By Andy Ho
NEWTONIAN physics can predict how a celestial body will move around another, like the Earth around the Sun. However, when a third body - the Moon, say - is included, the movement of one body alters the distance between the other two bodies, thus changing the gravitational forces involved. Here, Newtonian physics cannot predict their movements.
In 1887, Swedish king Oscar II was so intrigued that he put up a prize to entice thinkers to solve this 'three body problem'. Cracking the puzzle, French mathematician Jules Henri Poincare showed that when the initial positions and velocities of all three bodies are known, their subsequent positions and velocities may be ascertained. Thus the system may be called 'deterministic'.
But if initial conditions change by a tiny bit, a very different state of the whole system results. So such a deterministic system is also 'chaotic', in the sense it has certain behavioural regularities which, however, can't be predicted accurately. Poincare was the first person to identify a 'chaotic deterministic system'.
Now throw in 'n' number of bodies and the difficulty of predicting behaviours in the 'n-body problem' rises exponentially. In these complex systems with billions of parts - at the molecular level of things, say - the maths was intractable. Until now, that is.
From the latter half of the 20th century, when researchers began to have access to immense computing power, all these problems became part of a new area of study called complexity science, the theme of a conference that the Nanyang Technological University (NTU) co-organised this week.
Those partnering NTU were the US-based Santa Fe Institute and its European cousin, Institute Para Limes. These tiny, standalone nonprofits do trans- disciplinary science by co-locating physicists, biologists, economists, sociologists and everything else in-between to look at problems ranging from quakes and epidemics to stock markets and weather systems.
In fact, Poincare himself had suggested that weather cannot be predicted accurately because it is a chaotic deterministic system but his insight was lost until meteorologist Edward Lorenz rediscovered it. While re-running a simple computer model of the Earth's atmosphere in 1961, Lorenz decided to enter data culled from the midpoint of a previous run instead of starting from the beginning. And instead of entering the value 0.506127 as the start of the new run, he typed in 0.506 instead, having assumed that the minute difference wouldn't matter.
However, the fresh printout was completely different, implying that the 'weather' had developed in a radically different fashion. Thus, a tiny change in initial conditions could lead to a hugely different final state - a possibility that is now hyped as the 'butterfly effect'. (The butterfly effect, it should be said, is largely a myth. A butterfly flapping its wings in Singapore cannot literally cause a storm in Timbuktu.)
Even if the weather can always be measured precisely in the present, what will happen at a future instant can never be predicted accurately enough. But if the raison d'etre of science is prediction, shouldn't complexity scientists just admit defeat?
However, it has also been shown that while chaotic deterministic systems are unpredictable, they do have 'emergent' properties. That is, although their futures can't be predicted, such systems exhibit patterns, so their instability is bounded.
In other words, though their specific behaviours cannot be predicted, such systems do have an overarching general structure of behaviour that can be observed. And precisely because variability in such systems stays within a pattern, complexity emerges.
For example, when birds flock together in the sky, they evince gracefully coordinated, swift swirling patterns, even with sudden course changes, all without one bird being 'in charge'. We know now that all it takes is for each bird to keep constant the distance between itself and the one in front while flying in its general direction as well. Fish schooling - or the 'Kallang wave' - operates similarly.
Hence, simple rules enable very complex behaviours to emerge. Likewise, people who congregate in urban areas and interact in particular ways can give their cities emergent personalities of their own. Thus Singapore is very different from Jakarta. Small-scale interactions among many individual parts can lead to large-scale order. Conversely, think of a magnet being heated up until it melts and its magnetism disappears. If it is cooled down, the magnetism re-emerges at a certain temperature. Individual iron atoms have no magnetism but, collectively, those self same atoms in distributed interaction can cause magnetism to emerge. When perfectly integrated, each individual unit is apparently not really individualistic.
The brain is made up of dense networks of billions of neurons. While individual neurons are not self-conscious, networked together in interaction with each other, human consciousness emerges.
Organs are made up, in descending order 'downwards', of tissues, cells, molecules and atoms. Yet as the layers add up 'upwards' - from atom to molecules to cells to organs - life itself emerges. But how?
Right now, such phenomena can only be identified and described, not explained or predicted. But the latter would be complexity science's calling in the years and decades to come. Complexity is getting very exciting.
Daedalus (meaning "cunning worker" in Greek) was the man who built wings so he and his son Icarus could fly. Flying too close to the sun, Icarus' wings melted and he crashed to earth. Daedalus is a weekly column on the triumphs and challenges of science and technology.