What is Chaos theory?
Before we turn to Chaos, let’s have a quick look at Determinism.
Determinism implies that everything is preordained, that living life is somewhat like reading a book.
Universe and everything that exists in it, all our decisions and actions are already predetermined, they are prewritten and a man that lives his life is like a reader.
He does not know what will happen in the next chapter, but things he has already read, he cannot forget or change, they are his past.
He knows how the book started and everything that happened till the page he is currently reading, just like in life he knows when he was born and what has he done by now, but he doesn’t know how and when will the book end.
So he imagines all possible endings, they are all real in his head, just like he doesn’t know his next move in his real life and the date of his death. It seems to him that they are numerous possibilities and diferent endings of the book, altough the path is already determined.
This sound somwhat grimm because it denies free will. In determined universe we could say that we are just observers of our life with no influence on it, and that our experience of living is no different from discovering the unfolding of a good book, or a bad book, if you will.
This idea was best described in 1814. by a French mathematician Pierre-Simon Laplace.
He said this: „An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies ofthe universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.
“This is a best ilustration of a deterministic theory, theory that the fate of everyone and everything, past and the future is preordained by one specific mathematical equation.
If everything is determined, a man, if he could acquire enough knowledge, or better said, if it is writen in his destiny that he will acquire enough knowledge, would became in one sense godlike, all knowing.
Imagine a man knowing every thing that will happen next, like reading a book he has already read before, but he would not be completely godlike, as he could not do anything to change his fate.
The quest of science is to reach that Holy Grail – all knowing.
So we have tests, examinations, predicions.
Now, lets go back to chaos theory.
Chaos theory starts on a winter day more than 50 years ago with an American mathematician and meteorologist, Edward Norton Lorenz.
One day, Lorenz entered some numbers into a computer program simulating weather patterns and then left his office to get a cup of coffee while the machine ran.
The computer model was based on 12 variables, representing things like temperature and wind speed.
On this day, Lorenz was repeating a simulation he’d run earlier, but this time he was astonished with the results.
The simulation should have been the same as before, but this time computer program produced drastically different results.
He wondered why.
In first simulation he entered one variable 0.506127, and in the second simulation he rounded this number to.506.
To his surprise, that tiny alteration, and this is really tiny alteration, drastically transformed the whole pattern his program produced, over two months of simulated weather.
At first two lines the program produced were almost the same, but how the time passed, he got something very different.
So, Lorenz concluded that small changes in the initial conditions can result in large differences in a later state.
Before that, and even now, mathematicions were rounding numbers, making it a bit simpler but keeping its value close to what it was, and they were knowing that the result will be less accurate.
But they thought that the results will be approximately similar, however Lorenz now concluded that this small alterations, rounding numbers can result with a large differences over time.
In order to explain how important sensitivity the to initial conditions was, Philip Merilees, the meteorologist who organized the conference session where Lorenz presented his result, chose himself the title of Lorenz’s talk, a title that became famous: “Predictability: does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?
The unexpected result led Lorenz to a powerful insight about the way nature works: small changes can have large consequences.
The idea came to be known as the “butterfly effect” as the title of the presentation suggested that the flap of a butterfly’s wings might ultimately cause a tornado.
And the butterfly effect, also known as “sensitive dependence on initial conditions,” has a profound corollary: forecasting the future can be nearly impossible.
Because we can never know all the initial conditions of a complex system in sufficient (i.e. perfect) detail, we cannot hope to predict the ultimate fate of a complex system.
Even slight errors in measuring the state of a system will be amplified dramatically, rendering any prediction useless.
Chaos theory does not denies Determinism, it just implies that despite all of our super computers and all of our math discoveries, we will never be able to calculate the outcome of the man’s fate.
In a purely mathematical world where you can specify initial conditions exactly, chaotic systems are fully deterministic, and our lives are predetermined.
Chaos theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. These phenomena are often described by fractal mathematics, which captures the infinite complexity of nature. While classical geometry uses formulas to define a shape, fractal geometry uses iterations.
The shapes that come out of fractal geometry look like nature. This is an amazing fact that is hard to ignore. As we all know, there are no perfect circles in nature and no perfect squares. Not only that, but when you look at trees or mountains or river systems they don’t resemble any shapes one is used to in maths.
However with simple formulas iterated multiple times, fractal geometry can model these natural phenomena with alarming accuracy. If you can use simple maths to make things look like the world, you know you’re onto a winner. Fractal geometry does this with ease. An you can put randomness into fractal shapes and this is why some believe that God used fractals when he coded the world, but in a strictly philosophical sense this denies our free will.
As George Dallas, UK based Information engineer and Internet social scientist writes, there’s a whole debate to be had on the purpose of fractal math, but as an Engineer I am inclined to say that one of its purposes is to try and replicate the world around us.
I suggest you read his writing about fractals HERE