How Accurately Could Early (622-900 C.E.) Muslims Determine the Direction of Prayers (Qibla)?

Abstract

Debate has arisen over the ability of Muslim architects in the first two centuries of Islam to determine true qiblas accurately. Some believe that they had such a capability, while others think not. The argument could be more complex—perhaps some architects could, while others could not; perhaps their accuracy changed over time or over greater distances from qibla targets. Here, we investigated how the accurate qiblas of 60 mosques or related structures were, using data from Daniel Gibson’s books and websites. Contrasts were drawn between theories that the qiblas of early mosques were—or were not—generally accurate. If one were to assume that Mecca was the only qibla, qiblas would not appear to have been accurate. However, if one were to assume that qiblas changed, it would be found that qiblas were accurate to plus or minus two degrees in over half of the cases and accurate within plus or minus five degrees in over 80% of cases. Accuracy was not related to distance but did appear to improve over historical time, while distance from the target cities and historical time were positively associated. The average qibla accuracy had a near zero error, with random variations on either side of that zero error. The overall distribution was not normal—kurtotic—because a greater accuracy was found than would have been expected with a normal distribution; however, the pattern deviated more from a uniform distribution than it did from a normal distribution. To try to synthesize the competing theories, we analyzed data for only 14 of the 60 mosques, those presumed to face towards Mecca, and we found fairly high degrees of qibla accuracy with nearly 43% of qiblas within two degrees of accuracy and nearly 80% within five degrees of accuracy. Comparing the accuracy of Meccan qiblas with other qiblas of the same century, we found no significant differences in azimuth errors. While some architects were more accurate than others, early Muslim architects seemed, in general, quite capable of placing qiblas with reasonable accuracy, even though their accuracy may have improved slightly over the first two centuries of Islam.

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Rate Distortion Theory for Descriptive Statistics

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