Hi Jez,

I must respectfully disagree on two points. First, Raghunathan's point is not that random numbers can not be generated from an algorithm. Only that if you have a source for data from a random process, there may be no need to generate the number.

Second, it is possible to generate truely random numbers based on a purely deterministic process. I wrote a paper on this very subject some years ago, wherein I derived a mathematical definition for the randomness of a finite set of numbers which was independent of the process by which the set was generated.

The key is to understand that a process may be random, and still produce a non-random set of results. If you just randomly read the output noise from an ADC it is possible, however unlikely, that you could read the integer sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. After the fact, however, you would never believe that such a sequence had been produced by such a process. The reason you would disbelieve it is because the sequence is decidedly and obviously not random. Another example is the coin toss experiment. If you see 100 coins lying on the table, and each of them is heads up, you will immediately reject that the arrangement is the result of 100 coin tosses. You will assume that someone has gone through the set and arranged them heads-up on purpose. Even though the result set of all heads is precisely just as likely to occur as any other particular sequence-set of results, it is a decidedly non-random set.

Thus, it is shown, at least on an intuitive level, that the randomness of a result set is independent of the process by which the set is generated. Random processes can produce non-random results, and likewise deterministic processes can produce random result sets. The trick then becomes to define the randomness of a result set in a way that is independent of the process by which it was generated, and preferably also quantifiable, which is what I did in that paper.