Late in his career Marsilio Ficino wrote a treatise called the Fatal Number (De Numero Fatali) in which he focused on the difficult mathematical passage that occurs toward the beginning of Book VIII of Plato's Republic, where Socrates refers to this mysterious or "fatal" number in order to explain why ideal republics may be apt to deteriorate into tyrannies.
This leads Socrates into a discussion of the necessity to improve inborn or hereditary qualities in the human race. He argued that the State should regulate parenthood in order to ensure a continuance of harmony and balance in civic development.
In some way, the "fatal" number plays a role in determining the future prosperity of a republic.
In his treatise Ficino analyses numbers and explores their influence on a variety of interwoven topics, including eugenics, in order to discover the prevailing cyclical cosmic pattern and what steps might be planned by the State to overcome and control it.
Ficino was convinced that a marvelous power lay hidden in the depths of Plato's words and in his treatise attempted to unfold the mystery of Platonic mathematics and the Pythagorean tradition.
We might note that in his treatise Ficino plays close attention to Platonic musical proportions and harmonics, to Pythagorean numerical traditions, and to the symbolic associations of the decade, or the first ten numbers. He sets forth a Platonic astrology based on geometrical ratios that govern the heavenly bodies and their spheres of influence in such a way as to predict a Christian-Platonic Golden Age.