[oh_my_goodness]

Lemme go through details, not because anyone doesn't know the details, but to get them written down and discussable.

"Random" means I draw up a list of all possible outcomes. The probability of an event is defined as the fraction of outcomes in which that event is true.

Example. Choose two numbers "randomly" between 1 and 3. What's the probability that the two numbers are equal? The list of outcomes is: (1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3). There are 9 possible outcomes. In 3 outcomes the first and second numbers are equal. So the probability is 3/9 = 1/3.

The math part is just bookkeeping.* The math isn't random, it just uses the rule above. And there is no claim (within the math) that things are or aren't "really random" in the actual world.

*Can be very slippery bookkeeping. People who know what they're doing get wrong answers all the time. But bookkeeping.

[_8j50]

Thank you, my original comment was for ELI5, I was asking because I didn't know and clarifying like this helps.

Wouldn't it be more correct to say arbitrary instead of random?

[oh_my_goodness]

I think random is often used as a keyword that means "use ideas from probability." Those ideas are tricky and (I think) not well captured by any one word.

Example of a tricky situation: Say we play cards. You shuffle the cards well, and you don't show them to me. I might say the order of the deck is random, to indicate that I have no idea which card is in what position. But you might be looking at the faces of the cards. In that case you might say the same cards are ordered in a way that's not random.

Could we describe the same situation using the word arbitrary but not the word random? I'm not sure. Seems likely.

I know how to make up models and test the models by experiment. I don't know whether randomness is real or not. I don't think it's deeply meaningful what words we use, as long as it's clear what the math is and how we're applying it.

[_8j50]

I agree, but in crypto for example they use the term "cryptographically random" as in for the purposes of computing it is not possible to predict the value.

As a complete outsider to the field, I had no idea what is meant by random in a mathematical sense because I thought math was always realistic, as in it mirrors real things, you can't have 2+2=3 because reality doesn't work that way.