I want everyone to be able to achieve world they would really like; guess the best way to do that is to help people learn, build one’s strengths, build small-scale and large-scale projects, and also to cooperate.
Any gift must be accepted with gratitude and, if possible, with grace.
As of 2024-12-21, I have signed no contracts I cannot mention exist. I finally got to adding this notice thanks to the one in the-gears-to-ascension’s bio.
Intuition. Imagine a picture with bright spot in the center, and blur it. The brightest point will still be in center (before rounding pixel values off to the nearest integer, that is; only then may a disk of exactly equiprobable points form).
My answer: because strictly monotonic[1] probability distribution prior to accounting for external factors (either “there might be negligible aiming errors” or “the bullet will fly exactly where needed” are suitable) will remain strictly monotonic when blurred[2] with monotonic kernel[2] formed by those factors (if we assume wind and all that create a normal distribution, it fits).
in this case—distribution with any point close to center having higher probability assigned than a point farther
in image processing sense