# Believers in base 10 always seem to talk nineteen to the dozen!

Bad puns aside, math is a vast and dynamic language, a lens into the depths of the expanses of the universe and a global standard method of communication. The basics of math are taught to us at a young age, at a time when we’re so fascinated by it that we never get to question it. So, my hope is that this post will introduce you to something that you accepted readily as it was taught to you.

Base 12- The Dozenal or Duodecimal System.

It baffles me how every child who is taught to count in the decimal system {0,1,2,3,4,5,6,7,8,9} has never asked why there aren’t any more symbols!

If you’re a computer science student or math student you’ve probably understood what I’m talking about. But for those who are new to the concept of counting in different bases, heres a quick explanation:

Explanation (can be skipped by ones who understand it)

The number system we use to count is the decimal number system where there are ten symbols and the repetition of combinations of these symbols results in further counting.

For example:

After 9 comes the first repetition of 0, i.e., 10. Followed by the first repetition of 1, i.e., 11. Further down there is the first repetition of 9, i.e. 19. And then starts the second repetition of 0, i.e. 20, and so on.

So 100, being the 10th repetition of 0, in the decimal system signifies 10 x 10 objects.

But in the dozenal or duodecimal number system, there are 12 symbols. {0,1,2,3,4,5,6,7,8,9, X, E} (you can use any two other symbols). When you have 12 symbols 10 actually holds the decimal value of 12 and 20 → 24 and 30 →36, and 100 → 144.

Binary (used in computer science) is another numeric system, with, as the name suggests, two symbols, 0 and 1, works the same way. And the hexadecimal (again used in computer science) uses symbols {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F} which has 16 digits and is also commonly used.

For a more in depth explanation, check out the following links or leave a comment below!

//https://www.youtube.com/watch?v=EsLgiffa9Cc

//https://www.youtube.com/watch?v=U6xJfP7-HCc

//https://www.youtube.com/watch?v=snz-81omkFQ

What makes base 12 more useful than base 13 or 14 or 15 or well the regular decimal system?

To say it simply, the number 12 has more factors than 10, 13, 14 or 15.

Which means that fractions that are difficult to calculate of recurring in the base 10 system are a cake walk in the dozenal system. Example:

1/3 = 0.333… in base 10

1/3= 0.4 in base 12

and the same goes for other such fractions.

This means that the base 12 system makes daily math much easier as you dont have to think as much about recurring decimals, complicated division and such problems.

On thinking about this, we realise that the number 12 is already a pretty big part of our daily lives, there are 2 sets of 12 hours in a day, 30 sets of 12 degrees in a circle, 12 inches in a foot, 12 months in a year, etc. The calculation and conversion regarding these would become much easier as well.

For more interesting information regarding the dozenal system, check out these links: -http://io9.gizmodo.com/5977095/why-we-should-switch-to-a-base-12-counting-system -https://books.google.ca/books/about/New_numbers.html?id=zfXuAAAAMAAJ&redir_esc=y&hl=en -https://www.theguardian.com/science/alexs-adventures-in-numberland/2012/dec/12/dozenalists-world-unite-tyranny-ten

Hope that set you thinking. Do you think the dozenal system is something we can switch to in this day and age? Do you think the great amounts of short term effort it would take to make the change is worth the difference it will make? Leave your opinion in the comments below.

Here are links to a few dozenal societies which you could consider becoming an active part of.

Dozenal Society Of America : http://www.dozenal.org

Dozenal Society of Great Britain : http://www.dozenalsociety.org.uk

Dozenal Society of Reddit : https://www.reddit.com/r/dozenal/

Leave a link below if you are a part of a dozenal society I haven’t mentioned above!

-Nishka.