Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Friday, July 16, 2010

Is complexity post-Newtonian?

There are changes coming to our approach to science. But what is behind them?

In a word, complexity. What is it? It is actually very hard to define, but is frequently used to describe systems which behave unpredictably for one reason or another. By system we usually mean some interactive group of components, which may be living or not. Thus a system may be a single organism, a group of organs within an organism, a colony of related organisms, an entire ecosystem, a planet, or some portion thereof, such as the atmosphere or hydrosphere (or both together).

I will paint this in broad strokes and hopefully fill in details later. I will also link you to much better sources of information than poor me.

Complexity is frequently described as being either organized or disorganized. Disorganized complexity is used to describe systems which have so many disparate components and so many possible interactions that our ability to describe and characterize them all defies our computational abilities. The behaviour of the system might as well be random. In some senses this type of complexity is not of great intellectual interest as it is possible that as our computational and organizational skills increase, we may be able to understand the origin of the unpredictability of such systems.

Organized complexity is much more interesting. In this case we are looking at a simpler system with only a few interactions, each of which appear to be straightforward, and yet the system surprises us with unpredictable behaviours which are sometimes called “emergent properties”. (See here for a seminal paper on complexity in which emergent properties are described).
Complexity is often described as post-Newtonian, but issue is far from settled. For instance, an earlier version of the Scholarpedia article on Complexity began with such a statement, but has since been removed.
Apart from their disputes over who had precedence in the development of the calculus, Leibniz and Newton also had different metaphysical ideas about how science should proceed. 
The mechanistic approach to science is very closely associated with Newton despite having a much earlier origin. The central logic of the mechanistic view is that knowledge about a complex system can be gained by reducing it to simpler components, each of which could be understood. The reduction could be carried out repeatedly until hopefully the components were comprehensible. This approach, known as reductionism, was formulated by Descartes. The mechanistic approach to science is commonly considered to be the only approach to science. If we recall the key approach to science is the formulation and testing of hypotheses, then it is clear that the mechanistic worldview may be described as a paradigm, in that it does not define the scientific method itself, but restricts the types of hypotheses that are formulated and tested.

The mechanistic view would consider an organism to be a divisible collection of parts which, while interrelated, could be studied and understood separately.

Leibniz’s metaphysical view was considerably different. Leibniz’s metaphysics would consider the organism to be the sum or combination of an active and a passive principle: the passive principle representing the physical manifestation of the organism while the active principle was the organizing principle which caused matter and energy in the environment to form the organism. Under this approach then, it would make no sense to study an organism one component at a time, but only somehow in its entirety. Additionally, one could argue that the essential reality of the organism (or system) was the active principle, which was not something that could be perceived directly, but which would have to be inferred on the basis of observations of the passive principle.

In order to better understand the differences between these two systems, let us consider a particular complex system and look at how we would investigate it under these two different approaches.

A nicely defined complex system.

Under the Newtonian mechanistic approach we would study the system by studying all possible parts and making every possible measurement we could think of, and . . . where was I . . . we would hope somehow to gain a complete understanding of the system at the end of this process. Even with these measurements, common experience tells us that there is a little more to this system than meets the eye. We could not determine by direct measurement many of the important parameters of this system, such as her favourite music or indeed how to get her to agree to allow us to make the measurements we alluded to above.

The Leibnizian approach would suggest that the physical form of the system before us is merely a consequence of some inner truth which can't be perceived directly, but which causes the system to organize itself out of the ambient energy and matter of the surrounding environment. The Leibnizian approach would be . . . well, it's not really clear what the Leibnizian approach would be. It seems to be the central disadvantage of Leibniz's metaphysical approach to science. What sort of hypotheses can you formulate? And how do you test them? So while Newton is busily measuring the big toe, for instance, Leibniz can only wonder.

It is very difficult for us to think about this in the same way as did Leibniz, because our view is likely to be coloured by the recent concept of information as an actually quantifiable property. It is not clear to me whether or not information was viewed as a thing that could be measured in Leibniz's day, so while it is tempting for us to say that the active principle must be information—that it could be considered to be an intangible set of rules for constructing the system of which it is the active principle; I am not sure that Leibniz would have thought about it that way.

No doubt some readers are already thinking "Aha! Genetics!" And genetics could certainly qualify as information making up Leibniz's active principle in the complex system depicted above. But I am reasonably certain that Leibniz did not have secret knowledge of genetics either. So Leibniz would not be able to apply his metaphysical approach towards understanding the complex system standing in front of him.

All of this goes to explain why the mechanistic worldview came to be looked upon as the only approach to science. Under the mechanistic approach, it is generally clear what you do. You measure, codify, observe, and you will learn something, even if it wasn't what you set out to learn. Indeed, probably 99.9% of everything we have learned in science since Newton's time has come from testing hypotheses within a reductionist, mechanistic worldview.

And still . . .

There are some problems which we have not been very successful at solving, and we are beginning to doubt whether the reductionist approach will ever work. These are problems like the workings of ecosystems, and complex systems like climate. There are too many parameters to measure, we often don't know what parameters are important to measure and which can safely be ignored, the accuracy of measurements is limited, and there is a little problem called sensitivity to initial conditions.

It is only in the past thirty years or so that methodologies for codifying the behaviour of complex systems have been developed. And testing of interesting hypotheses concerning the organizational behaviour of complex systems is even more recent. The notion of self-organized criticality has a particularly "Leibnizian" feel to it. Phase space reconstructions, computational mechanics, the idea of self-organized criticality, multifractals, . . . are all ideas that are clearly moving us away from a mechanistic reductionist world view, and towards something that is more embracing of the organization of information at the centre of complex systems. However, this is not a paradigm shift, as the Newtonian approach will not be replaced, but merely enhanced by the new approaches. And, it is not a post-Newtonian approach either, as the basic idea was around in Newton's time. The difference is that we are beginning to learn how to apply it.

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