This is candy.
It's called candy because it was originally from India,
where sugar cane was first processed into sugar crystals
around the 4th century AD, with a piece of sugar referred to as
'khanda' (खण्ड) in Sanskrit.
*Simon surreptitiously deposits the candy into his mouth*
Now, as the knowledge of the cultivation and processing of sugar spread westwards into what was then Persia
some time in the 6th century, the word used to refer to the process of coating something in sugar syrup
became 'qandiyy' (قَنْدِيّ‎) in Arabic.
And then, as that knowledge made its way westwards to Europe, eventually we get the English word 'candy',
some time 13th century.
'Etymology', or the study of the origin of words, can reveal a story. How we got to an object, or an idea's
importance in the world- where it came from. But, unlike candy, 'sin' and 'cos', as words, don't really mean anything...
and their story tells us why.
To go back to the beginning, the concept of 'sin' originates in India in the Gupta Period around
the 4th or 5th centruty AD. Previously, Ancient Greek mathematicians had considered the relationship
between the length of a chord- that's any line that connects two points on the perimeter of a circle-
and the angle subtended at the centre of the circle by that chord.
But the writers of the Siddhantas- one of the most important texts in Ancient Indian maths-
instead considered the relationship between half the length of a chord, and half the angle subtended at the centre.
And this is directly related to the modern concept of 'sin'. If a circle has radius 1, then its half cord has length sin(x),
if (x) is half the angle subtended at the centre.
In Sanskrit, which was the liturgical language of India at the time, the cord was referred to as 'Jyā' (ज्या),
meaning 'bowstring'. It's kind of obvious to see why: the chord looks like a bowstring if the rest of the circle forms the bow.
And a common synonym of Jyā at the time was 'Jīva' (जीव) which was the word that ended up sticking to refer both
the chord, and the idea we now know as 'sin'.
Mathematicians working in Gupta Era India defined two huge concepts that we use all the time in maths today:
Sin, as we've already seen; and literally how we write numbers.
And around the same time that sin was invented, modern decimal notation was also invented,
where each column of a number is 10x larger than the previous column. That replaced earlier systems which
were a bit more unwieldy, like sexagesimal, where each column was 60x larger than the previous one.
It's no exaggeration to say that mathematicians working in Gupta Era India really defined a lot of how we currently
think about maths. But those ideas had to get from India to Europe, where it was eventually standardized
into the notation we use today. And the journey it took to get there is where we get the names 'sin' and 'cos'.
Exactly as with 'candy', as the idea of sin spread from India to what was then Persia, the word used to refer
to it was transliterated from Sanskrit into Arabic because there was no direct equivalent that already existed.
So, 'Jīva' (जीव) became 'Jiba' (جيب).
Now this next bit is important... because something's about to go wrong.
Because in Arabic, words can be abbreviated by omitting short vowels. And as such, for convenience,
when written down, 'Jiba' (جيب) became 'Jb' (جب).
But this only works if you know what the abbreviation was in full in the first place. Because there could be any
short vowels between the remaining consonants. Normally, of course, that's not a problem. If you speak Arabic,
and you're familiar with the conventions, you can substitute in the original vowels.
But when Western Europeans started translating Arab mathematical documents in the 12th century,
what with the 'increased contact' between the two cultures, there was a problem.
Europe hadn't been thinking much about maths for the past... well, nearly 1000 years, instead focusing on
salvation, and who the successor of the Roman Empire was.
So, when they gained access to Arabic texts, which brilliantly extended the works of Ancient Greek and
Indian mathematicians and scientists, they began fervently translating them, and they translated them into
Medieval Latin, which was the language of maths at the time.
A translator, and it's not universally agreed on who this was, but it was probably Robert of Chester
(who, incidentally, was the first person to translate the quran into Latin), or Gerard of Cremona, got their hands
a book, in Arabic, called 'The Compendious Book on Calculation by Completion and Balancing'.
And within this book were tables of the values of the sin of an angle, referred to as 'Jb' (جب).
But the translator, whoever it was, didn't realise that that was short for 'Jiba' (جيب), and instead interpreted it as
being short for 'Jayb' (جايب)- the Arabic word for 'bosom' or 'pouch'.
Therefore, he translated 'Jb' (جب) in Arabic into 'sinus' in Latin, which is the word meaning 'bosom' or 'fold' or 'cavity'
(Incidentally, why your sinuses in your head are called that: they're literally air cavities in your skull).
And this name stuck in Latin, which remained the language of maths for centuries- right up until
mathematicians, and in particular Euler [Leonhard Euler], standardized the notation 'sin(x)' (being short for 'sinus'),
and 'cos(x)', for trigonometric functions. 'Cos', incidentally, is short for 'cosine' or, more completely
in Latin, 'complimenti sinus', meaning the thing which varies with 'sin'.
But the word we use today- 'sine'- was an English corruption of the Latin word 'sinus'.
So, as a word, it only has a mathematical meaning. It simply didn't exist until English mathematicians started
using the Latin function 'sinus' some time in the 16th century.
So perhaps it's fitting, then, that after centuries of history and a dodgy translation into Latin, that the first person
recorded to use the word 'sin' in English... was called Thomas Fale.
So the next time that you're stuck in a trigonometry test and you're staring blankly at the questions,
take some comfort in the fact the the person who named sin and cos
didn't really know what they were doing either.
If you want to prepare for that test, though, then the best way you can do that is actively engage with some
problems that develop your mathematical toolkit, and give you a deep understanding of the concepts at hand.
And the best way to do that is through brilliant.org: a website that promotes learning through problem solving.
Time and time again, I get asked: "What's the best way to get better at maths?" And my answer is the same every single time:
Practise, practise, practise!
The more problems you do, the better you will get. And brilliant.org is a great place to do that, as even if you do
get a question wrong, it will correct you, and remind you it's OK- getting stumped is part of learning!
In particular, their courses on mathematical fundamentals and algebra through puzzles are
a great place for you to get started.
...(and get stumped.)
If you'd like to try Brilliant- for free!- then go to Brilliant.org/SimonClark,
where the first 200 people to go to that link will also get 20% off their annual premium subscription,
and it helps me grow this channel.
Thank you for watching! If you enjoyed the video, please do pop it a like.
If you're not already, subscribe to the channel, and I'll see you next time!
CAPTION AUTHOR'S NOTE: Oi you! Go check out some more of Simon's videos. They're actually not half bad.