What does randomness look like? • Hacker News Board

Re: What does randomness look like?

#121

Post by jwmerrill » Sun, Dec 23, 2012, 10:23 PM UTC

tome wrote: post #57

bluedanieru wrote: post #56

Earlier quoted context omitted.

Can you expand on this? I'm curious. It seems to me that with the glowworms, knowing the position of one worm tells you something about the position of every other worm in the sample. If it was truly random, wouldn't it tell you nothing?

No, in mathematics the eye colour and hair colour of a randomly selected human being are considered random, even though knowing one tells you something about what the other is likely to be. Mathematically, "random" means distributed according to some definite (though perhaps unknown) distribution whereas in common parlance it means something like "not distributed according to anything definite at all" (though it's no…

Common parlance "random" seems to mean something more like "uniformly distributed and independent."

Re: What does randomness look like?

#122

Post by jwmerrill » Sun, Dec 23, 2012, 10:35 PM UTC

baddox wrote: post #41

I'm a bit confused. What is this notion of "pure randomness" that this article and many comments seem to be eluding to? Perhaps I'm just not using the same definitions of terms, but I thought a uniform distribution is still considered random.

The concept you're looking for is "independence"

http://en.wikipedia.org/wiki/Independence_(probability_theor...

The glow worms are still distributed randomly in the mathematical sense, but knowing the position of one tells you something about the likely positions of others, so they are not independent.

Common parlance doesn't do a great job at talking about the features of random distributions, but when people say "purely random," they often seem to mean "uniformly distributed and independent." Both pictures have uniformly distributed points, but the glow worms are not independent.

Re: What does randomness look like?

#123

Post by martincmartin » Mon, Dec 24, 2012, 7:34 PM UTC

Zakharov wrote: post #67

fmx wrote: post #66

Earlier quoted context omitted.

You couldn't possibly miss all 8 pieces. As soon as you make one attempt you'll get one piece.

Henrik's math calculated the chance of missing the "I love you" piece each time. The chance of missing any one other piece each time is the same.

Yes, but they're not independent. Given that you missed piece X, the probability that any one piece it's piece Y it's 1/7, not 1/8, so the chance of missing both X and Y it's lower than the product of their individual probabilities.