[Sidenote: Cosmic mysticism.] Sometimes Plutarch’s cosmology carries Platonism to the verge of Gnosticism, a subject of which we shall treat in a later chapter. The diviner who had communed with demons, nomads, and nymphs in the desert asserted that there was not one world, but one hundred and eighty-three worlds arranged in the form of a triangle with sixty to each side and one at each angle. Within this triangle of worlds lay the plain of truth where were the ideas and models of all things that had been or were to be, and about these was eternity from which time flowed off like a river to the one hundred and eighty-three worlds. The vision delectable of those ideas is granted to men only once in a myriad of years, if they live well, and is the goal toward which all philosophy strives. The stranger, we are informed, told this tale artlessly, like one in the mysteries, and produced no demonstration or proof of what he said. We have already heard Plutarch liken gods, demons, and men to different kinds of triangles; he also repeats Plato’s association of the five regular solids with the elements, earth, air, fire, water, and ether.[955] He states that the nature of fire is quite apparent in the pyramid from “the slenderness of its decreasing sides and the sharpness of its angles,”[956] and that fire is engendered from air when the octahedron is dissolved into pyramids, and air produced from fire when the pyramids are compressed into an octahedron.[957] [Sidenote: Number mysticism.] These geometrical fancies are naturally accompanied by considerable number mysticism. In this particular passage the merits of the number five are enlarged upon and a long list is given of things that are five in number.[958] Five is again extolled in the essay on _The Ei at Delphi_,[959] but there one of the company remarks with much reason that it is possible to praise any number in many ways, but that he prefers to five “the sacred seven of Apollo.”[960] Platonic geometrical reveries and Pythagorean number mysticism are indulged in even more extensively in the essay _On the Procreation of the Soul in Timaeus_. The number and proportion existing in planets, stars and spheres are touched on,[961] and it is stated that the divine demiurge produced the marvelous virtues of drugs and organs by employing harmonies and numbers.[962] Thus in the potency of number and numerical relations is suggested a possible explanation of astrology and magic force in nature. [Sidenote: Occult virtues in nature.]