An activity of the Primer Group


A Special Integration Group (SIG) of the
International Society for the Systems Sciences (ISSS)
originally SGSR, Society for General Systems Research.






Excerpted from ISSS Proceedings
The Singer Singing His Song
By Thomas Mandel
Presented before
38th annual meeting
June 14 - 19 1994
Asilomar Conference Center on the Montery Peninsula


The Science of Simplicity & Complexity

A new science of complexity was recently formulated at the Santa Fe Institute in New Mexico, in response to 'the difficulty of pursuing multidisciplinary studies of complex systems in traditional universities,' SFI hopes, "that by understanding a complex adaptive system in one field, light will be shed on complex adaptive systems in other fields." They state in their pamphlet, Santa Fe Institute, a General Overview that, "Complex behaviors may emerge from a surprisingly few basic rules controlling individual parts of a system' Complex behavior is not readily predictable froom knowledge of the individual elements, no matter how detailed, but can be understood by studying how the elements interact and how the systems adapts and changes."

Physicist Murray Gell-Mann, co-chairman of SFI's science board, spoke at the University of Chicago recently. He mused about a need for, "aa generalist attitude" which is capable of producing at least a crude outline" of their new science. He comments further about this, in the book, Complexity, reminding his colleagues, "I think of the subject as the study of simplicity and complexity." [ 16.1 This is a major point to be noted.

On a more concrete or experimental basis, the new science of complexity reveals its irony stated by Cris Langton: "The most surprising lesson we have learned from simulating complex systems on computers is that complex behavior need not have complex roots."

Complexity, as a fact of life, cannot be disputed. It should not be taken to mean, however, that simplicity is therefore trivial. Consider this situation: the human brain consisting of billions of neurons, each with thousands of connections talking to each other trillions of times each second, constantly learning by producing new connections and leaving others to die off, all of which are mediated by at least fifty different kinds of neurotransmitters, which, in turn, may be attenuated or enhanced, the whole of which is constantly modulated by the six senses--is indeed a complex system. Yet, to do their work, the individual neurons themselves do no more than simply reverse an internal electrical charge. They simply turn on and off. We now know that the key lies in their relationships, the pattern of ON's and OFF'S.

Computer science is yet another example where roots are the simplest. The computer letter, the BYTE, is a pattern of ons and offs. Even DNA, so complex it will take decades to map, is a function of an on/off processing of bases between the pair-strands that DNA is formed of.

Indeed, most, if not all, major advances of knowledge were, at their roots, simple. Consider fire, tools, art, writing, to name a few. Writing is derived from the act of using marks to represent sounds. Simplicity is certainly not something we can assume can be ignored. What is problematic is oversimplification. In the end, if systemic principles are applied here, it is clear the simple and the complex need to be blended into a greater whole, a kind of "simplexity". The trick is to find the relationship that will accomplish this.

If Philosophy were General, THEN Science would be Specific

It is best to start with a definition of two complementary systems of thought, how philosophy and science are being used in this paper. When the two are taken together, philosophy is the study of the general and science, then, is the study of the specific. The dividing line, defined by science itself, is the principle of verification. In order to be verifiable, there would have to be something specific to verify. For example, the absolute cannot be verified by science, even in principle, and thus is not a problem of science. It is a 'category error," however, to further assume that the absolute does not exist. On the other hand, philosophy has no difficulty dealing with the absolute for the absolute defined is not the absolute.

A general philosophical theory without particulars does not explain anything and therefore is useless to science. A scientific theory containing particulars is limited by those particulars and therefore cannot be fully general. What is needed to construct a useful general theory, is a bridge between the general and the particular. between the analytic and synthetic, This can be accomplished if both are seen as aspects of a greater whole. Algebra for example, is such a bridge. It is general to begin with, but ends with particulars. Algebra, however, is limited to only those things which can be explained with numbers. What is being presented here is a kind of algebra of conceptualization.

The Simplest is not as Simple as we think

If the Universe operates as a unified whole, we can assume that a single, and first general principle of operation can be found as well. Any general single principle of operation would by necessity be the simplest Principle. Because any general theory would have to include the simplest and since only the simplest can express itself, complexity, because it adds to simplicity, can never be the fundamental principle. Therefore, the simplest is not only the most likely (Russell), it is the only possible way. It is necessary.

But the simplest is not as simple as we often assume. A single part is not a part. Thus we must always have at least two parts, and two parts always means some sort of relationship between them, hence three conceptual parts is the simplest form.

I am introducing at this point a new and different kind of notation called tetronic notation. In figure one, the four primary aspects of a system are denoted by horizontal and vertical lines. The horizontal lines denote elements while the vertical lines denote relationships.

The diagrams form a framework or model, a "canvas", if you will, of a simple process which "forces" us to follow the natural laws of the conceptual process. When properly used, they can form a kind of conceptual shorthand. The idea is to insert your particular conceptual elements into the appropriate general form of the diagram. The trick is not to leave anything out, especially relationships.

The advantages of expressing our concepts in a simple form are immense. The brain learns by changing its structure. It is likely, this structural change (understanding) cannot occur unless a simple or general framework is provided for it to follow.


This and That in an Appropriate Relationship is Whole

A number of general rules and principles of systems theory can be determined from the simplest conceptual system. These fundamental conceptual principles would then interpenetrate to all systems using the conceptual process.

At the very least, we have two relational elements and their relationship. Because the realm of relational elements approaches infinity, little more can be said, in general, about the "This and That" The realm of relationships, however, is limited quantitatively, and thus can be defined. Relationships include those that are internal and external; emergent and additive. They can be combined to form two basic systems - simple and complex.

An additive relationship adds no more than the sum of the relational elements, arithmetic for example, while an emergent relationship adds more than the sum of the relational elements, evolution for example. A simple system consists of internal relationships while a complex system includes external relationships.

This paper you are reading is a simple system. The relational elements are the black of the letters and the white of the background page. The forms of the black on white are internal relationships, while their meaning, upon reading, is an emergent relationship. The emergent relationship, in turn, is a relational element (or "holon") of a larger complex system.

Conceptually, we create a complex system when we add external relationships to a simple system. Conversely, we create a simple system out of a complex system when we isolate it from external relationships.

The diagrams can be linked several ways, and when placed back to back form boxes which can be used as transformational tools or as simple "black boxes" not unlike the block diagrams used in electronics. In addition, complex systems may be denoted by circular diagrams capable of illustrating many inputs and outputs in two or three dimensions. Punctuation usage is similar to the rules of the English language except that "sentences" can be read in both directions.

Practical applications


The elements of a General Systems View can also be found in the early philosophical writings of the Greeks. That is if we re-interprete them as such. In this exercise, we are going to apply these principles of contextual relations and general systems principles to our first philosophies and see what comes up.



It is rumored that Thales of Miletus was the first to predict an eclipse to occur the 28th of May, 585 B.C.. And in fact it did occur. Because there was no distinction between what was philosophy and what was science at that early time, it can be said Thales conducted the first scientific experiment and thus would be the father of science, and May 28th, 585 B.C. would be the day of birth. Isaac Asimov also held this view.

And it was around 585 B.C. that Thales formulated Western civilization's first philosophy in an attempt to break from the mythical gods of Homer and Hesiod. Thus, Thales' rational explanation was the first to replace the magical creation of the Cosmos by the various gods. His idea was simple: the world was constructed of a kind of "stuff", a single thing that made up the world, much like WATER made up the oceans.

But knowledge was not meant to stop evolving and soon afterwards Thales' student, Anaximander, took issue with Thales's model of stuff, water, suggesting that there also was a complementary, the Boundless, which was then further modified by Anaximenes to include a specificness about it, much like AIR.


Heraclitus then surmised that Change was an important part of the total picture, a movement from one thing to another much like FIRE consumes and creates new forms of matter. He also spoke of them as the opposites, "What is in opposition, is in concert."

A fifth Ionian philosopher, Empedocles, decided that all of these concepts should be integrated into a whole to include the many not unlike the EARTH integrates all forms of matter. Furthermore, these forces were modulated by the forces of love and hate. Hence the concept of Water, Air, Fire, and Earth was born.

Very little of what Thales actually wrote has been found. What we do have is a verbal account given us by Aristotle. Aristotle's interpretation, however, leads one to believe the four elements actually existed as things, that water, air, fire and earth were actual elements which everything was made of. He also added a fifth celestial sphere, presumably to make it original.

Unfortunately, Aristotle's atomistic treatment of the Ionian philosopher's System as "four elements" -- Water, Air, Fire and Earth missed the point. His approach of four distinct things resulted in a stagnant "elemental" age that lasted more than 1500 years as science sought, instead, to make gold. Secretly of course. Unprofitably, at end...


But what if water was merely an example of Thales "Stuff?" And what if air also was an example of the Boundless? And what if fire was an example of Change rather than the accepted version that everything was fire? And what if earth was an example of what happens when you put all these Together? We would have a Greek General Systems Theory that would rival any we have today, at least of the general sort.

Indeed, if we interpret these elements in this relational manner, we find that we have two primary elements, water and air, which combine like fire combines, the whole of which is one, like the earth. Certainly this idea is not different from our own general system principles. Could they have gotten it right to begin with? There is evidence that such a scenario could have existed.


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