A fixed total of probability 1, bell-shaped, divided into equal-width piles over the numbers from minus four to four. Two bar charts share that axis. The top chart shows the probability in each pile. The bottom chart shows each pile divided by its width — a density — with the smooth limiting bell drawn as a dashed line behind the bars. Two buttons chop every pile in two, or merge neighboring pairs back together. As the piles multiply, every bar in the top chart falls toward zero, while the bottom chart settles onto the fixed bell shape. Readouts track the number of piles, the tallest pile, that pile divided by its width, and the total, which is always exactly 1.

Cut the piles finer and finer

A fixed total of probability 1, bell-shaped, chopped into equal-width piles. Chop finer and watch what dies — and what doesn't.