28 March 2014

Welcome the duodecimal currency so says Mr Osborne

Well not quite. This by the way is not Mr Osborne the Green Goblin although he probably has been called worse. It's Mr George Osborne Chancellor of the exchequer.

Also he hasn't announced a new base for the currency, what he has done instead is announced that the humble £1 coin will have a different design. It will have 12 sides. Yes, this is where I have deceived you, I apologise.

What does 12 sides mean anyway? Does it look better?
Well have you ever wondered how machines recognise coins? They have holes which is just big enough for the coin to go through. 20p and 50p are 5 sided which means thanks to rotation and objects of constant width, they are easy to say what the width is. The issue with the 12 sided coin is it does not have that property, it's a bit of an issue, I'm not sure what the solution is. I personally find object of perfect symmetry ghastly but it depends on who you ask. The dozenal society in the UK would probably be quite pleased.

Who are the dozenal society?
They believe that changing the base of currency and counting to 12 will make things simpler, and they are right. Also there is a dozenal society in the UK and in America.
First of all counting. Every number you get in base 10 can easily be converted over to base 12. Take 2014 as a number, the first thing we have to do is work out the highest powers of 12 (power of 12 e.g. 12^0=1, 12^1=12, 12^2=144, ...) that is less than 2014. Which is 3 (12^4=20736 and 12^3=1728).

(12^3)*1=1728. 2014-1728=286.
(12^2)*1=144. 286-144=142.
12*11=132. 142-132=10.

Convert 11 and 10 into base 12 numbers i.e. 10=a and 11=b

There is other methods, this is just one of them.

If anyone does implement the base 12 system they need a symbol for 10 and for 11 and also a name. This I believe is where the fun comes in, for naming anyway. We already have a number which is in alphabetic order (forty) so can we have reverse alphabetic name like trone for example. The other thing we haven't got is a Palindrome (something that reads the same forwards or backwards e.g. racecar, hannah, 123321). For 11 we could have caac or ette. It probably should be only 1 syllable.

With base 10 we count on our fingers and thumbs, thats fine. In base 12 we only use the knuckles of our fingers of 1 hand (see already much more efficient) and the thumb can count along. If you count on one finger you can get to 3, do that on all 4 fingers we can get to 12. Now if use both hands we can get to 143 or 12^2-1, good lots of big numbers, but now you ask about learning the times tables.

Lets count this in base 10. Up to 10 times table there is 100 digits but thanks to patterns we don't need to learn them all, only 77 digits. Times tables 5 and 2 and 10 we can reduce. In the 5 times table, a number ends with a 5 or a 0. We only 2 numbers we need to know. In the 2 times table after 5 numbers it repeats 2, 4, 6, 8, 10. The 10 times table is the same as the 1 times table but with a 0, so we don't need to learn them.
In base 12 however there is a total of 144 digits but we only need to learn 85 numbers. This is more than base 10 but less overall. As a percentage you needed to know 77% of the 100 numbers. In base 12 we need to only know 60%(bit less) of 144 numbers. Why? In base 10 it has prime factors 2 and 5. In base 12 it has 2, 3, 4 and 6. More prime factors means less to remember.

Also base 12 means there is some interesting things you can do with symmetry, but that's a subject for another day.