Episode #189 – Gabriel’s Horn: The Shape of Everything

Episode #189 | Published April 23, 2026 In 1641, Evangelista Torricelli rotated the curve y = 1/x around the horizontal axis and obtained a shape whose interior volume converges to π while its surface area diverges to infinity. Mathematicians of the day called it an abomination. Three centuries later, Jacob Bekenstein proved that the entropy of a black hole scales with its event horizon, not its volume. This episode argues that Gabriel’s Horn is the universal blueprint for every structure that creates, stores, or processes knowledge, and that no horn stands alone. Episode Summary Torricelli used the proto-calculus of ind...