chaos theory is very real,
it is infact simply a term used to describe a certain kind of system,
one that is found in many places including nature.
so to say it does not exist is a bit like saying the colour yellow does not exist.
the word "yellow" is simply a term we use.
chaos theory is amazing though.
from order comes chaos - and yet, within that chaos there is always order and from that order there comes chaos etc. etc. and so on.
once you get your head around it, its amazing!
to give an example of chaos.
imagine a perfect hypothetical experiment in a perfect vacuum.
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there is a an upright tube with one end open (think pringles)
at the bottom of the tube there are 200,000 grains of sand.
when the experiment begins a mass is driven into the bottom of the tube,
at an exact force. say 100N.
driving the sand perfectly straight up into the air.
we are interested in where the sand lands. this is our output
now Newton tells us that as we know the mass of each grain of sand, the force applied to it, the friction force between the grains of sand etc. etc.
that we should be able to predict exactly where the sand will land.
after all the Newtonian equations are all pretty simple and any highschool/secondary school student could do them.
but as you can imagine.
there is no way to predict where the sand will land.
and all 200,000 grains will never fall in the exact same place again. even if the initial conditions were identical.
this is chaos.
we have a complex system that contains absolutely no random variables, yet the results are random.
and here is where it gets even deeper!!
obviously the sand will always fall within a certain radius of the tube. only everytime it falls in a different place.
now if you were to plot where the sand fell, and then repeat the experiment.
the sand would keep falling in completely random places (chaos from order)
but after enough repeats of this experiment a pattern would begin to form in the sand, perhaps waves, or a spiral or whatever. but a pattern will eventually emerge (order from chaos)
however this pattern will be unique. when you repeat the whole experiment the next day. you will get a pattern, but a completely different one (chaos from order)
and it gets deeper still!!!
have lets say 200,000 of these experiments all happening side by side in a big square,
and eventually (and were talking a long eventually here) a pattern will form within that square!!!
here are some vids that show order in chaos
YouTube - Order in the Chaos - Synchronicity through Fractals ささやくの庭の
YouTube - Strange Attractors by Whisper of the Garden 奇妙な アトラクタ
some say the whole universe is nothing more than one giant fractal!!
and if you think about it,
the galaxy is a series of bodies in orbit around a large mass (super black hole)
our solar system is a series of bodies in orbit around a large mass (the sun)
those bodies have smaller bodies that orbit them (moons)
these bodies are made of matter, which is made of atoms, which are made of electrons orbiting a large mass (protons - neutrons)
which in turn are made out of bodies of mass (quarks) and gluons.............................etc?
and what happens when we go the other way?
why is it that trees and the veins in our body have such similar shapes/patterns?
like i said. it goes deep.
this is why newtonian physics and past events (ie mini ice age) cannot be used to predict the climate or weather.
example:
if it has rained berlin on the 19th of january every year for the last 1000 years, you would not be able to use that information to say that it will rain on the 19th of jan this year.