Dialogue Concerning the Two Chief World Systems

...transition occurs only due to some deficiency (and thus from the line one moves to the surface, because the line is lacking in width); and since it is impossible for the perfect to be deficient, being complete in every direction, one cannot move from the Body to any other magnitude. Now, from all these points, does it not seem to you sufficiently proven that beyond the three dimensions—length, width, and depth—there is no passage to another, and therefore the Body, which has them all, is perfect?

SALV. To tell the truth, in all these discourses I have not felt myself compelled to grant anything else except that what has a beginning, a middle, and an end can, and must, be called perfect. But then, because the beginning, middle, and end are three, that the number three is a perfect number and has the power to confer perfection on those who possess it—I do not hear anything that moves me to grant this. I do not understand, and I do not believe that, for example original: "v. g." for "verbi gratia", the number three is more perfect than four or two; nor do I know that the number four is a source of imperfection for the Elements Elements: Earth, Water, Air, and Fire. In the Aristotelian view, the world was made of these four substances., and that it would be more perfect if there were three. It would have been better, then, to leave these fancies to the rhetoricians and prove his intent with necessary demonstration, as is proper in the demonstrative sciences.

SIMP. It seems you take these reasons as a joke, and yet it is the entire doctrine of the Pythagoreans Pythagoreans: Ancient Greek philosophers who believed that numbers were the fundamental building blocks of the universe., who attributed so much to numbers; and you, who are a mathematician, and I believe in many opinions a Pythagorean philosopher, seem now to despise their mysteries.

SALV. That the Pythagoreans held the science of numbers in the highest esteem, and that Plato himself admired the human intellect and judged it a participant in Divinity solely because it understands the nature of numbers, I know very well, nor would I be far from making the same judgment. But that the mysteries for which Pythagoras and his sect held the science of numbers in such veneration are the nonsense that passes through the mouths and the papers of the common folk, I do not believe in any way. On the contrary, because I know that they—so that marvelous things would not be exposed to the insults and contempt of the masses—condemned as sacrilege the publication of the more hidden properties of numbers and of the incommensurable Incommensurable: Quantities that cannot be measured by the same unit, such as the relationship between the side and the diagonal of a square; this led to the discovery of irrational numbers. and irrational quantities they investigated, and preached that whoever had revealed them would be tormented in the other world; I think that one of them, to give the common people something to chew on and free himself from their questions, told them that their numerical mysteries were those trivialities that then spread...