The division of time into 24 hours with 12 numbers on a clock is based on historical and cultural reasons rather than pure mathematical convenience.
The concept of dividing a day into 24 hours dates back thousands of years to ancient civilizations. The ancient Egyptians, Babylonians, and Greeks, among others, divided the day and night into 12 equal parts each. This division was based on the observation of the sun's apparent motion across the sky.
The choice of 12 divisions likely had practical reasons. The number 12 has many divisors (1, 2, 3, 4, 6), making it convenient for dividing time into smaller units like minutes and seconds. Additionally, the Babylonians used a base-60 number system, which is believed to have influenced the division of hours into 60 minutes and minutes into 60 seconds.
When mechanical clocks were invented, they retained the 12-hour division due to its familiarity and cultural significance. The 12-hour system became deeply ingrained in various cultures and has persisted to this day, even as we have adopted decimal systems for other measurements.
While a decimal system might have certain mathematical advantages, such as easier decimal calculations, transitioning from the 12-hour system to a 10-hour system would require substantial changes to our timekeeping conventions, including recalibrating the entire infrastructure built around the current system. Such a change would likely cause significant disruption and confusion.
It's worth noting that decimal time systems have been proposed and experimented with at various points in history. For example, during the French Revolution, a decimal time system was briefly implemented, dividing the day into 10 hours, each hour into 100 minutes, and each minute into 100 seconds. However, these attempts to adopt decimal time have not gained widespread acceptance or long-term usage.
In summary, the division of time into 12 hours on a clock and 24 hours in a day is a result of historical, cultural, and practical factors rather than pure mathematical convenience.