What is randomness?

We all know what is randomness: it is chaos, unpredictability, lack of structure, no pattern.

To generate a random result we use a coin or a die.But if you have a sequence of numbers, when can you say that they are random?

When you cannot find any recipe, any algorithm that will allow you not only to reproduce the sequence but also to predict the next number in the sequence.

Before quantum mechanics there was common agreement among scientists that God doesn't play dice:i.e. the randomness in the launch of a coin was only the result of our ignorance of all forces involved. If we knew everything about what is going on,randomness would disappear. Or just to say it in another way, only complex causes could produce chaos.

Quantum mechanics has shown that God does indeed play dices: the behaviour of matter at microscopic scale is unpredictable. There is no way to predict when a radioactive nucleus will decay.For this reason we can use quantum phenomena to produce a sequence of true random numbers.

The discovery of deterministic chaos has shown in more recent years that also in classical physics we get randomness and unpredictability. A simple cause can also produce chaos.

We have a simple recipe to produce our numbers but there is no way to predict future values. This allows us,for example,to produce with a simple algorithm a sequence of "pseudorandom" numbers that behaves exactly like a random sequence. This is how a computer generates random numbers. This algorithmically produced pseudo-randomness is so surprising that von Neumann's said (cited by Knuth in his volume 2: Semi-numerical Algorithms)

``Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.''

Computers with Linux/Unix operating systems, also generate random numbers by using the following method. They have a special device that gathers non-deterministic events in the computer environment, like:

Mouse movement
rate of packets coming in or out of system
interrupts timing

and transforms them in random numbers. The rate of random numbers production depends on the use of the computer.

Randomness and coincidence

There is a fascinating link between randomness and coincidence. Coincidences are the result of randomness! How can this be?

The problem is that if you have a truly random phenomenon than each occurence of it must be completely new.Let's put it in this way. A perfect random die must have an infinite number of faces and each time you cast it the result must be a completely new face, a face never cast before. Now, what happens with real dice:the phenomenon is random but the outcome can be only one of six. The die must decide for one of the six faces. The distribution of the frequencies of the six numbers must now follow some precise laws otherwise THE PHENOMENON IS NOT RANDOM. One of these laws dictates the presence of coincidences like the number 6 cast ten times continuosly. Strange eh...

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