The Edge of Knowing
“A skate blade presses down, a thin film of water melts, and you glide.”
What’s Inside
III.01.00 Things We Thought We Understood
III.02.00 Patterns at Every Scale
III.03.00 The Edge of Geometry
III.04.00 Light, Time, and Gravity
III.05.00 The Quantum Threshold
III.06.00 What Cannot Be Solved
III.07.00 At the Limit
III.08.00 Coda — The Nature of Mathematics
About the Book
In 1963, in a cookery class at Magamba Secondary School in Tanzania, a 13-year-old named Erasto Mpemba watched his hot ice cream mixture freeze before his classmates’ cold ones. His teacher called it nonsense. The boy persisted.
Everyone learns why ice is slippery. A skate blade presses down, a thin film of water melts, and you glide. James Thomson predicted it in 1849, Michael Faraday demonstrated it in the 1850s, and the textbooks agreed for over 150 years. The answer is also wrong.
Britain’s coastline is 17,820 kilometers, according to the Ordnance Survey. It is also 50,000 kilometers, and infinitely long, and all three are correct. Above Palazzo Massimo, a starling tracks six or seven neighbors in the Roman dusk and decides which way to turn. At Brookhaven in 1987, Per Bak watches a simulated sandpile, fed one grain at a time, collapse in a pattern nobody tuned it to follow. At a Saturday market, Maria breaks a head of Romanesco into smaller pieces, then smaller, and every piece is the whole thing again.
These are the things we thought we understood, and the simple questions underneath them that refuse simple answers.
A 19-kilogram granite stone slides 45 meters across pebbled ice. No current theory fully explains how the sweeping works.
Other Books in The Math Series
- Book I Everything is a Rate of Change
- Book II The Hidden Architecture