Well, that night his brother the computer scientist (yes, that Dijkstra) dropped in, and the subject of the donkey came up. The great man listened to the problem, and said, "When a program is doing something really strange, we install a "window" (ed. note: this was long before Microsoft took over the meaning of the word) in the code, so we can check the state of the critical variables and see what's going on." (This was also before the era of decent debuggers, except in APL).
That sounded good. The next day, both Dijkstras descended on the donkey and installed a window into its digestive system. It turned out that the donkey was stabled next to a particularly unclean goat, whose coat was all covered with purulent guck. This goat would rub against the donkey's feed bin, contaminating the contents, and that's why the donkey was sick. They wrote up a paper describing their work: "Goat Ooze Considered Harmful".
A few months later, the brothers happened to meet again, and went to check on the subject of their work. They found the farmer carefully harnessing the donkey, with a complicated rig designed not to break the window. The farmer said, "You know, this takes me an extra half an hour every day. To you it's a window in the donkey. To me, it's just a pane in the ass."