you remember how scientists in Armaggedon were perfectly able to calculate the path that the asteroid would be coming to earth. So far perfect, but we are before a problem related to mathematics. Differential equations, ie the governing almost all the phenomena we know, the so-called fundamental inequality satisfied. Well, this is, given as a differential equation x '(t) = f (t) y' (t) = f (t) two continuous functions and lipstzianas constant "k" and E approximate two solutions x (t) y (t) of equations x (t) = f (t) y (t) = f (t) with initial conditions x and y, then we have:
well looks like something horrible had nothing better than an example to demonstrate its operation. Suppose that we poor scientists behind the cumbersome task to calculate the asteroid's orbit that goes straight to the us and this is defined by a continuous differential equation and constant lipstzianidad 1, assume these conditions is not unreasonable since lipstzianidad is a little restrictive conditions and the movement of an asteroid is continuous. Yet our ultramodern instruments is not strange to think that we can make a small error of assessment in measuring its position at any given time, giving us his initial position X'O the we have measured, instead of Xo, its actual position. Now suppose that this deviation was only one meter, which is totally negligible in relation to astronomical distances. If we continue with our chain of assumptions we think that we can calculate the exact path starting from the initial position we measure. So if we now apply the fundamental inequality we obtain that after 10 seconds both DISTAR paths can reach up to 22 km away, after a minute this difference would increase to 1023 km. If we now assume that it must not have been able to calculate the exact path of the asteroid if not approximate this difference would increase with a new exponential factor, further increased the difference between the two paths. The same could also apply to the path followed by both fragments of the asteroid after the bombs explode. Not forget that when the bombs we are providing a speed burst to each fragment and the speed is the first derivative of the position. So might simply be that the fragments were not separated enough not to hit the ground, producing the Armaggedon. <||x-y||exp(k|t|) +((E1+E2)/k)||exp(k|t|)-1||
Anyway we should not forget that we are talking about an upper bound of the difference, so this bound is improved in general. But serves as an example to demonstrate that are less easy to predict the trajectory of an asteroid that is approaching from beyond the asteroid belt, approximately 400 million kilometers from Earth, with an accuracy as given in the film, I remember that spoke of a circle with a radius of several hundred kilometers. For something when they talk is talk about possible clashes between meteorites and earth speak of probabilities, not certainties such as those given in the movie.
Superstring Theory. Thanks to XKCD