After my first lackluster post i started to think and the idea of chaos got lodge in to my old think tank!
What exactly is chaos? The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data.
When was chaos first discovered? The first true experimenter in chaos was a meteorologist, named Edward Lorenz. In 1960, he was working on the problem of weather prediction. He had a computer set up, with a set of twelve equations to model the weather. It didn't predict the weather itself. However this computer program did theoretically predict what the weather might be.
One day in 1961, he wanted to see a particular sequence again. To save time, he started in the middle of the sequence, instead of the beginning. He entered the number off his printout and left to let it run.
When he came back an hour later, the sequence had evolved differently. Instead of the same pattern as before, it diverged from the pattern, ending up wildly different from the original. Eventually he figured out what happened. The computer stored the numbers to six decimal places in its memory. To save paper, he only had it print out three decimal places. In the original sequence, the number was .506127, and he had only typed the first three digits, .506.
By all conventional ideas of the time, it should have worked. He should have gotten a sequence very close to the original sequence. A scientist considers himself lucky if he can get measurements with accuracy to three decimal places. Surely the fourth and fifth, impossible to measure using reasonable methods, can't have a huge effect on the outcome of the experiment. Lorenz proved this idea wrong.
This effect came to be known as the butterfly effect. The amount of difference in the starting points of the two curves is so small that it is comparable to a butterfly flapping its wings.
The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does. (Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141)
This phenomenon, common to chaos theory, is also known as sensitive dependence on initial conditions. Just a small change in the initial conditions can drastically change the long-term behavior of a system. Such a small amount of difference in a measurement might be considered experimental noise, background noise, or an inaccuracy of the equipment. Such things are impossible to avoid in even the most isolated lab. With a starting number of 2, the final result can be entirely different from the same system with a starting value of 2.000001. It is simply impossible to achieve this level of accuracy - just try and measure something to the nearest millionth of an inch!
Ahhhhhhh i now feel abit better for venting
Untill next time.
Thursday, 23 April 2009
Why is special K so Special and whatever happened to regular K?
Dont be fooled by the title this little blog isnt going to detail my favourite breakfast treats i might save that for a later blog........ or not.
Anyway down to business ive finally decided to join the blogging comunity im not going to talk about much, just the random thoughts that pop in to my brain box.
Todays blog is just a quick one to pop my blogger cherry, nothing like a quick cherry pop in front of an audience.
This being my first day off in a while is not really a good day to start my wonderful blog because i have done absolutley nothing all day except play football manager so my usually chaotic mind has been silenced... well at least dulled for this i apologise i feel like i have deprived you of the true potential of my wisdom but please be patient i promise they will get better.
Anyway down to business ive finally decided to join the blogging comunity im not going to talk about much, just the random thoughts that pop in to my brain box.
Todays blog is just a quick one to pop my blogger cherry, nothing like a quick cherry pop in front of an audience.
This being my first day off in a while is not really a good day to start my wonderful blog because i have done absolutley nothing all day except play football manager so my usually chaotic mind has been silenced... well at least dulled for this i apologise i feel like i have deprived you of the true potential of my wisdom but please be patient i promise they will get better.
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