The natural occurrence of discreteness

Although the conventional experience of time gives a strong impression that time ‘flows’ in a continuous way, humans have always measured time in discrete units such as hours, days, months and years. In general, longer time periods require less sophisticated technology for their measurement. Stone Age observers could record the passage of days easily by the simple process of adding one more pebble to a pile of pebbles every time the Sun set. It would not take much data collection to create semi-permanent records of the passage of days, which could be analysed at leisure to reveal longer timescales such as the lunar month and the solar year. On the other hand, hours would require a theoretical division of a day into equal parts, which could in principle be recorded by counting turns of an hour-glass or burnt candles. But this requires relatively sophisticated technology and constant monitoring. One issue in antiquity was whether it was the period of daylight that was divided into twelve hours or whether it was the period from one midnight to the next midnight that was divided into twenty-four. The former definition of the hour had the unfortunate characteristic of depending on the season, being shorter in winter than during the summer.