The often used notion "random numbers" is misleading. Every number
is random. Randomness rather refers to *sequences.* Look at the following sequences. Which one is "random"?

A: 1,0,1,1,0,

B: 1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,

C: 1,0,0,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,1,

D: 33,23,9,79,89, 83,77,27,73,15, 73,51,81,27,97, 47,17,11,41,19,
73,71,13,67,57, 7,9,91,.................

### What is Randomness anyway?

You can *not* define randomness simply to be the outcome of a random
experiment like coin tosses. Though very unlikely, it is still possible to get a
sequence 0,1,0,1,0,1,0,1,0,1,0,1, as such an outcome.

Gregory J. Chaitlin and independently
A.N.
Kolmogorov defined a sequence of numbers to be random
if "it cannot be compressed"---every computer program creating it
would be at least as long as the sequence itself; every description of the
sequence would be at least as long as the sequence itself.

There is also a statistical
definition, where randomness is the opposite of (partial) predictability.

### Where is Randomness used?

For passwords (the more random, the more difficult to crack). Claude
Shannon showed in ... that if you use a key of the same length as the message
in ordinary (symmetric) one-key encryption, then it is impossible to break the
code.

In the Ethernet protocol.

in randomized algorithms.

random poetry?

### How to create random sequences?

Deterministic machines like computers cannot create randomness. The sequences
created by such algorithms (like example D, where
you multiply a number by 997, divide by 100, and take the remainder to be the
new number) are called **pseudorandom**. According to the Chaitlin/Kolmogorov
definition, they fail very much, but statistically some of these sequences have
rather good properties.

Therefore mostly physical events, like radioactive decay or thermal
electronic noise, is measured and used to create random sequences, even the
Pentium 4 has such a build-in random number generator.