hello welcome to the first and only episode of mathematical baking with Toby
today we're going to be making some delicious ancient Babylonian
mathematical tablets now Babylon was an ancient city whose ruins lie in
modern-day Iraq and the ancient Babylonian civilization was among one of
the first to be able to write they did this by inscribing things onto clay
tablets which could then be baked in a kiln and set hard and made permanent or
they could just be left uncooked and recycled hundreds of thousands of these
tablets have been excavated from the ruins of the civilization and many of
them relate to mathematics in fact many of the tablets found by archaeologists
were preserved by chance, being baked when attacking civilizations burned down the
buildings in which they were being kept before we get baking we first need to
cover our bases when it comes to ancient mathematics when we're talking about
numbers writing 2 3 4 is very different to writing 4 3 2
so in our number system it depends on the position of each digit specifically
when we write it like this it is really saying 3 times 10 and 4 times 100 in
fact we can rewrite this number as being equal to 4 times 10 squared which is a
hundred plus 3 times 10 plus 2 now our number system is in a base of 10
probably because we have 10 fingers and it's easy to start counting over again
once you reach 10 but not all number systems have a base of 10 you could
pretty much have you know whatever number you want for example if we had a
base of 7 any of the numbers higher than 7 could be re-written using the digit 7
or lower for example if we have that can be written as 1 times 7 plus 2
now let's talk about the ancient Babylonians they didn't use a base of 10
or of 7 instead they used a base of 60 now you might be thinking what kind of a
crazy base is 60 but we actually use it sometimes too for example telling the
time we've got 60 seconds in a minute and 60 minutes in an hour so we can
probably thank the Babylonians somewhere along the way for that one.
For the Babylonian's base 60 they had no symbol for zero and the other fifty nine digits
were written as a combination of only two markings in the clay made with some
kind of square-ish tool it appears they had the wedge for the units and the
corner for the tens they wrote numbers less than 60 like this this was a 1 2 3
4 5 6 7 8 9 10 11 12 13 14 15 20 30 40 50 and 59 and then when we reach 60 we
start again so one wedge is 60. two wedges could be two 60s. three 60s. ten 60s would be a
corner and 59 60s would be 5 corners and 9 wedges. If we had this it would be
equal to 12 and in our base 60 that would be times 60 squared because it
does depend on the position plus this which is 31 but that is times 60
and then adding on this that will be plus 25 now all of that will be equal to
and I did this calculation before, 4 5 0 8 5 so this is how
ancient Babylonian mathematics works and we're going to use that to see if we can
decipher some of the clay tablets now of course there is a little bit of room for
miscommunication here because say one wedge could be interpreted as one or as
sixty and something like a corner and two wedges because there is no symbol
for zero this could be ten eleven twelve or it could be ten sixties
so it would be 602 we're not really sure but we'd have to follow the context of
the rest of the calculation to be a bit more confident now we're going to take a
bit of a break from the maths a little bit of a mental break and we're going to
do some baking instead of using clay I'm going to make
a gingerbread tablet and then we're going to inscribe some cuneiform onto it
that is the name of this babylonian writing so we're going to recreate one
of the original tablets which have helped us to really understand how the
ancient Babylonians did math now in terms of ingredients I have them laid
out here I've got three cups of white flour half a cup of brown sugar
two thirds of a cup of molasses a hundred and seventy grams of butter and
then some little spices and things I've got one teaspoon of baking soda one
teaspoon of ginger half a teaspoon of cinnamon 1/2 a teaspoon of nutmeg 1/2
teaspoon of salt and some chili I've also got this egg here and we're just
going to mix all of these into this bowl
now that I've finished mixing all of this together I'm actually going to put
it into the fridge for a few hours to let it cool so I'll see you then
once it's cooled for a bit I need to roll it out and get it to about the size of my
baking tray I was aiming for it to be about one centimeter thick I then put it
back in the fridge overnight I wanted it to be nice and firm for the inscribing
process for my tools I used a chopstick for the wedge symbals and a cocktail
skewer for the corners
this is an image of the original tablet we will be replicating and here is a
clearer version of it I then made some lines I'm not going to tell you straight
away what the purpose of this tablet is because I want to give you a chance to
work it out you know everything that you need to
know but one hint is that this strange group that repeats in every line with
the strange sideways symbols that isn't a number that's a word so we have 10,
something, 1, 10. Then something, 2, 20. something, 3, 30. something, 4, 40.
something, 5, 50. I'll tell you what the word is it's the word for multiplication
this is a multiplication table and in the top left corner they've told us that
it was the 10 times table notice when we have 10 times 6 we get one wedge to
represent 60. ten times seven equals one wedge and one corner to give seventy. ten
times 12 is equal to two wedges for a hundred and twenty and that's all I had
space for then I put it in the oven for about 10 minutes at 175 degrees Celsius
here's what the baked version looks like next to the original and here it is with
a bit more of an authentic look it's not bad actually I might offer some to
my family but their collective response will probably be what the heck is this
but I enjoyed making it and there's actually a lot more that can be said
about ancient Babylonian maths and a lot more that we can learn so I'd love to
make some more videos like this granted that you enjoyed this one so please let
me know down in the comments or leave a like and I hope you have an absolutely
mathematical day
you