Complexity

Kepler's "laws":
1. The planets move in elliptical orbits with the Sun at one focus;

2. the time necessary to traverse any arc of a planetary orbit is proportional to the area of the sector between the central body and that arc (the “area law”); and

3. there is an exact relationship between the squares of the planets' periodic times and the cubes of the radii of their orbits (the “harmonic law”).

The concept of an emergent property (i.e. a property of a system that cannot be derived from properties of its parts) is not new. In the 19^th century, George Henry Lewes (English philosopher of science) distinguished between phenomena that are predictable from their constituent parts and phenomena that are not - emergence (such as salt which looks nothing like sodium or chlorine). Jules-Henri Poincaré made significant contributions to the theory of orbits - celestial mechanics, particularly three-body problem. It turned out that it is impossible to combine solutions of three two-body systems into a single solution for a three-body system - thus turning Kepler's "laws" into approximations.

However, the theory of emergent property did not take hold. British zoologist C. Lloyd Morgan established an opposite approach - nothing should be called emergent unless it can be shown (proven) not to be a resultant. This might have appeared as a healthy approach but the trouble was the most of those "potential" emergent properties could not have been proven to be a resultant either - and the impasse was obvious.

The last quarter of the 20^th century saw a rapid growth in computing power that brought very powerful machines to many offices and homes and with them an innocent "game" called "Life". It was basically a simulation of number of "cells" that had very few rules - when to divide, not divide or die. It was captivating to observe how complex patterns of "cells" emerged and sometimes "pulsated" through sequences of other patterns. Quickly many other similar "games" appeared simulating life based on complex math originally called chaos theory that nowadays has evolved into complexity theory. However, impressive results in replicating numerous phenomena of life that surrounds us are still waiting to be translated into - what is this "more" in "the whole is more than the sum of its parts".

As an introduction as well as a powerful call towards new dimensions of Artificial "Intelligence", I would recommend Klaus Mainzer's book "Thinking in Complexity". To those undeterred by the unfamiliar terminology, I would suggest a comparison between prototype vector approach described in 4.3 - Brain and the Emergence of Consciousness, with the concept in which "an intention can change the intrinsic dynamics by destabilising one pattern and stabilising the other one" (4.4).

Many phenomena, ranging from quantum physics and astronomy to psychology and sociology, are being modelled in complex non-linear dynamic systems. Based on the work of brilliant mathematician Henry Poincaré and many others, the interplay of numerous self referring variables is being modelled and simulated on a computer to catch emergence of an order from an apparent chaos.

The emergent property is a stabilised result (split symmetry) of interplays (interactions, communications, relations) between its constituent parts.

In a highly abstract and simplified form, it could be said that a phenomenon impacts (communication) its surroundings (other phenomena within a system) while, at the same time, it is being impacted by its surroundings. It is reasonable to assume that the impact of its surroundings will modify its behaviour that impacts its surroundings, thus closing the loop in which another phenomenon emerges - a phenomenon we call emergent property.

Depending on the "kind" of interplay, the system is initially unstable "oscillating" between few possible stable states. (Note the transition of continuum into discrete.) And then - something remarkable happens - the system "falls into" one of the states (symmetry breaking) gaining more and more stability with little if any chance to "fall back" into the initial state of instability. The only way that this could be interpreted, seems to be that the emergent property impacts the interplay between its constituent parts by amplifying interplays that stabilise the system and diminishing interplays that destabilise the system.

We cannot say, for example, that our culture (emergent property) resides at any particular physical location. In a sense it resides within us and among us. The fact that we cannot point our finger at it and say - "there it is", does not mean that it does not exist. Although it may sound counterintuitive, I would suggest that there is nothing in our world we can point our finger at and say - "there it is", for everything we see is a result of interplays between its parts. In other words, I would suggest that we do not see particles of a rock for example - but the result of their interplays that form an emergent property we call "rock".

The emergent property is often considered within terms of the phenomenon we call life. For example - the article "Flower arranging made easy" in Nature Science Update. However, the principle of the emergence extends to inanimate matter as well - saltiness, for example, of a molecule of salt that is not present in its parts (atoms/elements). Or - oscillating systems (like old fashioned clocks) that synchronise (or silence) themselves if their ticks are transmitted (communicated) between them when hanging on the same wall.

These two aspects are easily translated into the view from outside ("objectivity") and the view from within ("subjectivity"). Although I can only infer the "subjectivity" of others (or other species or inanimate matter), I am quite sure that it is there - in one form or another. The trouble is that I can neither experience nor prove the existence of the richness of the world and ourselves within it in others - not even in a human being next to me.

"Subjectivity", uniqueness, selfreference are "impossible" in the ("objective") picture of probabilistic/deterministic universe (closed system). A probability of a unique phenomenon in such a universe is zero (1/∞). And yet - I guess that all of us will agree that we are "subjective", unique, selfreferring human beings with feelings, a sense of beauty and humour... We all live our life taking or missing opportunities that are not a product of random chance, but rather "openings" in complexities of interactions within our world and ourselves within it. This is a quite different, "subjective" picture of the universe - a picture without boundaries around it (open system). In this picture we have something that simply cannot exist in our "objective" pictures - our uniqueness, selfreference, meanings, feelings, emotions, sense of beauty and humour... And this is that elusive "more" in "the whole is more than the sum of its parts".

We need both pictures, but we also need to recognise limitations of the "objective" picture and try to see how to overcome them in order to improve our "subjective" picture.