Final answer:
The Pythagoreans refrained from eating beans due to their belief in the transmigration of souls, where beans might be associated with housing these souls, not because of digestive reactions they might cause. Their dietary practices were shaped by a mystical and mathematical worldview, forming part of their strict community rules.
Step-by-step explanation:
The real reason that Pythagoreans refrained from eating beans is rooted in their philosophical and religious beliefs, particularly the concept of the transmigration of souls. This doctrine suggested that the soul is immortal, passing from one body to another upon death. Beans, because of their size and shape, which could be likened to an embryo with two lobes potentially representing the head and body, became associated with the potentiality of containing these transmigrated souls. It was not because of any audible emissions commonly associated with the consumption of beans. Pythagorean philosophy combined deep mathematical understanding with a mystical approach to the natural world, which they believed was generated according to numerical regularities.
Historical sources do not definitively explain the bean prohibition, but the explanation involving the spirits of the dead is one of several hypotheses. The abstention from beans could also relate to beans' role in ancient voting practices or other symbolic associations, as beans were used in various rituals and were believed to have different attributes significant in the Pythagoreans' cultural context.