The Slave Boy Who Knew Geometry In one of philosophy's most remarkable scenes, Socrates calls over an uneducated slave boy and proceeds to demonstrate something impossible. Through questioning alone, without teaching anything, Socrates leads the boy to discover the solution to a complex geometric problem. The boy has never studied mathematics. He cannot read. He has received no instruction in the properties of squares and their diagonals. Yet when Socrates asks the right ques

The Language Before Language Long before humans developed speech, they were painting. The caves of Lascaux contain images over seventeen thousand years old, rendered with sophistication that still startles modern viewers. These weren't idle decorations. The artists descended into absolute darkness, navigated treacherous passages, and worked by flickering animal-fat lamps to place specific images in specific locations. Bulls and horses and deer appear where acoustics amplify s