# : What is the butterfly effect?

168 views

: What is the butterfly effect?

In: Mathematics

It’s a description of chaotic systems. The saying goes that the weather is so chaotic that if a butterfly flaps its wings in Colombia, in a year, that will change the weather so much as to “cause” a hurricane in Florida.

It doesn’t actually cause anything, it’s just that the final outcomes of the two situations (flap vs no flap) are completely different. This is a result of weather being extremely sensitive to initial conditions.

In regards to time travel, it’s very similar to how the other guy made mention.

If a time traveler steps on a butterfly.

That butterfly could in theory have fed a spider, that spider could have poisoned some bird that ate it, and that dove could have been hunted by a person and that Hunter could called in sick to work, and survived an encounter that blew up the building for they would be at home.

HOWEVER, the butterfly that’s now dead by said time traveler, can no longer go through all of that, causing the Hunter to show up to work like everyone else and die causing a divergence in the timelines

In a chaotic system tiny differences can grow exponentially over time.

Since wheather is such a system (and basically any flow of liguids or gasses can be) the tiny detail like a butterfly flapping it’s wings **can** dramatically change the outcome.

If you look at the phase-space of the system it happens to be a fractal, wich means certain regions have infinitely high sensitivity.

Another such system is a magnetic pendulum. Place an iron ball on a string over 3 magnets and try to predict over wich magnet the pendulum stops after you released it in some point. If you paint that in 3 colours you will receive this amazing [pattern](https://upload.wikimedia.org/wikipedia/commons/thumb/8/88/MagneticPendulum.jpg/1280px-MagneticPendulum.jpg)

The butterfly needs to be in one of those regions of extremely fine switching to change the wheather on the other end of the world from friendly to hurricane.

The idea is that a minor change can have bigger consequences than you would expect. So maybe I have egg on toast instead of cornflakes for breakfast. But that means I don’t go to the store later to buy more milk, and don’t bump into my old friend Steve from school.

Because we don’t bump into each other, and go for a beer, Steve gets home in time to find the hooker he had chained up in his basement escaping, and is able to quickly put a stop to it. He is never reported to the authorities, and goes on to shoot Elon Musk with a .45

There are certain mathematical systems where tiny changes in the initial state of the system result in big differences later on. One of the simplest examples is the “full logistic map”. Take a number between 0 and 1, let’s call it “x”, then calculate 4*x*(1-x), where “*” means multiplication. Then treat this number you get as your new x and plug it back into the equation. Do this over and over again and you’ll get a sequence of numbers. If you do this whole process all over again starting with a very slightly different initial number between 0 and 1, instead of getting roughly the same list of numbers like you might expect, your list will eventually diverge from the original list and you’ll start seeing completely different numbers.

The main reason why this is so important is because quite a lot of mathematical systems turn out to behave this way, including many that model real-world behaviour such as turbulence in fluids. The full logistic map itself is actually a special case of a simplified model of how a population of animals changes over time. And if small changes to the initial state of a system can result in big differences later on, that means it’s very difficult to predict what the system will do, since in practice we can only measure the current state of a system to a certain level of accuracy.

Edward Lorenz discovered chaos while using computers to try and develop models of the weather. He liked to use a metaphor to describe the phenomenon in which a butterfly flapping its wings in one part of the world could eventually cause a tornado somewhere else.

Also chaotic systems turn out to have all kinds of interesting and complicated mathematical properties (google “strange attractor” for some pretty pictures of weird stuff they do), so they have remained a major area of study.

The butterfly effect is as other have described, a seemingly insignificant event causing huge consequences at a later time and place.
Most commonly we associate this with time travel and stepping on a butterfly and thus changing a fictional future.

But we don’t seem to realize that small incrimental and seemingly insignificant actions now may change your actual future. So go out there and step on those proverbial butterflies.

When a butterfly flaps its wings, it moves air, right? But the amount of air it moves is so tiny that its easy to think that on a large scale, it doesn’t matter. For example, if trying to track where a thunderstorm in Asia came from, it would sound ridiculous to think that a butterfly flapping its wings in North America would have anything to do with it. But as it turns out, it totally does. The gist is that small things do have big consequences. It is one of the foundations of Chaos Theory.

So back in the mid 20th century, some scientists were studying weather patterns. They had this big mathematical equation to account for wind, humidity, temperature, rainfall, etc etc. At one point, one of the scientists wanted to get some results from a certain point in the experiment. So he entered the numbers from an earlier starting point, but to save time, he didn’t type out the full values. For hypothetical example for one value instead to typing 5.72383, he just typed 5.723, because anything after the 3 is so small and unimportant that it just represents a gust of wind, or half a degree change in a football field or something. Small stuff, right? But the numbers that followed ended up being very different. The first day or so were the same, but after about two or three days, the entire global weather patterns were different.

It’s interesting stuff. One of those weird things where some people were just innocently studying one thing and stumbled upon some fascinating discovery that changed everything.

There’s a really cool book about it called Chaos by James Gleick that explains chaos theory really well to lay people.