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00:00:01the hero of this story is a master of disguise to some people he's appeared as
00:00:08a wedge shape to others as a comb but no matter what shape he may have taken on
00:00:20he's always been number one his story is our story it's a story of struggle of
00:00:35knowledge of where numbers come from
00:00:41we'll see how one helped create the first cities how we helped build empires
00:00:49how he inspired some of the greatest minds in history and we'll also find out his part in
00:00:55making money work as it does so where did one come from well his story begins at the dawn of
00:01:13time
00:01:13three billion forty two thousand six hundred and fifty nine years ago to the day the first
00:01:22primitive one crawled out of the primordial soup onto dry land
00:01:44not really just joking in fact the origins of one are shrouded in mystery
00:01:55it's a mystery that only our earliest ancestors can answer at some point one of them must have been
00:02:03the first human being to use one to actually count with but when ever since man could make marks on
00:02:15bones he's been well making marks on bones but what about the fellow who scratched marks like this 150,000
00:02:25years ago is it possible that he could have been counting
00:02:28could these scratches represent a series of ones well the experts tell us that giving due weight to the scientific
00:02:37and archaeological evidence they haven't a clue
00:02:43what they're now pretty sure about is that one is a lot younger than us it's not until quite recently
00:02:52a mere 20,000 years ago that we get the first really solid evidence that one existed and it's a
00:02:58lot younger than us
00:02:58and that someone was using it for counting
00:03:03of course it didn't look like this when he was born
00:03:07back then one was just a scratch on a bone
00:03:13this bone
00:03:15it's known as the
00:03:17ishango bone
00:03:19it was found quite recently in the congo and look
00:03:23you can see these scratches
00:03:26we know that each represents a one
00:03:29how can we be so certain
00:03:31well someone must have been counting
00:03:33because there are 60 scratches along this edge of the bone
00:03:36and another 60 along this edge
00:03:39and on the back they're in equally numbered groups
00:03:42and you can't do that without counting
00:03:46the ishango bone may mark a defining moment for mankind
00:03:50zoologists tell us that other mammals are able to count up to three or even four but not beyond
00:04:01by turning one into a scratch
00:04:04our early ancestors could count to four
00:04:07five six clever clogs
00:04:10in fact they could count any number of ones they wanted
00:04:20and that is what gave us the edge over the lions and the tigers
00:04:24from now on counting new no limits
00:04:27one is growing up into a big boy
00:04:47in the meantime human beings were moving up the property ladder
00:04:53and that would change one story forever
00:04:57they stopped living in caves and started to build their own caves
00:05:02houses
00:05:09the next great event in one's life was to happen in the ancient civilization of suma
00:05:16here in the middle east in about fourth
00:05:18oh there you are
00:05:21around this time the people of suma decided to give one his independence
00:05:26they stopped scratching on a bone and set him free
00:05:31by representing him as a token
00:05:37this transformation
00:05:40changed not only one's life
00:05:42but the course of history
00:05:49the invention of tokens allowed the Sumerians to do something that nobody had done before
00:05:55if you add notches to a stick or a bone you can do just that
00:05:59add
00:06:00but with tokens you can take away
00:06:03so say you've got six chickens and you eat five of them
00:06:11look what you've got
00:06:15indigestion
00:06:16no no no no no no
00:06:17you've invented arithmetic
00:06:20it was the biggest breakthrough in one's life so far
00:06:23but why did it happen here
00:06:26to find out we have to go somewhere where it didn't
00:06:37meet the walpui of central australia
00:06:40they're people who've been minding their own business here for 30,000 years or so
00:06:45until some anthropologists came along and noticed that they didn't use numbers
00:06:53people get very interested in warping
00:06:56because in our language we don't use numbers
00:07:00we have a word for one
00:07:01but that's about it
00:07:06until recently the walpui have got by without using numbers
00:07:10how on earth have they been able to manage
00:07:15the things that you do in your world are done differently here
00:07:19take up Jabalderi here
00:07:20he never grew up with any numbers at all
00:07:25but
00:07:26we're talking about
00:07:28no
00:07:28what they did
00:07:30what they did
00:07:30they did
00:07:30what they did
00:07:32what they did
00:07:32they did
00:07:33they did
00:07:34They did
00:07:39Jabalderi names his grandchildren
00:07:41what he doesn't say is four
00:07:43it's just not in his vocab
00:07:45yeah
00:07:46On
00:07:50older generation walkyrie
00:07:51don't talk in terms of exact times of day, just the position of the sun.
00:07:58They don't even deal in distances because their land is mapped out
00:08:01not with numbers but with songs, which contain all the information they need.
00:08:07These timeless songs, deeply rooted in their culture,
00:08:10are a source of huge national pride.
00:08:23The fact is, in traditional Walpuri life,
00:08:26they didn't really need a number system, let alone arithmetic.
00:08:34So why, on the other side of the world, 6,000 years ago,
00:08:38did the people of Sumer feel the need to turn one into a token and invent maths?
00:08:51What was so different about life in the Middle East?
00:08:54I mean, why were people here so keen to get into maths, of all things?
00:08:58Maybe it was because there were so many people living in the same place.
00:09:06Unlike the Walpuri, the Sumerians lived in cities.
00:09:10And cities need organising.
00:09:13Grain had to be stored and distributed.
00:09:15And working out how much each person should get required arithmetic.
00:09:22That's why the Sumerians turned one into cone-shaped tokens.
00:09:27Tokens made possible the arithmetic required to assess wealth,
00:09:31calculate profits and loss, and, more important perhaps, collect taxes.
00:09:37Yes, you can blame the invention of maths on city life.
00:09:46The ability to do arithmetic wasn't the only thing the Sumerians needed for their civic programmes.
00:09:53They also needed to be able to keep a permanent record of their calculations.
00:09:57But, hold on, the written word hasn't been invented yet.
00:10:01Numbers, it seems, were the world's first writing.
00:10:07It happened like this.
00:10:10Specific numbers of cones would be put into clay envelopes for safekeeping, and then sealed up.
00:10:18But, once you'd sealed the envelope, how could you remember how many cones it contained?
00:10:22Hmm, bit of a problem, that.
00:10:25But, wait a minute.
00:10:27They took another cone and made the same number of impressions on the outside of the envelope as there were
00:10:33cones inside.
00:10:36Then, some bright spark realised you didn't need the envelopes in the first place.
00:10:41In fact, you didn't even need the cones.
00:10:43You could just make the marks straight onto a clay tablet, and, hey presto, you had a record of the
00:10:49number.
00:10:50The notion of writing had been born.
00:10:57Sumerian mathematicians were now able to keep permanent records of their calculations, and these could become more complex than ever
00:11:04before.
00:11:08Only a select few were initiated into the mysteries of numbers, and they were trained from childhood.
00:11:14They became a powerful and highly paid elite that we still pay homage to today.
00:11:20That's right, the Sumerians' great gift to the world.
00:11:24The Chartered Accountant.
00:11:35Juan was now disciplined and organised as never before.
00:11:41He became a powerful tool.
00:11:44One that could be used to build empires.
00:11:48Which is precisely what happened to Juan in his next incarnation.
00:12:00They needed him to help out on the building site.
00:12:06The ancient Egyptians were enthusiastic builders, with a keen eye for beauty.
00:12:11But you can't create beautiful buildings without measuring things accurately.
00:12:15And you can't measure accurately unless you know what your unit is.
00:12:19That is, what you mean by Juan.
00:12:25In solving this problem, the Egyptians would do something nobody had done before.
00:12:31They defined their own version of Juan.
00:12:36They based it on the length of a man's arm, from elbow to fingertips, plus the width of his palm.
00:12:47One was now known as the cubit, the measure of everything.
00:12:52The undisputed ruler.
00:13:05These official wands, the master cubit sticks, were so important, they were jealously guarded in the temples.
00:13:12From them, copies were made and given out.
00:13:15So, right across the empire, whatever the building project, everyone knew what they meant by Juan.
00:13:22And with this simple measuring stick, the Egyptians were able to complete their vast construction projects with astonishing accuracy.
00:13:32If Juan hadn't become the cubit, some of the wonders of the world might have been, well, a little less
00:13:39wondrous.
00:13:47By transforming Juan from counting things to measuring things,
00:13:51the ancient Egyptians hadn't just opened up a whole new world of bespoke tailoring and fitted carpets.
00:13:58They had made Juan the measure of all things.
00:14:02Juan had become the ruler.
00:14:04But its destiny was even more special.
00:14:07Juan was about to become the essence of the universe.
00:14:28It all began about two and a half thousand years ago in ancient Greece,
00:14:33well, modern Greece as it then was, because of a chap by the name of Pythagoras.
00:14:38Pythagoras.
00:14:39Didn't he have a theory or something?
00:14:41The square of the hypotenuse in a right-handle triangle is equal to the sum of the...
00:14:50That's right, Pythagoras' theorem.
00:14:53Bit of a bore, I never quite understood it.
00:14:55Well, actually, I think that Pythagoras was a pretty interesting bloke.
00:14:59Oh, yeah?
00:15:00He had a school in which all his pupils had to give up their worldly possessions,
00:15:05eat only vegetables, and swear never to touch beans.
00:15:08Why on earth not?
00:15:10Pythagoras believed that when you fart, a bit of your soul escaped.
00:15:17Amazing what you learn in schools nowadays, isn't it?
00:15:22It's true that Pythagoras was a little, well, weird's about the only word for it.
00:15:27He studied in Egypt in the Middle East, and on his return home, set up his vegetarian school of math.
00:15:33Here, he devoted himself to exploring the wonders and mysteries contained in numbers.
00:15:39Pythagoras was the first man to come up with the idea of odd and even numbers,
00:15:43and he gave them sexes.
00:15:45One was male, two was female, and so on.
00:15:48He also had a thing about whole numbers, collections of ones.
00:15:52He realised that certain whole numbers make pleasing shapes.
00:15:56Three makes a triangle, four a square.
00:15:59One plus two plus three plus four makes ten, which forms a magic triangle.
00:16:04One plus three makes a triangle, and so on.
00:16:07Pythagoras was also convinced that one would eventually help explain
00:16:11one of the fundamental philosophical questions of the day.
00:16:15The Greek philosophers were forever trying to find out the one thing that everything is made of.
00:16:21One philosopher said everything's made of fire, another air, another water.
00:16:27Pythagoras said that everything was made of numbers, including music.
00:16:35To find out what Pythagoras meant, I've come to the Waterbury Garden Centre in Oxfordshire.
00:16:41Oh, thank you very much.
00:16:43All I need now is a mathematician.
00:16:46Oh, I'm a mathematician.
00:16:47Oh, what a bit of luck.
00:16:49But if you want to find out about Pythagoras' music and maths,
00:16:52we're going to need some pots of rather different sizes.
00:16:55Oh, good luck.
00:16:57Perfect.
00:17:00Pythagoras wanted to understand why certain combinations of notes
00:17:04sound is so beautiful and harmonious.
00:17:06So if we play a pot, we get a note.
00:17:10La.
00:17:11But if I combine it with the note of this pot,
00:17:15La.
00:17:16It's rather a bad combination.
00:17:18Let's listen to them together.
00:17:21Yes, that doesn't work at all, does it?
00:17:23But if I play this pot here,
00:17:25La.
00:17:27La.
00:17:28That's a beautiful combination.
00:17:29Let's hear them together.
00:17:32But why is it such a beautiful combination?
00:17:34And the answer is mathematics.
00:17:36The relationship between the weights of these pots
00:17:38is in a perfect one to two relationship.
00:17:41And it's that combination of whole numbers
00:17:43which makes this such a nice sound.
00:17:45As opposed to the first pot,
00:17:48this is sort of a one to one point two six four,
00:17:51not a nice whole number relationship,
00:17:53which is causing the bad sound.
00:17:55So Pythagoras is saying that the harmonies
00:17:58are combinations of whole numbers.
00:18:00That's right.
00:18:01Numbers of the collections of wands.
00:18:02Pythagoras realised that these whole numbers
00:18:04are really why things sound so beautiful.
00:18:07And it excited him so much
00:18:08he realised that really mathematics
00:18:09was the base of everything.
00:18:12That it would explain musical harmony
00:18:13and the cosmos.
00:18:15And this is why he coined the phrase
00:18:16the music of the spheres.
00:18:18So shall we?
00:18:19Oh, I don't see why not, yes.
00:18:28If the beauty of music relied on whole numbers,
00:18:31as Pythagoras reckoned,
00:18:32so too must everything.
00:18:40And since whole numbers are collections of wands,
00:18:44one must be the essential material
00:18:46out of which the universe is constructed.
00:18:52One had never been so admired.
00:18:58But ultimately,
00:18:59Pythagoras' whole belief system was doomed.
00:19:03And ironically,
00:19:04it was the triangle that made him famous,
00:19:06which was to prove his undoing.
00:19:15If one was at the heart of everything,
00:19:18it should also be at the heart of every triangle,
00:19:22even the right-angled triangle
00:19:23with two equal sides.
00:19:30Pythagoras kept trying to make all three sides
00:19:33an exact number of units,
00:19:34but it just couldn't be done.
00:19:41When one of his disciples tried to point this out,
00:19:45the others drowned him.
00:19:48Pythagoras' whole belief system
00:19:50that the world was made up of units
00:19:52was a lie.
00:20:09Poor old Pythagoras,
00:20:11brought down by his own favourite geometrical shape.
00:20:16One, however,
00:20:17was about to embark upon a new career.
00:20:19Only, first,
00:20:21he would have to become a little less real.
00:20:28Like everyone else before him,
00:20:30Pythagoras couldn't conceive of numbers
00:20:33unless they represented actual things.
00:20:35A one was not a one
00:20:37unless it stood for one chair
00:20:39or one step
00:20:40or one television presenter.
00:20:42But the mathematicians
00:20:44who followed Pythagoras
00:20:45broke three of these constraints.
00:20:48Yep, Archimedes,
00:20:50famous today as the world's first streaker,
00:20:52but in fact,
00:20:53the greatest mathematician of ancient times.
00:21:00Archimedes just loved playing games with numbers,
00:21:03and he took mathematics
00:21:05into the realm of the unimaginable
00:21:07because in these games,
00:21:09he allowed numbers
00:21:10to do impossible things,
00:21:13like working out
00:21:14how many grains of sand
00:21:15you'd need
00:21:15to fill the universe.
00:21:17And yet daft,
00:21:18as some of these mathematical games may seem,
00:21:21they sometimes came up
00:21:22with practical results
00:21:23that we benefit from to this day.
00:21:26For example,
00:21:28he was obsessed
00:21:29with what would happen
00:21:30if you took a sphere
00:21:31and turned into a cylinder.
00:21:33What would be the difference
00:21:34in area covered?
00:21:36Well, personally,
00:21:37I don't give a fig.
00:21:38But for Archimedes,
00:21:39it was the proudest moment
00:21:41of his life
00:21:41when he finally succeeded
00:21:43in working out the formula.
00:21:45And although it was
00:21:46a piece of pure mathematical bravado,
00:21:48it did actually prove
00:21:49to be amazingly useful in the end
00:21:51because, thanks to Archimedes,
00:21:54later mapmakers
00:21:55could take the globe
00:21:56and turn it into a flat map.
00:22:00One was no longer
00:22:02the essence of the universe,
00:22:03but he was helping
00:22:04to create a golden age
00:22:06of theoretical mathematics.
00:22:13But a new force
00:22:14was at large
00:22:15in the world
00:22:16and one
00:22:17was about to be dominated
00:22:18by a people
00:22:19who had
00:22:20rather different
00:22:29obsessions.
00:22:30Archimedes lived in Syracuse
00:22:32and when the Romans
00:22:33invaded in 212 BC,
00:22:36he was in the middle
00:22:36of a particularly gripping
00:22:38piece of calculation.
00:22:39In fact,
00:22:39he was so wrapped up
00:22:40in his work
00:22:41that all he could say
00:22:42was,
00:22:42I beg you,
00:22:44do not disturb this.
00:22:49Perhaps not a wise move.
00:22:56It was the end
00:22:57of theoretical mathematics
00:22:59in the classical world.
00:23:00The Romans weren't interested
00:23:02in airy-fairy abstractions
00:23:04like how to calculate
00:23:06the weight
00:23:07of all the goats
00:23:07who ever lived.
00:23:08They were interested
00:23:09in power.
00:23:12Whether he liked it
00:23:13or not,
00:23:14one was now
00:23:15a servant of Rome.
00:23:20He had to leave
00:23:21the dizzy world
00:23:22of abstract mathematics
00:23:23behind him
00:23:24and get on
00:23:25with more
00:23:25practical concerns.
00:23:33Why?
00:23:36He became the backbone
00:23:37of the Roman world
00:23:38as the Romans
00:23:39used him to impose
00:23:40a rigid numerical grid
00:23:42on their army.
00:23:44There were 10 men
00:23:46in a section
00:23:49and 10 sections,
00:23:50100 men,
00:23:51were called
00:23:52a century.
00:23:57Two centuries
00:23:58were called
00:23:59a manipulus,
00:24:00which means literally
00:24:01a handful,
00:24:02which I imagine
00:24:03200 Roman soldiers
00:24:04probably were.
00:24:08Even punishments
00:24:09were dealt out
00:24:10on numerical principles.
00:24:11If a legion
00:24:12suffered a humiliating defeat,
00:24:14the entire legion
00:24:15was decimated
00:24:16from the Latin word
00:24:18for ten,
00:24:18decen.
00:24:19Regardless
00:24:20of individual guilt,
00:24:22one soldier
00:24:23in ten
00:24:23was killed.
00:24:26Ooh!
00:24:28Ooh!
00:24:31Ooh!
00:24:32Ooh!
00:24:32Ooh!
00:24:35The great aim
00:24:36of the Roman world
00:24:37was to keep things
00:24:38kicking over.
00:24:39Theoretical mathematics
00:24:40just wasn't them.
00:24:44Mark you,
00:24:45I'm not surprised.
00:24:46I mean,
00:24:46the Roman numerals
00:24:47don't exactly make it easy,
00:24:49do they?
00:24:49I mean, look at them.
00:24:50They're just an elaboration
00:24:52of the old notches
00:24:52on a bone,
00:24:53the only sophistication
00:24:55being new symbols
00:24:56as the numbers
00:24:57get more unwieldy.
00:24:58V for five,
00:24:59X for ten,
00:25:00C for a hundred,
00:25:01up to their symbol
00:25:02for a million.
00:25:03But it's still
00:25:04just a simple
00:25:05counting system,
00:25:07fine for writing
00:25:08inscriptions on tombs,
00:25:09but not much cop
00:25:10for the complications
00:25:11of theoretical maths.
00:25:12Well, you try writing
00:25:14a billion like that.
00:25:15In modern numerals,
00:25:17it takes me about
00:25:18eight seconds.
00:25:18I tried it.
00:25:19In Roman numerals,
00:25:20it would take something
00:25:21like 16 minutes.
00:25:25It's no surprise, then,
00:25:27that Roman numerals
00:25:28weren't even used
00:25:29for calculating.
00:25:30The actual calculating
00:25:32had to be done
00:25:33on a counting board,
00:25:34an early version
00:25:35of an abacus.
00:25:41The numerals themselves
00:25:43were just used
00:25:44for recording the results.
00:25:47Maybe it's no coincidence
00:25:48that, unlike the Greeks,
00:25:50not a single Roman
00:25:51mathematician
00:25:51is celebrated today.
00:26:02As Roman power spread,
00:26:04so, too,
00:26:05did its numeral system.
00:26:08Over the next 500 years,
00:26:10all of Europe,
00:26:10from Spain to Turkey,
00:26:12came under Roman control.
00:26:14And even when their
00:26:16empire eventually crumbled,
00:26:18their numerals
00:26:19were left standing.
00:26:24But though the Roman system
00:26:26might have seemed
00:26:26indestructible,
00:26:28it wasn't.
00:26:29its nemesis
00:26:30came from the east,
00:26:31to be precise,
00:26:32from India,
00:26:33in 500 A.D.,
00:26:35to all thereabouts.
00:26:46One had an Indian cousin,
00:26:48who for some time
00:26:49had been living
00:26:50in a more rarefied atmosphere.
00:26:59The Indians
00:27:00seemed to have been
00:27:01less concerned
00:27:02about military organisation
00:27:03than about renouncing
00:27:05the world
00:27:05and finding enlightenment.
00:27:09But Nirvana
00:27:10isn't just down the road.
00:27:12To reach it
00:27:12is a very,
00:27:14very long journey,
00:27:15which takes
00:27:15a very,
00:27:16very long time.
00:27:18And to convey
00:27:19that fact,
00:27:20the Indians
00:27:20came up with
00:27:21with some stupendously
00:27:23big numbers.
00:27:28Take a Raju,
00:27:30for example.
00:27:31A Raju is the distance
00:27:33covered by God
00:27:33in six months
00:27:35if he travels
00:27:36a million kilometres
00:27:38in every blink
00:27:40of his eyelid.
00:27:43Or how about
00:27:44a pallia?
00:27:45A pallia
00:27:45is the length
00:27:46of time
00:27:47it would take me
00:27:47to build
00:27:48a cube of lambswool
00:27:49ten kilometres high
00:27:51if I were to lay
00:27:52one strand
00:27:53every century.
00:27:55Here's one
00:27:56I made earlier.
00:28:00Well,
00:28:01these were the sort
00:28:02of numbers
00:28:03that could have
00:28:03made one feel,
00:28:05well,
00:28:05small
00:28:06if he hadn't
00:28:08had a little help
00:28:09from his friends.
00:28:15Unlike the Romans,
00:28:16the Indians
00:28:17devised a system
00:28:18that could cope
00:28:19with vast numbers.
00:28:20they developed
00:28:21a different symbol
00:28:22for every number
00:28:23from one to nine.
00:28:25One,
00:28:26two,
00:28:28three.
00:28:29Or if you do them
00:28:30quickly,
00:28:31you get
00:28:32Arabic numerals.
00:28:40It's right,
00:28:42you know.
00:28:44The numbers
00:28:45we use today
00:28:46are called Arabic,
00:28:47but in fact
00:28:48they began life
00:28:49here in India
00:28:50as early
00:28:51as 500 B.C.
00:28:54But then,
00:28:55around 1,500
00:28:56years ago,
00:28:57or a little longer
00:28:57if you're watching
00:28:58a repeat of this
00:28:59programme,
00:29:00someone came up
00:29:01with a stupendous,
00:29:03incredible,
00:29:04extraordinary idea.
00:29:05The biggest revolution
00:29:07in numbers
00:29:07since the Sumerians
00:29:09invented maths,
00:29:10a creation
00:29:11that would
00:29:12change the world.
00:29:13they invented
00:29:15an entirely new number.
00:29:19And it's in here,
00:29:22inside this tiny,
00:29:241,100-year-old temple
00:29:25in Gwalior,
00:29:26northern India,
00:29:27is this new number.
00:29:30And after a 4,000-mile journey,
00:29:33I'm finally going to get to see it.
00:29:41Nick,
00:29:42it's locked.
00:29:50So we wait.
00:29:51And while we wait,
00:29:53I start to wonder,
00:29:54how was it
00:29:56that this new number
00:29:57wasn't invented sooner?
00:29:59It's such a simple
00:30:01little number
00:30:02that takes only a moment
00:30:03to say
00:30:04and even less to write.
00:30:07Ah, here he is.
00:30:09But once invented,
00:30:11it transformed
00:30:12the life of one
00:30:13in a way
00:30:14that would eventually
00:30:15change the entire world.
00:30:21Well, here we are.
00:30:23The first undisputed example
00:30:25of India's greatest invention,
00:30:27the new number,
00:30:30the holy grail of numbers.
00:30:34Zero.
00:30:35For the first time
00:30:36in human history,
00:30:38someone had made
00:30:39nothing a number.
00:30:43The inscription says
00:30:45that a garden was planted
00:30:47to produce flowers
00:30:48for the temple.
00:30:50And to ensure
00:30:51that they had enough,
00:30:52that garden
00:30:53had to be 187
00:30:55by 270 hastings.
00:30:57about 20 acres.
00:31:00Well, while the Romans
00:31:01were using numbers
00:31:02to record their conquests
00:31:04and count dead bodies,
00:31:06these people
00:31:07were using them
00:31:08to make sure
00:31:09they had adequate supplies
00:31:10for their flower arrangements.
00:31:14You might say,
00:31:15what's all the fuss about?
00:31:16I mean,
00:31:16what's so wonderful
00:31:17about inventing a symbol
00:31:19that means nothing?
00:31:20I mean,
00:31:21if somebody asks me
00:31:21how much I've got in my hand,
00:31:23I can just say,
00:31:23well, I haven't got anything
00:31:24in my hand.
00:31:25I don't need a zero
00:31:26to do that.
00:31:30Well, a zero on its own
00:31:31would be nothing,
00:31:32well, obviously.
00:31:34But when you teamed
00:31:35zero up with one,
00:31:36magic started to happen.
00:31:45And when they were joined
00:31:47by the rest of the troop,
00:31:48the results were spectacular.
00:31:50With just 10 digits,
00:31:52the Indians could make numbers
00:31:53infinitely large,
00:31:57as well as infinitely small.
00:32:01Now, the Romans
00:32:02couldn't do that.
00:32:05One had found
00:32:06his perfect mate in zero,
00:32:08and it was a partnership
00:32:09that was going to change the world.
00:32:16Together with the rest of the team,
00:32:17they enabled Indian science
00:32:19to storm ahead.
00:32:21Indian astronomers,
00:32:23for example,
00:32:23were centuries ahead
00:32:25of the Christian worlds.
00:32:33Indian scientists
00:32:34worked out
00:32:34that the Earth
00:32:35spins on its axis
00:32:37and that it moves
00:32:38around the sun,
00:32:40something that
00:32:41over Europe,
00:32:42Copernicus,
00:32:43wouldn't figure out
00:32:43until a thousand years later.
00:32:48Indian scientists
00:32:49also calculated
00:32:50the diameter of the globe,
00:32:52and they were less than
00:32:531% off
00:32:54what it actually is.
00:32:57All this was possible
00:32:59because of one,
00:33:00zero,
00:33:01and the rest of the troop
00:33:02of performing numbers.
00:33:07They were a sensation,
00:33:09and their fame
00:33:10soon began to spread
00:33:11across the globe.
00:33:15A conflict
00:33:16with the numbers of Rome
00:33:17was bound to happen
00:33:19sooner or later,
00:33:20but for now,
00:33:21one and zero
00:33:22and their friends
00:33:23made their way
00:33:24across the deserts
00:33:25of Arabia
00:33:25to take on
00:33:26one of the most
00:33:27sophisticated societies
00:33:29of the age
00:33:30in what is now
00:33:31Iraq.
00:33:40When Islam
00:33:41was little more
00:33:42than 100 years old,
00:33:43Baghdad was ruled
00:33:45by the great caliph
00:33:46Al-Mansur.
00:33:49Now,
00:33:49the caliph
00:33:50wished his people
00:33:51to live according
00:33:51to the Quran,
00:33:52so he set up courts
00:33:54and judges
00:33:54to apply the law
00:33:56of the prophet.
00:34:01Now,
00:34:02the law of the prophet
00:34:03is full of instructions
00:34:05that require
00:34:05serious mathematical
00:34:07calculations
00:34:08if they are to be
00:34:09carried out exactly.
00:34:14For example,
00:34:15unlike Christianity,
00:34:16the Quran insists
00:34:18that women
00:34:19share in any
00:34:20inheritance.
00:34:21The book says
00:34:22there is a share
00:34:23for men
00:34:23and a share
00:34:24for women,
00:34:25each share
00:34:26depending on
00:34:27the number
00:34:27of other relatives
00:34:28and their relation
00:34:28to the deceased.
00:34:30Working all that out
00:34:31required fractions
00:34:32and ratios,
00:34:34but these were people
00:34:35who counted
00:34:36on their fingers.
00:34:39It's not like
00:34:40they weren't up
00:34:40to complex arithmetic,
00:34:41it was just
00:34:42their number system
00:34:43was holding them back.
00:34:49But one day,
00:34:50there arrived
00:34:51in the court
00:34:52an ambassador
00:34:53from India.
00:34:55He had to present
00:34:56the great caliph
00:34:57with a gift
00:34:57of some sort.
00:34:58But the caliph
00:34:59was a man
00:35:00of infinite riches.
00:35:01It was hard
00:35:02to know
00:35:03what to give.
00:35:04I mean,
00:35:04an I Love India
00:35:05t-shirt
00:35:06was hardly going
00:35:06to do the job.
00:35:08The ambassador,
00:35:09however,
00:35:10had thought long
00:35:10and hard about this
00:35:11and had decided
00:35:12to present the caliph
00:35:13with the greatest
00:35:14gift he could think
00:35:15of.
00:35:16The gift
00:35:17of numbers.
00:35:38Actually,
00:35:39we don't know
00:35:40for certain
00:35:40exactly how
00:35:41Indian numerals
00:35:42came to be adopted
00:35:43in the Islamic world,
00:35:44but the ambassador story
00:35:46is my favourite.
00:35:57What we do know
00:35:58is that Muslim scholars
00:35:59were bowled over
00:36:00by one,
00:36:01zero,
00:36:01and the rest
00:36:02of the truth.
00:36:03And the most famous
00:36:04of these scholars
00:36:04was a man
00:36:05by the name
00:36:06by the name
00:36:06of Al-Qwarizmi.
00:36:07Al-Qwarizmi.
00:36:08Al-Qwarizmi.
00:36:11Al-Qwarizmi.
00:36:12Al-Qwarizmi.
00:36:12Al-Qwarizmi.
00:36:14That's right.
00:36:16Thanks.
00:36:21Al-Qwarizmi and his colleagues
00:36:23taught the performing numerals
00:36:25a whole host
00:36:27of brand new tricks.
00:36:30Quadratic equations.
00:36:33Algebra.
00:36:37Reversed logarithmic cubic cake handstands.
00:36:41Well, okay, I made that last one up.
00:36:43But these new numerical feats
00:36:45enabled science, mathematics,
00:36:47and astronomy
00:36:48to reach new heights
00:36:50in the Middle East.
00:36:51And the Indian troop
00:36:52became a smash hit
00:36:53throughout the Islamic world.
00:36:56But on the other side
00:36:57of the Mediterranean,
00:36:59Christian Europe
00:36:59was still in the static grip
00:37:01of the old army
00:37:02of Roman new ones.
00:37:04And being Romans,
00:37:05they weren't going to give way
00:37:07to the feisty newcomers
00:37:08that easily.
00:37:09A showdown
00:37:10between the two systems
00:37:11was inevitable.
00:37:13And when it came,
00:37:14it would shape the destiny
00:37:16of the Western world.
00:37:23The beginning of the end
00:37:25for the Roman numerals
00:37:26started on the shores
00:37:27of North Africa.
00:37:36Muslim traders
00:37:37had been quick
00:37:37to adopt one, zero, and co
00:37:39for their business dealings.
00:37:41By the end
00:37:42of the 12th century,
00:37:43the Indian numerals
00:37:44were in common use.
00:37:47And it was
00:37:48in the bustling port
00:37:50of Bidjaya
00:37:50that the young son
00:37:52of an Italian diplomat
00:37:53based in Algeria
00:37:54first witnessed
00:37:56their amazing act.
00:38:11When I had been introduced
00:38:13to the art
00:38:14of the Indian's nine symbols,
00:38:17knowledge of the art
00:38:18very soon pleased me
00:38:19more than anything else.
00:38:21And I came to understand it.
00:38:33That young man
00:38:34was known as
00:38:35Fibonacci
00:38:36and he was so
00:38:37knocked out
00:38:37by the Indian numerals
00:38:38that when he grew up,
00:38:40he decided
00:38:41to take them home.
00:38:45In 1202,
00:38:46Fibonacci wrote a book
00:38:48all about calculation
00:38:49called, well,
00:38:50the book of calculation.
00:38:52He's now regarded
00:38:53as one of the greatest
00:38:55mathematicians of all time
00:38:56and his book
00:38:57was pretty much
00:38:58a showcase
00:38:59for Indian numbers.
00:39:02Fibonacci wasn't just
00:39:03an ivory tower theorist.
00:39:05Part of his book
00:39:06of calculations
00:39:07was aimed
00:39:08specifically at merchants,
00:39:10showing them
00:39:10how useful Indian numerals
00:39:12could be for, say,
00:39:13calculating their profits.
00:39:16Not exactly a page-turner,
00:39:18you might think,
00:39:18but this was a time
00:39:20when capitalism
00:39:21was beginning
00:39:21to come out
00:39:22into the open
00:39:23in Europe.
00:39:24Fibonacci's book
00:39:24was a must-read.
00:39:31Unfortunately,
00:39:33ordinary people
00:39:33felt comfortable
00:39:34with the old numbers.
00:39:37After all,
00:39:37they'd lived with them
00:39:38for the best part
00:39:39of a thousand years.
00:39:42The old Roman numerals
00:39:44weren't going
00:39:44to make it easy
00:39:45for the Indian newcomers.
00:39:56And it wasn't
00:39:57just a question
00:39:58of tradition.
00:39:59Your average punter
00:40:00had some pretty good reasons
00:40:01to prefer the old system.
00:40:03For example,
00:40:04many medieval Italian cities
00:40:05had their own currency.
00:40:07So every time
00:40:08I found myself
00:40:09as a new town
00:40:10or a new set
00:40:11with extras
00:40:12and costumes
00:40:13in the case, maybe,
00:40:13I have to go
00:40:14to the money changer's
00:40:15bench,
00:40:16or banker,
00:40:17as it's called.
00:40:17A banker
00:40:18was a counting table,
00:40:20basically an abacus
00:40:21with counters
00:40:21instead of beads.
00:40:23The men
00:40:23who operated them,
00:40:24the bankers,
00:40:26had to swear an oath
00:40:27not to cheat
00:40:28their customers.
00:40:30Mind you,
00:40:30if the magistrate
00:40:31find he is cheating me,
00:40:32they'll come
00:40:33and break his bench
00:40:34because banker
00:40:35will be ruptor,
00:40:37which is the word
00:40:37for broken,
00:40:38and he'll be declared
00:40:39banker ruptor,
00:40:40which is where we get
00:40:41the word bankrupt from.
00:40:42Hi.
00:40:43Now,
00:40:44how much can I get those
00:40:46in whatever place this is?
00:40:50Well, he's counting it now.
00:40:52It's reassuring to see
00:40:53he's using numerals
00:40:54I'm familiar with,
00:40:55which are Roman numerals,
00:40:56of course,
00:40:57and he's using this abacus,
00:40:58so at least I can see
00:40:59what he's doing.
00:41:00And I get that much.
00:41:01Oh, right, fine.
00:41:02Well, thanks a lot.
00:41:04Nice doing business with you.
00:41:06But what if I was
00:41:07to go over
00:41:07to one of the smart chaps
00:41:09using the newfangled
00:41:10Indian numerals?
00:41:14Hi.
00:41:15Now, how much will you
00:41:16give me for that?
00:41:22Now, you see,
00:41:23this is the problem.
00:41:25You see,
00:41:25as a medieval punter,
00:41:26I've got no idea
00:41:27what he's writing.
00:41:29I mean,
00:41:29no wonder people
00:41:30were suspicious.
00:41:30I mean,
00:41:31if my bank started
00:41:32keeping my accounts
00:41:33in Chinese,
00:41:33I'd be suspicious.
00:41:35Oh, thanks.
00:41:36I've got no idea
00:41:38how you arrived at that.
00:41:39But thanks anyway.
00:41:41This distrust
00:41:42went right to the top.
00:41:44In 1299,
00:41:46the city of Florence
00:41:47actually banned merchants
00:41:49from using
00:41:49the new numbers
00:41:51and accounts.
00:41:52They had to use
00:41:52Roman numerals.
00:41:56But no number
00:41:57was treated
00:41:58with more suspicion
00:41:59than one's partner
00:42:00zero.
00:42:02One writer called
00:42:03zero a sign
00:42:04which creates
00:42:05confusion and difficulties.
00:42:12Zero was called
00:42:13cipher,
00:42:14and it was regarded
00:42:15with such suspicion
00:42:16that that word
00:42:17became our word
00:42:19for secret code,
00:42:20a cipher.
00:42:22But the days
00:42:23of the old system
00:42:24were numbered.
00:42:25I suppose you could
00:42:26blame good old
00:42:27human greed.
00:42:30The traditionalists
00:42:31who clung to the
00:42:32abacus and Roman numerals
00:42:33had never had to
00:42:35calculate interests
00:42:36on loans
00:42:36because the Catholic
00:42:38church said charging
00:42:39interests on loans
00:42:40was a sin.
00:42:41It was called usury.
00:42:43But come the
00:42:44Reformation,
00:42:45the Protestant churches
00:42:45were more business-friendly
00:42:47and the long-held
00:42:48Christian objections
00:42:49to capitalism
00:42:50seem to,
00:42:51well,
00:42:52disappear.
00:42:55So,
00:42:56in this new
00:42:57money-lending,
00:42:58interest-charging
00:42:59environment,
00:43:00which would prove
00:43:01the more useful?
00:43:02Indian numbers
00:43:03or the abacus?
00:43:05Well,
00:43:06let's find out.
00:43:09On my right,
00:43:10one first-class
00:43:11mathematician.
00:43:12On my left,
00:43:13one first-class
00:43:14abacist.
00:43:16So,
00:43:16supposing I
00:43:17lend someone
00:43:18£10
00:43:19at half a percent
00:43:22interest a month,
00:43:23how much
00:43:24do they owe me
00:43:25at the end of the year?
00:43:27OK?
00:43:28Ready?
00:43:29Steady?
00:43:30Go!
00:43:34Kimmy's been
00:43:35an abacist
00:43:35since she was
00:43:36just 15
00:43:36and is using
00:43:37a modern
00:43:38Soroban model.
00:43:39But just as they
00:43:39did in the 16th century,
00:43:41she's rounding
00:43:42her numbers
00:43:42to the nearest penny
00:43:43as she goes.
00:43:44Let's hope she can
00:43:45round herself up
00:43:46into first place.
00:43:51Marcus is using
00:43:52a pen and paper,
00:43:53so he's working
00:43:53to an eye-popping
00:43:5412 decimal places.
00:43:56He lives in
00:43:57North London
00:43:57with his lovely wife
00:43:58Charlie
00:43:58and three charming
00:44:00children.
00:44:00He's not big,
00:44:02but he is
00:44:05clever.
00:44:07Kimmy has
00:44:07got an answer.
00:44:08Kimmy, what's
00:44:10your answer?
00:44:10£10.60.
00:44:12£10.60.
00:44:13So compound
00:44:14interest after a year
00:44:15would be £10.60
00:44:17and the abacus
00:44:18seems to have
00:44:18got there before
00:44:19the mathematician.
00:44:20Well, I don't want
00:44:20to put a damper
00:44:21on things, but I
00:44:21think that answer
00:44:22is actually wrong.
00:44:23I've got an answer
00:44:25of £10.61.677.76640.35
00:44:31to be precise.
00:44:32I've actually
00:44:33picked up the
00:44:34subtlety of compound
00:44:35interest, which is
00:44:35it's a little bit
00:44:36each month, but it
00:44:37adds up, so I've
00:44:38got this extra
00:44:391.67p.
00:44:43For the medieval
00:44:44businessman, it would
00:44:45mean the difference
00:44:46between making a living
00:44:47and not.
00:44:48Maybe that's why the
00:44:49abacus user looks so
00:44:51miserable.
00:44:53As capitalism gained
00:44:55respectability,
00:44:56calculating interest and
00:44:58compound interest
00:44:59became de rigueur for any
00:45:00self-respecting businessman.
00:45:02And for doing that,
00:45:03even with an abacus,
00:45:05the old Roman system
00:45:06was simply no match
00:45:07for the Indian
00:45:09new rules.
00:45:12So, centuries after
00:45:14Fibonacci had brought
00:45:15them to Europe, the
00:45:16Indian numbers finally
00:45:18outmaneuvered the
00:45:19lumbering old Romans.
00:45:25They were quick and
00:45:26versatile, and with
00:45:28one and zero in the
00:45:29lead, just better at
00:45:30teamwork.
00:45:36When the end came,
00:45:37it was a pushover.
00:45:39The old Roman
00:45:40numerals were at last
00:45:43Bankerupta.
00:45:45But one and zero had
00:45:48even bigger plans for
00:45:49the future, and they
00:45:51didn't include the
00:45:52other numerals.
00:45:57In the meantime, the
00:45:58full troop of Indian
00:45:59numbers took over the
00:46:00Western world.
00:46:03With them, European
00:46:05navigators found it
00:46:06easier to calculate
00:46:07the Latvian, and so
00:46:08dared to cross the
00:46:09great ocean out of
00:46:10sight of land.
00:46:11That's how they
00:46:11stumbled on America.
00:46:14And the new numbers
00:46:15became the vocabulary of
00:46:16modern banking, as we
00:46:17know it.
00:46:18Hello!
00:46:20But there was still
00:46:21plenty of room for that
00:46:22old problem, human
00:46:23error.
00:46:34Columbus thought he'd got to
00:46:36Japan, when in fact he'd
00:46:37got to the West Indies,
00:46:38half the world away.
00:46:42He'd made a mistake.
00:46:43Humans do, which was
00:46:45something one man was
00:46:46determined to stop.
00:46:47It all happened around
00:46:49about 16...
00:46:50Oh, I don't know why I'd
00:46:51bother.
00:46:57Gottfried Wilhelm Leibniz
00:46:59was one of the greatest
00:47:01mathematicians of all time.
00:47:03He set out to rid mankind
00:47:05of the curse of human
00:47:07error.
00:47:13In trying to do this,
00:47:15Leibniz invented something
00:47:16that still affects us every
00:47:18day of our lives.
00:47:19What's more, it's an
00:47:20invention that was to give
00:47:22our old friend Juan the
00:47:23chance to rule the world.
00:47:28Leibniz was convinced that
00:47:30he could eradicate error by
00:47:32inventing a mechanical
00:47:33calculating machine.
00:47:35And in fact, he built one
00:47:36using all the numerals from
00:47:38zero to nine.
00:47:39But then, he had a better
00:47:41idea.
00:47:42And it was one that was
00:47:43inspired by his philosophy.
00:47:47It is true that as the
00:47:49empty voids and dismal
00:47:51wilderness belong to zero,
00:48:01so the spirit of God and
00:48:04his light belong to the
00:48:05all-powerful one.
00:48:07In other words, to paraphrase
00:48:10Leibniz very, very, very loosely,
00:48:11the universe is a bit like a
00:48:14Swiss cheese, which some of us
00:48:16have suspected for years.
00:48:18The holes are just as important
00:48:21as the cheese itself.
00:48:23So to construct the world, you
00:48:25need both something, good old
00:48:26number one, and also lots of
00:48:29nothing, which is where zero
00:48:31comes in.
00:48:34Leibniz was convinced that
00:48:36one and zero were the only
00:48:39numbers that anyone really
00:48:40needed.
00:48:44With these two numbers, he
00:48:46claimed, he could achieve
00:48:47every mathematical dream and,
00:48:50what's more, eliminate human
00:48:52error.
00:48:53So he got rid of the other
00:48:55numbers and developed a system
00:48:57using just ones and zeros.
00:49:01It's called the binary system.
00:49:05Wait a minute.
00:49:06How could you possibly express
00:49:08all numbers just with a one and a
00:49:11zero?
00:49:12I think it's time I spoke to
00:49:14someone who knows what he's
00:49:15talking about.
00:49:17Marcos!
00:49:19I need to understand the
00:49:20binary system.
00:49:22Binary.
00:49:23OK, let me give you a number in
00:49:24binary.
00:49:24OK.
00:49:25Here is the number nine written
00:49:27in binary.
00:49:28So this is just using ones and
00:49:30zeros to express any number?
00:49:32It's just zeros and ones.
00:49:33So that's nine in binary.
00:49:35Well, it looks like a thousand and
00:49:36one to me.
00:49:37That's because you're obsessed with
00:49:39your ten fingers and you like to
00:49:40keep track of things in tens.
00:49:42Well, this one keeps track of how
00:49:44many ones, the second column of
00:49:45how many tens there are, next
00:49:47how many hundreds and one lot of
00:49:49a thousand.
00:49:50But in binary, things work rather
00:49:52differently.
00:49:52In binary, what the columns keep
00:49:54track of is how many ones, how
00:49:57many twos, how many fours and how
00:49:59many eights there are.
00:50:00Here we have an egg.
00:50:02We're only allowed to represent
00:50:03these numbers using zeros and
00:50:05ones.
00:50:05OK, so we're only allowed either to
00:50:07put an egg in or not have an
00:50:09egg.
00:50:09An egg in is one.
00:50:10An egg represents one.
00:50:12So let me show you what nine is in
00:50:14binary.
00:50:14One lot of eight.
00:50:15So I have an egg in the fourth
00:50:17column.
00:50:17That's a one.
00:50:18Yeah, that's one lot of eight in the
00:50:20fourth column.
00:50:21And nine is eight plus one.
00:50:23So I need a one in the ones column.
00:50:26So in binary, the number nine is one
00:50:31lot of eight, no fours, no twos, and one
00:50:34one.
00:50:35Amazing.
00:50:37But what about the other numbers?
00:50:39Well, after just three short hours of
00:50:41tuition, I began to see that it was
00:50:43possible, after all, to make every number
00:50:45using just ones and not ones.
00:50:49What's more, I became convinced that you
00:50:51don't need to do it with eggs.
00:50:58It's a sort of mechanical system.
00:51:00It's very mechanical to add the ones and
00:51:02zeros, and that's why it's perfect for a
00:51:04machine.
00:51:04And a machine doesn't really care too much
00:51:06about how big the numbers get.
00:51:08It can keep track of very long numbers,
00:51:10whilst we're not very good at doing that.
00:51:11What it's interested in is a very efficient
00:51:13way of adding numbers.
00:51:15That's why machines love to put numbers
00:51:17into binary.
00:51:20And Leibniz designed exactly such a binary
00:51:24machine.
00:51:25Only his was using metal balls dropping
00:51:27into slots instead of eggs and egg cups.
00:51:31From now on, mistakes would be a thing of
00:51:34the past.
00:51:35The digital age, it seemed, was ready to
00:51:38take over the world.
00:51:42Unfortunately, he never built it.
00:51:51One and zero would have to wait another
00:51:55265 years before they could step into
00:51:58the limelight.
00:52:06Meet Colossus, the world's first working
00:52:09binary computer.
00:52:11It's Leibniz's dream made real.
00:52:14But instead of dropping metal balls into
00:52:16slots, Colossus is electronic.
00:52:20In here, one and zero, something and
00:52:24nothing, have finally come into their
00:52:26element as electrical currents on,
00:52:31and off.
00:52:34Colossus was created during the Second World War
00:52:36and installed here in Britain's code-breaking
00:52:38centre at Bletchley Park.
00:52:40It has 1,200 valves, miles of wires, hundreds of
00:52:45mechanical components.
00:52:50But just like all computers today, the beating heart of this
00:52:54machine is one and zero.
00:52:57In their electronic binary form, one and zero performed millions of rapid calculations, enough to crack the
00:53:05enemy's codes before the Germans had even sharpened their pencils.
00:53:11Thanks to Colossus, the Allies knew what the German messages said, even before Hitler did.
00:53:18And it may be that this extraordinary contraption helped shorten the war by as much as two years.
00:53:26The technology that started here in Bletchley has changed our world forever.
00:53:34You remember all those reasons for using and understanding numbers, doing astronomical calculations, working out measurements, juggling with the divisions
00:53:43of property?
00:53:43Computers can do it, working out percentages, currency exchange rates, compound interest, all that calculation that preoccupied and sometimes perplexed
00:53:55the great minds of antiquity.
00:53:57Just leave it to the computers and we can all simply be happy ignoramuses, not even knowing whether the answer's
00:54:04right or wrong.
00:54:06Well, that's got to be a good thing, isn't it?
00:54:13Terry?
00:54:15Where are you going, Terry?
00:54:19In the computer age, our whole world runs on a stream of ones and not ones.
00:54:26From our bank statements and medical records to the barcode every time I buy a tin of cat food.
00:54:31And the rest of the numbers can be consigned to the dustbin of history.
00:54:37One and zero are all we need.
00:54:40The old performing duo have come out on top.
00:54:50Let's just hope we can control the little blighters.
00:54:53Let's just check those.
00:54:54Oh, yes, yes, yes.
00:54:56Of course, he's going to be the blues.
00:54:57Oh, yeah, yes, yes.
00:55:01Oh, no!
00:55:07Oh, there's nothing else.
00:55:08Oh, there's nothing else from him.
00:55:08Oh, there's nothing else from him.
00:55:10Oh, my.
00:55:11Oh, no.
00:55:13Oh.
00:55:14Oh, oh.
00:55:15Oh, oh, oh.
00:55:16Oh, oh, oh.
00:55:19No!
00:55:20Oh, oh, oh!
00:55:21Uh, oh, no, oh.
00:55:21Oh, no!
00:55:26Oh, oh, oh, oh, oh, oh.
00:55:54Well, I thought I was rather good, didn't you?
00:55:56I thought you were mild.
00:55:57I would, then.
00:55:59I much preferred working with Michael Palin.
00:56:04Why did it happen here?
00:56:06To find out, we have to go somewhere where it didn't.
00:56:17Meet the Walfrey of Central Australia.
00:56:21They're people who've been minding their own business here for 30,000 years or so,
00:56:25until some anthropologists came along and noticed that they didn't use numbers.
00:56:33People get very interested in Walfrey,
00:56:36because in our language, we don't use numbers.
00:56:40We have a word for one, but that's about it.
00:56:46Until recently, the Walfrey have got by without using numbers.
00:56:51How on earth have they been able to manage?
00:56:55The things that you do in your world are done differently here.
00:56:59Take out Jabaljeri here.
00:57:01He never grew up with any numbers at all.
00:57:05He never grew up with any numbers at all.
00:57:08We have died.
00:57:19Jabaljeri names his grandchildren.
00:57:22What he doesn't say is four.
00:57:24It's just not in his vocab.
00:57:30older generation walkyrie don't talk in terms of exact times of day just the
00:57:35position of the Sun they don't even deal in distances because their land is mapped
00:57:41out not with numbers but with songs which contain all the information they
00:57:46need these timeless songs deeply rooted in their culture are a source of huge
00:57:51national pride the fact is in traditional walkyrie life they didn't really need a
00:58:08number system let alone arithmetic so why on the other side of the world 6,000
00:58:18years ago did the people of Sumer feel the need to turn one into a token and
00:58:23invent maths
00:58:31what was so different about life in the Middle East I mean why were people here
00:58:35so keen to get into maths of all things maybe it was because there were so many
00:58:41people living in the same place
00:58:46unlike the walkyrie the Sumerians lived in cities and cities need organizing grain
00:58:53had to be stored and distributed and working out how much each person should
00:58:58get required arithmetic
00:59:02that's why the Sumerians turned one into cone-shaped tokens tokens made possible the
00:59:09arithmetic required to assess wealth calculate profits and loss and more
00:59:13important perhaps collect taxes yes you can blame the invention of maths on city
00:59:26life the ability to do arithmetic wasn't the only thing the Sumerians needed for
00:59:31their civic programs they also needed to be able to keep a permanent record of
00:59:36their calculations but hold on the written word hasn't been invented yet numbers
00:59:42it seems were the world's first writing it happened like this specific numbers of
00:59:51cones would be put into clay envelopes for safekeeping and then sealed up but once
00:59:59you'd seal the envelope how could you remember how many cones it contained bit of a
01:00:04problem that but wait a minute
01:00:07they took another cone and made the same number of impressions on the outside of
01:00:12the envelope as they were cones inside then some bright spark realized but when ever
01:00:24since man could make marks on bones he's been well making marks on bones but what
01:00:32about the fellow who scratched marks like this 150,000 years ago is it
01:00:38possible that he could have been counting could these scratches represent a
01:00:42series of wands well the experts tell us that giving due weight to the
01:00:47scientific and archaeological evidence they haven't a clue what they're now
01:00:55pretty sure about is that one is a lot younger than us it's not until
01:01:02quite recently a mere 20,000 years ago that we get the first really solid
01:01:07evidence that one existed and that someone was using it for counting
01:01:14of course it didn't look like this when he was born back then one was just a
01:01:21scratch on a bone this bone it's known as the ishango bone it was found quite
01:01:32recently in the Congo and look you can see these scratches we know that each
01:01:38represents a one how can we be so certain well someone must have been
01:01:44counting because there's 60 scratches along this edge of the bone and another 60
01:01:49along this edge and on the back they're in equally numbered groups and you
01:01:54can't do that without counting the ishango bone may mark a defining moment for
01:02:00mankind zoologists tell us that other mammals are able to count up to three or even four but
01:02:06not beyond
01:02:13by turning one into a scratch our early ancestors could count to four five six
01:02:20clever clogs in fact they could count any number of ones they wanted
01:02:29the hero of this story is a master of disguise to some people he's appeared as a
01:02:35wedge shape to others as a cone but no matter what shape he may have taken on he's
01:02:47always been number one his story is our story it's a story of struggle of knowledge of where numbers
01:03:04come from we'll see how one helped create the first cities how we helped build empires
01:03:16how he inspired some of the greatest minds in history and we'll also find out his part
01:03:22in making money work as it does
01:03:33so where did one come from well his story begins at the dawn of time three billion forty two thousand
01:03:43six
01:03:44six hundred and fifty nine years ago to the day the first primitive one crawled out of the primordial soup
01:03:52on to dry land
01:03:56yeah
01:03:57yeah
01:03:58yeah
01:04:04yeah
01:04:06yeah
01:04:12not really just joking in fact the origins of one are shrouded in mystery
01:04:22it's a mystery that only our earliest ancestors can answer
01:04:27at some point one of them must have been the first human being to use one to actually count with
01:04:39and that is what gave us the edge over the lions and the tigers from now on counting new no
01:04:46limits
01:04:47one is growing up into a big boy
01:05:06in the meantime human beings were moving up the property ladder and that would change one story forever
01:05:16they stopped living in caves and started to build their own caves houses
01:05:28the next great event in one's life was to happen in the ancient civilization of suma
01:05:34here in the middle east in about fourth oh there you are
01:05:40around this time the people of suma decided to give one his independence
01:05:46they stopped scratching on a bone and set him free by representing him as a token
01:05:56as a token
01:05:57this transformation
01:05:59changed not only one's life
01:06:01but the course of history
01:06:08the invention of tokens allowed the sumerians to do something that nobody had done before
01:06:15if you add notches to a stick or a bone you can do just that add
01:06:19but with tokens you can take away
01:06:22so say you've got six chickens and you eat five of them
01:06:30look what you've got
01:06:34indigestion
01:06:35no no no no no no you've invented arithmetic
01:06:39it was the biggest breakthrough in one's life so far
01:06:42but
01:06:43see
01:06:43what maybe
01:06:43you
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