“If a butterfly flaps its wings in China, it could cause a typhoon in Miami a month later.”
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Surely it has happened to you, at some point in your life, to go to sleep and as soon as you lie down and shut your eyes, you hear the broken tap dripping. Tip, tap, tip, tap, tip, tap, tip, tip….
The next time it will happen to you, don’t get mad. You can do something much more beneficial since you won’t be able to sleep: study the chaos theory!
All you need is an atomic clock. Surely you have one lying somewhere, in a drawer or in your laboratory. If you don’t, then just nip off to a nearby kiosk or N.C.F.S.R. Demokritos and borrow one.
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There are two possible ways that the maddening drips can fall: either they will follow a regular rhythm (tip, tap, tip, tap) or a chaotic one (tip, tap, tip, tip, tip…tap, tip,….tap etc). Do you think it’s funny to give some thought to the matter?
And yet, a research team of young students back in 1978 at the University of California spent their prime years striving to predict the periodicity of the falling drops.
They came to the following conclusion: if you know precisely the timing of the first three drops, then you can also predict precisely the future of the system until the end of time!
In this very ‘precisely’ is where chaos theory comes into play which renders the prediction of the weather, the roll of the dice, horse racing, football and the economy impossible.
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The students who had a state-of-the-art atomic clock at their disposal figured out that if they measure precisely the periodicity of the first three drops to an accuracy of nine decimal places (0,000000001 seconds), then they could predict the future of the following…nine drops!
If they would like to know what will happen after, say, two days (one billion drops) it would require a clock which could measure 0,00000000000000000000000000000000000000000……… (I need a lot of space to type one billion zeros).
This unforseeability can be overcome –sort of- with the aid of strange attractors.
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Since we can’t get any sleep due to these chaotic drops that keep falling, let’s go and make a cake.
To do this, we use a blender which possesses two totally predictable (Newtonian) whisks. The only thing they are made to do is rotating round and round. If, by any chance, you have witnessed a whisk doing something else like dancing to Cha-Cha then you’d better quit drugs.
But the behavior of the ingredients we use for the cake is completely chaotic in the container.
Imagine that you are able to trace the motion of every sugar grain you poured in the container. Each goes its own way as the whisks beat them. We can’t predict where the grains of sugar or the molecules of the egg or the melted butter will go.
But after some beating the result is seemingly always the same and it resembles –with just a little imagination- the dunes of the desert.
Through chaos emerges organization, order.
It’s the strange attractor that shapes typhoons, galaxies and the formations of your coffee into spiral shapes.
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“What does it all matter?” you are going to ask.
A great deal if you want to have really sparkling dishes.
A group of mathematicians and physicists tried to find a way to utilize the butterfly effect (or, more scientifically, “sensitivity to initial conditions”) to our advantage. They arrived to chaotic control and the…chaotic dishwasher!
The chaotic dishwasher is a Japanese invention which possess two arms which spin chaotically (they stop abruptly, resume the process any time they mean to, sometimes they rotate slower and some others faster) and they spray water also chaotically (but the force varies).
The result is sparking clean dishes, way better than the common and dull dishwashing you do, consuming less energy, to boot.
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Chaos theory has everything to do with your empty refrigerator since the quantity of food you put or you don’t put in there is totally dependent on your financial situation which, in turn, depends on the socioeconomic situation of your country.
Since we indulged ourselves in cake and the sugar keeps us awake, let’s give rebellion a once-over – never mind the tap.
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As the mathematicians of nonlinear dynamics (the chaos theorists) have proved, if you want to predict precisely how a chaotic system will move and change, then you need to know everything for all of its elements.
The ultimate chaotic system is human society for the simple reason that it consists of…humans.
There is nothing more unpredictable than the human factor, in fact many books have been written and many movies have been made based on this unforseeability.
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Man, this fundamental element of society, is unpredictable but thankfully the strange attractors, statisticians and economists are also around.
We can’t predict the behavior of a single person, but we can guess the behavior of the mass.
In order to take place a general uprising, a revolution in other words, then the best part of a society must be stretched beyond its limits.
One, ten or a thousand people going mad will not do. This is not a revolution, this is collateral damage.
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The governments and the real powers behind the throne work on this principle: they keep pushing and exploiting the people until they perceive that things are about to get out of hand.
Then they concede some privileges and rights to ward off explosion or they create external/domestic enemies as a diversion.
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But “slight changes to the initial conditions lead to big changes in their subsequent behavior”.
The butterfly effect: “the bankruptcy of a small Balkan country could, after a month, cause the collapse of the world economy.”
Usually, this is not the case. The politicians, the statisticians and the economists are well aware of it. Most of the times the cake rises, pretty much like the deposits of the moneychangers who play dice (with people’s lives) in underground penthouses.
But ‘usually’ doesn’t mean ‘never’.
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I drew inspiration and material from Ian Stewart’s book Nature’s numbers.
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Translated by Alexandros Mantas:
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