For they divided it into twelve parts, which they called “al-dākhil,” each zodiacal sign comprising twelve degrees. This is the extent of his knowledge: your determination of the distance between the two at a particular time and place. This is what he can establish by calculation. Whether the crescent can actually be seen, however, is a matter of sensory perception and natural conditions, not mathematical calculation.

The most he can say is: “Through repeated observation, we have established that when its separation is such-and-such a number of degrees, it is certainly visible, or certainly invisible.” This is ignorance and error, for the matter does not follow a single, unvarying rule governing both visibility and invisibility. Rather, if its separation is twenty degrees, for example, it will be visible unless something obstructs the view; if it is one degree, it will not be visible. Around ten degrees, however, visibility varies with several factors.

First, visibility varies according to the sharpness or weakness of eyesight. When the crescent is very fine, someone with keen eyesight can see it, whereas someone with weak eyesight cannot. When it is of moderate size, most people can see it. People’s eyesight is not confined between two fixed limits. Nor can the matter be decided by saying that most people can see it or that most cannot: if two people see it, the Lawgiver makes the ruling dependent upon their sighting, by unanimous agreement, even if the majority have not seen it. Thus, if he declares it invisible on that basis, his judgment is mistaken under Islamic law. If, on the other hand, he declares it visible, meaning that someone with keen eyesight can see it, there may happen to be no one with keen eyesight among those looking out for it.