Cosmopoeia
κοσμοποιία · the making of the world
How an ordered world arises from number and form: in geometry, in the primes, in sound and in the old teachings of creation. The key is a small figure, the Pythagorean tetractys.
Introduction
The small figure where everything begins: what the tetractys is, how we know about it and why it has occupied thinkers for two and a half thousand years.
The seven liberal arts
A guide for young adepts: how to read closely, reason soundly and speak honestly, how number, form, sound and the heavens train the mind, and why all learning ends in knowing oneself. The old curriculum of the schools, read anew as a tool for the present.
Geometry
How points become forms: simplexes and star polygons, the Platonic solids and the lattice that fills space without gaps.
Number theory
The order behind the numbers: divisibility and primes, read as figures rather than strings of digits.
Harmonics
The world as sound: intervals as ratios, the lambdoma and the harmony of the spheres.
Cosmos
What modern science finds about number and form: resonances and Trojans in the sky, quasicrystals, atomic shells, the light of hydrogen and the primes as a spectrum, plants, viruses and honeycombs, and sounds that draw figures.
Mysticism
How religions and secret teachings put the order of the world into images, from the Kabbalah and the Rosicrucians to the throne of God.
Philosophy
Number as the ground of the world: from the Pythagoreans via Plato and Kepler to the question of why mathematics can describe nature at all.
Foundations
The mathematics behind this website, step by step and for non-specialists: what a proof is, how a few basic assumptions lead to numbers, divisors and figures, and why the theorems about the ten and the primes really hold. With proofs to unfold and checks by computer.
Number theory and geometry are two views of the same thing: one counts, the other sees.