PHILOSOPHICAL WORD DESCRIPTIONS can never be wrong, for what is described has been created by the process of description. Words like ‘self’, ‘consciousness’, ‘free will’, ‘humour’, ‘motivation’, ‘learning’ and ‘insight’ are useful as catalogue descriptions for the purpose of communication, but useless as explanations. They create themselves in a manner that has its own consistency but does not explain what is being described.
‘Suicide is caused by the self-destructive tendencies inherent in mankind.’ At first sight this sentence seems to offer a useful explanation of the phenomenon of suicide. But does it? Suicide is clearly self-destruction, and one can use the latter phrase instead of the word. When members of a species do actually commit suicide then it is fair to say that there is a suicidal tendency in that species. Since the species in question is mankind, the tendencies are inherent in mankind. Thus the sentence, ‘Suicide is caused by self-destructive tendencies inherent in mankind’, explains no more than a sentence which reads, ‘Suicide is accounted for by the fact that people do actually commit suicide’.
As explanation, the sentence offers nothing except tail-chasing, but as description it does have a value. It suggests that suicide may not be an abnormal aberration, or due to external pressures, but the expression of an inclination which is part of the make-up of mankind. That may be so, but as mere description one is not entitled to build on it as if it were some real phenomenon. Otherwise one just ends up with words chasing words into a pattern of great intricacy and little use.
The sort of mess one can get into with words is shown by some of the old arguments about determinism, free will, responsibility and punishment. The argument is that if a person’s actions are entirely determined then he is no longer responsible for them, and hence it is unjust to punish him. One might equally well argue that the only possible justification for punishment was that the actions were determined. One would hope that the memory or anticipation of punishment would become one of the determining factors. It all depends where one draws the boundary for self: whether self includes the determining factors or is supposed to stand apart from them.
In order to make any progress one tries to get away from words as things in themselves and tries to use them only as descriptions of other things which exist in their own right. If the behaviour of a car is determined by its design and the power of its engine, then a description of the system still involves words but they rest on the car system and not on each other.
If you use a child’s construction set to make a working model of a crane, then the way the crane works will depend on the pieces that have been chosen and how they have been put together. Once the pieces have been chosen and put together then the model will work according to its nature. The creator no longer controls but only watches it. Usually the model will behave as expected, but it can also go beyond what the creator expects. Once it has been constructed the model has a life and working of its own. If instead of actually constructing a crane you had just imagined one then you would have been free to imagine all sorts of behaviour for this crane, but this behaviour would never have taught you anything since you would be supplying it all. With a model, however, you only put the pieces together and then learn from what happens.
A model is a method of transferring some relationship or process from its actual setting to a setting where it is more conveniently studied. In a model, relationships and processes are preserved unchanged, though the things that are being related may be changed. In order to study the proportions of Westminster Abbey one might take a photograph and then study this. The photograph is a model of the abbey, and the relationships are preserved, even though it is now differently shaded areas of paper that are related. A better model would be a three-dimensional one made of wood or cardboard which would preserve even more of the relationships.
All models involve this transformation of relationships from their original setting into another. A map is the transformation of the relationships of the countryside into relationships on a piece of paper that is much more convenient to study. Once the transformation has been made then the relationships within the model itself indicate what can happen. The paths of sub-atomic particles in physics are transformed into lines of minute bubbles which can be photographed and measured. A watch is a method of transforming time into the position of one bit of metal relative to another. All scientific measuring instruments are just methods of transforming some phenomenon into something else that is easy to handle, be it a curve on a piece of paper, a pointer on a dial, or a printed figure. A book is a transformation of ideas into a black and white pattern of some permanence. Money is the transformation of work into pieces of paper.
All these transformations result in the setting up of models which represent processes or relationships in ways that are more easy to handle and examine. For instance, a temperature-recording device may transform the fluctuations in temperature in a warehouse into a wavy line on a piece of paper. Here the transformation of time into space is most convenient since it makes all the information available at a glance.
Some working models may actually carry out processes which can be examined. Other models merely represent the relationships, and the observer has to do the work. The line which represents the projection of a cone onto a piece of paper is just a line, but working from it the observer elicits the mathematics of conic sections.
A child making a model house might cut the whole thing out of cardboard or out of a cardboard box. Alternatively he could use those ready-made plastic building blocks. These blocks can be used to build any shape of building. All one has to do is to fit them together in their special way and then one can proceed to make any design one likes.
So it is with other models. One can make a special model to fit the situation, or one can make use of multipurpose model-building kits. Mathematics is the most obvious of such kits. There are pieces which fit together in certain ways and these ways are the rules of mathematics. Using the standard pieces one can represent a real-life situation by means of a model. Once the transformation has been done then the model is allowed to work according to its own rules. One follows along and sees what happens, and then translates this back into the real world to see what would have happened there. Mathematics is no more than a pencil-and-paper model-building system worked with certain rules.
Any notational system is a model-building system. Mathematics happens to be a system of notation with which there has been a huge amount of experience. This means that people have become very good at recognizing particular types of models and knowing exactly how to work them. Ordinary language is another notational system with its own working rules.
Because notation seems so arbitrary, it is often difficult to appreciate just how important it may be in the development of ideas. It is rather like the design of a child’s building blocks. If the design is good then there is great flexibility in what can be built. A cumbersome design may make progress impossible.
The development of mathematics was held up for a long time by the cumbersome notation of the Greeks and then the Romans. The Roman system was good for adding, subtracting and tallying, but very awkward for multiplication or division. Then came the Arabic system, with its emphasis on the position of a symbol as well as its shape. Then there was the invention of the zero, which has had an immense usefulness in the development of mathematics. The invention of the decimal notation again made things easier.
Descartes’s invention of co-ordinates made possible the development of analytical geometry. Newton and Leibniz independently discovered the calculus, but Newton’s notation was so very cumbersome compared to that of Leibniz, that those who followed Leibniz made much more progress. This is surprising when one realizes that the basic principles were the same in each case and only the notation was different.
The effect the different types of notation have had on the development of mathematics is very striking. With the notation of language the effect is probably also very large, but it is less obvious. Choice of a convenient notation may have made possible the development of different ideas. A more important effect is the way choice of notation can make a great deal of difference to communication. It is also possible that the more complicated the notation the longer it takes to learn, and hence the more prolonged education must be. When one compares the twenty-six-letter alphabet to the huge number of Chinese characters one can appreciate the huge difference in convenience, for instance on a typewriter.
Symbolic logic is a further notational development of language that brings it closer to mathematics. It is possible that the notation of language, both as regards visual and auditory notation, may be developed further. For instance there does not yet seem to be in language an equivalent of the zero in mathematics.
Notation is quite arbitrary and quite passive. Notation may even seem insignificant beside the subject being described, just as the choice of a particular language may seem to be much less important than what is being said in that language. Yet notation is immensely important. Notation and its rules form a model in themselves, and it is the fluency of this model that determines how well the real-life situation can be explored. One would hardly set out to explore the intricacies of flight with a model aeroplane made of clay.
In this book the function of the brain system is not described with words but with working models. The models are set up to imitate certain processes, and then one observes how they function. One watches what happens when various processes and relationships are put together. There is no question of words chasing words, creating and justifying each other in an endlessly circular fashion. Words are only used to describe the behaviour of the model, and this is independent of the words used.
The models are simple functional ones which embody basic processes that are easy to follow. It is true that many of the relationships and processes shown by these models could be just as easily shown by mathematical models, but except to those who work with them all the time mathematical models can be difficult to follow, whereas a model which makes use of the behaviour of an ordinary fruit jelly is much more accessible. The process itself may be just as subtly described by the one as by the other. The advantage of having an accessible model is that the reader can visualize it and play around with it in his mind.
In so far as mathematics is the handling of relationships, the physical models are mathematical models if they obey certain defined rules. Mathematics in its proper sense is not just the arrangement of symbols on paper. Stonehenge is a mathematical model, and so probably are the pyramids.
The advantages of using a model that can be actually played with or visualized are great when compared with mere description. A description only uses one particular way of looking at something; it describes what is noticed at the moment, what makes sense at the moment. A physical model, however, contains all that could be noticed at any time; it includes all the possible ways of looking at the situation. Should the point of view change, one can go back and find the new point of view.
Here is shown a simple physical figure that could be described as an ‘L’ shape. This is an adequate description, but it is much less use than having the actual figure. With the actual figure one can go back again and again, paying attention now to the length of the limbs, now to the width of the limbs, now to the orientation of the figure. It is true that all these things could be included in an elaborate description, but that would be tedious. It is much better to have them stored in an accessible model so that one can have them only when one needs them.
Some new notations are introduced in this book. These notations have been invented to ease the business of describing certain processes and relationships which it would otherwise be awkward to describe. Like all new notations they may take some getting used to, but once one gets to know them they do make things easier.
Imitation of behaviour does not imply similarity of the mechanism underlying that behaviour. The behaviour of the information-processing system described in this book may resemble that of the brain, but this does not prove that there must be a similar mechanism acting in the brain. Nevertheless there are several reasons why such an approach may be useful.
1. The information-processing mechanism described may be of interest in itself, as an example of a self-educating and self-organizing passive system that is capable of effective information-processing by means of a few basic operations.
2. The system described is capable of such processes as ‘self’, ‘direction of attention’, ‘thinking’, ‘learning’ and even ‘humour’. These and other related processes are usually regarded as being specifically human in nature. That they can be imitated by a mere mechanical machine – and a passive one at that – must affect the notion that the human brain functions in some unique and magical fashion.
3. Although the system is basically very efficient, there are certain inherent faults and limitations which lead to definite types of error in the processing of information. Such inescapable errors permeate the thinking processes in the system. The idea that there may be inbuilt errors in an information-processing system may have a relevance to human thinking, even if the system itself does not.
4. Instead of the more usual verbal philosophizing as to what goes on in the mind, the system offers a mechanical philosophy. In its own right this is just as valid as the verbal descriptions, and it also avoids some of the circular tendencies of verbal descriptions. Like any myth, this mechanical one can have a useful consistency as an organizing idea, whether or not its truth can be checked.
5. By far the most important function of the system described is to throw up definite ideas which can then be examined for their own sake. The validity of the ideas is not proved by the way they come about, but once they have come about then they might prove to be valid in themselves. In this capacity the system acts as a method of generating ideas which can then survive on their own.
6. Even though no formal attempt is made to prove that the information-processing system described is the one operating in the brain, there is evidence to suggest that it may be. The actual details of the system may be different, but the broad class of system is probably the same. In a later section the resemblance between the functional units used in the information-processing system and those operating in the brain is discussed.
Whatever else it does, the description of the information-processing system ought to stimulate the reader’s own ideas about the dependence of brain function on its structure.
One talks of a computer having a memory. This is using a human analogy to describe a mechanical process. In the course of this book the processes that occur in the model are often described as if they were occurring in the human brain. This is carrying the same analogy process further, for it would be quite impossible to describe the processes in other terms. It is not meant to be a back-door way of implying that similarity of behaviour proves similarity of mechanism.
