Analysis of systems characterized by relatively fast-paced change has been impaired by the application of methods suitable for systems that feature slower rate of change. More specifically, research into biological, socioeconomic, artificial intelligence, art, linguistics, and other such systems is affected adversely by the use of the methodology more suitable for such extensively explored system as the physical system. The investigation of the universe aims to uncover the laws that govern the physical processes. This methodology was deemed appropriate because the physical system was perceived as changing very slowly (in time and in space). Once discovered, the law (such as the law of gravity) was thought fixed and universal for the entire physical from elementary particles to galaxies. This raises the following question: What are the specific features regarding fast changing systems that preclude the use of the methodology that is widely adopted in physics?

The one distinguishing mark of a changing system is the presence of two-ended source of development. I call it Janus processes following the image of the Roman's god Janus. In accordance with the Roman mythology, Janus, as the patron of beginnings and endings, has two faces looking in opposite directions: one in front, the other at the back of his head. The features of Janus processes require a new methodological approach, which leaves room for the classical methods, but now these methods must be integrated into the new scheme (and new methods) that is adequate for the study of changing systems.

Let me elaborate on this rather odd term. It denotes a process where the changes in the system are triggered both at the end and at the beginning but the beginnings and the ends are not fixed for ever and the way between them is not complete, that is, it can have gaps.

Classical methods are quite adequate in situations where we can start at the end (the final state) and link it to the current state in a complete and consistent manner. By the same token, if extrapolation is admissible, we can start at the beginning (the initial state) and proceed indefinitely (or until the system reaches a definite state).

But how are we to proceed if we start at the beginning, before we reach a definite state? We might have information regarding the feasible space of the system's behavior and the initial conditions. Granted, this case allows us many degrees of freedom, but it confronts us with a very difficult task of how to proceed within this feasible space and, at the same time, satisfy certain ordering constraints?

Over the course of my work (Katsenelinboigen, 1984, 1989, 1992, 1997), I have discovered that scholars in many different disciplines are exploring, albeit implicitly, similar ideas to combat this confrontation. Many researchers do not realize that, in effect, they are dealing with the same issues. These issues are including at least in such areas as the evaluation of a chess position, formalized by Claude Shannon (1950) and implemented in many computer programs, Russell Ackoff's (1981) concept of development of social systems via a multistage planning process, the concept of invisible assets and evaluation of performance by Japanese corporations (Itami, 1987), the nonclassical analysis of firm behavior elaborated by Sidney Schoeffler (1991), the index of vulnerability in strategic minerals devised by Alvin King (1981), the measurement of Modern Economic Growth proposed by Simon Kuznets (1966), the concept of balascopy as a tool for heuristic diagnosis developed by Vadim Kvitash (1983), Willem Stemmer idea (1995) to consider biological evolution as a chain of recursive cycles, each of which operates on a limited set of elements and where at each cycle "only the most promising sequences are selected and used as the basis for further mutagenesis and selection", the elaboration of the hypothesis of positional information in biology by Stuart Kauffman (1993), the usage of positional parameters in psychotherapy by Daniel Giacomo and Mona Weissmark (1997), the formation of predispositions in literary works, in particular Leo Tolstoy War and Peace by Saul Morson (1987), and Anton Chekhov's plays by Vera Zubarev (1997), the aesthetic measurement of art works elaborated by George Birkhoff (1933), "Algorithmic aesthetics" in computer models for criticism and design in the arts, by George Stiny and James Gips (1978), the heuristic methods of pattern recognition by Alex Petland (Discover, 1992), the idea of connectivity in mathematics suggested by Ron Atkin, and so forth.

The lack of a unified results in critical mistakes in applications of different techiques used in the above mentioned fields. This is where the new calculus of assessing system's dynamics come in; these methods help coordinate and link the various stages of the new procedure.

Before we proceed with the more concrete analysis of the new calculus, I would like to make a brief digression into the methodological framework underlying my analysis. This framework is predicated upon the philosophical category of determinism/indeterminism. I regard determinism as inevitability, independent of the degree of uncertainty of the outcome.

My next step was to link the concept of indeterminism/ determinism with the axiological scheme, underwritten by a new concept entitled spectrum of conditionality of the valuations. In keeping with the general systems theory I want to portray values as isomorphic to a variety of systems ranging from natural to man-made systems (values are generally thought to be the prerogative of the latter).

Mathematical models proved highly effective in describing deterministic processes. Mathematical procedures devised for the indeterministic domain have come under the guise of satisficing solutions (Simon, 1979) and heuristic programming. However, I am not familiar with any attempt to construct a general typology of these procedures and certain procedures, notably the formation of predispositions, have been omitted altogether.

The concept of determinism-indeterminism has given rise to a typology of decision-making methods applicable to settings (phases) characterized by different degrees of indeterminism.

It is claimed that there are several phases in the spectrum of measurement of indeterminism. Among the phases in the spectrum of indeterminism there is a phase which requires the introduction of the category of predisposition and the respective technique for creating predisposition - the method of predispositioning or calculus of predisposition. The new term underscores the distinction between the new procedure and the entrenched notion of probabilities based on observed frequencies.

The heart of this calculus is a weight function reflecting the indeterminate nature of change. This function, which is only partly objective, involves the essentials (material parameters), weighted by semi-conditional objective evaluations, and in addition relational (positional) parameters as independent variables with corresponding semi-conditional subjective evaluations. The development of such a weight function yield an explicit and quantitative analysis of situations which today are regarded as pervasively qualitative and have only been subject to implicit "intuitive" examination.

Via the aesthetic method, the degree of beauty (ugliness) measures "perception" by the given subject of the predisposition for development of "observable" objects. Measuring, a predisposition is akin to forming the category of beauty. Beauty is something that enables us, however incompletely and inconsistently, to determine the influence that the present state of development has on future progress. In this sense the development of beauty is the striving towards the creation of completed (in the sense of maximum possible accomplished balance) incompleteness (in the sense of creating conditions for future development and disposal of dead ends).

Such a notion of beauty is quite parallel to its philosophical definitions. Thus, Immanuel Kant wrote, "Beauty is a form of worth of an object, which is appreciated without any idea of a goal."

This idea seems to be intuitively sound reasonable because beauty, without being a full and complete program for achieving desired ends, is still an ordered structure that creates predisposition to development.

The striving to find components, on which the potential is built, as well as the methods of their synthesis is none other than a rather ambitious attempt to demonstrate that the category of beauty can be represented structurally, i.e. it can be dismembered and synthesized.

Things are less familiar with the weight function measuring the beauty of a work of art. The honor of constructing it belongs to the well known American mathematician George Birkhoff (1933). In subsequent years this book provoked great interest, expressed not merely through corresponding theoretical studies but also through attempts at an experimental verification of theses advanced in the book.

From a traditional perspective, the aesthetic method is limited primarily to human evaluation of beauty via feelings. My approach to the aesthetic method is based on the idea that this method could be used to analyze interrelationship among different objects in any field where relations between objects are not complete and consistent but do exhibit some regularities.

These regularities are more pronounced than they would be under chaos but at the same time they are not sufficient to give rise to probabilities based on statistical observed frequencies. In such a case the operationalization of measurement of the degree of development calls for the calculus of predispositions.

The complexity of predisposition varies from field to field, ranging from a simple pattern to an artistic image. Exploring different systems, I will elaborate on the extent of complexity of the respective category of predisposition.

Verifiability of the idea of measurement of predispositions ranges from such experimentally verifiable methods as those employed in chess programs to logical speculations concerning new interpretations of old theological questions. The extent of verifiability of the methods used to measure predispositions oscillates between these two extremes.

Systems that are amenable to formal description of a predisposition merit special attention, if only because they provide an experimental substrate for testing the viability of the proposed theory. Conversely, systems that yield relatively inexact results may contribute to the elaboration of a general theory of predisposition, since these systems may possess features that are lacking (or hidden or insignificant) in other systems.

As an illustration of my approach, compare chess and economics. Of course chess is much less complex than the economic system. For one thing, chess is zero sum game, which is only one mode of interaction (there is win-lose). Moreover, when we confront a unique situation in chess, we can be sure that the known material objects (pieces) are fixed, in the sense that chess rules preclude the introduction of new pieces. The same does not hold true for the economy where unique situations may feature the emergence of new objects (products) or means of manipulating them (technologies).

Still, chess does disclose various methods of operation, notably the creation of predisposition methods which may be applicable to other, more complex systems.

Considering the novelty and the importance of the predispositioning, I organized a symposium called Calculus of Predisposition, held March 26 - 29, 1992, in Philadelphia and sponsored by the Research Foundation of the University of Pennsylvania. The primary aim of this symposium was to bring together specialists from different branches of arts and sciences and organize a dialogue on the problem of formation and measurement of predisposition. I realized the chance I took in organizing such a gatheringeach participant talked about his/her professional field using his/her professional lingo.

I am a big fan of the Bible, and I hold the book in high esteem. I am well aware of the sad outcome of the endeavor to erect the Tower of Babel after all the languages were intermixed. I failed to heed the biblical tale, hoping that my venture will help construct an edifice featuring the language of a new calculus.

This book represents another step. The collection of essays were written over the years by my former students from my course, An Aesthetic Approach to Decision Making, which is a joint-program of the Benjamin Franklin Scholars/General Honors Department of the University of Pennsylvania and the Operations and Information Management Department of the Wharton School.

The power of the collection is two fold: firstly, many essays deal primarily with subjects never before discussed in writings or in the course. I appreciate the creativity of the authors for choosing such unique topics to show their understanding of the concepts. Secondly, and perhaps more importantly, the collection brings together a broad range of fields, Life, History, Society, Business, Science, Art & Literature, and discusses them using similar language based on the concepts of predispositioning. Predispositioning serves as a bridge linking the disciplines. By understanding the concepts and the breadth of their application, one can have an openness to life and an access new ideas, curiosities, adventures, and enlightenment.

For the reader, I hope this book will stimulate your mind, enrich your intuition and spur your creativity. I ask you to think of new parallels and new applications for this language. In an age of holistic thinking, communicating within a wide-variety of disciplines and understanding the connectiveness between them becomes crucial for personal and societal development.

I would like to thank the Benjamin Franklin Scholars/General Honors Department of the University of Pennsylvania and its associate director, Linda A. Wiedmann, for financial help with this compilation. I also thank Joshua Marcus for his computer troubleshooting skill, Howard Mandelbaum for his technical assistance and Maurry Apple and Vivek Bantwal for sharing some of there internet know-how. I thank the authors for the honesty and openness of their writings, particularly in the Life section - these authors deeply analyzed their feelings and beliefs about personal subjects. I hope the reader can reap some benefits from all of the authors work, as I am certain their investigations were personally beneficial. I note that the texts have been dated purposefully as the dates signify the complete incompleteness of the papers and serve as benchmarks for the authors' further development Finally, I am especially grateful to Matthew Mandelbaum, my co-editor, for his work in compiling this collection. His efforts were extremely instrumental in its success.

Ackoff, R. Creating the Corporate Future. New York: Wiley, 1981.

Atkin, R. "From Cohomology in Physics to q-connectivity in Social Sciences." International Journal of Man-Machine Studies 4 (1972a): 139-67.

Birkhoff, G. Aesthetic Measure. Cambridge, MA: Harvard University Press, 1933. "Face Space." Discover (August 1992): 9.

Giacomo, D., and M. Weissmark, Doing Psychotherapy Effectively. Chicago, Ill.: University of Chicago Press, 1997.

Itami, H. (with T. Roehl). Mobilizing Invisible Assets. Cambridge, MA: Harvard University Press, 1987.

Katsenelinboigen, A. Some New Trends in Systems Theory, Seaside, CA: Intersystems, 1984.

___. Selected Topics in Indeterministis Systems. Seaside, CA: Intersystems,1989. 

___. Indeterministic Economics. New York: Praeger, 1992.

___. The Concept of Indeterminism. New York: Praeger, 1997.

Kauffman, S. The Origins of Order. New York: Oxford UniversityPress, 1993.

King, A. The US Stategic Minerals Position-The 1980's and Beyond.

Carlisle Barracks. Penn.: Stretegic Studies Institute, U.S. Army War College, 1981.

Kuznets, S. Modern Economic Growth. New Haven, CT: Yale University Press, 1966.

Kvitash, V. "Balascopy as a Tool for Heuristic Diagnosis." In Proceedings of the Congress of Medical Informatics, vol.1, Bethesda, MD:

Morson, G. S. Hidden in Plain View. Narrative and Creative Potentials in 'War and Peace.' Stanford, CA: Stanford University Press, 1987.

Schoeffler, S. "The Role of Science in Business Strategy." Handbook of Business Strategy. Boston: Warren, Gorham, and Lamont (1991): 4-1 to 4-26.

Shannon,C. "Programming a Computer for Playing Chess." The Philosophical Magazine 41 (1950): 256-75.

Simon, H. Models of Bounded Rationality: Economic Analysis and Public Policy. Cambridge, MA: MIT Press, vols. 1 and 2, 1982.

Stemmer, W. "The Evolution of Molecular Computation." Science 270 (1995): 1510.

Stiny, G., and J. Gips, Algorithmic Aesthetics: Computer Models for Criticism and Design in the Arts. Berkeley: University of California Press, 1978. 

Zubarev, V. Systems Approach and the Mytholiterary Continuum. Westport, CT: Greenwood Press, 1997.

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