this story is a master of disguise to some people but he's appeared as a wedge
to others as a coach
but no matter what shape he may have taken on he's always been number one
his story is our story
it's a story of struggle of not
numbers come from
will see out one helped create the city
how he helped build and parts
inspired some of the greatest minds in history and also part that his part
making money work
we'll see how one teamed up with very well could dominate the world we live in
today that digital world the world runs on one hand dealers were first written
down my computer using the code of ones and zeros even my image coming into this
digital TV has been sent through the ether as a series of what and how these
two digits come to dominate in fact most of human history
20 simply didn't exist why
to win did one come from
well his story begins at the dawn of time three billion forty two thousand
six hundred and sixty-nine years ago
day the first limited one pulled out of the primordial soup onto dry land
really just joking in fact the origins of 10 shrouded in mystery
it's a mystery that only answers one of them must be the first human being to
use one actually count but when I could make marks on bones he's been well I can
box but the fellow who scratched marks like this
hundred and fifty thousand years ago is it possible that he could have been
counted good these scratches represent a series of one's while the experts tell
us that giving due weight to these scientific and archaeological evidence
they haven't a clue
pretty sure about is that one is a lot younger than us it's not until quite
recently twenty thousand years ago that we get the first really solid evidence
that one existed and someone was using it
County
of course he didn't look like this when he was pulled back then one was just a
scratch on a bone this bone it's known as the shank bone it was found quite
recently in the Congo and look you can see these scratches we know that each
represents a 10 can we be so certain well someone must been counting because
the sixty scratches on the edge of the bone and another 60 along this age and
on the back
equally numbered groups and you can't do that without counting may mark a
defining moment for mankind
tell us the other models are able to come to three or even four but not
beyond
by turning into a scratch our early ancestors could count all six of her
room
clever clogs in fact they could count any number of ones they won
that is what gave us the edge over the lions and tigers from now on
counting new nodes and one is growing up into a big boy
in the meantime human beings living in caves and started to build their houses
the next great event in one's life was to happen in the ancient civilization of
human here in the Middle East in about this time the people of Sumer decided to
give one is independence they stop scratching on a boat and set him free
but I represent
transformation changed not only ones life but the course of history
the invention of pogroms allowed the Sumerians to do something that nobody
had done before if we had not choose to a stick found you can do just that but
with tokens you can take away so that you got six chickens and you eat five of
them look what you've got
indigestion in Vienna know you've invented arithmetic was the biggest
breakthrough in one's life so far but why did it happen here to find out we
have to go somewhere where I didn't
meet the world free of Central Australia that people have been minding their own
business here for thirty thousand years or so until some anthropologists came
along and noticed that they didn't use number people get very interested in
Marbury was in a language we don't use numbers we have one but I think about it
until recently the world go by without using numbers how long he been able to
think differently here in every group of any numbers at all
began
General Jerry names his grandchildren but he doesn't say is full it's just not
an easy
generation don't talk in terms of exact times of day just the position of the
Sun
they don't even deal in distances because their land is mapped out not
with numbers but with song which contain all the information they need these
timeless songs deeply rooted in their culture was sort of huge national pride
in the fact is in traditional while free life they didn't really need a number
system let alone a rhythmically so why on the other side of the world
six thousand years ago did the people of Summa feel the need to turn one into a
token and invent math
different about life in the Middle East
why would people here so keen to get him to maybe it was because there were so
many people living in the same place the wealthy the Sumerians lived in cities
and cities need organizing way to be stored and distributed and working out
how much each person should get required and that's why the Sumerians turned one
into koshen Perkins made possible the arithmetic required test well how can a
profit and loss and more important perhaps collect tax yes you can blame
the invention of mass on city life
needed for their civic programs they also need to be able to keep a permanent
record of their calculations but hold on the written word hasn't been invented
yet numbers it seemed with the world's first writing it happened like this
specific numbers of cones would be put into play envelopes for safekeeping and
then sealed up but once its sealed envelope how could you remember how many
contained but wait a minute
another cone and made the same number of impressions on the outside of the
envelope as they were cones inside then some bright spark realized you didn't
need the envelopes in the first place if you didn't even need the cones you could
just make the mark straight onto a clay tablet and a presto you had a record of
the number that notion of writing had been born
mathematicians were now able to keep permanent records of their calculations
and these could become more complex than ever before
a select few who initiated into the mysteries of numbers and they were
trained from childhood they became a powerful and highly paid elite that we
still pay hommage due today right
the Sumerians great gift to the world but chocolate one was now disciplined
organized as never before he became a powerful tool was used to build
which is precisely what happened to one next incarnation
egyptians
even
walking very slowly formation egyptians
big big building they came up with some pretty big and the way they wrote them
down
provides a fascinating reflection of the hierarchy of Egyptian side
numbers of drudgery and everyday toil one was a plain unadorned life
100
workaday numbers numbers numbers to impress
unnoticed symbol of pleasure 10,000 bonding finger and then the number of
number this means
million sort of number
it was the first ever and a simple they used was a prisoner begging for
forgiveness or counted begging to be let off County Animal prisoners in any case
one had never been busier
but one had another job injections wanted to do perhaps the most important
job needed to help out
building site
addictions were enthusiastic builders with a keen eye for beauty but you can't
create beautiful buildings without you can't measure accurately unless you know
what your unity that is what you mean by one
in solving this problem the Egyptians would do something nobody had done
before they defined their own version of what they based it on the length of a
man's arm from elbow to think it plus the width of its parts
one was now known as the cube
the undisputed ruler
the official ones the master cubed steaks with some important they would
jealously guarded in the temples from them copies were made and given up so
right across the Empire whatever the building project everyone knew what they
meant by one simple measuring stick the Egyptians were able to complete their
vast construction projects with astonishing actors
if we hadn't become cubit some of the wonders of the world might have been
well a little less onerous
by transforming one from County things to measuring things the ancient
Egyptians haven't just opened up a whole new world of bespoke tailoring and
fitted carpets they had made one
the measure of all things one had become the ruler destiny was even more special
one was about to become the death of the universe
two and a half thousand years ago in ancient Greece Greece then was the cause
of a check by the name of Pythagoras theorem
it's a boy understood it all his pupils had to give up their positions to such
things that when you
even so he also had to think about
whole numbers collections of what you been I that certain whole numbers make
pleasing shapes 3 makes a triangle square miles 210 which forms a magic
trial was also convinced that one with it venturi help explain one of the
fundamental questions of the day the Greek philosophers were forever trying
to find out the one thing that everything is made of one philosophy
said anything made of leather and other water pythagoras said that everything
was made of numbers including music to find out what pythagoras meant I'd come
to the world Perry garden center
all I need now is a mathematician logician a bit of luck but if you want
to find out about Pythagoras music and matts gonna need some putts are rather
different sizes got lost together but we're not together but why is it such a
beautiful combination and the answer is mathematics the relationship between the
weights of these parts is an imperfect 122 relationship and it's that
combination of whole numbers which makes this such a nice sound as opposed to the
first part is about 12 1.26 fall not not a nice hole number relationship which is
causing the bad sound so that the combinations of whole numbers numbers
that are the ones I realize that these poll numbers are really why things sound
so beautiful and excited him so much he realized that really mathematics was the
was the pace of everything that it would explain musical harmony and the cosmos
and this is why he coined the phrase the music of the spheres so shall we say yes
beauty of music relied on whole numbers I take respecting so too must everything
and since the universe's construct one would never know it but I thought missus
holt belief system and ironically it was the triangle that made him famous which
was approved
was at the heart of everything it should also be at the heart of the triangle
even the right angle triangle with equal signs it's not
I thought with kept trying to make all three sides an exact number of unit
could be
when trying to point this out
others I think was his whole belief system units
down by
like one was not a chair one step one television presenter but the
mathematicians who followed by side was broke free these constraints yep
archimedes famous today is the world's first Street up but in fact the greatest
mathematician of ancient archimedes just playing games with numbers and he took
mathematics into the realm of the unimaginable because in these games he
allowed numbers to do
possible fifty like working out how many grains of sand you'd need to fill the
universe and get down to some of these mathematical games may seem they
sometimes came up with practical results that we benefit from this day for
example he was obsessed with what would happen if you took a spare turned into a
selling them
what the difference in area covered person I don't give a fix but for
archimedes it was the proudest moment of his life when he finally succeeded work
here and it did actually proved to be amazing because thanks to our
communities they do match makers could take the globe and turning into mom was
no longer the essence of the universe but he was helping to create a golden
age of theoretical mathematics
but a new course was at large in the world
one was about to be dominated by a people who had rough different
obsessions
and when the Romans invaded in two hundred and twelve BC he was in the
middle of a particular gripping piece of calculation in fact was so wrapped up in
his work that all you could say was I do not disturb this
not a wise move
it was the end of theoretical mathematics in the classical world the
votes weren't interested in me ferry abstractions like how to calculate the
weight of all the goats who ever lived
they were interested in power
whether you like it or not one was now a servant of Rome he had to leave the
disney world of abstract mathematics behind it and get on with more practical
concern
the backbone of the Roman world as the Romans used him to impose a numerical
grid
and in the section 10 sections hundred-man called a century to century
called a manipulator which means literally handful which I imagine two
hundred soldiers probably work
even punishments without doubt on numerical principles of Allegiance
suffered a humiliating defeat the entire lesion was death made from the Latin
word for 10 Dec regardless of individual guilt one soldier in 10 was killed the
Great Ape of the Roman world was to keep things ticking over mathematics just
wasn't there I'm surprised I mean the Roman numerals don't exactly make the
easy I mean look at them just an elaboration of the old notches on a
baton the only sophistication being new symbols as the numbers get more unwieldy
be 45 exit n c400 up to their symbol four million but it's still just a
simple counting system fine for writing inscriptions on tombs but not much cop
the complications of theoretical math would you try writing a billion like
that in modern new malls it takes me about eight seconds I tried it in Roman
numerals it would take something like sixteen minutes it's no surprise then
that Roman numerals weren't even used to calculate the actual calculating had to
be done on accounting board an early version of an abacus
the numerals themselves would just used caught in the result it's no coincidence
that unlikely not a single Roman mathematician it celebrated today
as Roman power spread so too did its newer system over the next five hundred
years all of Europe Spain Turkey came under Roman control and even when their
empire crumbled their new moves left
but though the Roman system might have seemed indestructible
wasn't its nemesis came from the east side in 580 the cold there about
engine cover some time living in a more where if I
the Indians seem to be less concerned about military organisation them about
announcing the world and finding enlighten
never isn't just down the road to reach it is a very long journey which takes a
long time and to convey that fact the Indians came up with some stupendously
number
covered by God in six months if you travel a million kilometres every blink
is the length of time it would take me to build a cube of lambs will 10
kilometres high if I want to leave one strand every century
numbers that could have made one feel well
bowl if you hadn't had a little help from the Indians divide the system that
could cope with vast numbers they developed a different symbol for every
number from 1 to 9 1230 quickly you get new moves you know
numbers we use today but in fact they began life here in India as early as
five hundred BC
around 1,500 years ago a little longer if you're watching a repeat of this
program
someone came up with a three appendices incredible extraordinary hydeia numbers
since the Sumerians invented maths creation that would change the world
they invented an entirely new number in here inside this tiny seven hundred year
old templeton value of northern India is this new number and ask the four
thousand mile journey I'm finally going to get to see
so we wait while we wait I start to wonder how was it
this number wasn't invented sooner it's such a simple number that takes a moment
to say and even less to write
invented it can't for the life of one in a way that would eventually change the
entire
time history nothing
inscriptions says that in garden was planted to produce flowers temple and to
ensure they had enough
that garden had to be a hundred and eighty-seven by two hundred and seventy
about 23 using the recalled their conquest is the people who use them to
make sure they have adequate supplies for what's all the fuss about having
what's so wonderful about inventing a symbol that means nothing I mean
somebody asked me about my hand I can just say I don't need 20 to do that well
0 would be nothing but when you team 0 up with lung magic started and when they
were joined by the best of the crew the results must tackle with just 10 digit
engines could make numbers in large as well
infinitely small how the Romans couldn't do that wrong had found his perfect made
in 08 it was a partnership that was gonna change the world
together with the rest of the team they enabled Indian science to storm ahead
Indian astronomers for example where centuries the head of the christian
worlds
but it moves around the thought of something that I couldn't figure out
until a thousand years
Indian scientists also calculated the diameter of the glow and they were less
than one percent of what it actually is
all this was possible because of 10 and the rest of the troupe of performing
and their fame soon began to spread across the globe
the numbers of Rome was bound to happen sooner or later but for now
10 and their friends made their way across the deserts of Arabia to take on
one of the most sophisticated societies of the age in what is now Iraq
hundred years old
baghdad was ruled by the great Calif now wished his people to live according to
the current setup courts and judges to apply the law of the Prophet and resume
now he law of the prophet is full of instructions that requires serious
mathematical calculations if they are to be carried out on the number of other
relatives and their relation to the decease working all that required
fractions and ratio at least four people counted it's not like we went up to
complex arithmetic it was just their number system was holding them back
but one day they arrived in the court and ambassador from India he had to
prevent the great Calif with a gift of some sort but the Calif was a man of
infant pictures it was hard to know what to get I love India t-shirt was hardly
going to do the job they have thought long and hard
decided to present the Caliph with the greatest gift we could think of
the game
actually we don't know exactly how adopting the Islamic world but the
Ambassador story is
what is that Muslim scholars were bowled over by 10 and the rest of the trip and
most famous these colors with a man by the name of Calgary's I'll however
recently however I don't how it is me and his colleagues thought the
Performing numerals a whole host of brand new tricks
quadratic equation
well ok I made these numerical feature enabled science mathematics and
astronomy to reach new heights in the Middle East Indian group became a smash
hit throughout the Islamic world
but on the other side of the Mediterranean Christian Europe with
still in the static grip of old army of Roman noodles and they weren't going to
give way to the feisty newcomers that easily
a showdown between the two systems was inevitable and when it came a good shape
the destiny of the Western world
the beginning of the Roman numerals starting on the Short North Africa
muslim traders have been quick to adopt 10 and code for their business deal by
the end of the 12th century Indian numerals in common use
and it was in the bus in court the judge that the young son of an Italian
diplomat based in algeria
witnessed that amazing
when I had been introduced to the art of the Indians 9 symbols
knowledge of the art very soon please me more than anything and I came to
understand
calculation called the book of calculation is now regarded as one of
the greatest mathematicians of Paul and his book was pretty much a showcase for
Indian number wasn't just a part of his book of calculations was aimed
specifically at merchants showing them how useful Indian numerals could be for
calculating net profits not exactly a page-turner you might think this was a
time when capitalism was beginning to come out into the open in your book what
are not screen
ordinary people felt comfortable with the old number
live with them thousand years the old Roman numerals weren't going to make it
easy for the Indian newcomers wasn't just a question of tradition you have
fun too had some pretty good reasons to prefer the old system for example many
medieval Italian cities had their own currency so every time I found myself in
a new tab a new step with extras and customs in the case may be I have to go
to the money changers bench or bank as it's called a banker was accounting
cable basically an abacus with counters has said a beat the man who operated
them the bankers had to swear an oath not to treat their customers the
magistrates welcoming his bench like that will be tough to broker and he'll
be declared bankrupt up which is where we get the word bankrupt
how much can I get to cease using numerals on familiar with using this
site and see what he's doing well thanks a lot
doing business with you but what happens to grab them on the smart chaps using
the newfangled indian girls that this problem he has a medieval part of my
family my bank started keeping my cousin Chinese I had no idea how you arrived
but thanks anyway
distrust went right to the top in 1299 the city of Florence actually banned
merchants from using the new numbers they had pues Roman numerals but no
number was treated with suspicion than one partner 2010 sign which creates
confusion and difficulty
0 was called FIFA and was regarded with such suspicions that that word became
our word for secret code for the day of the old system as opposed to the blame
good old human greed
the traditionalists who come to the abacus in Roman numerals had never had
the calculate interest on loans because the Catholic Church to charging interest
on loans was a city that was called usual but come the Reformation the parts
and churches were bombed business-friendly and the long held
Christian objections to capitalism seem to well disappear so in this new money
lending interest charging environment which moved the more useful Indian
numbers for the add
my right one first-class mathematician on my left one first-class
surprising I lend some 110 pounds at half percent interest per month how much
they owe me at the end of the year
ok ready steady
has been inhabited since she was just 15 and he's using the buttons but just as
they did in the 16th century she's Ramagundam penny actually goes let's
hope she can round up into first place
markets is using a pen and paper so he's working to an eye-popping 12 decimal
places in North London with his lovely wife Shaunie and treat children not big
but he is clever
jimmy is gonna kill me but what's your temp and sixty
compound interest after year will be pimp and sixty in the abacus seems to
get there before the mathematician I don't want to put a damper on things but
I think that answer is actually wrong I gots an answer in 10 pounds and 61.6
7776 6403 fully pass to be precise I'm actually picked up the subtlety of
compound interest which is a little bit each month but it adds up so I got this
extra 1.6
the medieval businessman it would mean the difference between making a living
and not maybe that's why the abacus you look so miserable as capitalism gain
respectability calculating interest compound interest became any
self-respecting businessman and the doing that even with an advocacy the old
Roman system was simply no match for the Indian numerals
your engine number
outmaneuvered the lumberyard quick and birthday with one and zero in the lead
just better teamwork came up push out the old Roman numerals
banker or even plans for the future and they didn't include took over the
western world with them
European navigators either so plus the great ocean out of sight of land that's
how they stumbled on america
the new numbers became the vocabulary of modern banking as we know but there was
still plenty of room for that old problem
human Columbus thought he got to Japan when it got to the West Indies
the world away he made the mistake
humans do which was something one man was determined to stop it all happened
around 60
Gottfried Wilhelm Leibniz with one of the greatest mathematicians of all kinds
he set out to rid mankind of the curse of human
and trying to do invented something that still affects us every day of our lives
what's more it's an invention that was to give our old friend won the chance to
rule the world like it with convinced that he could ever invented a mechanical
calculating she had in fact he built using all the new rules from vero
tonight then he had a better idea was inspired by his philosophy it is true
that has the empty voids and Desmond along 20
belong to the all-powerful in other words to paraphrase life in the universe
like a Swiss cheese which some of us are you know we hold I just as important as
the cheese itself so construct the world you need both something nothing which is
where the hero comes in
with convince at 10 with the only numbers and one really need these two
numbers he claimed he could achieve every mathematical dream more eliminate
human error
got rid of the other numbers and developed a system using just one year
it's called the binary system how could he possibly express all numbers just
within 10 I think it's time I spoke to someone who knows what he's talking
about models to understand binary ok let me give you a number in binary here is
the number nine written in boring hurry this is just using 10 just someone's
that's nine in binary well it looks like someone that's because you're obsessed
with you like to keep track of things in 10 mins
well this one keeps track of how many ones the second column of how many tens
their own next how many hundreds and one lot of thousands but in binary things
work differently in binary what's the Collins keep track of how many ones and
twos how many pools and how many here we have allowed to represent these numbers
using zeros and ones ok so so we're only allowed to put a net gain will not have
an egg and egg represents one let me show you what nine is involuntary 10
tonight in the fourth column yeah that's one loss of 8 fourth column and nine is
a plus one so I need to one in the ones column so
in binary number nine is one of them right now foods may 2011
but what about the other numbers well after just three short hours of tuition
to see that it was possible at all to make every number using just bones and
not convinced you don't need to do it it's very mechanical to have the ones
and zeros and that's why it's perfect for a machine to machine doesn't really
can't do much about how big the numbers guess he can keep track of real numbers
whilst we're not very good at doing that what it is interested in is a very
efficient way of adding numbers that's why machines love to put numbers into
binary
and the live in its design exactly such a machine and he's using metal Bulls
dropping the slot instead of eggs and a from now on
mistakes in the past digital age it seemed was ready to take over the world
he never built it 10 would have to wait another two hundred and sixty-five years
before they could step into the line
colossus the world's first working by now we compute its lightness his dream
made real but instead of dropping metal balls into slot blot US is electronic in
here 10 something and nothing surprisingly coming to their element as
electrical currents on and off
was created during the second world war and install here in Britain's
codebreaking Center at Bletchley Park it is 1200 valves miles away hundreds of
mechanical components
but just like all computers today the beating heart of this machine is one in
their electronic buying reform and they were performed millions of rapid
oscillations enough to crack the code for the German
even sharpened their pencils to Colossus the allies new the German messages said
even before maybe that this extraordinary contraction help shorten
the war by as much as two year
the technology that started here in Bletchley has changed our world
reasons for using an understanding numbers
astronomical calculations measurement of juggling with the divisions of property
do it
compound interest all that calculation preoccupied and sometimes the great
minds of antiquity just leave it to the computers and we could all simply be
happy ignoramuses but we've known whether the answers right or wrong
will care
in the computer age a whole world runs on a stream of ones and not bank
statements medical records to the Buckeyes every time I box of cat food
and the rest of the numbers can be consigned to the dustbin of history
10 the old performing have come out on top
just hope we can control
good