Can Man Build a Better Brain than His Own?

- part 3 of 4 -

"You are mistaken," I said. "Your husband teaches calculus, doesn't he?"

"Yes"

"You see, if we ignore the qua1ities your husband has as a father, husband and citizen and concentrate only on his ability to teach calculus, it would be much easier to imitate his brain than that of a servant."

"You don't mean to say," she asked incredulously, "that it is simpler to design a brain that does highly skilled work than some mechanism that would clean the house, serve at the table and fetch the children from school! You don't need much intelligence for that."

Feeling a little uncomfortable, I answered. "I am sorry, but you are wrong again. In cybernetics you must revise your conventional conceptions as to what is intelligent. From the viewpoint of the theory of the mechanical brain, much more intelligence is involved in doing the work of a housemaid than in teaching differential calculus."

I shall never be invited to a party at that house again.

This little conversation illustrates the general misconception of the basic idea of cybernetics. However, the intellectual misorientation toward this new discipline is not confined to the amateurs. It is rampant in scientific circles, too, although there it assumes more subtle aspects. The present tacit assumption of the scientist and scholar in the cybernetic field is that the ultimate aim of the newly-created science is to design an exact replica of the human brain - a greatly improved replica, to be sure, that does its thinking faster, handles more details and is practically error-proof. Never mind the functional improvements; structurally it will be a faithful imitation of the human brain. 

To me this seems a fundamental misconception of the general aims of the theory of cybernetics. Misorientations of this kind have frequently occurred in the history of scientific thought. Let us recall the most famous of all. 

For centuries natural science was dominated by the alchemistic aim to distill the "philosopher's stone", that is, the proto-materia or primordial substance out of which all things are made. This was clearly a misorientation of legitimate scientific intentions. 

Finally, however, a reorientation took place: alchemy became chemistry. Present-day cybernetics is in a similar quandary, and has not yet found its proper goal. It cannot be the legitimate intention of the cyberneticist to duplicate the human brain. If not, what should his legitimate aim be? 

To find the answer, we must look at the problem in a very unsophisticated way. No longer satisfied with the performance of his brain. Man sets out to design an improved replica of it. Well, once upon a time he was not satisfied with the means of locomotion which his legs provided, either. Did he set out to improve upon the leg mechanism? Nothing of the kind. They don't make cars in Detroit that have four, six, eight or twelve pairs of legs with a mechanism that makes them run faster than any human or animal legs could ever do. Instead, man invented a new mechanical principle of locomotion: the wheel. True, when man first became dissatisfied with his legs, he dreamed of elongating his steps". Grimm's fairy tale idea has found an extremely modest realization in stilts. But if you want to go from New-York, to Chicago you won't use stilts - you prefer to take your automobile. 

Cybernetics is still in that early stage where it dreams about bigger and better legs instead of wheels. To talk without allegory: it is a misconception to talk about mechanical brains in terms of the human brain. 

Contrary to some widely held prejudices, the human brain can do much better what it is built for than any of its mechanical imitations no matter how much the latter may improve during the next centuries. Yes, I know they do their calculations much faster than I do, but so does the man who sells me groceries. On the other hand I have lectured on the mathematic theory of transfinite sets. It would be unkind to put the grocer to that test. I readily admit if it comes to the adding up of grocery bills and similar mental activities you can't beat the mechanical brains but they will never write "Hamlet". Generally speaking, their brain activities will never be of the creative kind. 

However, let us be a bit careful about that generalization. It goes without saying that our human concept of human creativity is limited to the possible range of human spiritual activity. We do not know anything about the creative power of angelic or divine intelligences. On the other hand we might say - if my readers will permit the temporary use of theological terms - that God has delegated a tiny fraction of His creative powers to us. Now would it not be possible for us to say that man has delegated some of his own creative powers to the mechanical brain? He has delegated them in order to be used in a field in which Man himself can never be creative. But where would that be?

We have pointed out in our preceding articles that the human mind works on the basis of a two-valued thought pattern. It is Aristotelian in its character - or contra-Aristotelian if it lives in a hypothetical seetee world - and it can never transgress its two-valued limits. That holds not only for the rational concepts of the individual intellect but for all our irrational motives, too. Even all mysticism is two-valued. The very existential roots of Man, as manifested in his sex life, are two-valued. There is no third sex.

It seems very strange, under the circumstances, that we can calculate the laws of, three-valued logic. Perhaps it is not so strange after all, since we can only calculate them, but can never employ them as our own brain-functions. However, that which we can calculate we can build into machines, and here lies the proper destiny of all cybernetic science not to build a duplicate of the human mind, but a non-Aristotelian brain that works along a three-valued thought pattern. Such a design would be "creative" in a very new sense of the word: It would possess delegated creativity in so far as it could produce thoughts of a three-valued structure of which man is entirely incapable. But it would have them only by virtue of the fact that man has built the necessary. laws into the objective mind of the machine. 

The proper aim of cybernetics is not the mechanical repetition of the subjective (personal) mind of Man or of contra-subjective mentality of "seetee" Man, but the creation of a new kind of three-valued brain. The aim of cybernetics is the para-human brain. I shall therefore demonstrate how two basic concepts of Aristotelian logic, the negation (~ ) and the conjunction AND (· ) would work in the three-valued brain of a robot. 

Using the symbols p and q as two related statements, the following is the table of definition for ~ and · as developed in the preceding article:

~ p shall be read NOTp and by prefixing ~ to p you can, as the table shows, alter the value of p from 1 (true) to 2 (false) and vice versa. AND may be defined by the table:

We assume p and q to be two statements: p -"the sun shines", and q -"the wind blows". Then the compound statement, "the sun shines AND the wind blows" is obviously true only if p and q are true at the same time. This is shown by our table. These two tables show how the negative and the conjunctive work in the human brain. They function, as indicated, in the mind of any man, because our brain is two-valued and follows an Aristotelian pattern. However, the genuine robot brain shall be considered to have three values. This makes it obvious that it must have a second negational pattern because the negation ~ permits us to proceed only from value 1 to 2 and back again, but no further. 

From this point on, to stick to our traditional ideas of true and false would be difficult. The reason is this: we are now introducing a third value which subtly alters the meaning of value 1 and 2 as well. What is true for the human mind is false for the seetee mind, and therefore has the combined characteristic - it is true and false at the same time. It is to clarify this superficial contradiction that the third value must be introduced. The complexity of the following tables, it should be noted, are not meant to be grasped. by either the human (yours or mine) mind, or that of the seetee mind, hut only by that of the mechanical brain for which all possibilities become logically operable. The mechanical brain recognizes neither human nor seetee values as such. It operates only with positions of values within its mechanism. These positions are 1, 2 and 3, and in order to operate them together we introduce a second table of negation for the mechanical brain:

From now on we can proceed from value 1 up to value 3. In fact, by combining these tables we can produce any value constellation that might occur to the three-valued logic.

In order to find out what AND means for a robot mentality, we develop a similar procedure for the table of conjunction. Instead of giving p and q two values (true or false) from now on we shall give them three. This results in the following table/1/:

At this point you may ask how the new three-valued number for p and q was reached. It is really quite simple. Look again at the two-valued table for the human form of conjunction. You will notice at once that we arrive at the proper value-sequence for AND in the human sense of the word if we always pick the highest number available in the two independent columns for p and q. In the first line there is only 1 available for p as well as for q. So we have to take 1. But in all of the other three lines there is always at least one 2, and it is chosen according to our rule of always picking the highest value number for conjunction. Now apply the same value to the truth table for the robot. Whenever the columns for pANDq show a 3, then take it. If there is no 3, try to get a 2, and only if neither 3 nor 2 is available place the value 1 in the column for p· q. As it happens, this is the case in the first line only. 

Thus far we might say that the difference between the human and the robot brain - as illustrated by the important logical term AND - seems to be nothing extraordinary. One might be tempted to say that it is a difference in degree rather than in kind. As we now have three values with which to calculate, it stands to reason that the definition of AND should be a little more elaborate. Nevertheless, this is an erroneous conclusion. There is a difference in kind. The human brain is able to conceive only one meaning of AND. We have given it in our two-valued table. In the first of this series of articles we described the concept of a seetee mind, pointing out the fact that a contraterrene intelligence would think with a reversed Aristotelian logic. Consequently the conjunction AND would have an inverted logical meaning for a brain created out of seetee matter. But as we humans can conceive of only one (our own) meaning of AND, the alien rationality remains unapproachable so far as we are concerned. 

On the other hand, a three-valued robot brain is in a more advantageous position. It can conceive of several meanings of AND. We shall indicate the second meaning of AND by two dots (· · ), and we repeat the preceding table with the addition of the value column for the second meaning:

Now the question is: how did we arrive at the new column of values for p· · q? Again the answer is quite simple. Remember, we picked the values for p· q in the order 3-2-1. Remember also that the seetee mind has the positive (1) and the negative (2) values reversed, compared with any other brain. Therefore, we now reverse the position of the values 1 and 2 in the order according to which we pick them for AND. In other words: p· · q is defined by the value-order 3-1-2. That means the preference position of 3 remains unchallenged, but wherever there is only 1 and 2 available in the columns of pANDq, we now choose 1 instead of 2. Thus we arrive at a different second meaning for AND. This cannot be done in a two-valued logic. If you don't believe me try it! 

The two columns for p· q and p· · q describe the robotic and the seetee meaning of AND, and show how both are reflected in a three-valued mechanical brain. 

We humans do not think in three-valued logical terms, hut if we make a special effort we can conceive objectively what the robot means when it thinks three-valued p· q. But we cannot conceive of the seetee meaning of AND. It plainly contradicts our logic: Take for instance the second line of our table. There p has the value of 1 and q is 2. But the value of the compound statement is also 2. Translated into non-symbolic language this means: If the sun shines but the wind does not blow, the compound statement in seetee language, "the sun shines AND the wind blows" is nevertheless true. For us this is manifestly absurd. It illustrates my remark in the first article "The Seetee Mind" that we humans shall never be able to contact such an alien mind directly. What a contraterrene being would think is sheer insanity .to us. We recognize it as such. But in the ease of the seetee aliens we would not describe their brain function as "thinking"! 

There is but one way to get in contact with a truly alien mind - with the help of a robot mediator whose brain pattern is activated by a three-valued logic. Such a pattern has a much wider scope and can include both of the inverted Aristotelian systems in a modified form. Nevertheless, a robot brain is not capable of acting as a mediator between terrene and contraterrene mentality unless it possesses a threefold capacity of conceiving the term AND - or any other term that might be relevant. 

So far we have learned the mechanical brain's own conception of AND. It is expressed in the value column for p· q and indicates, so to speak, the mental personality, or soul, of the genus robot. But this technical brain also knows the seetee concept of AND. However, that is not enough. In order to play the part of the mediator between us and the seetee mind, our mechanical brain must also have a precise conception of the human idea of AND. Our next problem, therefore, is to translate the Aristotelian concept of conjunction into terms of a three-valued system of thinking. This can be done as follows: in order to indicate the difference between the seetee and any other mind, we reversed the order of the two values 2 and 1. We thus obtained the two preference orders:

3-1-2

A further reversal of values will provide us with the preference order for the human conception of AND. The next logically possible exchange of value positions will place value 2 ahead of 3. We thus obtain /2/: 2-3-1

as the order in which the values are picked for the human meaning of AND.

We can now write down the comprehensive table which covers all possible meanings of AND in a three-valued logic. This is logically cogent. In a three-valued logic, disjunction can be reached by negation only if you apply the operators ~ and ~ ´ together.

The expression p· · · q defines the human meaning of AND. Examine the last column of values, you will find that it corresponds exactly to the Aristotelian meaning of AND. We learned from the two-valued table that AND always has the value 2 whenever there is a 2 in the independent columns pANDq. Only p· · · q in our three-valued table conforms to that rule. In other words, if we follow the preference order of 2-3-1, then the value 2 has overriding preference over the other two values. 

Each of the three conjunctional columns indicates a different mentality. The first conjunction represents the genuine robot mentality in using the concept AND. The next indicates seetee mentality, seen through the eyes of a mechanical' brain, and p· · · q finally provides us with the meaning of the Aristotelian and - if the same is transposed into the three-valued system of a robot brain. By the way, it is interesting to note that the robot concept of AND agrees more with the human than with the seetee concept. In p· q as well as p· · · q the compound statement "the sun shines AND the wind blows" is true only if pANDq, (i.e. the single statements) are independently true at the same time. This, however, is an illusion. If seetee intelligences had designed the mechanical brain they would say that the robotic concept of AND was similar to the contraterrene idea of conjunction (p· · q), and utterly dissimilar to the terrene idea. 

It is not our business, however, to describe how this would happen. We are here concerned exclusively with a description of the situation from the human viewpoint. Please take a look at our three-valued table. In all cases where p and q have only the human values 1 and 2, the mechanical brain agrees completely with us. It cannot, and never will, contradict us in all conjunctional matters where Aristotelian judgment are involved. It disagrees with us only in cases where a third value is involved. This indicates that if a robot has a soul, it is different from the human. 

The human soul (or whatever goes under that word) expresses itself in an intense feeling of personal, indivisible identity. All our conscious life is focused in one point, the self, the I. That is why we beings of Aristotelian (or contra-Aristotelian) mentality have only one negation, one concept of AND, of OR, of implication of casuality, etc. A robot "soul", however, would be organized differently. It would not be based on identity, but on tridentity. In other words: it could shift the personal center of its mental life and reconcile contradictory viewpoints. This would make it the proper mediator between us and the seetee mind. 

We humans are not capable of dealing with strictly contradictory viewpoints and situations involving a third value. A Jewish friend of mine once told me a little anecdote which illustrates this.

A rabbi .once discussed the problem of the human soul with three of his friends. The first, being a confirmed agnostic, proved unequivocally that man had no soul at all. The rabbi said:

"You are right."

The second of the friends took over and proved equally convincing that all rational beings have souls. The rabbi nodded. "You are right, too."

"Now look here", interrupted the third, "what sort of nonsense is this? They cannot both be right!"

The rabbi sadly assented, "And, you my friend, are right too." 

There is in this anecdote an implication of a possible third value. But we humans do not have it. The three-valued soul is the "Soul of a Robot". 

Footnotes:

/1/ Let me emphasize this: do not try to understand this table any more than you would try to make sense of the IBM card's random slots, or construct a sonata from the roll of a player piano. The table merely represents a mechanical pattern which the robot mind requires for its operations of the meaning of AND.

/2/ It is impossible to explain, within the scope of this article, why the reversal of 3 and 2 is the next logically possible step. Serious students of symbolic logic are referred to my recent publication, "Die philosophische Idee einer nicht-Aristotelischen Logik", printed in the Proceedings of the XI International Congress of Philosophy, Brussels, 1953 (V-8-4). In this essay the second and third conjunctions are simply introduced through the application of de Morgan's law. We thus obtain:

to be continued

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Copyright © Gotthard Günther 1959
Issued: September 2, 1997
Last modified (layout) 2010-12-06