3 ms·
This comment was what made this article make sense to me. Just to add to add to the mathematical intuition here (please correct me if I'm wrong): if you're thi
by saeranv 6y ago
This comment was what made this article make sense to me.
Just to add to add to the mathematical intuition here (please correct me if I'm wrong): if you're thinking of it as a unit line/square/cube then total n-dim area is 1^n, and the portion in the 50% range is (1/2)^n, where n = number of dimensions. So that should simplify to 2^(-n).
Note this works out to 10th dimension as 0.09765% or 0.1 person per 1000.
ETA: As one of the comments below points out, you can also model it as a binomial distribution.
Probability of getting all heads, given p=0.5 is (n!)/((n-k)!k!) / 2^n. Since n=k since we're looking to get all heads at all times, this also simplifies to 2^(-n).
- spappal 6y agoP(simultaneously within middle 50 % of n independent distributions) = 0.5^n = 2^(-n), like my parent comment says. But interestingly, every relevant comment here either got something wrong about the final frequency or percentage, or corrected the wrong thing. (Parent comment, grandparent, 2 aunts and 1 cousin.) 0.5^10 = 2^-10 = 1/(2^10) = 1/1024 [i.e. exactly 1 person per 1024] ~= 0.00097656 ~= 0.09766 %.
- saeranv 6y agoHah, you are correct. I even had access to numpy and still managed to get this wrong.