The Complexity of Simplicity

By: Dr. Sam Vaknin


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Read these essays first:

Parsimony - the Fourth Substance

Bestowed Existence

Anthropic Agents and the Increase of Entropy (Abstract Only)

 

 

 

 

Everything is simpler than you think and at the same time more complex than you imagine.
(Johann Wolfgang von Goethe)

 

 

 

Complexity and simplicity are often, and intuitively, regarded as two extremes of the same continuum, or spectrum. Yet, this may be a simplistic view, indeed.

Simple procedures (codes, programs), in nature as well as in computing, often yield the most complex results. Where does the complexity reside, if not in the simple program that created it? A minimal number of primitive interactions occurs in a primordial soup and, presto, life. Was life somehow embedded in the primordial soup all along? Or in the interactions? Or in the combination of substrate and interactions?

Complex processes yield simple products (think about a newspaper article, a poem, or a sewing thread). What happened to the complexity? Was it somehow reduced, "absorbed, digested, or assimilated"? Is it a general rule that, given sufficient time and resources - the simple can become complex and the complex reduced to the simple? Is it only a matter of computation?

We can resolve these apparent contradictions by closely examining the categories we use.

Perhaps simplicity and complexity are categorical illusions, the outcomes of limitations inherent in our symbols system. Complexity would then be when we use a large number of symbols to describe something. Surely, our need to employ this or that number of symbols teaches us nothing about reality and its characteristics. A straight line can be described by three symbols (A, B, and the distance between them) - or by three billion symbols (a subset of the discrete points which make up the line and their inter-relatedness, their function). But whatever the number of symbols we choose, however complex our level of description - it has nothing to do with the straight line or its traits. It is not rendered more (or less) complex or orderly by our choice of level of (meta) description and language elements. 

The simple (and ordered) can be regarded as the tip of the complexity iceberg, or as part of a larger, interconnected whole, or hologramically (the same way all particles contain all other particles) - but these merely reflect choices of descriptive language, with no bearing on reality.

Perhaps complexity and simplicity are not related at all, either quantitatively, or qualitatively. Perhaps complexity is not simply more simplicity. Perhaps there is no organizational principle tying them to one another. Complexity is often an emergent phenomenon, not reducible to simplicity.

The third possibility is that somehow - through human intervention - complexity yields simplicity and simplicity yields complexity (by the application of the human activities of identifying patterns, applying rules, classifying, etc.). It would explain the convergence of the behaviours of all complex systems on to a tiny sliver of the state (or phase) space (sort of a mega attractor basin). This, in a way, is an anthropic principle - Man is the creator of simplicity and complexity alike but they do have a real and independent existence thereafter (a Copenhagen interpretation of Complexity). 

Still, these twin notions of simplicity and complexity give rise to numerous theoretical and philosophical complications. 

Consider human life.

Applying a technological metaphor, every thing and every action has a function within a "scheme of things". Goals are set, plans made, designs help to implement the plans. But most of human life is dedicated to disorientated thoughts, or the absorption and processing of absolutely irrelevant and inconsequential data. Moreover, these laboriously accumulated databases vanish instantaneously with death. It is akin to a computer which processes data using elaborate software and then turns itself off after 80 years, erasing all its work. 

Most of us believe that what appears to be meaningless and functionless supports the meaningful and leads to it. The complex and the meaningless lead to the simple and the meaningful. Why not, therefore, consider the complex to be meaningless (or the least humanly incomprehensible)? If the complex is meaningless and disordered then order must somehow be connected to meaning and to simplicity (through the principles of organization and interaction).

Moreover, complex systems are inseparable from their environment whose feedback induces their self-organization. Our discrete, observer-observed, approach to the Universe is, thus, deeply inadequate when applied to complex systems. These systems cannot be defined, described, or understood in isolation from their environment. They are one with their surroundings.

Many complex systems display emergent properties. These cannot be predicted even with perfect knowledge about said systems. We can say that the complex systems are creative and intuitive, even when not sentient, or intelligent. Must intuition and creativity be predicated on intelligence, consciousness, or sentience?

Thus, ultimately, complexity touches upon very essential questions of who we, what are we for, how we create, and how we evolve. It is not a simple matter, that...

TECHNICAL NOTE - Complexity Theory and Ambiguity or Vagueness

A Glossary of the terms used here

Ambiguity (or indeterminacy, in deconstructivist parlance) is when a statement or string (word, sentence, theorem, or expression) has two or more distinct meanings either lexically (e.g., homonyms), or because of its grammar or syntax (e.g., amphiboly). It is the context, which helps us to choose the right or intended meaning ("contextual disambiguating" which often leads to a focal meaning). 

Vagueness arises when there are "borderline cases" of the existing application of a concept (or a predicate). When is a person tall? When does a collection of sand grains become a heap (the sorites or heap paradox)?, etc. Fuzzy logic truth values do not eliminate vagueness - they only assign continuous values ("fuzzy sets") to concepts ("prototypes").

Open texture is when there may be "borderline cases" in the future application of a concept (or a predicate). While vagueness can be minimized by specifying rules (through precisifaction, or supervaluation) - open texture cannot because we cannot predict future "borderline cases".

It would seem that a complexity theory formalism can accurately describe both ambiguity and vagueness: 

Language can be construed as a self-organizing network, replete with self-organized criticality. 

Language can also be viewed as a Production System (Iterated Function Systems coupled with Lindenmeyer L-Systems and Schemas to yield Classifiers Systems). To use Holland's vocabulary, language is a set of Constrained Generating Procedures.

"Vague objects" (with vague spatial or temporal boundaries) are, actually, best represented by fractals. They are not indeterminate (only their boundaries are). Moreover, self-similarity is maintained. Consider a mountain - where does it start or end and what, precisely, does it include? A fractal curve (boundary) is an apt mathematical treatment of this question. 

Indeterminacy can be described as the result of bifurcation leading to competing, distinct, but equally valid, meanings.

Borderline cases (and vagueness) arise at the "edge of chaos" - in concepts and predicates with co-evolving static and chaotic elements. 

(Focal) meanings can be thought of as attractors. 

Contexts can be thought of as attractor landscapes in the phase space of language. They can also be described as fitness landscapes with optimum epistasis (interdependence of values assigned to meanings).

The process of deriving meaning (or disambiguating) is akin to tracing a basin of attraction. It can be described as a perturbation in a transient, leading to a stable state.

 



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