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The Mathematics of Existence

“The highest form of pure thought is in mathematics.” – Plato The universe is often seen as a vast and complex machine, yet at its core lies an elegant simplicity. Mathematics, the language of this cosmic order, offers a glimpse into the profound structures that underlie all existence. Among these structures, one of the most fascinating is the Phi Ratio, also known as the Golden Ratio. This unique proportion, approximately 1.6180339, has captivated minds for...
Descartes

Descartes radical shift in mathematics

If you have been the proverbial fly on the wall in Descartes’s bed-room in La Flèche, in southern France, in 1636, you may have watched Descartes laying in bed observing you. His most remarkable idea came to him while observing a fly crawl along a curved path, which he thought about illustrating in terms of its distance from the walls. A revolution in thought was in the making; mathematics would certainly never be similar. The...

The Glass Bead Game

Gelegentlich ergreifen wir die Feder and schreiben Zeichen auf ein weisses Blatt, Die sagen dies and das, es kennt sie jeder, Es ist ein Spiel, das seine Regeln hat. —Hermann Hesse. Das Glasperlenspiel From time to time we take our pen in hand and scribble symbols on a blank white sheet. Their meaning is at everyone’s command; It is a game whose rules are nice and neat. —Hermann Hesse, The Glass Bead Game, When Hermann...
checkerboard

This statement is a lie

Paradoxes appear in all shapes and forms. Certain are uncomplicated paradoxes of reasoning with minimal potential for investigation, while others sit atop icebergs of full scale scientific disciplines. Many may be solved by mindful consideration of their hidden assumptions, one or more of them could be faulty. These, strictly stating, really should not be referred to as paradoxes at all, because as soon as a puzzle is solved it stops to be a paradox. “One...
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