Chaos
We’ve all heard the maxim that the flap of a butterfly’s wings in Tokyo can stir up a hurricane in Chicago. Perhaps you’ve heard it with different place-names, but the notion is equivalent; that a tiny change in initial conditions can result in a vast change in outcome, given a sufficiently complex system like the atmosphere.
An important issue arising from this is that of an invertebrate conspiracy to bring down mankind. If butterflies are responsible for hurricanes, do snails control snowstorms? Are ladybirds in control of the World economy? Can we blame ants for the poor quality of British railway timetabling? The train companies would certainly try.
But can this all be turned around?
With sufficient computing power, it would be possible to predict the necessary butterfly motion to train a team of aerobatic butterflies and prevent tornadoes and hurricanes worldwide. Butterflies would no longer be agents of destruction, causing fractal, off-the-Beaufort-scale meteorological phenomena, but saviours of communities which would otherwise have been ravaged by the terrible winds.
This concept is presumably extensible to other natural disasters. Using knowledge of the chaotic behaviour of tectonic plates, could aphids be used to prevent earthquakes? Would a team of synchronised-swimming pond skaters be able to stop tsunamis in their tracks? Should crack teams of cockroaches be deployed to dance near subduction zones and stop volcanic eruptions?
Chaos theory says it’s possible. The question is, could a prevented tsunami in the Pacific cause a stock market crash resulting in a rapidly-fluctuating oil price end up causing Saudi Arabia to go bankrupt, inducing a US-led invasion during which a troop who was to give some chocolates to his girlfriend on Valentine’s day dies horribly in a case of friendly fire, meaning the girlfriend never gets her chocolate and goes home for tea hungry on February 15th, having been unable to snack on them during her long day in the lab working on a cure for ebola, which, had she stayed, she would have worked out, but when she returns in the morning an incompetent cleaner has knocked her solution onto the floor, meaning that when ebola is brought from darkest Africa to Paris by an infected monkey posing as a businessman, there is no cure, and thus be the architect the destruction of all mankind?
If it happens, I blame the butterflies. Don’t say I didn’t warn you.
April 1st, 2005 at 08:53
Doesn’t the very nature of Chaos Theory prohibit the calculation of it’s results to any meaningful purpose - any model you make that exhibits characteristics of the world, affects the world. So you’d need an even bigger, better computer to calculate the effect that the first computer would have on the world, and possibly adjust butterfly flight paths to accomodate for it’s effects, and so on ad infinitum.
The only way to break this cycle would be to put the computer a sufficient distance away that no information generated by it could affect the earth - so if, for example, it really is impossible to travel faster than the speed of light, you could put the computer a light year away and have a year to plan your caper before your plans are affected by the fact that you’re making plans. Of course, this would make it impossible to communicate your plans back to the butterfly trainers on earth within the timeframe. They would be left in the dark and have to guess your orders, which reintroduces chaos.
You can’t escape it.
April 1st, 2005 at 11:46
I’m not sure I like the first sentence, “any model you make that exhibits characteristics of the world, affects the world“; it’s not really the act of making the model which affects it, but the tiny variations themselves.
But your point is a valid one: you would need to model the effects of the computer, the nerd typing at it, the fact that you’ve assembled all the parts to this large supercomputer changing the Earth’s gravity…
Move your supercomputer away, and then you need to take into account the effects of the radio waves to beam the information back…and the instructions being sent will obviously be subtley different depending on the instructions being sent, creating a wonderful infinite vicious regression…
I think the answer is that you can get something useful, though; the small changes in initial conditions only manifest after a long period of time. The animated GIF below illustrates this; it shows the variation of one chaotic variable with time, using initial conditions that differed by somewhere in the region of 0.2%. As it flicks between, you can see that the systems start out with approximately the same behaviour that, at some point, diverges massively. This is why weathermen can gleefully wave their arms about in the studio when giving their reports; they’re confident that the tiny change in conditions they’re causing won’t manifest for a significantly longer period of time that they’re forecasting.
A chaotic variable plotted against time with two slightly different initial conditions
There follows is another picture from the same computing project, illustrating a feature called a “strange attractor”. I included it largely because it looks pretty, but the interesting thing to note is that the line (which now is two different chatoic variables plotted against one-another) orbits around these points in a non-random but difficult-to-predict way, without ever actually reaching them. Craziness.
Two chaotic variables plotted against one-another, displaying strange attractor behaviour
So, in summary, we’d need a largely isolated computer, and a bloody lot of butterflies.
May 7th, 2006 at 22:18
Isn’t a big part of the problem that no one could ever find out - or at least prove that they had - the “right” model (or equation, or whatever), since we can only make our measurements of the past to a given degree of accuracy, and chaos being chaotic, any variations within these error bounds could lead to slightly different models, with vastly different predictions? Assuming of course that there is a “right” model. And assuming that we live in an inductive world - no point in having the perfect model if all the rules change tonight. Or if there aren’t any rules, just a big coincidence so far.
Also, what if the World isn’t deterministic? Your computer would have to be able to predict, for instance, my buying a particular brand of ham on Tuesday in three weeks time. If I consulted the computer, being a mischeivous devil, I could decide to buy a different brand of ham. Or - shock, horror - not even buy ham at all! Maybe I’ll go to London for the day instead, just to exercise my inaliable right to free will.
Apologies for the many Earthquakes, tsunamis and hurricanes I have caused by typing this. On that note, why do people focus on the bad things? Why don’t they say that a butterfly in Japan could cause John Smith to win the lottery in England? Or him to meet his future wife? Or just cause a lovely sunny day? Keep the glas half-full.