Base 10 is the way we write numbers.
One, two, three, four, five, six, seven, eight, nine, 10.
And I assume we do it because we’ve got 10 fingers.
Yeah, so I guess you would just go like well this has been useful.
So let’s write that down.
I just think that everyone should know, it doesn’t have to be that way.
Base 10 is just…
irritating.
So 12 is an amazing number because you can divide it by two,
you can divide it by three and four
and six and get whole numbers.
So it’s very special.
In a dozenal world
it would be much easier to use currency,
anything that you were trying to measure
if you wanted to have a third of it or a quarter of it
it would make it much easier to do.
And that would make young children’s experience of maths smoother.
So bases are all about at what point you go from
just having a single character to represent a number
to having two characters.
For us in the decimal society,
we do that when we go from nine through to 10.
And we use numbers that have already been used.
We use a one and a zero.
I hadn’t even considered that.
That actually there are no symbols past nine
because then it’s just zero and one again.
So base 12 would mean that you need 12 symbols,
zero through to nine as we have and then two more symbols as well.
Ten…
Eleven.
And it’s only now,
when we get to 12 that we have to go into two columns.
One, zero, it would look like 10, it would represent 12.
I’ve never done this, so…
Four times table in base 12.
OK.
Four times one.
Is four.
Four times two.
Is eight.
Four times three.
Is 12.
Right?
That’s right, yeah, because it’s one lot of…
No it wouldn’t be that it would be…
No, no, no because that’s…
10, 11.
And then we start again because we’ve got a whole thingy of 12.
Oh, it keeps repeating.
Some times tables work more nicely in base twelve,
some work more nicely in base 10.
I guess there are more of them that work nicely in base 12
because there are more numbers that divide exactly into 10.
Two, three, four, six.
That’s what makes it useful for writing fractions,
with nice things after the decimal place.
A third, which is really difficult to write normally…
Nought point three, three, three…
You could write nicely using base 12
because this means four twelfths but you still couldn’t do a seven.
It’s not rare, I don’t think, to have to share something
amongst three people or four people and base 10 is just…
irritating.
I wouldn’t say we have to use the number system 10.
Why must we use the number system 10?
If you go back to classical antiquity
you tend to find that other systems were more predominant,
the sexagesimal decimal system of the Babylonians for example.
Base 60,
so rather than having columns with powers of 10 like we have,
they have columns with powers of 60.
So there’s a units column, there’s the 60s, there’s the 360s,
and you add that up.
360 is very close to the number of days in the year.
That’s where this idea of using 60 comes from.
The fact that we have 60 minutes in an hour comes from the Babylonians.
We convert in and out of base 60 quite a lot
when we work out how many hours, things like that.
I didn’t even know I was doing fancy mathematics.
Yeah.
There are some legacies of some previous counting systems
in everyday life.
When we’re measuring things we use lots of different bases.
Civilisations have switched between bases throughout history
and we could do it again and I hope that we do.
The entire world has grown up with base 10.
You would have to completely rewire everyone’s brains into being like,
“Oh, let me get my base 12 times tables.”
Be like, “Oh my gosh.”
I really want to switch to base 12
so that when I’m using maths it’s a more pleasant experience.
Why can’t we be using the best base?
It’ll be so confusing for me and for everybody else.
But I can see on a mathematical level why base 12 is cool.
