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## Order vs. Organization

November 14, 2011

This paper deals with man's taste in configurations and consequences arising therefrom. "The Problem of the Orchard" may introduce the subject better than any abstract statement.

## The Problem of the Orchard

Let there be an apple orchard and two distinct groups of school children. The first group is assembled in class and is asked the following question: "In a given orchard, 100,000 apples are to be picked and collected in heaps. How should the heaps be formed?" No child will regard the problem as indeterminate; most will answer that the apples should be collected in a hundred heaps of a thousand apples each. Possibly some few may give different answers, but always in round numbers of heaps with equal numbers of apples to the heap.

In the meantime let us send out the second group of children actually to heap up the 100,000 apples. When their task is completed we will find a varied collection of uneven mounds.

Thus the same problem has been given contrasting solutions: A in the classroom, B in the field; A by a process of thought, B by a process of action. This affords us our first general statement: given a set of factors, there is no necessary coincidence between their arrangement by a process of thought (type A) and their arrangement by a process of action (type B).

After the apples are gathered, an observer strolls into the orchard. He beholds the B arrangement, and its irregularity faintly displeases him, while his eye would be gladdened by a more regular distribution of the A type. Indeed the unseemliness of the B arrangement may affect him sufficiently to evoke action — he may apply his own labor or that of others to a rearrangement. This affords us our second and third general statements loosely worded: man delights in perceived order; he is willing to expend labor on its achievement.

## The Feeling of Orderliness

We are enamored of order; this passion runs through all of mankind, from the housewife to Einstein. True enough, but what is "Order"? So Platonic an approach is to be shunned.

It is a more sensible and modest course to note that some arrangements evoke an immediate pleasure and approval, while others do not. We shall call the first "seemly" and the second "unseemly," hoping that we thereby emphasize that we start from subjective appreciations. We do not then have to answer the question, "what is Order?" Our concern is merely to detect when the feeling of seemliness is experienced.

Tests of seemliness can easily be devised. On your desk, next to the visitor's chair, place twelve pencils, six blue and six red ones, arranged in two heaps, six red and one blue in one heap and then five blue ones in the other. A visitor will itch to transfer the "mislaid" blue pencil to the blue lot, while he will remain quiescent if two heaps of six each contain three blue and three red pencils. Or again, if the pencils are arranged by size with one discrepancy, the visitor will experience something like relief if you restore the continuity of the series.

As one goes on to less naïve experiments, it becomes apparent that the feeling of seemliness is experienced when we grasp the law of structure according to which the factors are arrayed. If five beads are presented, three large ones in succession and then two small ones, the individual will want to place each small one between two large beads, but if the pattern of three large ones and then two small ones is frequently repeated, its periodicity will make it acceptable.

An office has a stock of envelopes of various sizes. Their arrangement pleases if they are stacked by sizes in a progression. Let there be two collections on two different shelves, each containing the whole range of sizes.

A new secretary undoubtedly will set out to assemble all same-sized envelopes, substituting one series for two. She will, however, refrain from this rearrangement when she finds that the envelopes on the first shelf carry an engraved address on their back while those on the second shelf do not. The principle of classification has become clear to her and she now regards as orderly an arrangement which did not seem so at the outset.

We want factors to "obey" some understandable principle by reference to which each has and falls into "its place." The understanding can be either artistic or intellectual. Every eye enjoys the shapes of shells, but few minds could formulate that the shapes are generated from an equi-angular spiral. The eye may thus jump to a conclusion while the mind may recognize an organizing principle which does not jump to the eye, as in the foregoing example of the envelopes. Thus there are two modes of understanding; appreciation of seemliness involves one or the other form of recognition of an organizing principle.

Our desire to find things "obedient" to some principle is the mainspring of intellectual inquiry. We seek "hidden" principles of organization whose discovery reveals the orderliness of phenomena that seem disorderly to us.

Our achievements in so marshalling phenomena have been connected with and are dependent upon the progress of mathematics. Mathematics mainly consist in the thinking out of more complex configurations. When an additional "function" or "series" is studied, one more "shape" is thereby added to our intellectual store of "orderly configurations."

Let us take a grossly simplified example. Let us assume that we have been unable to form any idea of a closed curve other than the circle. We are then told that the earth "circles" around the sun. But by some means we find that the earth does not in fact describe a circle around the sun.[1] Its movement therefore does not conform to any model of orderliness held in our mind, ergo we adjudge it disorderly. This is meant to stress that the probability of our experiencing orderliness is a function of the store of configurations worked out in our minds. A lognormal distribution[2] may seem orderly to a mathematician but to no one else.[3]

## Fitting and Tidying-up

A scientist may be thought of as having access to a great store of patterns into which he delves to find one that will fit the facts he seeks to integrate into a theory. Such a pattern may not be available to him, in which case he must acknowledge failure. For to him the facts are supreme; the theory must fit them. Success may come later in this field because some mathematician, possibly quite ignorant of his concern, has worked out a pattern [4] which will now suit the phenomena.

The inverse relation holds true in the case of those many diverse human activities which we may blanket under the term "tidying up." Take the simple example of the housewife who holds in her mind a given pattern of arrangement to which the objects of "tidying-up" are made to conform.

In terms of our orchard example, the progress of science depends upon the ability of the mind to move away from the simplest type A arrangements to the conception of more intricate shapes. One of these shapes will bear a great likeness to the B arrangement which actually occurs. This is an achievement of science. On the other hand, tidying-up activities consist in moving objects from B configurations, which just occur, toward type A arrangements which are recognized as orderly and therefore desirable.

We can there reformulate our second and third general statements: Men have a tidiness-preference for arrangements of which they grasp the structural law, and they have a tidiness-propensity to recast arrangements in accordance with models held in their minds.

## Contrasted Meanings of Rationality

The root of the word "rationality" is ratio, i.e., proportion. Considering a given arrangement of factors, we may call it "rational," because the proportions obtaining between parts are such as to spring immediately to the eye, or to be immediately (or readily) understood by the mind.[5] Our pleasure is then bound up with the assent we grant to existing proportions. But an arrangement may be "rational" in quite another sense: if the proportions between factors are suitable to produce the result at which the arrangement is aimed. We thus find two distinct meanings of "rationality": subjective enjoyment of proportions, and objective adequacy of proportions to the purpose of the arrangement.

To be more precise, in the first case the arrangement is judged as "a sight"; in the second case, as "an organization for results."[6]

In everyday language, people tend to call arrangements "rational," "reasonable," and "orderly" if their principle is simple enough to be immediately grasped; conversely, they tend to call them "irrational," "unreasonable" and "disorderly," if the principle is not clear to them. Thus order and reason tend to be identified to seemliness rather than to operativeness.

## The Case of the Library

In the course of his life an author has collected a private library attuned to his needs. The volumes he uses least have been relegated to the highest and least accessible tiers, while the works of reference are ready at hand. Regardless of authorship and formal subject-matter, those works that hold for him some affinity of significance and that are apt to be used simultaneously are placed together. The owner could not easily account for the distribution of his tools (which indeed shifts over time), but it serves his purpose.[7]

While he is on a holiday, a well-meaning daughter decides to tidy up and aligns the volumes according to format and alphabetical order. Having wrought, she feels that "it looks better now"; and so it does, but a working arrangement has been destroyed in the name of seemliness. No doubt, the previous arrangement was imperfect and could have been reformed to serve the author's purpose even better. But such an improvement would have been based on a considered judgment of the operator thinking out his process, or by someone else capable of seeing the problem from the operative angle — an "operator-judgment." The reform effected by the daughter was not "operator-based," if I may so express it.

Thinking in general terms, let us consider an arrangement of factors that serves some purpose and is instrumental to some process. Let us call it an operational arrangement.

A mind concerned with this purpose, well aware of the process, dwells upon the operational arrangement and finds that it might be made more effective by certain alterations. We shall call a judgment passed from this angle an O-judgment to denote that the arrangement is appreciated from the operational standpoint. O-judgments are the principle of all technical progress made by mankind. Quite different in kind is the judgment passed upon the same arrangement of factors by a mind that regards it without any intensive interest in or awareness of the process. Such a judgment is then passed as it were from an external, extra-processive standpoint. We shall call it an S-judgment (S for sightseer).

## The Genesis of Absurdity

Whenever I recognize that an arrangement of factors is instrumental to an operation, I cannot call this arrangement irrational (this would be saying in the same breath that it is related and unrelated to the same operation). But being concerned ex hypothesi with this operation, I may well call the arrangement more or less rational. In this case I am really comparing a current method or path which I have explored with another method or path which I have discovered. This is an O-judgment.

Addressing myself to the same arrangement, I may fail to identify it as processive and instrumental to an operation, or I may fail to interest myself in this operation, or again I may fail to sufficiently scrutinize the process and arrangement to recognize their complex connection.

If I nonetheless pass a judgment upon what I perceive of the configuration, this must be an S-judgment whose principle is a spontaneous and undeliberate comparison of the shape perceived to simple models of seemliness. If this is my attitude, the more complex the process is to which I have denied my attention, and the more complex the attending configuration, the more unseemly I shall find the latter, and the more unfavorable must be my S-judgment. I shall then call the arrangement disorderly and irrational.

An O-judgment is costly in terms of attention and time. It cannot be formed immediately or without effort; therefore, the number of such judgments which I may form is limited.

But while I must focus my attention intensively on the process and arrangement in question, a great number of other shapes float into the field of my attention, and my glimpses at them immediately call forth uncostly S-judgments. The more extensive the field over which I may thus roam effortlessly, the greater the number of my S-judgments.

Therefore, my store of judgments will tend to be made up of a small minority of O-judgments and a great majority of S-judgments. But while my O-judgments tend to improve arrangements whose processiveness I have grasped and which I endeavor to make more rational (i.e., effective), my S-judgments tend to impeach arrangements of which I considered only the seemliness and which I therefore pronounce irrational.

Therefore the larger the number of arrangements upon which I venture to pass judgments, the higher the proportion of the arrangements examined which I shall pronounce unseemly, and the more the world will seem to me to be made up of "bad" and "wrong" arrangements.

But O-judgments are also in a small minority within every other mind. Moreover, diverse minds do not form O-judgments on the same subject matters. It follows that a summation of individual judgments arrived at independently within a society would show that there is of necessity a huge majority of S-judgments over O-judgments. And second, there must be a majority of S-judgments over O-judgments on every arrangement.

S-judgments generally entail a verdict of unseemliness, disorder, and irrationality; therefore, a summation of all judgments must result in a general verdict of unseemliness, disorder, and irrationality. It must result in a condemnation of "the absurdity of the universe," and more specifically of all social arrrangements.

We actually find that such a philosophy has arisen in our times possibly because we have overextended the field of individual judgment.

## The Case of the Judge

Of course, it runs contrary to the principle of division of labor that I should pass judgment on a great number of arrangements. Take a simple simile. As a judge I have to rule on a number of cases per year. It has never been suggested that every litigation in the country should be submitted to every judge. If this would be the case a great number of minds would be conscripted for each case, but no attention at all could be paid to each. Such a procedure would seem inane, and yet consider how many "cases" the daily paper brings to our private court and tempts us to adjudge.

It takes no great psychological acumen to observe that we enjoy passing judgments on matters of which we know very little. This is bound up with our taste in configurations. Problems to which we have devoted scrupulous scrutiny and arrangements which we have delved into deeply offer no scope for application of the simple models that we inherently prefer.

It is a relief to turn to problems of which we are ignorant and to which we therefore may apply our models. Be it noted that the greatest scientists who have mastered prodigious complexities are apt to come out with the most naive views on social problems, for example. Their minds are taking a holiday, reverting to the effortless and invalid judgment of seemliness.

We could assume that those who are best aware of the difficulties of grasping a process in their own fields, should be most chary of passing S-judgments on other matters; but this is contrary to reality. Our affection for simple patterns is so basic to our nature that the more we must bow to the actual complexities of organizations we understand, the more we want to find simplicity in other organizations.

## The Attraction of Simple Figures

All that is known of man's past is testimony to the fact that he has ever associated the idea of perfection with simple figures, which he therefore used to denote Divinity. Basic to every ritual is the circle in which the eye finds no lack and which thus represents (or indeed suggests) the concept of Wholeness. The circular crown seems to have been invented independently by all human societies; the operations of magic have involved everywhere the tracing of figures within a circle.[8] We are told that primitive places of worship and assemblies of worshippers were circular.[9] Movement forming simple geometric patterns was a form of homage to Divinity. Military parades have also been derived from this, as well as our word "theory," which in barrack language still meant quite recently "training in geometric marching."

The setting of effective values upon the simplest geometric figures is strikingly exemplified in the history of warfare. The Macedonians were so enamored with the squareness of their phalanx that they thoughtlessly adhered to their order of battle even when circumstances made it most inadvisable. Frederick the Great and Napoleon's victories owed much to the aesthetic sense of their opponents who arrayed their troops with an eye for symmetry. Frederick and Napoleon gave themselves the advantage of an operative arrangement over a seemly one.

## The Threat of Orderliness

This train of thought leads us to regard the simplicity preference and tidiness propensity of the human mind as potentially destructive. Such tendencies run counter to the diversity and intricacy of operative structures. Practically all men enjoy the orderliness of a military parade, but they are dangerously prone to mistake this enjoyment for the recognition of a supreme form of organization. In fact, the men assembled on the field achieve no operation whatever beyond offering a sight.

The idea of over-all organization is frequently aligned to an image of perceivable regularity in human movements as can be found in a parade. But this is the very opposite of organization.

A parade is costly; equally costly is the parade spirit with which we approach the operations of men in general. We tend to believe that society is at its best when its functioning offers to our minds a clear, distinct, and simple pattern. But the only thing then maximized is our intellectual enjoyment.

We are prone to mistake our endeavors to maximize our intellectual enjoyment for the spirit of reform. But we have no warrant for the belief that a simplification of pattern that would please our minds would constitute an improvement of society, unless we define improvement as increasing coincidence of arrangements with the figures held in our mind — an extreme of intellectual pride.

[product:121]

Let us now picture a group of operators, each engaged in a process and therefore prone to arrange factors at hand in a manner suitable to his process. Imagine that they meet at regular intervals to devise a general structure. Now if they all individually and responsibly perform the same operations, we can assume that their general decisions as to the over-all structure will take into account operational needs that are experienced by all participants.

This cannot be so, however, if the participants are engaged in very different processes and if only a minority of them are in fact responsible for the performing of operations. Then the common ground for the participants will be provided by those general shapes and figures that inhabit our minds and of which the simplest are the most common to all of us.

Agreement shall then most easily be reached on orderly arrangements adverse to operational arrangements in proportion to the intricacy of the latter. The rule of order and the operational urge shall thenceforth be in conflict. This is, of course, in itself a pattern of deceitful simplicity. But it may serve to explain some tensions of contemporary society.[10]

##### Notes

[1] Though in fact we would presumably have no means of establishing this if our geometric knowledge were so restricted.

[2] See the notable paper on lognormal distributions by Prof. J. H. Gaddum (Nature, Oct. 20, 1954) to which our attention was drawn by Prof. Allais.

[3] A collection of phenomena becomes orderly for me if and when I can tersely formulate the law of structure whereby each item is assigned the position which it holds.[4]

Consider the number of processes which come to be recognized as orderly when related either to the Verhulst-Pearl logistic curve, or even better to Gaston Backman's more elastic model. For an inspired eulogy of these patterns cf. D'Arcy Thompson: On Growth and Form, new ed. Cambridge, 1942.

[5] Let us recall that the eye of an ignorant man may appreciate the harmony of proportions of an arrangement the structural law of which he could not formulate; conversely, a mathematician may formulate a law of arrangement which cannot be transcribed in a visible form.

[6] A third meaning of rationality need not concern us here; any configuration whatever is, of course, the outcome of its causes and therefore may be called "rational." In this sense, everything that is real is rational, but then the term becomes so all-embracing as to be useless.

[7] For a striking treatment of the general problem of arrangement of tools around an artisan, see Gerald K. Zipf, Human Behavior and the Principle of Least Effort, Addison-Wesley Press, Cambridge, Mass., 1949.

[8] Cf. for instance Robert Ambelin, La Kabbale Pratique, Paris, 1951.

[9] Cf. among many other sources Louis Hautecoeur, Mystique et Architecture; Symbolisme du Cercle et de la Coupole, Paris, 1954.

[10] Much more could be said on the subject. It might, for instance, be useful to dwell upon our natural tendency, when sight-judging a mechanism or process, to reform or improve it by breaking down whatever feedback it is provided with. But what use, if any, can be made of the views advanced here must be left to better judgments.

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