Why do moving clocks run slow?

A moving clock runs slow because each tick has further to travel at a speed that never changes. Take a clock of two mirrors one meter apart with a pulse of light bouncing between them, riding on a train. Seen from the platform, the mirrors slide sideways while the pulse is in flight, so the pulse runs along a slant, which is longer than the gap. Light has one speed for everybody, so the longer path takes longer and the tick stretches. By Pythagoras, at eighty percent of light speed a tick lasts five thirds as long. Cosmic-ray muons should decay long before reaching the ground, and they arrive anyway, on stretched ticks. Underneath the mirrors, a duration is a count of records in small regions strung along a path, and a moving path collects fewer of them.