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Thursday
Apr082010

the oxbow lake effect

Aardvarks, especially smart ones, have an aversion to complexity. Their burrows can become veritable warrens until, at a certain critical moment, they are abandoned. Whereupon it is those natural lovers of complexity, nay, even chaos, the wild dogs who take over, and make more complicated the already labyrinth-like underground dwellings so recently vacated.

The labyrinth- navigated by Theseus with the help of Ariadne’s ball of string. A sliver of a link but one worth making. String, you see, can bundle up as we all know into one hell of a complex knot, a Gordian knot no less that only a lateral thinker like Alexander can defeat- slicing through it rather than trying to untangle it. He knew, you see, that tangle complexity can never be defeated.

Tangle complexity appears too in the strange case of the Norwegian coastline. As students of fractal geometry will know, the coastline of Norway is riven into fjords, and fjords on fjords and fjords on fjords on fjords. You get the picture: in a variation on Zeno, the coastline is potentially of infinite length and can certainly be never measured. What I’m projecting here is a sort of speeded-up vision of the coastline over eons of time, the fjords just multiplying and lengthening all the time. This is tangle complexity- it just gets worse. It just gets more and more complicated over time.

There’s no feedback mechanism to control the growth of the complications.

But not all complexity is tangle complexity, which is akin to, but not identical with, entropic decline. When we think of unavoidable complications which are brought on us in order to alleviate or solve some ongoing problem, then we’re in different territory; then we are in the realm of the oxbow lake effect.

As students of geography know, the oxbow lake is the result of a river running through easily erodible land. As it wobbles the curves are carved out (water flows fastest on the outside of a curve thus digging it wider) and eventually the river begins to loop back on itself. Finally, though, the two sides of the loop meet and a redundant lake- the oxbow- is formed- and the river is much shortened and much straighter. Until the process starts all over again.

So, in terms of complexity, the river gets more and more complex, ie. loopier and less straight, until at that sudden breakthrough point when the levels connect together and shorts out the bit that becomes the oxbow lake.

Shorting-out, or shortcutting-out is a good description. In any system, that becomes too complicated, but has some over riding purpose, the levels will shortcut out after a while. As Steven Strogatz has shown complicated architectures very often develop the ‘small world effect’; ie. six degrees of separation. (if a sample of 100 people each know 50 more people and this is repeated through six people the total pool is 31 billion- in other words much bigger than the world’s population. So you can connect to anyone in 5 or 6 people, even Saddam and Stalin). Implied is a certain degree of non-isolation. Inuit in the 14th century would have to be excluded I imagine. The ‘mechanism’ of six degrees is: shortcuts happen when there is lots of connecting going on.

What the ‘oxbow lake effect’ does is take this further, it suggests that any system that is non-trivial will develop shortcuts causing an oscillation in states of complexity. In the oxbow lake effect the shortcuts happen because of the nature of the erosion. Over time the erosion effect exaggerates any wrinkle in the river’s length. It is pure positive feedback- making left turns more left and right turns more right. But when this uninhibited positive feedback effect is contained within a bigger system that limits it (in this case the limitation is the water flowing downhill to the sea) then the positive feedback eventually negates itself and the system as a whole exhibits negative feedback characteristics.

Students of history will be familiar with the law of unintended consequences: politicians, usually, set out to rectify something and end up exacerbating the very thing they wanted to improve. There’s some joyous poetic justice involved here- but only if your heart is a little cold. One of my favourites was the UN anti-desertification program that actually found the largest increase in desertification where all the research vehicles at the study centre were turning in and out and driving around and actually causing a major increase in…desert.

Then there’s the second world war, to change pace a little, where an attempt to avoid another catastrophic war by making the aggressor weak, ended up fuelling such resentment that another war broke out.

In fact you only have to study a few cases to realise that the law of unintended consequences is the RULE rather than the exception. People see something complicated, they try to fix it, they make it worse…until it somehow ‘shorts-out’ and fixes itself.

There is fixing something complicated by making it more complicated and fixing something complicated by creating an ‘oxbow lake’. Maybe we should look for potential oxbow lakes before we rush in to fix things that have defeated many many people before and are hideously complicated.

Perhaps the oxbow lake effect is evidence too of a motive power for the mysterious ‘black swan effect’ invented by Nicholas Taleb. Here, big strange things- like the recent credit crunch- just ‘happen’. Of course one needs to be wary of trying to predict a real world phenomenon from a few nice analogies, nevertheless, if one flies over a river a few months, years even, before the breakthrough is made and sudden redundancy happens, one can safely predict some pretty major falls in riverside real estate values on the soon to be formed oxbow lake.

One should, as a smart aardvark, be on the look out for the oxbow lake effect. What is overcomplicated and just begging for a shortcut? You might need only add one more plank to create a massive saving or create a great innovation. 

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