Tom: We tend to think that numbers are a universal language
like if there was a
extraterrestrial single the hit Earth, that it would start with one plus one is two
and it would work up from there and work from there and work up from there and then eventually
we're building a machine
opens a wormhole to Vega. And that's a really good idea
for formal mathematics and formal logic it might work...
but the way that humans actually use numbers and we talk to each other it is not
nearly as universal as you might think
I mean I should say I'm a linguist not a mathematician. I've kind of moved over to numberphile
briefly here but to my background's linguistics and the number of ways
that humans use numbers... The number of ways that humans use numbers? Doesn't even make sense...
And you might say okay this there's some weird examples where
English is base 10, but it's not entirely because we still have dozen
which is based 12, we still have Gross, which is 12 times 12, which is 144
that's all base 12 that's duo-decimal we still have 'score' in the language
in the language, we still have 'four score and seven years ago' with Abraham Lincoln
he meant eighty-seven
but 'four score and seven' resonates because we used to have base 20 counting. We used to have
vigesimal, and that still resonates well in the language today. We still have all of that.
I looked up specifically one linguist called Glendon Lean who spent
twenty years touring round Papua New Guinea, Oceania, all kind of south
eastern areas he found languages that were base 6. He found languages that were base 15.
He found all sorts of outliers that you would find if you have isolated populations on isolated islands.
They're not that weird though. I mean you've done a French video before
right you have 'quatre vingt sept' which is four 20s & seven.
That's strange before you even get
outside Europe. Hindi is so irregular
that for the numbers 1 to 100 you essentially have a hundred different words.
There is a pattern in there behind them but the forms are so irregular and they change so
much that you basically have to learn a hundred different words.
Danish ... Danish is an astonishing one
the Danish number for 58 is
I'm totally not going to pronounce this correctly
'otteoghalvtreds' I think I apologize to the people of Denmark
'otte' is eight, that's easy, I think the 'o' is in there as well
ignore the 'g', that's just to link things together, and then you've got this, which is
'halvtreds' -- 'half third'
now hang on, that's meant to mean 'fifty' so what's going on there?
so dot is the freebie action that
so that is an abbreviation, it's 'halvtredsindstyve'
again I'm sorry but that is 'half thrice times 20'
which still doesn't make any sense because how can you manage, half times three times ...
how does that make fifty?
well then you get another catch because this bit here 'half thrice' is like Roman numerals
what you got there is 'half away from thrice' this literally means 3 minus 1/2 times 20
which if you actually do the maths is two-and-a-half times twenty which is
50 so you finally have 58 you have
half thrice two-and-a-half times twenty plus eight, 58
so the complete opposite end of the scale is Tonga. Which is wonderful
there there are a few more formal ways you can say them but essentially if
you're saying
a really complex number like 771,216
you say the numbers for 7 7 1 2 1 6
in order that's it. It is as simple as that you just say the numbers
for one thing I suspect most of your viewers will think is that at least we've agreed on
Arabic numerals now. At least we've we've got the standard
5, 6, 7, 8 standard 0 to 9
that everyone uses. Ehm, Not Quite
someone languages, particularly those in India and China still use
their own numeral system particularly for formal things like we still use Roman numerals
for clock faces they might use them in similar places Brady: And the SuperBowl
Tom: And the SuperBowl! Of course, yes. although SuperBowl 50
is going to be SuperBowl 50 (five zero) because Super Bowl L
doesn't really sound all that impressive. There's a few other obvious
points mainland Europe
uses a comma for the decimal point and a full stop
to separate thousands UK and US are the other way around
If you're using currency then there are a whole load a different ways to say
'and no cents' you might put a slash. You might put a comma and a slash, you might put
dot double '0'. And then there's the big one 'cos I said
thousands separator a while ago and that's not universal either
and I really got surprised by this when I looked it up
there is not a universal thing for how many digits
should be in each group if you go to South Asia
to India to Pakistan to areas around there
you will find they don't use, I mean they do, they can use that as well but
frequently the system that is used is the 'crore' and the 'lakh'
watch a British guy try and explain 'crore' and 'lakh'
your lack is 10^5 and your crore is 10^7, and here's the thing
they are written like this
your least significant group is three digits
and each group that's more significant than that is two
so you can have a lakh crore, which is going to be 10^12
and watch me mess this up
that's 5, that's 7, that's 9, that's 11 which is going to be written like that
that's a trillion and there's no reason why that should be a trillion instead of a lakh crore
its just what we happen to decide
you might be able to argue that constant threes is
maybe a bit more understandable but that's coming from a really English
perspective. I would be absolutely certain that someone who grew up with this system
would have just as good a reason why theirs is more logical
let's say all written spoken language fails, let's say you have
someone who you have about absolutely nothing in common with at all
at least you can gesture. At least you can say, you know, 8, 9 these are ... no
... no. I even thought that was universal
until someone I know came back from China
and told me that if you are going to be in certain regions in China
you are going to be using hand gestures that are complete different
so you get 1, 2, 3, 4, 5
I'm gonna try this, and I know someone in the comments is gonna call me out for hand positions
being a little wrong, but it is roughly
6, 7, 8, 9, 10
or sometimes 10 are which are based
on the shapes of the original Chinese characters for those numbers
that kinda blew me away but then I found
the paper from Glendon Lean I mentioned right at the start about
Papua New Guinea and languages in that area who use a brilliant thing called a
body count tally system so they will go
1, 2, 3,4 5, 6
7, 8, 9, 10
and then depending on which language it will follow different points around the face
of it might go across and down the other side
okay there are a lot differences between languages but the majority who use that system?
base 27 because you have 27 points that that they refer to
to keep tally. We're not going to be doing advanced calculus in this
we're going to be you know during everyday conversations but that means
you can do things like
one man and here. 37.
you can start keeping tally with things and that's wonderful because that
is something but I hadn't even thought
of. I haven't even come up with before reading about it that wasn't
something that my
my mind was open to. What I wanted to do here, kind of a grand finale,
was to look at what science fiction writers have done with alien languages
but they're nowhere even close to that. I looked up
Klingon, from Star Trek Klingon on is base 10
with words for thousands and millions
it's clearly written by an English speaker and it's more English
and more normal for us
for those with over here than
half the languages i've talked about! And it's meant to be an alien species and I know
in Star Trek they're all meant to have come from a common ancestor but
we did come from a common ancestor and we've got much
much weirder numbers in our own
human speech than science fiction has ever come up with. I think that's one of the
best things about linguistics, about being human,
about all of this is that someone on the other side the world
something that they will consider absolutely normal
can completely blow your mind
Brady: We'd like to thank Squarespace for supporting this video if you want a
simple
powerful and beautiful website then check them out. I use SquareSpace myself for my blog
and I could tell you I'm a really happy customer but if you're a bit more
advanced than me and really want to fine tune all aspects of your site
then SquareSpace's developer tools really let you get under the hood and
tinker with everything so if you've got a great idea for a website
online store podcast or anything else that needs a web presence
check them out. You can even give it a trial run, set up a site, see what you think, with
no credit card required
and then if you do sign on for a year they'll throw in a free domain name
use the offer code numberphile and you get 10 percent off
your first purchase. Go to squarespace.com/numberphile
remember that offer code (great stuff) and thank you to Squarespace
for supporting numberphile.