by Kees Vuik [mailto:jcvuik@chello.nl]

Can humans gain a complete understanding of the world, or are there limits to what we can know? How does one acquire knowledge? And how certain can you (suppose to) know something? Philosophers from Plato and Aristotle to Kant, Wittgenstein and Quine have been struggling for centuries with these questions from epistemology (the theory of knowledge).

Put two philosophers in one room and within the minute they’ll disagree. Therefore, definitive answers won't probably come from them but rather from natural scientists. Their explanations are often clearer - and more disturbing. The mathematician Kurt Gödel, for instance, proved in 1931 that no mathematical system can ever be fully explainable. He showed that even within the narrow and strict logical boundaries of number theory there will always be propositions that can't be proven true or untrue. If such a small domain of mathematics already contains so much uncertainty, how can we ever hope to know everything about the world?

Matter is made out of elementary particles and those particles obey a small set of known laws. Nevertheless, their behaviour can not be predicted. An elementary particle is not real, in a sense, not substantial. It can best be seen as a probability wave, a mathematical function that predicts the chance of finding the particle at time t on location p. Strictly speaking, elementary particles do not exist at all. Until the moment that someone tries to measure one of its properties and the wave function miraculously 'collapses', giving rise to tangible matter... Not "I think, therefore I am" as Descartes once said, but "I'm being measured, therefore I am".

The behaviour of systems with billions of identical building blocks can often be predicted by using statistics. This has been done for gases, for example, resulting in the laws of thermodynamics. However, gas molecules exist independently from each other. Calculating the behaviour of systems with elements that can interact with one another is much harder... For example, a long time prediction of the movements of three celestial bodies that are circling each other is virtually impossible - even if you know their initial velocity and position with a certainty of a hundred decimals. The combined gravity's are so complex that the dynamic behaviour of the system as a whole cannot be calculated, no matter how big and fast your computer might be.

And what is a system of just three bodies, compared to such complex adaptive systems as brains, dolphins or ant colonies? These kind of structures are composed of huge amounts of elements that can - one way or the other - respond to each other's state. Adaptive systems can adjust themselves to varying circumstances and never reach thermodynamical equilibrium. Unlike gases, they constantly change by taking in and digesting food and producing waste materials. If you want to understand the behaviour of such a system, searching for mathematical equations is useless and the only thing you can do is: simulate it on a computer.

Stunts in three rules

Some birds are proficient stunt flyers. With hundreds at a time they can speed up in one direction, suddenly in unison decrease their velocity and turn to follow a different route. No matter how complicated their acrobatic path, the birds always stay close together and never collide. They resemble elite soldiers who blindly follow the orders of their drill sergeant. But is there a leader..? Computer simulations reveal that the complex behaviour of a flock of birds can easily be imitated by following three simple rules: 1. steer to move toward the average position of local flockmates, 2. steer towards the average heading and speed of local flockmates, and 3. steer to avoid flockmates and all other objects. The first two rules produce the cohesion and alignment of the flock, the third rule ensures the necessary separation.

In 1986 Craig Reynolds, a computer animator from California, wrote a software program according to these principles. He named it Boids, and every expert was deeply impressed when seeing his digital birds fly around on the computer monitor. The birds behaved exactly like they do in nature, with fluid and elegant movements that were indistinguishable from those in real life. Even the obstacles Reynolds introduced on their path - solid software-pillars of various heights - didn't lead the Boids astray: they approached the first pillar, split up at the right moment and reassembled themselves effortlessly at the end of the pillars to resume their flight.

Reynolds' investigations illustrate a basic principle of adaptive systems and Artificial life (Alife): when individuals are able to observe their closest neighbours, as well as to react upon each other's state, complex global behaviour can spontaneously emerge. The Boids-simulation proved that there's no need for a leader to dictate the other birds how fast they must fly and in which direction. Every individual sorts this out for itself, solely by watching their nearest neighbours and adjusting its reaction to theirs.

Whether flock simulations enrich epistemology, is a different question. What do we learn from such experiments? It's perfectly possible that real birds follow the same rules as Reynolds' Boids (perhaps you'll even think this is plausible), but the laws of logic prevent us from drawing this conclusion - although some Alife adherents would love to do so. When two systems show identical external behaviour, this doesn't mean at all that they are ruled by the same internal mechanisms. A bold person might even endow Reynolds' birds with some sort of intelligence, since they developed 'natural' behaviour all by themselves (or at least a behaviour that can be observed in nature). Notwithstanding the validity of this reasoning, the simulation is of course much too trivial to generate intelligence of any kind. For this to happen, a system should at least be capable of learning and reproducing.

Therefore, the only conclusion we can safely draw from Reynolds' program (and from all kinds of other Alife-experiments) is: local interaction between individuals that follow simple rules may - on a much larger scale - induce complex behaviour and intricate patterns. So much is for sure. Whether our own super-complex society is also founded on a small set of simple principles, remains an unsolved puzzle. Up to this moment no scientist or philosopher has successfully revealed the contents of this black box.

Boids has given birth to followers. A good point to start a Net hunt is Reynolds' homepage [new-address] with a lot of information about Alife and click-throughs to all sorts of other places (like The Lion King from Disney, where Boids-principles were used to model a realistically galloping herd of animals on the silver screen). Reynolds' page is also one jump away from a beautiful site where you can play on-line with famous Alife-programs like John Conway's Life, a Boids-variation called Swarm and Biomorph, the evolution simulation of biologist Richard Dawkins (http://www.fusebox.com/cb/alife.html). Of course, Santa Fe (http://alife.santafe.edu/) also offers lots of Alife.