Why is it hard for a program to generate random numbers?

Question

My kids asked me this question and I couldn\'t really give a concise, understandable explanation.

So I\'m hoping someone on SO can.

Answer 1

It's easy to come up with an algorithm that generates unexpected numbers, that appear random in some sense. But to design an algorithm that generates true random numbers, well, that's hard.

Imagine designing an algorithm to simulate a dice roll. You can easily formulate some procedure to generate different numbers on each iteration. But can you guarantee that, in the long run (I mean, up to the infinity), the amount of times that 6 came out will be the same as any other number? When designing a good random number generator, that's the kind of commitment that you have to assume. You have to provide strong guarantees (i.e. mathematical proofs) about the randomness, if the application (e.g. lottery) requires it.

Answer 2

Computers can only execute algorithmic computations, and a truly random number isn't an algorithmic thing. You can get algorithms that produce numbers that behave like random numbers; such algorithms are called 'Pseudo-Random number generators'.

At various times in the past, people have made random number generators from analog-digital converters connected to sources of electronic noise, but this tends to be fairly specialised kit.

Answer 3

Because the only true source of randomness exists at the quantum level. With suitable hardware assists, computers can access this level. for example, they can sample the decay of a radioactve isotope or the noise from a thermionic valve. But your basic PC doesn't come with this cool stuff.

Answer 4

As surprising as it may seem, it is difficult to get a computer to do something by chance. A computer follows its instructions blindly and is therefore completely predictable. (A computer that doesn't follow its instructions in this manner is broken.) There are two main approaches to generating random numbers using a computer: Pseudo-Random Number Generators (PRNGs) and True Random Number Generators (TRNGs).

Answer 5

Had to be done really

Source: http://xkcd.com/221/

Answer 6

Computers just don't have suitable hardware. Ordinary computer's hardware is meant to be deterministic. With suitable hardware like mentioned here random numbers are not a problem at all.