## Encountering Complexity – In Need for a Self-Reflecting (Pre)Epistemology

## Vasileios Basios, 2005

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### Abstract

We have recently started to understand that fundamental aspects of complex systems such as emergence, the measurement problem, inherent uncertainty, complex causality in connection with unpredictable determinism, time-irreversibility and nonlocality all highlight the observer’s participatory role in determining their workings. In addition, the principle of ‘limited universality’ in complex systems, which prompts us to ‘search for the appropriate level of description in which unification and universality can be expected’, looks like a version of Bohr’s ‘complementarity principle’. It is more or less certain that the different levels of description possible of a complex whole – actually partial objectifications – are projected on to and even redefine its constituent parts. Thus it is interesting that these fundamental complexity issues don’t just bear a formal resemblance to, but reveal a profound connection with, quantum mechanics. Indeed, they point to a common origin on a deeper level of description.

### 1 Introduction

The main thesis of this presentation is that Complex Systems afford many and distinct levels of descriptions, dynamical, structural, geometrical or topological, metric or probabilistic, or even a hybrid interplay of the above. Moreover, especially for ‘real-life’ complex systems, any observation will necessarily be partial, incomplete and always depending on the observer’s choices due to incompressible initial conditions and f or approximate parameter estimation. This points to the fact that no single set of mathematical or other formalism – as we know them – is or could be capable of both a complete and consistent description of a complex whole.

Therefore a new double-edged approach is called for. A concertated approach which, on the one hand, would synthesize and unify, at different levels, using different tools and descriptions. And, on the other hand, being able to discriminate among several given aspects of the facts under scrutiny, and how these facts were acquired based upon the specifics of sets of objects and relations which provided these facts.

In short, we are fast reaching the point where we need to concern ourselves not only with the study of nature, but with the nature of that study. Being aware of the limits of our descriptions we can describe the limits of our awareness. That, as a consequence, will set the search of a ‘Science towards the Limits’ as William James called the scientific endeavour which is capable of reflecting not only upon its abstractions – a discourse that epistemology provides – but also reflecting upon its fundamental objectifications – that is one step beyond considering a pre-epistemology able to provide such a discourse.

### 2 What is Complexity that We should be Mindful of?

Looking into Webster’s dictionary the word ‘complexity’ is defined as ‘the quality or state of being complex’ and in the entry ‘complex’ we see that it means:

Main Entry: (1) complex, Function: noun,

Etymology: Late Latin complexus totality, from Latin, embrace, from complecti,

Date: 1643, (1) : a whoZe made up of complicated or interrelated parts. Self-referential as this definition might seem places the emphasis on ‘whole’ and ‘interrelated parts’.

As we came to understand, something complicated is not necessarily complex although a complex system could be complicated. The terms ‘whole’ and ‘interrelated parts’ are emerging as fundamental notions upon which the nonlinear relations among constituent parts rely and as such are identified. This has been the case mainly in physical sciences but it is not necessarily restricted to only there.

Indeed, this connection between complexity studies and nonlinear science brings forth a deeper understanding across the divide of subjective and objective narration in fields as diverse as physics, chemistry, biology, cognitive and consciousness studies, and even sociology and economics.

In complex system studies one is confronted with nonlinear relations which give rise, usually, to a great number of states. This multitude of states most of the times signifies many levels of ongoing processes of different time, and space, scales. The signature of complexity is the presence of multistationarity and/or chaotic regimes of motion.

All these aspects unavoidably lead to the breaking of symmetries both in the spatial (pattern formation) and the time (irreversibility) domain.

It is, now, well understood that these emergent patterns and rhythms are due to ‘nonlocal’ – in the sense that the correlation lengths of the patterns and rhythms emerging are orders of magnitude larger than the correlation lengths of their constituent parts – as well as an associated limited horizon of predictability due to strong sensitive dependence on initial conditions and parameters, which is the sine qua non of chaotic motion.

Of course complexity of form and structure is not a new or alien concept in the field of scientific investigations. Intricate patterns and forms, structures with great beauty and delicate design have captured the attention and admiration of scientific thinking since the dawn of time. A classic reference remains D’Arcy’s ‘On Growth and Form’ [l]. Recently, the studies of structural complexity in relation to information processes, from physicochemical and biological systems, to man-made networks such as electricity’s power-grid, the ‘World Wide Web’ and the internet, various social groups, etc., have made an impact on the scientific literature and created lively discussions (see, for example, [2, 31 for an introduction, specialized references can also be found therein).

Nevertheless, aside from the structural aspects of complexity the dynamical basis of it has been a path-breaking area of research during the sixties and onwards. Owing to the early, seminal, contributions of Hermann Haken, Ilya Prigogine, Brian Goodwin, their co-workers, and many others, the role of nonlinear relations and fluctuations to self-organization, synergetics, pattern formation, irreversibility and, in general, to what now tends to be called ‘emergence’ has been ellucidated. For an overview of their work, one might consult [4, 5, 61.

These pioneering contributions go well beyond qualitative descriptions, analogies and metaphors. They address fundamental issues such as the interplay of structure, function and fluctuations; they invoke a non-classical – sometimes circular – causality (since the parts collectively determine the macroscopic order parameters and the macroscopic order parameters determine the behavior of the collective of the parts) and they offer a new apprehension of the fact that determinism does not necessarily imply predictability (a corollary due to sensitive dependence on initial conditions and parameters).

Through the analytical tools of theoretical physics and mathematics unexpected relations between topological and geometrical aspects (structure), dynamical laws (function) and stochastic processes (fluctuations) were discovered in complex systems.