{"id":5808,"date":"2026-02-14T19:45:03","date_gmt":"2026-02-14T19:45:03","guid":{"rendered":"http:\/\/jwilliamcupp.name\/blog\/?p=5808"},"modified":"2026-02-14T19:45:05","modified_gmt":"2026-02-14T19:45:05","slug":"fun-with-ai-what-ai-is-good-at","status":"publish","type":"post","link":"https:\/\/jwilliamcupp.name\/blog\/fun-with-ai-what-ai-is-good-at\/","title":{"rendered":"Fun with AI: What AI is good at"},"content":{"rendered":"

Question:<\/strong><\/p>\n

Consider the situation in which an individual seeks to maintain physical health by swimming every day. The pool is 50 ft x 25 ft, and the individual swims 30 lengths of this pool, thus totaling 500 yards. The pool does not have lane markings, but on the narrow end there are symbols in the middle and one quarter from each side. By unspoken social contract all of the morning lap swimmers use these markers to remain clear of each other. Up to three swimmers can comfortably enjoy use of this pool at the same time. The preferred position is next to the wall remote from the steps in one corner entering the pool, because this position is least bothered by other swimmers. The position next to the wall along which the steps is complicated by their existence. The steps form a 45-45-90 triangle projecting outward from the corner, with the lowest step reaching to the first mark, that is, one quarter of the width of the narrow side. There are only one set of steps, at the shallow end — none at the deep end of the pool.<\/p>\n

Suppose an individual intending to use these marks while swimming laps often arrives at one end or the other up to one foot off to the side of the mark, in either diretion. Clearly, the person swimming along the side where the stairs are cannot swim the full 50 ft length of the pool if they are off the mark toward the steps, as they are in the way. Such a swimmer must, upon arriving at the shallow end and find he is facing the steps angle over to reach the mark exactly. This adds distance to the total swim.<\/p>\n

If this swimmer arrives at the end of the pool within 1 foot of the mark in a uniform distribution of error calculate the total distance traversed, that is to say, the excess beyond the intended 500 yards. Keep in mind there are no steps at deep end of the pool, and on arriving at the shallow end if the swimmer is off the mark away from the steps, no extra distance is traveled. More over at each end the swimmer corrects and leaves exactly from the mark, intending to swim directly to the other mark, 50 feet away.<\/p>\n

Repeat the calculation assuming instead the swimmer arrives at each end of the pool within 1 foot of the mark using a normal distribution of error.<\/p>\n

ChatGPT said:<\/strong><\/p>\n

Alright, let\u2019s carefully go step by step<\/strong>. We are trying to quantify the excess distance traveled<\/strong> due to lateral deviations from the marks at the shallow end where the steps interfere. I\u2019ll assume we\u2019re focusing on the wall with steps<\/strong>; the deep end has no obstacles, so deviations there don\u2019t add extra distance.<\/p>\n

We are given:<\/p>\n