-PUSS a close, interactive link with Teacher, we defer the need for an adequate walking-and-talking body until such time as we can provide it.
PURR-PUSS is unique, to my knowledge, in being a system that could be given a body-in-the-world.

Looking Ahead
The main results of this book are to be found in Chapters 6 and 7, where Figs 6.6, 6.7, 6.9, 7.3 and 7.5 to 7.12 represent a continuous interaction between PURR-PUSS and her body and world. Teacher, who is part of her world, attempts to teach PURR-PUSS a number of things during this interaction. I am Teacher.

The next four chapters (2 to 5) provide the reader with the detailed information necessary for a full understanding of each step of the main interaction in Chapters 6 and 7. Here, in this section, we look ahead in an informal, imprecise way to capture the highlights of PURR-PUSS's behaviour and to indicate the organization of the book.

In Fig 6.6 (Chapter 6), PURR-PUSS is taught to count objects using the fingers of her HAND. To get the gist of this interaction.

After teaching the COUNTING OBJECTS task in Fig. 6.6, Teacher goes on to teach PURR-PUSS another counting task, COUNTING BEADS, in Fig 6.7. The beads to be counted are on ABACUS, a part of PURR-PUSS's world. The details are deferred to Chapter 6, but here we can notice in Fig. 6.7 how the finger-raising technique of COUNTING OBJECTS is fully transferred to the new task with only one bit of prompting by Teacher (steps 193 and 195). PURR-PUSS applies the learned technique to the new task because the context is appropriate. In this way PURR-PUSS accumulates and transfers experience with the minimum of teaching. The more detailed discussion of Figs 6.7 and 6.9 in Chapter 6 explains how PURR-PUSS learns "naturally" to tell which of the two tasks, COUNTING OBJECTS and COUNTING BEADS, she is engaged in at any time.

In Fig. 7.3, I am attempting something more ambitious. Counting is a familiar operation and the teaching shown in Figs 6.6, 6.7 and 6.9 is quite straightforward. (Nevertheless, I know of no other existing artificial system that can be taught in this way.) In Fig. 7.3, however, I am trying to teach PURR-PUSS to say HELLO to a stranger and it is a surprising fact that no one knows what people do when they converse. The interaction listed in Fig. 7.3 combines talking, talking to oneself, raising eyebrows and face-scanning in a way which seems reasonable to me but may not appear so to the reader. Before being too critical, the reader should decide how he or she would have done it! Remember that PURR-PUSS should not treat a familiar face as a stranger, nor a strange face as familiar. This is, roughly, how PURR-PUSS encounters a stranger, Mr Triangle Face:-

Stranger says: "HELLO PUSS HELLO PUSS"

PURR-PUSS raises her eyebrows, looks at the stranger's face and says: "HELLO"

PURR-PUSS says to herself: "I MUST REMEMBER HIS NAME"

PURR-PUSS looks at stranger again and scans his face from bottom left, up across the top and down across to the bottom right.

Stranger says: "MISTER TRIANGLE FACE HOW DO YOU DO"

PURR-PUSS looks at the stranger's face and says aloud: "HELLO"

PURR-PUSS says to herself: "I MUST REMEMBER HIS NAME"

PURR-PUSS scans his face and says aloud: "MISTER TRIANGLE FACE HOW DO YOU DO"

The details are given and discussed in Chapter 7. The HELLO task is as much an experiment in psychology as a test of PURR-PUSS. It is an example of thinking with PURR-PUSS.

The ROOMS task occupies the largest part of the interaction, extending from Fig. 7.5 through all the figures to Fig. 7.12. The reader is given a ringside view of Teacher's attempts to make PURR-PUSS "want" to go into a particular room. As Teacher, I found it an interesting experience. You may decide whether, or not, I succeeded. The ROOMS task illustrates better than the earlier tasks how PURR-PUSS can act on her own, following her own hypotheses and being distracted by her own memories of past events.

Some readers may wonder how PURR-PUSS can use English words, when she starts with no knowledge of these words or even of their possible existence. She learns in a paradigmatic way, that is, by being given examples. I have taught her with English words because I am familiar with them and it is easier for me to remember what I am teaching her if I use English. If I had been Russian, say, then I would have used Russian words. A Frenchman can teach PURR-PUSS in French.

To understand how PURR-PUSS works, it is essential to recognize the part played by context in the remembering and recalling of events. Chapter 2 is devoted to the PUSS memory mechanism. PURR-PUSS contains five PUSSes, each of which provides memory for different aspects of her experience. The multiple context obtained from a number of PUSSes bestows on PURR-PUSS powers that we are just beginning to appreciate. Chapter 3 summarises our current understanding of multiple fixed contexts.

Chapter 4 places the reader at the console typewriter of a small digital computer programmed to behave like PURR-PUSS. There is a detailed account of what happens in a short illustrative interaction. The main decision processes of PURR are introduced in Chapter 4 with straightforward examples of how they occur in an interaction. The reader is given a full and precise description of PURR-PUSS and of her body and world in Chapter 5. The procedures for memory storage, prediction, hypothesis formation and action selection, given in Chapter 5, are derived directly from the computer programs that simulated PURR-PUSS for the interaction described in Chapters 6 and 7. Anyone wishing to write a program to simulate PURR-PUSS on their own computer should start from these same procedures....

The Appendix has not been given the status of a chapter, because it is less precise than the chapters and it is somewhat more speculative. However, as a model of the brain based on PURR-PURPUSS, it not only points to a way of discoverig the working principles of the brain but takes the first step.

Appendix

A.1 A Neurochemical Version of PURR-PUSS
Could the operation of PURR-PUSS be similar to the working of the brain? How could we tell? The brain is a neurochemical network of vast complexity and, physically, it is quite different from the digital computer in which PURR-PUSS is programmed. If we designed a neurochemical version of PURR-PUSS, would it be a model of the brain? That is the possibility that I discuss in this Appendix.

Mew-brain is a neurochemical network designed to be as similar to PURR-PUSS as possible. Unlike the mew-gram version of PURR-PUSS described in chapters 1 to 7, mew-Brain has not been properly tested. This is one reason why this section has not been given the status of a chapter. Another reason is that the current state of neurophysiology does not permit a detailed comparison of the neural processes proposed for mew-Brain with neural processes in the human brain. Nevertheless, the reader will find a carefully worked out system with some intriguing implications.

Mew-Brain offers certain advantages over the mew-gram version of PURR-PUSS and also suggests improvements to the latter. Thus, hypothesis formation in mew-Brain is more effective than hypothesis formation in either the mew-gram or the PUSS net versions of PURR-PUSS. In the PUSS net version hypothesis formation begins with a "working back" from the novelty goals through the network to guide the forward generation of hypotheses. In mew-Brain there is a similar "chemical leak-back" to mark out forward paths to novelty, but, being a neurochemical network, mew-Brain is not limited to the slow serial operation of the PUSS net version. The mew-gram version of PURR-PUSS would be as fast as mew-Brain with comparable "hardware", but, lacking the possibility of a fast working back process, the random forward generation of hypotheses in the mew-gram suffers from the disadvantages elaborated in Note 3 of Chapter 5.

Multiple context is another feature of PURR-PUSS that receives a somewhat diferent treatment in mew-Brain because of the different constraints encountered in designing a neurochemical network. The "cortical-PUSSes" into which mew-Brain is divided have been made partly sequential and partly spatial (see Note 1, Chapter 3) to avoid using composite events like pattern-actions and action-patterns. To include such composite events in mew-Brain would have made excessive demands on the chemical aspects of the neurochemical network. However, the mew-Brain contexts have virtues of their own and we plan to study them by introducing them into PURR-PUSS.

Mew-Brain is a physical system with all its parts working at the same time. Only a very small mew-Brain could be simulated in real time on a serial digital computer. PURR-PUSS is a similar, but not identical, structure which operates efficiently in a digital computer. PURR-PUSS may enable us to get a reasonably reliable idea of how a large mew-Brain would behave in complex environments. If there is some correspondence between this behaviour and the behaviour observed of humans, then we may be able to modify mew-Brain and PURR-PUSS to achieve a better correspondence. Even if this psychological approach provies unfeasible, the mechanisms proposed in mew-Brain may provide a working hypothesis for neurophysiologists studying the neurochemistry of the brain... .

A.5 Mew-Brain as a Complete System
This section is highly speculative so it will be kept brief. First I offer a rough calculation to show that known facts about the human brain are not inconsistent with a large mew-Brain.

A.5.1 A Very rough Calculation
A rough calculation shows that the kind of system we are talking about is possible . None of the figures used in the calculation is sufficiently reliable to make the results of the calculation likely.

We start by assuming that the brain (the neocortex, to be specific) receives input at the rate of 2 events per second. This is slower than rates attributed to the senses, but allows for pre-processing between sensors and neocortex. Estimates of the overall information rate of the brain have been as high as 40 bits per second, i.e. a million alternatives per half second. Let us assume, therefore, that we have a system which can accept any one of a million different possible inputs per half-second. If each of the three inputs to a context neuron in Fig. A.2 [Fig. A.2 is a diagram of a mew-Brain.] has a million different possible identities, there will be a trillion (10^18) different possible contexts. (I am using the British trillion which is a million million million). However, since a lifetime contains only about four thousand million half-seconds and there is likely to be a considerable amount of duplication of input sequences, we assume that only a thousand million contexts actually occur. In other words, about a quarter of the new inputs in a lifetime introduce a new context.

The number of neurons in the brain is estimated to be five thousand million or more. If a thousand million of these are context neurons for the thousand million contexts that can occur in a lifetime, three thousand million can correspond to integrating neurons in the upper, middle and lower layers of mew-Brain. Another thousand million neurons can be input, output and prediction neurons.

It has been estimated that a neuron in the brain can be within range of the connections (axons and dendrites) of up to five thousand other neurons. Suppose that each context neuron is within range of a thousand neurons in each of the layers of the integrating neurons. This means that each context neuron has a millin million million (i.e. a trillion) possible contexts, only one of which becomes coded to it. Assuming the inputs are randomly (or pseudorandomly) distributed throughout the neocortex, the thousand million context neurons, each with its thousand million possible contexts, presents a total potential of a trillion (thousand million times thousand million) possible contexts. But a trillion, being a million million million, is the number of possible contexts that can be produced by a million different inputs taken three at a time.

A.6 The Clay of Man's Mind
Mew-Brain is the last example of thinking with PURR-PUSS. By attempting to design a neurochemical version of PURR-PUSS, we have found something which promises to be more powerful than PURR-PUSS, something which suggests modifications to the design of PURR-PUSS, and something which takes us into the area of modelling the brain.

Arbib (1972, page 3) has complained that "too many psychologists and biochemists are not model builders. The opposite criticism, of lacking a practical experience of psychology and biochemistry, can be levelled against me. For this reason, I have not forced similarities between mew-Brain and the real brain. For example, the neurons in mew_Brain could have been arranged in a manner closer to neurophysiological proposals that I have read about. However, there seems to be a lack of general agreement on the physiological organization of neurons in the cortex, and the amateur like me finds no authoritative source to quote. My model is, therefore, a mechanistic model, not a physiological model. If neurophysiologists and neurochemists find the model compelling, they will be able to turn my model into acceptable neurochemical form. It is better that they do this than that I attempt it on the basis of their writings and my poverty of experience.

This Appendix has been speculative. My students and I are busy exploring the consequences of PURR-PUSS and mew-Brain. We are encouraged by the pleasantness of the journey. No dreadful threats of science fiction loom ahead of us. If the brain is like PURR-PUSS and mew-Brain, then we shall be able to talk about how the brain works without spoiling the mystery of its nature. We are discovering the clay, not analysing the sculptures. The brain will continue to be an infinite mystery evolving in each life from body, world and experience.

The clay of man's mind, grey matter and white,
Is a network of neurons and chemical codes.
The clay of man's mind is plastic, yet firm:
It allows him to choose and helps her to learn. It grows!
The clay of each man's mind
Is shaped by hands divine
And, leaving the Child behind,
Is set by the life it finds.
Mysterious clay of all mankind --- It knows!