|InterJournal Complex Systems, 378
|Manuscript Number: |
Submission Date: 503
|Why We Don't Understand Complex Systems|
Category: Brief Article
Physics has sought to understand physical systems that once were considered baffling in their behavior, and by the discovery of new abstractions - initially the creation of a new descriptive language, the infinitesimal calculus - was able to help provide theoretical explanations that have led to one revolution after another in the past 300 years. But as is usually the case, prior to the development of any real understanding of (say) thermodynamics, humanity was able to successfully harness the power of steam to launch the industrial revolution. This is characteristic of the successes we have had with many complex systems: humanity's successes in dealing with these systems, great as they have been in some cases, have occurred more by trial and error exploration than by the application of any fundamental organizing principles. Extending this classic model of progress to other kinds of complex system, this paper presents two fundamental theses. The first principal thesis is that complexity is in the eye of the beholder, and is a euphemism for perplexity. Seeming complexity can be dissolved with appropriate new ways of looking at complex phenomena, leading to the corollary that in order to understand complex systems, we will need to develop wholly new abstractions. Humanity has typically come across these by accident rather than systematically, so the hunt for new abstractions could be greatly facilitated by the systematic study of the history and evolution of a variety of types of notational systems (not just mathematics). I call this proposed subject "notational engineering". I believe we need new abstractions in many areas, including (e.g.) new ways of representing value besides money, and new ways of representing large systems of complex rules besides the current tools of mathematics, logic and natural language. The second principal thesis of this talk is that seemingly-complex systems are so because we are trying to represent or study the wrong level of the systems; we need a higher level of abstraction than rules. In traditional science, scientists look at the complex behavior of a system and try to develop a few simple rules that account for that behavior. With seemingly-complex systems, there will be many rules that must be defined. I call the complex behavior of a system its "surface structure", and the thousands of rules that govern it "middle structure". These rules in turn can be grouped by their form, and these the "deep structure" of the system. Families of systems share the same deep structure. This permits a very practical, highly abstract and formal way of organizing and representing rules. I call this approach "Ultra-Structure", and have applied it to a number of types of systems. I think this may be a serious candidate for a new general approach to representing any kind of complex, or seemingly-complex, system.
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