My hair grown too long, I was about to cut it, when one question come to mind:

Let's suppose I cut each of my hairs to a length uniformly random, how will my head look like?

instead of uniform random, other distributions like normal, binomial, can be applied.

Your hair would look terrible.

do you have proof?

Looks pretty ugly to me.

codeSo which haircut algorithm do you recommend?

Maybe cutting each hair by a random distance between 0 and the length of my shortest hair?

Or some convex function that depends on the distance of the center of my head?

Ok boomer go to a barbershop. The masters of hair cutting know these functions very well

I prefer to do it my self. I don't want a stranger touch my head with a weapon in his hand

Then you can ask your mom to cut your hair!

Am I the only one that sees layers here? Does a brain just try to find patterns even in a random thing?

When I saw this comment 7 months ago, I also thought it was weird that the uniform heights are sorted into seemingly-discrete layers.

Upon re-reading and taking another look, I think it makes sense that we see discrete layers here, because the discrete layers are actually not the heights (which are continuous), but rather "N consecutive adjacent white lines" with N = 1, 2, 3, ... (which are discrete).

For you, it'd probably look like this.

Why is everyone on CF down-voting you all the time??? Your posts are pure gold

I'm sure I have a bunch of people downvoting me automatically because they're mad I'm a higher quality shitposter than them. Whatever.

what do you mean exactly by uniformly random?

This is why you're green.

what do you mean exactly by uniformly random?

That's why you don't have a name

Why are you red?

I don't get the question, there is just one uniform distribution, right?

What kind of properties would this "one uniform distribution" have? Each number (integer/real, whatever) is equally likely and the sum/integral of probability value/density is 1? Figure out yourself what's wrong with that.

Yup, so what's wrong with that? I honestly don't know.

(and we're talking about some interval, not all real values)

Who's talking about it? You're only now talking about it, proof by Ctrl+F. That's the point. Even then, if it's "some" interval, what good is it? It's like asking you to lend me three fiddy and I'll give it back to you at some point.

The problem with all real/integer values is obviously that a distribution with such properties doesn't exist (sum/integral of a constant is 0 or +- inf).

Naming a distribution is useless if you don't give it specific parameters.

well, unless you can cut hair so that it becomes longer then it was, there's only one reasonable way to understand original post

No, even with that assumption, there's an infinite number of possible intervals.

I said reasonable, not possible

There's an infinite number of reasonable intervals too. You could want to cut your hair from 12 cm to uniform([5, 10]), uniform([1, 2]), uniform([1, 10]), etc. That's not even getting into the question of how you define reasonable for a normal distribution.

Out of nowhere, you wrote

"each number (integer/real)"so I specified that the problem makes sense only for an interval and I obviously meant interval $$$[0, currentLenth]$$$.I thought that I would learn something new :(

Why exactly that interval? Why not any other?

What else can it mean that we cut a hair of length $$$5$$$ uniformly at random? Cutting to interval $$$[2, 4]$$$? Come on.

How about to an interval [0, 2]? Or [0, 1]? What the hell is wrong with those choices? Are you the fashion police?

As you mention it is not possible to choose at random a point "uniformly" over the real line, but it is maybe worth pointing out that it is possible to choose at random a sequence of points in R in such a way that the distribution of these points is invariant under translations. These random sequences are provided for instance by the Poisson point process and can be used for instance as a toy model for stars in the firmament, that wherever you look it is equally likely to find the same number of stars.

r/destroyedbywords