Please Register or Log in to view the hidden image! no you need 10 billion butterflies to get a "El Niño" year. Please Register or Log in to view the hidden image!
If a butterfly flapping its wings causes a hurricane, does that mean that me breaking wind kills thousands of people each year in natural disasters? Just a thought.
NO, but you could post something on the Internet that could start a chain of events which could lead to the world war III. We know how Gautama became Buddha or how Gandhi took up the struggle to free India...
The butterflies: it's a nice story, an analogy. Why do people get carried away by it so much??? Please Register or Log in to view the hidden image! Have you ever considered the effect of a one-winged butterfly trying to fly? Now that can cause massive destruction!
Merlijn, In a previous post you discussed attractors in relation to complex systems and I understand (I think?) what you are talking about. I have also heard the term "strange attractors" in reference to quantum physics. Are you familiar with this? If so, can you describe what they are? Thanks, Noktvs
thanks Noktvs, Here is the story (if I get it right). I hope it is not too boring, since it is quite abstract: A complex system is composed of several interlinked elements that influence each other in a dynamical way. This means that the behaviour of the system can be described as a collection of differential equations. The variables in the equations span up the specific state space of the system. If there are n (unique and independent) variables describing the the system's behaviour, the state space is n-dimensional. A point in that state space defines the values of all n variables at a specific time. Every point is also part of one unique 'phase path', a trajectory through the state-space which describes how the system evolves over time. An attractor is a point or region in the state-space of a system toward which all trajectories from whithin a larger region of the state space evolve. No wonder it is called an attractor. There are also repellors, I guess you need no explanantion here. An example of an attractor point: a simple (damped) pendulum has a state space that is defined by the variables φ and dφ/dt (the angle and the angle velocity). From every point in the state space a phase trajectory spirals inward to the origin: φ=0 and dφ/dt = 0. That is where the pendulum stops swinging. Mind you, it is not the pendulum that is spiraling. the pendulum just goes from left to right and back again. It's the tarjectory through the state space that spiral towards a single point. Thus, the pendulum has a state space with a point attractor. Now there are also some other (more interesting) attractors: There are four kinds of attractors in total: point attractors periodic attractors torus attractors strange attractors [/list=1] The group we like to call strange attractors are attractors that behave in a strange way (in an unpredictable manner). Projections of the state space of complex systems with a strange attractor are fractals (you know those exotic beautiful mathematical pictures). Systems with a strange attractor are the field of study of the chaos theory. (*so.. there you have it!*Please Register or Log in to view the hidden image!) Please Register or Log in to view the hidden image! Thus: strange attractors have a very well defined bahaviour, but it is just impossible to predict it without knowing precisely what the starting point in the state space is. I am not very much familiar with quantum mechanics (or quantum electro dynamics), so I have no clear picture of what part strange attractors play in that field. Very interesting though! some interesting links (may be a bit hard to read though): Chaos without the math ThinkQuest: chaos theory I have been typing and editing now for about an hour. I hope the result is satisfactory. I have had it for now Please Register or Log in to view the hidden image! But feel free to ask for more.
Here's what we need to do. We get a trillion gallons of insecticide and kill all the butterflies thus solving our weather problems for good.
Merlijn, Wow, that's some pretty interesting information. I've had to read it a few times to get the gist of it, not because you weren't clear in your explanation, but because I only have a limited knowledge of the subject. It is, though, one of my new found interests. Please Register or Log in to view the hidden image! Thanks for posting the links, I've gone to the sites and poked around a bit. I'm somewhat familiar with Chaos theory (if that's the proper term for it?). I've read the Dancing Wu-Li Masters , Chaos, Making a New Science and am in the midst of reading the Elegant Universe I have only a low-level understanding of math, so this limits me to sources that aren't "math heavy"in their explanations. I'm more into the *ideas* then the mathmatical proof, although it's cool to know there is a mathmatical formula that represents these ideas. Anyway, thanks again for such a great post. Hope to hear more from you in the future. ~Noktvs
One may also check out: The Tao of Physics : An Exploration of the Parallels Between Modern Physics and Eastern Mysticism by Fritjof Capra
again: thanks Noktvs. Kmguru, even though I think Capra may do some good science, his philosophical conclusions are sometimes dubious. I read his The Web of Life, wicth was nice but had to take it with a pinch of salt so now and then. I would reccomend Ian Stewart Life's Other Secret on chaos theory in biology (and ther life sciences). No math, just theory, nice examples and very challenging. Fun to read. Merlijn
its pretty good but i think that 1st 3min was more interesting but its worth reading if you have free time
