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

Here's a kid friendly explanation:

1. Get a Dice (the number of sides doesn't matter)

2. Write these down on a piece of paper:

   • Move right
   • Move up
   • Move up
   • Turn the dice over
   • Move down
   • Move right

3. Show them the dice and paper. Explain that the dice represents the computer and the paper represent the math or algorithm that tells the computer what number it will return.

4. Now, roll the dice. Tell them that you are "seeding" or asking the computer to start at a random dice position.

5. Follow each step in the paper (move right) by moving the dice.

   • Let's say that you threw a 6 sided die and it was seeded at 5. By moving right, you get a 4.

6. Explain that the computer must start with a starting value. This could be given by any number of sources such as the date or mouse movement. Show them that how they throw the dice determines the starting value.

7. Explain that the piece of paper is how the computer get the next number. Tell them that the instructions on the paper can be changed as easily as the algorithm for the random generator can be changed by the programmer.

8. Have fun showing them the various possibilities that is only limited by their imaginations.

Now for the answer to your question:

Tell them that when a good mathematician knows the starting value and what step the computer is currently at, the mathematician can tell what is the next value of the random number.

1. Ask the child were to hide the paper and throw the dice.
2. Then ask the child to follow the steps on the paper, you then write down how he gets the next random number.
3. Afterwards, show them your paper. Now that you have a copy of their random number generator, its easy for anyone else to "guess" the next random to come out.

No matter how creative the child is with their algorithm, you should still be able to deduce their algorithm. Tell your child that in the computer world, nothing is hidden and just by observation, even if its just the numbers that was observed, the random number algorithm can be discovered.

...as a side effect, if the child was able to come up with a good algorithm that confused you, in which you can't deduce the next sequence, then you have a bright child. :D

Answer 2

Ask them to devise a step-by-step method to generate a random number.

And don't accept "pick a number from 1 to 10" as an answer ;)

Trying out a problem should illustrate the difficulty of having to generate random numbers from a set of instructions, just like what computers actually have to do.

Answer 3

To make the computer generate a random number, the computer has to have a source of randomness to start with.

It has to be feeded a seed that can't be expected or calculated by just looking at the seed, if the seed comes from a clock then it can be predicted or calculated by knowing the time, if the seed comes from like filming a lavalamp and get numbers from the picture stream then it's harder to just look at the seed to know what next number will be.

The computer does not have an built in lava lamp to generate that randomness, thats whats make it hard, we have to substitute real randomness with some input that exists in the computer, maybe by logging passing tcpip-packets or other things, but its not many ways to get that randomness sources in.

Answer 4

Primarily because computers don't have any functions that behave in discrete, non-random ways. A computer is predictable, which allows us to program reliable software. If it wasn't predictable it would be easier to generate a random number (since our software could rely on this unpredictable method).

While it's possible to generate pseudo-random numbers, and numbers that are distributed randomly, you cannot generate truly random numbers without separate hardware. There is hardware that generates truly random numbers based on "quantum" interactions (at least according to the manufacturers). Online poker sites sometimes use these adapters for their generators.

Apparently there are even online services to provide random numbers - random.org for example.

Answer 5

Actually, on most modern computers it's not hard to produce numbers that are "random enough" for most purposes. As others have noted, the critical thing is having a source of randomness. You can't just write a program that will produce randomness algorithmically, but you can observe randomness in the various activities of most computers of reasonable complexity, i.e., the ones we typically think of when writing programs. One such source is timing data of interrupts from various system devices.

At one time many computers had no way to get at this data and could only offer pseudorandomness, that is, a random, but repeatable distribution of numbers based on a particular seed. For many purposes this is sufficient -- choosing a different seed each time results in good enough randomness. For other purposes, such as encryption, this isn't strong enough and you need some randomness to start with that isn't repeatable or predictable. Today, most computers (with the exception of embedded devices, perhaps) are sophisticated enough to have a source of randomness that can generate encryption-strength random numbers. For instance, Linux has /dev/random and the .NET framework supports the cryptographically strong RandomNumberGenerator class which has a number of implementations.

Answer 6

Here's my attempt at explaining randomness at an approximately eighth-grade level. Hope your kids find it useful!

Surprising as it may seem, a computer is not very smart. Computers must follow their instructions blindly, and are therefore completely predictable. A computer that doesn't follow its instructions in this manner is, in fact, broken! We want computers to do exactly what we tell them.

That's precisely what makes it hard to do things randomly. Computers must be told a sequence of instructions on how to generate random numbers. But that's not really random, because if you gave anybody else the instructions and the same starting point, they could come up with the same answers. So computers can't be truly random just by following instructions.