Their punishment in the next life would be to return to earth in the form of the beasts they had grown to resemble. So a dishonest person would return in the form of a rat; an ignorant person in the form of a jackass and so on.
The spirit element was also held to be the correspondent between the elementals and to the symmetrical solids. Pythagoras found a more elaborate understanding of the ether element most likely by the Hindus, which refer to it as Akasa. Ether is the inner substance which infuses all of the other elements and acting as a common solvent common denominator and connector of them all.
It is legend that Pythagoras possessed hypnotic power not only over man but also over animals. It is said his mental powers would cause a bird to change the course of its flight, a bear to cease its ravages upon a community, and a bull to change its diet. He was also gifted with second sight, being able to see things at a distance and accurately describe incidents that had not yet come to pass. There is a legend where with his disciples drinking water from a spring and Pythagoras predicted an earthquake which was fulfilled and devastated the local communities. Pythagoras with his higher students practiced divination to predict future events. This divination was most likely a form of arithmomancy or hydromancy that he learned from the Egyptians.
Hydromancy is the divination through the observations of ripples in a bowl of water in a trance like state. It is likely that Pythagoras used a brass bowl; he believed that brass had psychic powers because of how rates of vibration were found in the metal. Pythagoras observed that even when everything was perfectly still and calm there was always a sound of vibration in his brass bowl. It is said that during a hydromancy session he addressed a prayer to the spirit of a river and out of the water arose a voice, which granted him the ability to cause demons to enter into the water and disturb its surface, and by means of the interpretations of the ripples certain things were predicted.