Random Stuff

The title is meta 🙂 . I’ll describe a little about ‘randomness’ which is an important topic about which I studied in my course project in CS682: Quantum Computing.

What does it mean for something to be random? Or if we get more precise mathematically, given a string of numbers how can one say whether the string was produced by a random or a deterministic process.

Consider the string all zero string 0000000…0 ‘n’ times. Is it really ‘random’? It seems like most people wouldn’t agree with that. But, how does anyone know? Intrinsically, what is the difference between the strings 000,000,000and 164,236,334? If we assume that our device produces any digit from {0,1,…9} with equal probability, then the probability for both the strings is 10^(-9). Surprisingly, what this means is that both the strings are equally probable. Then, how does it make sense to call 164,236,334 ‘more random’ than the the all zero string?

Aaaah! Now, we realise that ‘randomness’ is not as trivial as it might seem. We need a strong definition of randomness before we discuss anything about the randomness of a given string/event. I encourage you to ponder over this question for some time as this is really interesting and trying to understand the nature of randomness can lead to profound philosophical and physical truths which you might have never thought of before. I encourage interested readers to check out this link where you can find out more about randomness 🙂