Why is it hard for a program to generate random nu

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

How about, "Because computers just follow instructions, and random numbers are the opposite of following instructions. If you make a random number by following instructions, then it's not very random! Imagine trying to give someone instructions on how to choose a random number."

Answer 2

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 3

A simple explanation for the children:

The definition of randomness is a philosophical and mathematical question, beyond the scope of this answer, but by definition there is no such thing as a "random" number. In a metaphysical sense, a number is only random in sequential form; however, there is a probability that a sequence follows certain statistical distributions depending on the sample size. A random number generator (in our case a pseudo-random number generator, or PRNG) is simply a device to produce a quasi-random sequence of numbers that we can only estimate (based on the given probability inherent within the sequence) to be random.

You should explain to the children that programs can only mimic these devices using complex mathematical formulas (which guarantee a lack of "randomness" by definition because they are a result of some function, or procedural algorithm). Typically, rigorous statistical analysis is necessary in order to differentiate the use of a quantum hardware PRNG (use this as an opportunity to explain to your kids the Heisenberg Principle!) and that of a strong software PRNG.

Answer 4

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 5

Awhile back I came across the "Dice-O-Matic"

http://GamesByEmail.com/News/DiceOMatic

Kind of interesting real world application of the problem.

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.