REFERENCE: Wikipedia | Chaos
Chaos (derived from the Ancient Greek Χάος, Chaos) typically refers to unpredictability, and is the antithesis of cosmos. The word χάος did not mean "disorder" in classical-period ofancient Greece. It meant "the primal emptiness, space" (or, void) Chaos (mythology). Chaos is derived from the Proto-Indo-Euopeanroot ghn or ghen meaning "gape, be wide open": compare to "chasm" (Gr) χάσμα, a cleft, slit or gap), and Anglo-Saxon gānian ("yawn"), geanian, ginian ("gape wide"); see also Old Norse Ginnungagap. Due to people misunderstanding early Christian uses of the word, the meaning of the word changed to "disorder". (The Ancient Greek for "disorder" is ταραχή.).
Chaos is the complexity of causalityor the relationship between events. This means that any 'seemingly' insignificant event in the universe has the potential to trigger a chain reaction that will change the whole system. A well known saying in connection with this issue is "A butterfly flapping its wings in one part of the world can cause a hurricane on the other side of the earth." This is also known as the "butterfly effect".
BLOG LIST | powered by NetKismet
Mathematically, chaos means an a-periodic deterministic behavior which is very sensitive to its initial conditions, i.e., infinitesimal perturbations of initial conditions for a chaotic dynamical system lead to large variations of the orbit in the phase space. (editor's note: RE: Lorentz, make note from textbook) Chaotic systems are systems that look random but aren't. They are actually deterministic systems (predictable if you have enough information) governed by physical laws, that are very difficult to predict accurately (a commonly used example is weather forecasting). 
REF: 'Chaos and Fractals: The New Frontiers of Science', Peitgens, Jurgens and Saupe; Springer Publishers (a textbook from my library)
The Lorentz experiment from 1956 is probably the most important work to discuss here. He is famous for his theories on Lack of Predictability (...in deterministic systems) specifically, using a meterology model and a computer. He wrote an article called "Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" made him well-known for what is called "The Butterfly Effect". In a nutshell (albeit it tiny and inadequate) his experiments showed the same thing repeatedly; a break-down of predictability due to the inability to accurately calculate on two different events (but using the same fractions and starting point) a number past a certain number of decimal places.
Also, the remarkable thing is the way the variance grew over time. It grows exponentially on a variety of different iterations, depending on the predicted stability of the initial conditions. But even environments that are as stable as possible produce a variance at some point or another, then on the next iteration the accuracy between the two columns of numbers begins to vary more and more from each other, sometimes even crossing over to the left side of the decimal place from a tiny variation in the 12th or more decimal place on 15 of 50 iterations. (done on a 10-base.)
In an experiment with 2 different calculators, (a Casio and an HP, the Casio computer is on a 10-base and the HP is on a 12-base) Lorentz ran the numbers through again and again, sometimes changing a factor in the initial test environment. Even using the same computer there was a variance at some point during the iterations. Unpredictability always seemed to seep in, no matter what. Lorentz would say, that 'chaos' was inherent in the system. 
Experiment on your own.
This was fun for me. While writing this part of the article; I had to conduct research into the topic of Chaos Mathematics, being only a little familiar with it from seeing pictures of the Mandelbrot Set. I soon realized there was no way I'd ever be able to fit most of it in. During research (I read the textbook from 11:30 PM to 6:00-ish the next morning, finally stopping on page 101) I found it a helpful and fun way to get a better grasp on the subjects by doing some little experimentation.
To make a Video Feedback Machine, for example. Just put a video camera (I used my webcam) in front of a monitor (I used my flat-panel computer monitor) so that the monitor is filling the lens view and record. You will see infinite pictures of the monitor within the monitor. It's called a "monitor within a monitor" view (see video, 'Chaos & Fractals, Video Feedback, Part 1), because the monitors will appear to be infinite, each one nested in and smaller than the one around it, and multiplying into ever infinitesimally smaller views. So pretty cool stuff. You can also move the camera back out and get a larger view, also multiplied by the monitor, to emcompass the stuff around the outside of your monitor, or closer in to capture views of a part of the monitor.
Topics covered that are relevant will be linked to in the Mathematics section, or covered in a video (or both) because there are so many of them. The 'Chaos and Fractals' section of the Mathematics topics covered in this website could be a section all to itself, because it is the framework on which we must build any kind of understanding of the topics covered in the Physics section of the website, and even some of the larger topical stuff (like Symbology, Religion, Scientists, News and other parts of the Mathematics section) will be able to relate to it. As such, related topics are spread out throughout the Mathematics section of the website.
WHAT IS CHAOS?
People generally think of Chaos as just sheer randomocity that makes no sense, but scientists are studying it more and more for it's features; specifically, the tendency towards a pattern from within chaotic systems, the introduction of chaos into an ordered system (Lorentz: once the variance is introduced into an iteration - or loop, the numbers' variance is progressively larger and more unpredictable, ad infinitum) the duplication of its patterns in nature, and objects (even on the particle scale) that manifest a kind of behavior called 'auto-assembly' (or self-assembly) into a pattern. On that note, the rest that can even be explained through a website, should be seen. (the visuals will go a long way towards explanation, so if a related section has a video in it, you may want to watch it.) The topics covering Fractals was almost included here, but again, it turned out to be a section unto itself; so in relating Chaos Mathematics to Fractals you may find it helpful to view the videos (see Mission Heavens on YouTube).
[ TOP of page ]