A Parallel Between Time Zones and Radices
Consider the total number of fingers of as many persons as there are fingers in one of your hand. That number exists independently of how you call it. In English, you call it fifty.
50 = 101
However, fifty is how you pronounce this number. How do you write it down, apart for this five-letter word?
In Roman numeration, you note it D. By the way, this is how it was noted in Europe until as late as the 13th century, when Leonardo Fibonacci popularized the positional numeral system invented in India, based on the description by Muhammad al-Khwarizmi in the Arabic mathematics.
In the decimal positional system, fifty is noted 50. Meaning 5 times ten plus 0 times one. The symbols 0 and 5 are a conventional notation, the factors one and ten come from the choice of the decimal system. Also called “radix ten”.
Let us choose another number as our radix, for example seven. To know how to write fifty in the radix seven positional system, we have to decompose it along the powers of seven. Fifty equals fourty-nine plus one, that is, 1 time seven times seven, plus 0 times seven, plus 1 time one. Hence, fifty is noted 101 in radix seven.
Instants and their notations
The previous example illustrates that on the one hand we have the numbers, such as fifty; and on the other hand we have the notations for the numbers, such as D, 50, 101, etc. There are many different notations for a given number, but it’s always the same number, independently of the notation system or of the radix if you choose a positional system.
In the same way, we have the instants and the notations for the instants. Consider for example the birth of Nadia Comăneci, which occurred in Romania on November 12, 1961 at 10 am. At the very same moment in Papeete, French Polynesia, it was November 11, 1961 at 11 pm. Different dates and time, but the same instant.
Here, time zones act in a similar way to radices in the previous example. The lead to a different notation, giving the impression that we’re not talking of the same thing. But regardless of the radix or time zone, it’s the same number or instant we’re taking about.
One additional thing that makes things even more difficult in the case of dates and time, is the fact that we have no common way of referring to an instant independently of any location. In the case of numbers, we can resort to the written form of the way we pronounce the number, like fifty (as opposed to 50, which assumes radix ten). In the case of instants, the best we can do it refer to the instant by something that happened then, like the birth of Nadia Comăneci. What we’re missing is Star Trek’s “stardate”.
This story reflects a discussion I had with my colleague Guillaume Vantroeyen while I was preparing a presentation on Dates & Time in Modern Java.
