Grey Lodge Occult Review™
MANHOOD of HUMANITY: The Science and Art of Human Engineering
by ALFRED KORZYBSKIBack to Manhood of Humanity Contents
Appendix 4
Some Non-Aristotelian Data on Efficiency for Human AdjustmentThe summary of Graicunas' work given at the end of this supplement, in a practically unchanged form, was a personal communication in 1934 from Walter N. Polakov, the outstanding engineer and industrial diagnostician in the United States. It was originally written for the Tennessee Valley Authority, which was then passing through acute managerial difficulties due to confusion of function and control. Mr. Polakov, writing about the T.V.A. project, evaluated the situation thus:
The youthful T.V.A. inherited the language and metaphysics of a bygone age. It encounters unprecedented difficulties in expressing new relations in terms of vanished fancies. The night fear of ghosts remains.... The difficulties in building the T.V.A. without a language having correspondence to reality, are not difficulties peculiar to this project. They are signs of our time-a sort of dangerous epidemic, springing out of our slow adjustment to a profoundly changed environment.
In my work with students I have utilized Mr. Polakov's summary with his diagram adapted from the original data concerning the 'span of attention' or 'span of control', as well as related foundations formulated in my own writings. I have found empirically that these are invariably useful for the elimination of the individual's inability to handle personal life situations adequately.
At the root of the problem lies the significant fundamental difference in the rate of growth between arithmetical progression, which grows by addition, for example, 2,4,6,8,10, etc., and geometrical progression, which grows by multiplication, for example, 2,4,8,16,32, etc.
We must mention here permutations and combinations, and even combinations of higher order which also follow an exponential law. The different orders in which things can be arranged are called their permutations. The different collections which can be formed from things without regard to the order in which they are placed are called their combinations. For example, the four letters, a,e,m,n can form but one combination, but they occur in the English language in several permutations, as name, amen, mean, mane. The question may arise, 'How many changes can be rung with 10 bells, taking 7 at a time ?' The answer is 604,800, quite a respectable number for a problem so seemingly simple on the surface.
The work of Graicunas, Urwick, etc., is based on empirical data from military and managerial experiences, where complications dealing with human reactions grow in a geometrical ratio. The disregard of the above considerations has led to many military and managerial disasters. I must stress that the same principles apply also to our personal life difficulties. For instance, in what psychiatrists call 'family attachment' (infantile clinging to 'papa' or 'mama'), in the notorious interference of mothers-in-law, or in the tragedies of marital triangles, it is not a question of just an 'added' factor, but the difficulties accumulate in some geometrical ratio. Similarly, a childless couple 'adds' a baby to the family, and the complications grow following some exponential law. Organism I responses to 'one more glass of whiskey' are certainly not additive. The followers of sick Schicklgruber-Hitler may have learned by now that the 'addition' of one more country introduces non-additive complexities not included in a naive fool's paradise gained by brute force. And so it goes all through life in the more fundamental relationships.
If in personal life we undertake or have to carry too many responsibilities, interests, involvements, etc., the complexities often grow beyond the capacity of one human brain to manage them adequately, and human tragedies, disorganizations, etc., follow, very often culminating in maladjustment and even neurosis or psychosis.
Many times a single painful event in childhood or even later in life distorts the attitudes and colors the whole life. Thus, the 'addition' of a single factor results in unnecessary complexities which are certainly not additive, but spread all through life in some geometrical ratio.
We hear remarks by some scientists that 'It is impossible to express the conduct of a whole animal as the algebraic sum of the reflexes of its isolated segments.' Yet later we find that same author saying, 'The individual represents heredity plus environment.' another writes, 'Thus a clock-work is as little the mere sum of its little wheels as a human being is the sum of his cells and molecules'; and later on, 'to be exact the ego consists of the engrams of all our experiences plus the actual psychism.' These two examples, out of many, are given to show how even with those scientists who realize the fallacy of additivity, some 'plus' creeps in, which is obviously false to facts, demonstrating that ingrained additive tendency inherent in the aristotelian prescientific orientation.
On the other hand, a few modern psychiatrists familiar with the latest scientific developments by necessity realize those additive aberrations, and do not plant a falsifying 'plus'. We read, therefore: 'Before therapy can be discussed or put into practice, three fundamental concepts must be thoroughly understood: (1) the nature and characteristics of neurotic symptoms; (2) the formula, "Constitution times Environment times Stress"; and (3) the role that "attitudes" play in the creation of symptoms.' Although Dr. Kraines has definitely a non-additive attitude, his 'times' does not represent the situation correctly. The correct representation would be functional, N=f(x1, x2, x3,. . . xn), where N represents neurosis, f represents function of, x1, constitution, x2, environment, x3, stress, and the etc. ( . . . xn) indicates special functional factors in a given case, all of which are interrelated. Such psychotherapeutic observations indicate why in a 'therapy of attitudes' it is so important to change from an aristotelian to a general non-aristotelian attitude, not only for psychiatry, but for prevention of misevaluations in life by everyone.
As a matter of fact, most psychotherapy depends on efforts of the physician to eliminate, through reinterpretation in treatment, some of those original factors which produced worries, fears, anxieties, and other disorganizations. These factors were responsible for the introduction, because of exponential laws, of an enormous number of artificial complexities which made life adjustment difficult or impossible. In my personal experience and the experience of many of my students, who are physicians, educators, etc., it is found that the explanation of the above non-aristotelian principles is very useful, as the patients or students realize that with the old attitudes they are up against impossibilities. They become conscious of the mechanisms of the difficulties, which is the only way to make a solution possible.
Mathematicians, in their often deliberate detachment from life, unfortunately have not forewarned us of these kinds of methodological traps, and in fact often repulse their students by the lifelessness of their teachings. Mathematicians quite glibly speak about their students being 'mathematical imbeciles'. Often I wonder whether this is true, or whether the responsibility has to be laid frankly on the mathematicians, who may be 'life imbeciles'. If before they begin to teach they would study in a 'mental' hospital and analyze the 'treatises' of the patients, they would become better teachers, better research workers, as they would understand what it means to be detached from living life.
The problem of additivity in life as well as in mathematics, where it is called 'linearity', is of great antiquity because it was the simplest. The mathematical formulation of additivity (linearity) is f(x+y) = f(x) + f(y). One of the most striking consequences of additivity is the predictability from the characteristics of the elements to those of the results. In other words, no characteristic absent in the elements appears in the result. It is obvious that when we combine elements, and the results have new characteristics absent in the original elements, the new problems are structurally no more of an additive character, and the synthesis must be different. If our attitudes are limited to the additive principle alone the results in the most fundamental issues of science and life are bound to be false to facts. For example, one pound plus one pound in weight results in two pounds, but one gallon of water 'added' to one gallon of alcohol results in less than two gallons of liquid because profound inter-molecular issues enter which are not additive, and so 1 + 1 2. Similarly, one atom of mercury 'minus' one electron becomes one atom of gold. And so the results are not predictable by the principle of additivity. As Graicunas shows, the 'addition' of a sixth assistant by a supervisor may add 20 percent to his human resources, but adds approximately 100 percent to the complexity and difficulty of his task of co-ordination. And so it goes.
We have discovered by modern science that the world and life are not additive in their fundamental aspects. Even the epoch-making work of Einstein, the founder of a non-newtonian system, depends on the transformation of linear (additive) equations into non-linear (non-additive) more complicated equations. But the structure of our ordinary subject-predicate language and corresponding attitudes is still aristotelian, and therefore in the main additive. Unfortunately extremely few of us, even among my readers and students, realize that fundamental gap between additive and non-additive relations and attitudes.
My whole life work, and particularly since 1921, has been based on the life implications of this neglect to differentiate between the laws of growth of arithmetical and of geometrical progressions. Such neglect was partially responsible for most historical spasms of civilization such as wars and revolutions, and accounts for many disasters in private lives. This point must be stressed to the utmost. Because Graicunas, Urwick, etc., deal with human relations without disregarding mathematical issues, their work is based on the same principles, which automatically involve permutations and combinations. The interested reader is urged to consult his elementary algebra about the arithmetical and geometrical rates of growth, and the simple formulations of permutation and combination. It is sad to say that combinations of higher order are usually omitted in the textbooks and regarded as mathematical curiosities without application. Unfortunately life facts and complications, ultimately on the electronic and electro-colloidal levels, in principle follow these combinations of higher order. The computations as such are of little or no practical value; however, the methodological implications for life orientation, disregarded by mathematicians, are of primary importance. For further details the reader is referred to Jevons' and my own work.
In human life one of our difficulties is that we are 'both the marble and the sculptor', as Carrel says, and so we are both the managed and the manager of our personal lives, the supervised and the supervisor, the co-ordinated and the co-ordinator. Perhaps one of the main sources of a great many maladjustments is exactly that self-reflexiveness and circularity which we do not know how to manage simply because we don't know that there are non-aristotelian methods to do so.
In such a brief paper it is impossible to go into details short of writing a book. Plenty of books on modern science are available, but they have only very limited applications because the issues had not been formulated methodologically. It is generally not realized that with the advance of science the old aristotelian methodology, by which the majority of us still live, is thoroughly obsolete and unworkable today, and even harmful for the best of human adjustment.
This 'epilogue' was written to emphasize and partially explain the necessity of passing from the aristotelian orientation to a non-aristotelian, functional orientation, and to stress to what extent the issues have application in daily life. This non-aristotelian system is based frankly on physico-mathematical methods, which, as this volume shows, have general human application, even on the level of nursery education. These are not problems for speculation or verbal arguments or debates; the issues are empirical and have to be tested by application. This paper is based on experience of how this non-aristotelian system works in practice, no matter whether the theoretical issues are formulated satisfactorily for everyone, or satisfy the author himself.
In the present unprecedented world crisis we are not facing a 'new order', we are witnessing the death-bed agonies of the inevitable dying of the old aristotelian system which has been applied to its deadly limit. I personally have no doubt that after this world crisis is over, and the dead are buried, the future of mankind will depend on some new non-aristotelian systems which would be frankly based on scientific extensional principles, and so ultimately on physico-mathematical methods. I emphasize that the title of my book 'Science and Sanity: An Introduction to Non-aristotelian Systems and General Semantics,' indicates that science and sanity are interrelated, which seems only natural. The reader should notice that I utilize 'non-aristotelian systems' in the plural, because the non-aristotelian system I have produced is not the system, but a system among many other possible ones.
Surveying the chain of historical world tragedies as they accumulate with accelerating acceleration and intensity, one naturally looks for the factors which are responsible for such cataclysms. This problem may be analyzed in many different ways, but here in this first non-aristotelian system we take frankly and explicitly an engineering point of view, in which there is no 'philosophy' for 'philosophy's' sake, nor science for science's sake, nor mathematics for mathematics' sake, but we consider all those activities as products of the human nervous system, to be applied for its optimum efficiency. When formulated methodologically, the interrelation between science and sanity becomes obvious, and the new child-like methods can be applied for more efficient management of our private as well as public lives, and in particular for prevention of maladjustments, i.e. misevaluations in life.
From this, perhaps a new point of view, we must squarely put the responsibility on 'philosophers', because of their innocence of science, their 'superiority', aloofness from non-aristotelian issues, and so their inability to take into serious consideration our neuro-semantic and neuro-linguistic environment as environment. The 'philosophers' somehow feel 'above' experimental methods; they will argue endlessly on the verbal level, but they will not experiment with the new extensional methods. I must repeat that the new methods are not a problem for arguments or debates, but simply for empirical investigation of how they work. 'Philosophers' should have discovered long ago that maximum teachability is found in method, and in our case ultimately physico-mathematical method, even on the nursery level. Through their errors of omission, 'philosophers' are largely responsible for the sterility of education, be it on the primary or the university level, and for the naive 'isolationists' in science, and/or in life. For example, it is pathetic to watch university faculty members at meetings, where many have nothing in common, because they are not united by a general method. Under such conditions the effectiveness of scientists as human beings is lowered and often does not even command the respect of the layman, who does not realize the handicaps of specialization without a general method. In my experience with classes we have students who belong to widely separated fields such as medicine, mathematical physics, education, social work, linguistics, law, etc., and in a few days they become a more and more closely knit unit because they get a general method which applies to all their professions, as well as daily life. The present day isolationism paralyzes the isolationists themselves, preventing them from taking a general extensional attitude. We must become and remain conscious that scientific work as well as our private reactions in life are the end product of the electro-colloidal processes going on in our nervous system. As experience shows, these processes are deeply affected, in different ways, depending on whether we use intensional or extensional methods. This correspondence and close interrelationship between neurological processes and the method used is the key problem in passing from one system to another, in this case from an aristotelian to a non-aristotelian system. The empirical demonstration of the above facts through actual application of the extensional method is, I believe, entirely new, and amounts to a 'therapy of attitudes'.
Is the blame to be put entirely on the shoulders of scientists or laymen? The answer is 'no'. With the old, aristotelian, two-valued orientation it is humanly impossible to have the modern, infinite-valued, non-aristotelian process orientation, and therefore it is impossible to 'think' about ourselves in electro-colloidal neurological terms. So once again the responsibility is the 'philosophers', who have neglected this most important neuro-methodological field, and so have not given educators, scientists, etc., and laymen a foundation for mutual co-operation. This reflection is rather heavy in consequences, because the failure of 'philosophers', which is a matter of historical record, has actually prevented the co-ordination of diverse efforts for optimum human adjustment. 'Philosophers' of course will try to talk their way out of this dilemma, but this will not help because this work has not been done by them, and the only way for them is to investigate, experiment, and find out. A great many 'philosophers' will be shocked and consider sacrilegious a mere suggestion that 'philosophy' should become experimental, like any scientific theory is.
As to politicians, diplomats, rulers, etc., the situation seems hopeless because of their ignorance, lack of preparation for their human responsibilities, and in fact refusal to accept professional guidance when help is offered them. I will not go into details, as many hundreds of volumes have been written exhibiting the utter stupidity and incompetence of those who are supposed to guide our destinies. with the result that we are bled white in blood as well as in taxes, becoming more and more disorganized for years to come.
In the history of science and civilization we discover that living emergencies forced us to find some solutions to make adjustment to life more efficient, in spite of 'philosophers'. So far it has been done by men like Graicunas, Urwick, Polakov etc., who based their work on the application of mathematical methods to empirical data about the limitations of what the human nervous system can stand. Their work dealt particularly with industrial and military fields, where lack of efficiency brings obvious disasters. In my own work I felt that mathematical methods should have broader applications, and apply to daily life, as even the smallest managerial unit, which we call the 'family', also must have some method for optimum human efficiency based on the understanding of human nature and the limitations of what one human brain can stand. Otherwise disasters, in different degrees, are bound to follow, which may even end in maladjustment, neurosis, or psychosis.
I admit that I can not see how anyone who has to deal with human affairs, be he the responsible member of a family, a teacher, a physician, or a politician, etc., can be competent at all to deal with the problems confronting him if he is entirely innocent of the problems raised in this paper, including the summary by Polakov taken from the work of Graicunas and Urwick, which follows. Original sources were published abroad in 1933. In 1937 the Institute of Public Administration, Columbia University, New York, reprinted the two fundamental papers referred to, with some new material, under the title Papers on the Science of Administration, edited by Luther Gulick and L. Urwick. I suggest that all my readers study this book.
SUMMARY OF SPAN OF ATTENTION BY WALTER N. POLAKOV
For a full exposition of Mr. V. A. Graicunas, theory, see Bulletin of International Management Institute, Vol. VII, No. 3, March, 1933, article entitled: 'Relationship in Organization.' Reference to this theory is also made in a paper read to the Department of Industrial Cooperation of the British Association for the Advancement of Science, Leicester, September 7, 1933 by Major L. Urwick, O.B.E., M.C., M.A., entitled: 'Organization as a Technical Problem.' Quoting from the last reference:
Students of administration have long recognized that, in practice, no human brain should attempt to supervise directly more than five, or at the most, six other individuals whose work is interrelated. Mr. V. A. Graicunas of Paris has recently shown why this is so. [His work is the second of the contributions of importance to the technique of organization since 1930.] An individual who is coordinating the work of others whose duties interconnect must take into account in his decisions, not only the reactions of each person concerned as an individual, but also his reactions as a member of any possible grouping of persons which may arise during the course of the work.
The psychological conception of 'the span of attention' places strict limits on the number of separate factors which the human mind can grasp simultaneously. It has its administrative counterpart in what may be described as 'the span of control'. A supervisor with five subordinates reporting directly to him, who adds a sixth, increases his available human resources by 20 percent. But he adds approximately 100 percent to the complexity and difficulty of his task of co-ordination. The number of relationships which he must consider increases not by arithmetical but by geometrical progression.... Neglect of the limitations imposed by 'the span of control' creates insoluble problems in coordination.
The proposed formula for the number of direct group relationships is:
R = n (
+ n-1)
where R=a+b+c represents total direct and cross relationships; n = number of persons supervised; a=number of direct single relationships; b=number of cross relationships; c=number of direct group relationships. Thus computed on the maximum basis direct and cross relationships arising for the given number of subordinates is:
Number of assistants or functions
1 1 (1)* 2 6 (4) 3 18 (10) 4 44 (21) 5 100 (41) 6 222 (78) 7 490 (148) 8 1080 (283) 9 2376 (547) 10 5210 (1068) 11 11374 (2102) 12 24708 (4161) * Figures in parentheses are computed on the minimum basis.
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