the crescent’s visibility. Yet this method is neither sound nor consistent; rather, it frequently produces errors, as experience has shown. They disagree greatly over whether the crescent will be visible or not.

The reason is that they have sought to determine by calculation what cannot be known through calculation, and have thus missed the correct approach. I have discussed this at length elsewhere and explained that what authentic revelation teaches accords with sound reason. I have also discussed what marks the beginning of day, explaining that it cannot be precisely determined by calculation, because daylight appears through rising vapours. Anyone seeking to derive the duration of evening twilight from that of morning twilight would be correct only if the appearance and disappearance of light depended solely on the sun’s position relative to the horizon, which can be calculated. But if vapours affect this—and there is more vapour in winter and over damp ground than in summer and over dry ground—and this cannot be precisely determined by calculation, then the method of mathematical inference is invalid.

This is why morning twilight lasts longer in winter than in summer. This puzzles anyone relying solely on mathematical inference, since, in his view, the duration of morning twilight varies with the length of the day. This too has been discussed at length in its proper place. Allah, glorified be He, knows best. May Allah bless Muhammad.