Chaos Theory is a broad field of study concerned with the way that tiny differences in the initial state of a system can have profound effects on its outcome, such as, awesomely, causing lawyers to be eaten by dinosaurs, as explained by Jeff Goldblum
To understand Chaos Theory is to force your brain into a cage match with common sense while dressed in an elaborate chicken suit (just how elaborate is up to you). This is largely due to the distinction between chaotic and random. The two can look similar to a casual observer, since both types of systems can be difficult, or even impossible, to predict. The difference is that a chaotic system, once starting conditions are set, follows the rules, however simple or complex, very strictly, whereas a system with random elements basically makes shit up from time to time. Think about that: you can know the all rules, and exactly where everything starts, and you still can't predict the outcome. How? Read on.
Suppose you are in a forest. You are also naked, but that's nether here nor there. In the forest, you are to choose a spot to start from, facing any direction you like. Don't be shy. Now, walk forward, and every time your wood meets a tree (Ha!) turn left. Do this 20 times and see where you end up. Now imagine having started three feet to your right. The trees are all in same place, but since the initial conditions (namely, where you started from) are a bit different, you could have ended up on the other side of the forest, and been eaten by a bear. Bad, yes, but at this point, if you had a map with every tree in the vicinity marked, you could do a pretty good job of predicting where you end up. "Hey, that's not what you just said!" you shout. Well, lets just step it up a notch.
Now, suppose that, instead of the forest, you are in Times Square (yes, you are still naked). Pick a starting place and, again, turn left every time something gets in your way. After 20 moves, mark your position on a GPS and go back to where you started, and begin in the EXACT same spot facing EXACTLY the same way and try again. You didn't end up in anywhere near the same place, did you? Even though you duplicated your initial position, everything else around you was different. Still not impressed? Prepare to be skull-fucked by logic.
You're still in Times Square, and you want to predict where you are going to end up after 20 moves. Simple, all you need is to know is the location of each place where you will turn left. Take this moment to hear the universe laughing at your human arrogance. Oddly, it sounds a lot like your uncle Frank. Frank is laughing because in order to know where your turning points will be, you will have to know the entire history of every person close enough to run into. "What?!?!" we hear you ask as you spit your beer all over your computer. Think about it: You start walking and you see a person that you might run into. In fact, you sort of hope you do, because she's really hot, and doesn't seem to be upset by your as-yet-unexplained nudity, and if you don't turn left soon, you'll end up in the street at the mercy of New York taxi drivers. So you get ready to apologize and make a left when she sees you and slows down to let you by.
DAMMIT, WHY DID SHE DO THAT? To know, you would have to know everything about every aspect of her behavior and mental state at the time, both of which are the result of her genetic makeup, and the way she was raised, and the way her friends and TV shows and EVERYTHING SHE HAS EVER SEEN AND DONE influence her behavior. Unless you know all of that, you won't be able to predict her behavior accurately enough to depend upon. Maybe she saw a movie once where the pretty yet down to earth protagonist met the man of her dreams by being polite to him on the sidewalk in Times Square, and she was hoping to do the same with you, except instead of talking to her, you walked out into the street and got your naked ass run down by an angry foreigner driving a taxi on the wrong side of the road. Look at the girl now: she's crying. You dick.
What's that? You want to try again in a week? We don't recommend it, after how that last one just went, but ok, if you really want to. Now you have to figure out which people will be in Times Square in a week, and how they will behave. To do that, you need to know the entire history of THE WHOLE WORLD. "JESUS FUCK!" you shout, "Why!?" Well, suppose that ten years ago a person in London was looking at Big Ben and commented to themselves, "This is so very different from American architecture." (English people do talk like that, right?) At that same moment, a young girl walked by and heard them. This girl got to thinking about architecture and started paying attention to buildings around her. Ten years later, she's getting her masters in architecture in NYC, and one week from now, she will be on her way to class, walking through Times Square while you get ready to try your experiment again. To predict whether or not you will run into her and turn left, you need to know, just like before, everything about her, but you will also need to know everything about every person she will encounter between now and a week from now, because any or all of them may change the way she walks through Times Square, and in order to predict how those potentially thousands of people will interact with our grad student, you will have to know about every encounter they have ever had that could change any aspect of their behavior, and every encounter those people had, etc, all the way back to cavemen living in a cave in France. And that's just to predict the behavior of ONE PERSON, out of more than a THOUSAND that will be in Times Square next week.
"Bullshit," you say. "Most of those encounters would be so small that they wouldn't make a difference, fuck you, crazy Cracked people." Excuse us while we snort cocaine off of a hookers' ass in derision.
That's better. Now, meet Edward Lorenz. He was a meteorologist working with computers in the early 60's, when one day he accidentally rounded to three decimal places instead of six and got a completely different prediction for the weather. To be clear, we're talking something like .309 vs. .308612 being the difference between sunshine with a chance of puppies, and thunderstorms with hail big enough to smash your windshield. "Holy shit!" we imagine Lorenz said when he realized this. He also concluded that weather predictions could only be reasonably accurate up to a week out, at best. Lorenz didn't stop there, either; he went on to coin the term "Butterfly Effect," which manages to explain the conecpt very well while sounding like something your wise old karate teacher would say. Sadly, howver, the term is now also associated with Ashton Kutcher, and Edward Lorenz is now weeping in his grave, each tear taking a different path down his creepy dead guy face. Screw you, Ashton Kutcher.