Wednesday 9 March 2016

Can I be 21 forever?

One of my colleagues celebrated a birthday yesterday. To maintain the illusion of youth, he suggested that we start counting years in hexadecimal rather than decimal.

Hexadecimal (counting in Base 16) is used a lot in computing. Hexadecimal is used to represent numbers to the programmer, which are stored internally with 4 binary bits (2 to the power of 4 is 16). Instead of decimally counting 8,9,10,11,12,13,14,15,16 etc, hexadecimal numbers increment as 8,9,A,B,C,D,E,F,10, etc. In maths terminology, we describe this as counting in base 16 (sometimes called radix 16).

Although most of the world counts in base 10 (decimal), other bases have been used historically as well: from base 12 we get the concept of dozens, 12 inches in a foot, and 12 old pennies to a shilling. 12 is very useful for trading, cooking and measuring because it can be divided by 2, by 3, by 4 and by 6 (whereas 10 can only be divided by 2 and by 5). The sexagesimal system (base 60) originates in ancient Sumeria, and is still used today on our clocks and in the way we keep time.

The most important question in the world is of course whether I can remain 21 for the rest of eternity. Can I be 21 forever just by changing the base of my counting system?

Most people are happy to use decimal until their 21st birthday. Upon reaching 22 (decimal), most people prefer not to divulge their true age in polite conversation. So, can I write my age as "21" by assuming a different base system?

In the tables below, each column represents a different base system: on the left is decimal (base 10), followed by base 11 and base 12. On each row is the same number (e.g. the same number of elapsed years) but represented in that base system.

So, I could celebrate being 21 (in decimal), then a year later I could celebrate being 20 (in base 11), then a year later I would be 21 (in base 11). I could continue doing this, being 20 then 21 in each subsquent base system ... which would confuse my friends, so it might be easier to be 21 for two years at a time.

By the time I get to my 60's I should really be counting in hexadecimal, which is quite nice really, because I'll still be in my '30s (hex) when I'm 63 (decimal).

For practical purposes, however, lying about one's age is hard work. I'm relaxed enough to tell people how old I really am, and just use decimal for everything - especially inches and minutes.*

* You will turn 11 million minutes old about 2 hours 40 minutes into the day before your 21st birthday (assuming counting in base 10).