Mandelbrot set by Fractal DesignerThis essay is rewritten from a presentation given in October 1989
to the Middle Atlantic States Philosophy of Education Society entitled, "Authorship as a Social Enterprise".


Edited 8/29/19

The Fractalization of Social Enterprise

Complexity in Practical Decision

©2004 Edward G. Rozycki, Ed.D.



The Basic Tensions

Conflicts of the Normative, Technical and Political Aspects of Enterprise

From "Pure Telos" to Real World

Images of the School

The Concerns of Authors

An Ancient View of Authorship

A More Modern View of Authorship

An Ancient View of Understanding

Another Conception of Understanding

Complexes as Iterations


Conflictual Fractals

Areas of Fractalization

The Tensions of Scholarship

The Tensions of Securing Readership

The Tensions of Pedagogy

Further Fractalization

More on Scholarship

More On Readership


More On Pedagogy

The Practically Critical Points

The Fractal Model of the Enterprise




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Policy  is not made once and for all; it is made and remade endlessly.
Policymaking is a process of successive approximation to some  desired objectives
in which what is desired itself continues to change under  reconsideration.
-- Charles Lindblom1

Those of us lacking omniscience and omnipotence well recognize that Lindblom's characterization of policymaking is also applicable to most, if not all, of our undertakings. Time and again we experience the struggle between Aspiration and the constraints of both Nature and the Social Group.

This essay explores the interactive, iterative nature of decision-making and implementation. The concept of "fractal," ripped, in a sense, from the womb of mathematics, is employed to illustrate -- to suggest -- that rather complex social interactions may be understandable as simple items in simple relations that, through particular reiterative processes, develop into quite complex and opaque configurations.

The author's practical experience participating in developing a college textbook2 will provide the examples from which generalizations are drawn. Theory developed in the course of writing that book will be used to examine and structure the considerations that supported the enterprise.

The Basic Tensions

Every social activity is subject to three basic tensions: those created by the competing claims of authority, efficiency and consensus.

fig. 1

This provides the basic structure of the enterprise. Fractalization, reiterative embellishment, will generate, from these simple relationships, a quite complex map of the social and organization interactions involved.

Conflicts of the Normative, Technical and Political Aspects of Enterprise

Recast into other terms, the tensions can be seen as the result of competing normative, technical and political concerns.


We normally are quite aware of means-ends conflicts. Social contexts tend to complicate these even more with issues of consensus, as we see immediately below.

From "Pure Telos" to Real World

In some religious traditions, God is conceived of as pure telos. Omnipotence obviates the need for consideration of means, since to will is to create.

One way of understanding how the tension develops for us mortals is to consider how our pursuit of an end in a real-world situation generally requires consideration of means some of which may compromise that end.

When group support is needed consensus concerns may affect both the end and the means chosen.


Aristotle remarked that only gods and animals escape this tension: gods by their power, and animals, by their lack of understanding.

Images of the School

The basic tensions are reflected in the different images, or expectation models, of the school. In Understanding Schools 3 we analyze the tensions of schooling practice in terms of different images of the school which correspond to the basic social tensions:

the Temple image: ends, norms, authority

the Factory image: means, techniques, efficiency

the Town Meeting image: consensus, participation, politics.

Conflicts about schooling arise, we argue, because parties to the conflicts harbor conflicting expectations of the schools.


Of course, it is rare that any real school is a paradigm of a single image. More often, a given school muddles along unreflectively, incorporating competing images, expectations, within itself.

The Concerns of Authors

Authoring a book, a remarkably social activity despite the common image of authors struggling alone to articulate their insights into language, reproduces the basic tensions in a similar manner.

Concerns for scholarship give the normative aspect of the configuration; those for pedagogical effectiveness, the technical; and those pursuing readership, e.g. wide acceptance of the book, the consensual.


The next section brings up another set of concerns we had to deal with: what is authorship, and what is understanding? These concerns were formative in setting the norms we pursued for scholarship.

An Ancient View of Authorship

Scholarly authorship is commonly seen as a special apprehension of reality, of heretofore undiscovered or unconsidered truth, followed by the careful crafting of somewhat original ideas into text. Platonic and prophetic traditions assume this theory.


Variations of the correspondence theory of truth are invoked to define instructional outcomes, e.g.

1-2: Truth

2-3: Good writing

1-3: Written knowledge

2-4: Community of Mind

3-4 : Skillful reading

1-4: Enlightenment through text

Of course, it is problematic to establish these correspondences. 1-2 fails immediately: it cannot be established.4

(The notion of "clarity of text", for example, invokes a problematic correspondence.)

We worked from a different conception. This conception is defined not so much by a conscious theoretical construct, but by an aggregation of commitments forced upon us by practical concerns. The next frame illustrates a theory that economically captures these concerns.

A More Modern View of Authorship


A very important point is this: no crucial correspondences are assumed here which cannot be verified. We can recognize some relationships between different phases as instructional successes

1-2: Getting the idea (putting it into words.)

2-3: Good writing 1-3: (No relationship here)

2-4: (No relationship here)

3-4: Hypothesis Testing

1-4: (No relationship here)

2-5: Communication

Truth becomes a relation external to the author-reader relationship. It is a matter of author success in practice connected to reader success in practice.

Written knowledge is an ascription by a successful reader practitioner to a text generated by a successful author practitioner. (By way of comparison, "clarity of text" is a judgment of hypothetical decidability or of author-reader consensus.)

Our concern here as authors was to avoid writing a text that insinuated authority to be accepted uncritically. Rather, we wanted our book to support the kind of critical thinking that might bring even our own positions into rational dispute.

An Ancient View of Understanding

Our conception of understanding, also, bore on the norms for the enterprise.

Socrates asks Meno what virtue is. When Meno replies by mentioning virtues, Socrates objects that he wants to be told what virtue is "as a whole." This search for logical simples models understanding on the giving of definitions, particularly definitions which analyze items into constituents.


This "simplification" theory leads to the skeptical query, "How can we know we understand one another?" Thus begins the search for atoms of knowledge and relations which can be combined into more and more complex forms (statements) of knowledge.

It is important not to overlook that approaches to "simplification" are tied to notions of intelligence. (Recall, also, that Skinner's infamous teaching machine foundered on his failure to define such things as "the smallest possible instructional increment.")

Another Conception of Understanding

Vademecum, vadetecum.

The approach we adopted is that understanding is dialogic consensus, i.e. we understand each other when our belief that we do so is not contradicted by our practice. (Of course, dialogical consensus is achieved on the other theory, too, if at the cost of casting out those who persist in not "understanding.")


What a theory of dialogical consensus offers is respite from a potential infinite regress -- not to mention a presumptuous elitism. It implicitly accepts a theory of paradigms, or what psychologists call "prototypes."5

Complexes as Iterations

Authorship decisions are complexes of the basic tensions. Understanding them is a matter of seeing how they reiterate themselves in particular situations.


The kind of reiterative analysis we will present is intuitive to small children who can understand complex relationships as reiterations. To the question, What makes a pie an apple pie? they will answer,

The apples in it.

Ask them what makes an apple an apple and they are not likely to analyze apples into simpler characteristics, but may likely answer that it is like a pear but round, grows on an apple tree, comes on a stick at Halloween, you buy it at the fruit stand next to the oranges, etc.

This might not have satisfied Socrates, but it is a very satisfactory way of dealing with the world.



Changes in policy and policy implementation rarely result from a linear process of generating research, laying out policy options, choosing between alternatives, and evaluating the implementation of the selected option. Rather, changes come about through a process of iterative interactions among three "streams" of activity: defining the problem, suggesting solutions, and obtaining political consensus. -- Porter & Hicks6

We will be looking a special kind of reiteration called a fractal. The Koch's Island below is a construct that involves our imagining how a figure would look if we followed its development through an infinity of iterations while keeping each developmental stage in view.

Each side of a triangle counts as an initiator. On each side the generator constructs a new triangle, and so on, and so on...


The Mandelbrot Set from the very top of this document is, in effect, an infinity of graphs of the equation, f(z,x) = sqr(x)+z, throughout a section of the imaginary plane, looked at over an infinity of iterations. Different colors indicate different points on the graph where the iterative sequence goes to zero in the limit (black) or escapes to infinity at different numbers of iterations.7

For our purposes below, a unit element, the triadic tension illustrated above, will be reiterated to generate an increasingly complex figure. These basic tensions of a social enterprise will be found to reiterate themselves at finer and finer levels.

Conflictual Fractals

When we examine any constituent of the basic tension, the basic tension reiterates itself at that "lower" level.


This is not mere embellishment. New issues arise as the iterations continue, yet they bear a similar relation to each other as in the original triad.

Areas of Fractalization

To focus in on subparts, we will divide our original figure into three areas.


If scholarship is our concern, then, how the norms are to be decided, by whom, and how we will achieve them, are concerns.

Similarly, if pedagogy is our concern, then norms of pedagogical efficiency and consensus on them crop up as concerns, too. But so do technical concerns and circumstances which might offer impediments.

Finally, securing readership is a big concern, directly to the publisher and indirectly, at least, to the authors. For example, what constitutes sales adequate to keep the book in print? How and by whom is this decided?

The Tensions of Scholarship

Here we see how the basic tension manifests itself at this lower level.


Our normative concerns are addressed by availing ourselves of the theories of others or by arguing for our own novelties.

The technical aspect is dealt with by using accepted techniques or argued-for novelties.

The consensual dimension is particularly focussed by our concerns for improving the status of the field of foundations of education.

Clearly, what counts as scholarship, will depend upon how these tensions are dealt with.

The Tensions of Securing Readership

The area of securing readership, too, recapitulates the basic tensions.


What is the desired market? (Students? Instructors?)

By whom is it desired? What is the consensus on who might buy the book?

What promotional techniques will be used to address this market?

The Tensions of Pedagogy


In the pedagogical area, our personal normative commitment is -- and was in the book -- to critical inquiry.8

The technical question to be addressed is whether the contents of our text promote the development of critical inquiry skills in those students who will be the users of our books.

We hoped our commitment to critical inquiry would enjoy the consensus of many colleagues in the field.

Further Fractalization

We will fractalize down one more level, because certain practically important considerations show up with further refinement.


How many iterations can we make? There is probably no theoretical end; however, we would practically get no more complex than is necessary to deal with practical problems. For example, avoiding increasing marginal production costs (e.g., too many expensive media elements) or loss of consensual support for the project (e.g., content seen as too esoteric for the market) are two kinds of resistances more frequently encountered as fractalization progresses.

More on Scholarship

Note the way the consensus issue plays itself out here. Our commitment was to enhancing the status of the field. We have rather concrete objectives in mind


Note how the normative elements (lower left) of each sub-triad relate to the technical elements (lower right). For example, coherence and economy are norms by which we evaluate methods, and persuasiveness is a norm -- not the only one -- by which arguments are evaluated. Of course, consensus on both what constitutes the relevant norm and the extent to which the methods offered meet it is a source of tension in each enterprise triad.

More On Readership

On this element, consensus was hard to come by. Power relationships, contractual or otherwise play a large role here.


We, the authors, found the publisher's approach to reviewing to be haphazard and unscientific in the extreme. Yet this was the process that determined ultimately whether the manuscript would be published. Also, the question of seemliness of marketing approach is a concern not well-thought out by the publisher. Our sense of what our colleagues might find off-putting was not shared by the publishing staff.

More On Pedagogy

In order to maintain instructor authority and promote good class evaluations for those ordering the book for their classes, we committed ourselves to providing a detailed instructor's manual -- with tests -- for the 60% of instructors in foundations of education who have no advanced degree in the field. This concern is illustrated immediately below.


Production -- asterisked in the figure above -- became the tail that wagged the dog. For example, illustrations were rejected because they weren't "vertical." Cuts were made and footnotes abbreviated to reduce length irrespective of content. Photos were added supposedly to "increase appeal" but no adequate reasons were given to support this claim. Speed of production dictated relinquishing much authority to editors who sometimes missed the points being discussed. Also stylistic and grammatical changes were made that were not improvements.

The Practically Critical Points

Despite the many considerations we brought to the task, the basic priorities were established by the outcomes of reviews, the commitments to production and whatever counterbalance the authors' concerns could offer.

The indeterminate nature of the market, the size of the publishing company and the nature of its concerns, and the institutionalized nature of the productive processes had a great deal to do with transforming the authors' original intents into the text that resulted. Asterisks in the figure below indicate the most critical components of the process.

By asserting a great deal of control early in the process, we managed to maintain much of our original conception through the production process.


Conception, however, is not execution. A month before the book was to go to press, the company was acquired by a conglomerate, our editorial and support staff was changed, and the book was rushed to print without undergoing editing for typos and other last minute corrections.

The Fractal Model of the Enterprise

This essay has been, so to speak, a thought experiment. We have seen, in the particular context of writing and publishing a textbook, how the notion of fractalization helps us see an apparently labyrinthine structure of decision-making can be understood as the confrontation with and handling of a simple, recurrent pattern.

Intuitively, we all -- I suspect -- feel there is such an iterative aspect to many of our activities. What goes around comes around, we say. March and Simon have noted how organizations vacillate over time in the degree to which they pursue one kind of policy over another.9 Indeed, the ability to reverse direction while maintaining a facade of constant progress is no mean feat of leadership.10 Whether or not a "fractal" analysis would be enlightening in these areas remains to be seen.11





1 Charles E. Lindblom, "The Science of 'Muddling Through'", Public Administration Review, 19, Spring 1959, 79 - 88.

2 Gary K. Clabaugh & Edward G. Rozycki, Understanding Schools: the foundations of education. New York: Harper Rowe 1990.
(Unfortunately, in the middle of the book's production, the publishing company acquired new ownership that relocated the editorial staff. Editorial correction, especially of reference numbering in citations and graphics was not done. Yet, the book was rushed to print and put on the market. Despite good initial reviews, the errors made it frustrating to use. The change of venue had a profound effect on a critical element of consensus, i.e. adoption for use with students. - EGR)

3 Clabaugh & Rozycki 1990 Chapter 2. See also

4 See E.G. Rozycki, Conditions of Knowledge, online.

5 See, for example, E.G. Rozycki, "Multi-Leveled Individuation (The relativity of the paradigm)" , online.

6 Robert W. Porter with Irvin Hicks, "Knowledge Utilization and the Process of Policy Formation"

7 An excellent, well illustrated, yet rigorous, introduction to the fractal can be found in Michael F. Barnsley, Fractals Everywhere, 2nd Edition. Boston: Harcourt Brace, 1993.

8 By critical inquiry we understand something more provocative and honorable than partisan special pleading.

9 James G. March and Herbert A. Simon, Organizations. New York. Wiley. 1958. See, also, online Basic Organizational Conflicts based on March's and Simon's book.

10 For a rhetorical mechanism to enable reversal of policy see E. G. Rozycki, "Mechanisms for Policy Reversal," online.

11 Other possibly heavily reiterative activities: justifying a knowledge claim, or diagnosing a mechanical failure. These are reiterative not necessarily in terms of action, but structurally in terms of the kinds of acts undertaken and their relationship to each other.