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See also: fundamental

Outline

While physics has had an amazing success in describing most of the observable universe in the last 300 years, the formalism appears to be restricted to the fundamental workings of nature. Only solid-state physics attempts to deal with collective systems. And only thanks to the magic of symmetry one is able to deduce fundamental analytical solutions.

In order to approach real life complex phenomena, one needs to adopt a more systems oriented focus. This also means that the interactions of entities becomes an integral part of the formalism.

Some ideas should illustrate the situation:

• Most calculations in physics are idealizations and neglect dissipative effects like friction
• Most calculations in physics deal with linear effect, as non-linearity is hard to tackle and is associated with chaos; however, most physical systems in nature are inherently non-linear
• The analytical solution of three gravitating bodies in classical mechanics, given their initial positions, masses, and velocities, cannot be found; it turns out to be a chaotic system which can only be simulated in a computer; however, there are an estimated hundred billion of galaxies in the universe

Systems Thinking

Systems theory is an interdisciplinary field which studies relationships of systems as a whole. The goal is to explain complex systems which consist of a large number of mutually interacting and interwoven parts in terms of those interactions.

A timeline:

• Cybernetics (50s): Study of communication and control, typically involving regulatory feedback, in living organisms and machines
• Catastrophe theory (70s): Phenomena characterized by sudden shifts in behavior arising from small changes in circumstances
• Chaos theory (80s): Describes the behavior of non-linear dynamical systems that under certain conditions exhibit a phenomenon known as chaos (sensitivity to initial conditions, regimes of chaotic and deterministic behavior, fractals, self-similarity)
• Complex adaptive systems (90s): The “new” science of complexity which describes emergence, adaptation and self-organization; employing tools such as agent-based computer simulations

In systems theory one can distinguish between three major hierarchies:

• Suborganic: Fundamental reality, space and time, matter, …
• Organic: Life, evolution, …
• Metaorganic: Consciousness, group dynamical behavior, financial markets, …

However, it is not understood how one can traverse the following chain: bosons and fermions -> atoms -> molecules -> DNA -> cells -> organisms -> brains. I.e., how to understand phenomena like consciousness and life within the context of inanimate matter and fundamental theories.

Illustrations

Category Theory

The mathematical theory called category theory is a result of the “unification of mathematics” in the 40s. A category is the most basic structure in mathematics and is a set of objects and a set of morphisms (maps). A functor is a structure-preserving map between categories.

This dynamical systems picture can be linked to the notion of formal systems mentioned above: physical observables are functors, independent of a chosen representation or reference frame, i.e., invariant and covariant.

Object-Oriented Programming

This paradigm of programming can be viewed in a systems framework, where the objects are implementations of classes (collections of properties and functions) interacting via functions (public methods). A programming problem is analyzed in terms of objects and the nature of communication between them. When a program is executed, objects interact with each other by sending messages. The whole system obeys certain rules (encapsulation, inheritance, polymorphism, …).

Some advantages of this integral approach to software development:

• Easier to tackle complex problems
• Allows natural evolution towards complexity and better modeling of the real world
• Reusability of concepts (design patterns) and easy modifications and maintenance of existing code
• Object-oriented design has more in common with natural languages than other (i.e., procedural) approaches

Algorithmic vs. Analytical

Perhaps the shift of focus in this new weltbild can be understood best when one considers the paradigm of complex system theory:

• The interaction of entities (agents) in a system according to simple rules gives rise to complex behavior: Emergence, structure-formation, self-organization, adaptive behavior (learning), …

This allows a departure from the equation-based description to models of dynamical processes simulated in computers. This is perhaps the second miracle involving the human mind and the understanding of nature. Not only does nature work on a fundamental level akin to formal systems devised by our brains, the hallmark of complexity appears to be coded in simplicity (”simple sets of rules give complexity”) allowing computational machines to emulate its behavior.

It is very interesting to note, that in this paradigm the focus is on the interaction, i.e., the complexity of the agent can be ignored. That is why the formalism works for chemicals in a reaction, ants in an anthill, humans in social or economical organizations, … In addition, one should also note, that simple rules - the epitome of deterministic behavior - can also give rise to chaotic behavior.

The emerging field of network theory (an extension of graph theory, yielding results such as scale-free topologies, small-worlds phenomena, etc. observed in a stunning veriety of complex networks) is also located at this end of the spectrum of the formal descriptions of the workings of nature.

Finally, to revisit the analytical approach to reality, note that in the loop quantum gravity approach, space-time is perceived as a causal network arising from graph updating rules (spin networks, which are graphs associated with group theoretic properties), where particles are envisaged as ‘topological defects’ and geometric properties of reality, such as dimensionality, are defined solely in terms of the network’s connectivity pattern.

A list of open questions in complexity theory.

From: http://j-node.homeip.net/knowledgebase/overview/

tags: complex, systems thinking, algorithmic, self-organization, simple rules, complex systems

This entry was posted on Wednesday, March 28th, 2007 at 12:20 pm and is filed under This'n'that, science overview. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.