Chaos Theory - "The Butterfly Effect"
Ok, you might be thinking I'm going a little off topic with this one, and yeah, you'd be right! But I find it fascinating to understand this concept. This morning after looking up some movies to hire tonight I stumbled accross "The Butterfly Effect" with Ashton Kutcher. This lead me to look into this effect in more detail. I'll try explain Chaos Theory in the next few sentences:
- In a chaotic system, the use of the laws of physics to make accurate long-term predictions is impossible, even theoretically.
- To make long-term predications it would require giving the initial conditions to infinite precision ( i.e. measure to their exact size with discrepancies. Unfortunately measuring equipment will never be able to measure to infinite precision. E.G. try measuring to a millionth of an inch. Try measure a coastline - the closer you go, the more inlets and thus greater distance.).
- Even the smallest imaginable discrepancy between two sets of initial conditions would always result in a huge discrepancy at later or earlier times. This was noticed by Lorenzo when he wanted to start his weather predicting computer program mid-way to save time. In stead of entering the usual 0.5673456 he just entered 0.5673 expecting no significant alteration. However, the difference was huge.
- This means that in order to make long-term weather forecasts with any degree of accuracy at all, it would be necessary to take an infinite number of measurements.
- Even if it were possible to fill the entire atmosphere of the earth with an enormous array of measuring instruments---in this case thermometers, wind gauges, and barometers---uncertainty in the initial conditions would arise from the minute variations in measured values between each set of instruments in the array.
- This principle is sometimes called the "Butterfly Effect." In terms of weather forecasts, the "Butterfly Effect" refers to the idea that whether or not a butterfly flaps its wings in a certain part of the world can make the difference in whether or not a storm arises one year later on the other side of the world.
-It is now accepted that weather forecasts can be accurate only in the short-term, and that long-term forecasts, even made with the most sophisticated computer methods imaginable, will always be no better than guesses.
Examples of such systems are: the atmospher, plate techtonics, population growth, the solar system and Economies.
- In a chaotic system, the use of the laws of physics to make accurate long-term predictions is impossible, even theoretically.
- To make long-term predications it would require giving the initial conditions to infinite precision ( i.e. measure to their exact size with discrepancies. Unfortunately measuring equipment will never be able to measure to infinite precision. E.G. try measuring to a millionth of an inch. Try measure a coastline - the closer you go, the more inlets and thus greater distance.).
- Even the smallest imaginable discrepancy between two sets of initial conditions would always result in a huge discrepancy at later or earlier times. This was noticed by Lorenzo when he wanted to start his weather predicting computer program mid-way to save time. In stead of entering the usual 0.5673456 he just entered 0.5673 expecting no significant alteration. However, the difference was huge.
- This means that in order to make long-term weather forecasts with any degree of accuracy at all, it would be necessary to take an infinite number of measurements.
- Even if it were possible to fill the entire atmosphere of the earth with an enormous array of measuring instruments---in this case thermometers, wind gauges, and barometers---uncertainty in the initial conditions would arise from the minute variations in measured values between each set of instruments in the array.
- This principle is sometimes called the "Butterfly Effect." In terms of weather forecasts, the "Butterfly Effect" refers to the idea that whether or not a butterfly flaps its wings in a certain part of the world can make the difference in whether or not a storm arises one year later on the other side of the world.
-It is now accepted that weather forecasts can be accurate only in the short-term, and that long-term forecasts, even made with the most sophisticated computer methods imaginable, will always be no better than guesses.
Examples of such systems are: the atmospher, plate techtonics, population growth, the solar system and Economies.
posted by the author at 1:48 AM
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