Serendipity Daily Thoughts

Hey. How are you doing? The war in Iran seems to continue for more than weeks, so I am really worried about the future situation around the Mid-East Asia.

In the last post, I introduced the concept of Roman numbers. I also discussed that one of the downsides of using Roman number is that it can be complicated and difficult to interpret the letters as the number increases. To overcome this problem, Arabic numerals were gradually replaced for Roman numerals around the 15th century. (Surprisingly, the concept of Arabic numerals evolved much longer before the replacement though.) So, how was Arabic numeral superior to Roman?

The answer is hidden within the way in which we count using Arabic numerals. Firstly, let’s compare these two counting system. When we want to describe the height of Tokyo Skytree, it can be expressed as “DCXXXIV” in Roman and “634” in Arabic. It is clear that the letters used in Arabic is much less than those of Roman. One of the reasons of such reduction is that Arabic utilizes place of letters efficiently. To put it simple, we usually locate the number which has a value of 10^0 at the right hand side, and the power increases by one as the letter goes to the left. In this way, we no longer need to calculate letters to understand the number they represent. Therefore, Arabic numerals had the bigger advantages than Roman.

But why does the base has to be 10? One assumption is that it is because we have 10 fingers in our hands. Ancestors were used to count objects using hands, so it was easier for humans to adjust the counting system to base-10. Even there was base-20 counting system in Maya. Additionally, some civilization used base-12 or base-60, because the universe can be easily explained using these bases. The most familiar example of such base is time. One day is 24 hours, one hour is 60 minutes, one year is 12 months, etc… If a number is expressed using the base-12, it is required to use two additional letters, alpha and beta. For an instance, 32 in base-10 becomes 28 in base-12.

Thank you for reading today’s piece of writing. Please feel free to leave any comments, including some other ways of counting system possibly better than Arabic numerals.