I have been aware of the 'span of control' or 'span of attention' problem since I first read Korzybski's Manhood of Humanity twenty years ago. My awareness of this problem led me recommend smaller groups of organization within the ORTEGRITY than I might otherwise of suggested. Perhaps the ideal size of a heterarchy is five humans. Certainly, no more than seven.
Alfred Korzybski writing in 1941 explains: 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' by Graicunas.
 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-laws, or in the tragedies of marital triangles, it is not a question of just an 'added' factor, but the difficulties accumulate in some geometrical ration. Similarly, a childless couple 'adds' a baby to the family, and the complications grow following some exponential law. Organismal response 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. ...
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.1
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.2
The proposed formula for the number of direct group relationships is:
R = n ( 2N/2 + 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-minimum basis direct and cross relationships arising for the given number of subordinates is:
|
Number of assistants or functions |
Number of relationships or problems arising (maximum) |
Number of relationships or problems arising (minimum basis) |
| 1 |
1 |
1 |
| 2 |
6 |
4 |
| 3 |
18 |
10 |
| 4 |
44 |
21 |
| 5 |
100 |
40 |
| 6 |
222 |
78 |
| 7 |
490 |
148 |
| 8 |
1080 |
283 |
| 9 |
2376 |
547 |
| 10 |
5210 |
1068 |
| 11 |
11374 |
2102 |
| 12 |
24708 |
4161 |
References:
1) Alfred Korzybski, Papers From the Second American Congress on General Semantics, 1941, Institute of General Semantics, Lakeville, Conn., 1943
2) L. Urwick, Organization as a Technical Problem, Department of Industrial Cooperation of the British Association for the Advancement of Science, Leicester, September 7, 1933
3) Luther Gulick, Relationship in Organization, Bulletin of International Management Institute, Vol. VII, No. 3, March, 1933
4) 'Span of Control' Diagram (large)
9:26:11 AM 
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