I have always been fascinated by a theory called the "Simulation Hypothesis". This theory basically states that we are probably living in a computer simulation. The idea is that any sufficiently advanced civilisation will have the ability to create a computer simulation which is indistinguishable from the real world, and that such a civilisation will likely run a great many of these civilisations, in the same way that we create many computer games and other works of fiction.
This means, therefore, that the chances of being in a virtual worldare much higher than the chances of being in a real one. But, how could you prove that you were in a virtual world? Some scientists from the University of Washington are working on a method of testing the theory by observing the behavious of cosmic rays at the edge of the space-time continuum: Link But what if there was an easier way?
It is widely known that computers, no matter how advanced, cannot generate truly random numbers, only pseudorandom. So, if our reality is in fact a complex simulation, there should be very slight patterns in what should be random occurences. If you find a source of something that should be truly random, such as atmospheric noise or the decaying of an atomic nucleus, and measure it with extraordinary accuracy, a predictable pattern may emerge. This pattern would prove that the phenonenon is not truly random, as it should be, proving that we are living inside a computer.
Of course, a simulation sophisticated enough to create our reality could also have access to a hardware random number generator of it's own, capable of producing truly random numbers...
I am building a true random number generator as one of my projects, I should have the parts next week, so I have been thinking about the concept of random numbers a lot.