Zeno's Paradox
Suppose that Achilles and a tortoise are in a race. Because this is unfair, Achilles gives the tortoise a head start. Lets say that the tortoise only has to go half the distance. So the race starts. Quickly , Achilles, who travels twice as fast, gets to the half-way mark. By then the tortoise has made it to the 3/4 mark. Once Achilles reaches that point, the tortoise has traveled to the 7/8. This can continue ad infinitum. Using this logic, no one can ever make it from point A (the start) to point B (the finish line).
This is an interesting paradox, because it was only recently solved after thousands of years. Using modern mathematics, mathmaticians have shown that 1 + 0.5 + 0.25 + 0.125 ... = 2 Some people still regard this as an insufficient solution. It is also important to note that the situation could never occur in real life, as anyone who has ever raced knows.
The paradox here apparent when viewing the consequences. The traveler has told the truth, so the hangman cannot hang him. But if the traveler goes free, then he would have been lying.
String theory
This is widely regarded as a recent theory, but is in fact many years old. In the 1970s, some scientists attempted to write a "Theory of Everything," essentially a unification of all forces (strong interactions, weak interactions, magnetism and gravity.) The theory of everything may not have been discovered as of yet, but many think that string theory is the key.
String theory requires you to lose any preconceptions. It is very important to remember that what we think is reality is merely common sense that only applies to our moderate size and speed of movement.
The basic tenet of string theory is that everything is composed of tiny strings, essentially infinitesimally small. These strings make up quarks, protons, neutrons, and you. Different effects are achieved with string vibrations (much like a violin string at different tunes), each making a different variety of string. Another major effect of string theory is more than 4 dimensions. While most people are familiar with height, depth and breadth, and many know time is a dimension, more than a few mathematicians think there are more dimensions. Different flavors of string theory have different numbers of dimensions, ranging from 5 to 12. This is impossible to visualize, and don't even attempt it. The reason you don't normally notice these dimensions is that they are rolled too small to see. Imagine you have a sheet of paper. 2-D, right? If you're really good and can roll it tightly, it will appear to be one dimension, a line. This is what extra dimensions would always be like.
While String Theory is an interesting study, and is fairly highly regarded, remember that it has not been proven or verified and is at present merely the best attempt to explain different phenomenon and to unify the four forces.
