this happens when the only requirement you have is that the pins occupy space and can't overlap

soo

right after the begining and end there is a strong suggestion to not have a pin

and goes up and down untill you get to a baseline where its fairly certain to be a pin, but

why is this intresting

it is much more likely for pins to be close to the ends

it's interesting because the only thing that causes this is that the pins can't overlap

the exclusion of volume creates a force

https://en.wikipedia.org/wiki/Depletion_force#The_Asakura-Oosawa_model

i must be understanding this pattern wrong then, to me i read it as the beginings and ends have pins that overlap on multable

chart is probability vs position

and by that reason wouldnt there be multable instances of a pin being at the beginings since its a chart?

explicitly stated not to happen or something

Hope everyone is having a lovely day, being productive, eating your meat and greens. Have a blessed day 🤗

the point is that you get phase transitions as you increase the amount of pins

you get something that acts like a liquid or a solid depending on how many pins you are randomly placing

"""this prooves nothing"""

idunno

how this works

I just find it fascinating that you get physical phenomenon like phase transitions with particles that only have the interaction that they can't overlap

but if they dont get to overlap, then how do they do it

you get forces from the fact that they can't overlap

but doint they

idunno

oh

wait

do you mean that every clothespin per string doesnt get to overlap?

not the general

it's a very unintuitive result

if you put a bunch of clothes pins on a string they can't overlap

yeah

this is looking at randomly placing them in a way that they don't overlap

if they overlap that configuration isn't allowed

and the statistics from that show ends and beginings have generally more clothespins?

yes

and that they group together to

i thought it was way more complicated and overthunk it i guess

ooooooooh

group togheter in the middle?

yeah, what's fascinating is that this is the simplest possible system and you still get effects