Cosmopoeia
Sections

Section

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.

  1. 01Number theory + geometry = philosophyThe motto of this site. Joining analytical thinking in numbers with visual thinking in forms leads to questions that go beyond both.
  2. 02Plato's Timaeus: the world from number and triangleThe most influential text between Pythagoras and Kepler: how Plato built the world soul from the numbers 1, 2, 3, 4, 8, 9 and 27, composed the elements from two triangles and called time a moving image of eternity. What of it is wrong and why it shaped physics all the same.
  3. 03The tetractys analogy tableThe four start figures alongside the fournesses of physics, philosophy, Hermeticism, Kabbalah, Freemasonry and religion. A comparison, partly explicitly speculative.
  4. 04The masculine and the feminineWhy the Pythagoreans called the odd male and the even female, what Yin and Yang, the alchemists with sun and moon and the Gnostics with their pairs meant, what Eros has to do with it all and what of it still holds today.
  5. 05The union of oppositesHeraclitus' bow and lyre, Aristotle's mean, the coincidence of opposites in Cusanus, the chymical wedding and Bohr's coat of arms with yin and yang. What kinds of opposites there are, in how many ways they can be joined and which are better not united.
  6. 06What a secret isMysteries, lodges and secret teachings live by the secret. But there are three quite different kinds: the kept, the hidden and the unsayable. Why only the first can be betrayed, how to recognise a false secret and why silence still makes sense.
  7. 07Measure, number and weight: number in Christian thought“Thou hast ordered all things in measure and number and weight”: how a verse from the Book of Wisdom carried Pythagorean number teaching into Christianity. Augustine and the 153 fish, Boethius and the quadrivium, the school of Chartres and the Trinity as unity, equality and connection.
  8. 08The tetractys in J. G. Herder's MetacritiqueHerder set a fourfold formula of categories against Kant's forms of intuition and explicitly called it a tetractys.
  9. 09Giordano Bruno: the monad, number and figureThe philosopher burned in 1600 described the numbers from 1 to 10 as figures in a circle. Four points of agreement with the geometry of the tetractys.
  10. 10Johannes Kepler: the most beautiful error and the harmony of the worldFive Platonic solids between six planets: Kepler's first great idea was beautiful and wrong. How he let it fail over eight minutes of arc, found the ellipses along the way, discovered the third law in the Harmony of the World and why it was precisely his error that led him to the truth.
  11. 11Great thinkers on the structure of the worldFrom Pythagoras and Plato through Kepler and Newton to Planck and Dürr. How scientists thought about the order of the world.
  12. 12Death and reincarnation: spirit and matterThe transmigration of souls was a core of Pythagorean teaching. What philosophy and the religions say about it, what physicists suppose, what studies of near-death experiences have really found and where the line between belief and knowledge runs.
  13. 13The true masterA parable about paper, interest and the four things of nature, about the right measure. With an honest test: what is right about the parable’s critique of interest, what is not, what is disputed and what dark history it has.