 Science is dependent upon isolating a system in order to study it, but this is literally impossible. Everything has an effect on everything else in our universe. Every single particle of matter has some gravitational effect on every other particle of matter. Irrespective of how much we try to isolate something, the concept of an isolated system that has zero interaction with its environment is really just a theoretical one that does not exist in reality. This simple insight literally destroys the entire scientific enterprise because science is dependent upon this capacity to isolate systems, because if we want to say A causes B, then we need to be able to control for all other variables, that is, remove them from the equation. As we have stated, this is not possible, so how do we get around this stumbling block as it appears that the scientific endeavor goes on without this causing too much of a problem? What we do, because we can't fully isolate any system, is essentially define what are significant effects and what are negligible effects, and simply forget about the negligible effects. So for example, if I'm doing research in my lab on the interaction between two particles of matter, under this premise I do not need to take into account the gravitational effect that some planet, the other side of the universe, is having on these particles because it is deemed negligible. This basic premise that small causes can only cause relatively small effects is one of the basic assumptions and principles that gives our world some order. We depend upon it almost all day, every day. I feel confident in the fact that if I forget to pay my bank overdraft this week, it is not going to bring the whole global economy into meltdown, or that a teeny little pinprick is not going to kill me. We find order in this world in the fact that the chances of these phenomena happening are so small that they are negligible, and we can thus forget about them. Without this being the case in linear systems, our world would be extraordinarily random and chaotic. But as we've previously discussed, nonlinear systems through feedback loops can grow exponentially. This means that negligible effects or differences within nonlinear systems can themselves grow in an exponential fashion, where small effects and errors are fed back into the system at each stage of its development. To compound the size of error as it grows at an exponential fashion. As was the case in the famous Edouard Loren's computer experiment, where when he fed values into the computer that he thought were exactly the same, the output results that the computer gave him were widely divergent. He eventually traced this back to small differences in the rounding errors that made the values only very slightly different, but through iteration these very small errors would grow not in a linear fashion, but exponentially, making the resulting outputs widely divergent within a relatively short period of time, and thus giving us the phenomena that is called sensitivity to initial conditions. Sensitivity to initial conditions is popularly known as the butterfly effect, thought to be so cool because of the title of a talk given by Edward Lorenz in 1972 called Does the Flap of a Butterfly's Wings in Brazil set off a tornado in Texas. The flapping wing represents a small change in the initial conditions of the system, which causes a chain of events leading to some large scale phenomena. Had the butterfly not flapped its wings, the future trajectory of the system might have been very different. Something to note here is that the butterfly does not directly cause the tornado. This is of course impossible. The flap of the butterfly's wings simply defines some initial conditions. It is then the set of chain reactions through feedback loops that enable a small change in the initial conditions of the system to have a significant effect on its output, rendering long term predictions virtually impossible. With respect to the unpredictable nature of the butterfly effect, you might say this, well if our initial measurement is wrong, then obviously our prediction of its future state is also going to be wrong. But this is missing the point, which is firstly that this inaccuracy is growing exponentially as the system develops. It is not just staying the same, and secondly that in these nonlinear systems we can never know exactly the starting conditions, as our accuracy of measurement must grow in an exponential fashion in order to achieve just a linear growth in our horizon of predictability. Chaos and the butterfly effect, after being shunned by the scientific community for many decades, are today accepted as scientific facts, a fundamental and inescapable part of the dynamics to nonlinear systems. They show again how, when things can grow exponentially, we can get extraordinary and counterintuitive results.