194. Empire of Numbers: Fibonacci and the Birth of Modern Money

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0:29Hello and welcome to Empire with me, Anita Arnon. And me, William Durimple. Now on this podcast, hello dear friends, you know we talk about a number of empires, but today we're talking about empire of numbers. We are. Good, isn't it? It's quite neat, isn't it? You came up with that all of your own. Yes, and I really didn't, but I just stole it. Okay, look, in the last episode, we were following the story of numbers from India to Baghdad. Today, we're looking at how these ideas, these concepts made their way to Europe. And it's all based on William's brilliant book, The Golden Road, which, of course, you've heard about.

1:08It's everywhere. You're bloody everywhere. Can't turn on a TV or a radio without hearing you talking about it. I have been working hard for the last month on all this. You have been singing for your supper. But look, let's talk about how these concepts, these ideas, these just simply, you know, number breakthroughs changed the world that we recognize today. Exactly. And the story that we've got to tell today is the story of how these Indian numbers, which in the last episode, thanks to first the Barmakids, then Al-Qarizmi, reached first of all Baghdad, and then from there filtered out right across the Islamic world as far as Spain, how those numbers came to be adopted by Europeans.

1:55And it happens very, very late. The big surprise, I hadn't really sort of taken this in, as late as the 1100s, all calculation in Europe was still taking place with sort of MVCCMV1 times XV11XV. You know, it was those clumsy Roman numerals that you struggle to understand the date of a BBC series or something. They were still being used for calculation. across Europe. And 400 years after these numbers have been adopted by the Arabs and Al-Kharizmi's work has been copied and recopied right across the Islamic world, Europe still hasn't got it, except Spain, which is part of the Islamic world. Yeah, I mean, part of the Islamic world, but also a melting pot of ideas, because as we've talked about, these are places where Arab, Jewish, Christian communities, particularly in Spain, get together, swap ideas, swap thoughts, and a whole sort of culture comes out of this melting pot that is new and alien to all, but also familiar to all.

3:04Exactly that. And I think in the Roman Empire, even in a place like Britain, you had all sorts of different nationalities mixing together as you do today. So when you go to those Roman legionary fortresses on Hadrian's Wall or the museums attached to them in Newcastle and around the place there, you come across letters written by Dacians from the Balkans or legionaries writing home for socks from their mothers in Tuscany or people even from Syria and Palmyra. I mean, distant parts of the empire. Ancient Persian iconography. We talked about this, you know, winged figures and things, all of that.

3:42Exactly. We even have a Mithraic temple on Hadrian's Wall. But by the end of the Roman Empire, that ends again, and you get a kind of, you know, solidly monocultural Christian world in Britain and Europe. But in Spain, you've still got living side by side the Spanish Christians who are called the Mozarabs, who are the descendants of both the Romans and the Visigoths who conquered Spain in the early Middle Ages. Then you have a huge Jewish community who are full of contacts and brilliant intellectual pathways to other Jewish communities across the Levant and across the Middle East. And many extraordinary thinkers and mathematicians like Maimonides and so on are associated with the Jewish communities in Spain.

4:30And then you get the Arabs and you get people coming from across the Arab world. There's this character called, is it Zeriab, the blackbird, who is a famous entertainer and singer and fashionista. And all these sort of different characters all mixing together in what Spanish historians call the convivencia, the living together. And the place I think that we're going to focus in on is a real beautiful exemplar of that. That's Toledo. Set this in a timeline. Where are we zooming in or what point in time are we looking at this place? So Spain is conquered by the Arabs in the late 5th, early 7th century.

5:07They cross over from Gibraltar, which is named after an Arab, Jebel Tara, the hill of Tara. And the Arabs get as far as the Pyrenees, and there the advance stops. There's the famous story of the Song of Roland and the French kicking out the Arab raiding party that got as far as Tours, I think it's 732. I I think that was the date. Did you hear? You're going all Murray Pittick on us and just remembering dates. Look, look at you. Not normally something I do. But I used to love this period. I'd say this whole episode today is the stuff that I got so excited about as a schoolboy. I love this whole world of Islamic Spain and very much my A-level area, which I just adored this stuff.

5:52But by the 11th century, the great center of Cordoba is no longer quite as influential as it had been. and a lot of the manuscripts and learning of Cordoba had migrated northwards to the town of Toledo, which is just south of Madrid. I went there earlier this summer, funnily enough, because I had never been there before, and it was the one place in the book that I hadn't visited. So in May this year, I went to Toledo for the first time. And it's just an hour's drive south of Madrid Airport. And it's this beautiful, beautiful hill town with very steep steps, two rings of walls dating back beyond the Arabs to the Visigoths.

6:32And the importance of Toledo to our story is that it got caught up in the complicated Christian Muslim politics of the time during the period of El Cid. Do you remember the Charlton Heston film? I do. And he was this character who lived in the borderlands between the Arabs and the Christians, changed sides multiple times. but he's central to the story. And in this muddling period when individuals like El Cid are crossing sides and changing their allegiance according to what suits them, you find that the emir in charge of Toledo finally realizes that he cannot resist the Christians and comes to a peaceful transfer of the city.

7:18So that's fascinating because it's normally at force of of arms. So, I mean, how do they accomplish this peaceful handover? It's a siege, but the king eventually concedes and there is no looting of the town. Normally, what happens, of course, when a town falls to an army, and particularly if it's an army of a different religion, is they pour in, rape, loot, pillage, burn everything down, and everything's destroyed. What's remarkable about Toledo and why it's the centre of our story today is two things. First of all, just before the Christian conquest of Toledo, it had become the main intellectual center of Spain.

7:56And there's this particularly this amazing scholar judge or called Said Al-Andalusie, who is a fantastic writer, who is a historian of thought and philosophy. And he writes in the 1020s in Toledo, a history of mathematics and astronomy, and a look at the relationship of the Arabs to the Indians. And so he amasses all these books of Indian learning, which had once been in Baghdad, copies of it. He amasses the works of al-Qurizmi and astrolabes. He has this extraordinary astrolabe maker who's much younger than him, who lives beyond him to the time of the Christians. And so when in 1085, the city of Toledo opens its gates to King Alfonso VI of Leon, who calls himself the king of two religions, he marches in with El Cid by his side, with Charlton Heston standing beside him or marching beside him, or possibly actually on horseback beside him.

9:01And he marches in and he declares that there will be no looting. All the privileges of the Muslims will continue. They'll be allowed to live there. They don't have to leave. Anyone that wants to leave can leave. Anyone who wants to stay can stay. And he promises that the main mosque will remain a mosque, and no one will be forced to convert to Christianity. And in actual fact, many of these promises are later revoked by his successors. And there are some forcible conversions of both individuals and buildings. But the crucial point is the library of Said al-Andalusi and the other scholars of Toledo survives intact.

9:39And I mean, we still call it Andalusia, but it comes from the Arabic name for the place. I mean, they held onto that. So they really didn't sort of fire burn everything, including the names to the ground. Can I just give you a little fun fact? Yes, please. Toledo, why I'm obsessed with Toledo. I mean, I've got children who are obsessed with chess. I think this is right. The first ever book on chess, which is warfare, telescope down to a one board, was produced in Toledo. Is it Toledo that first does a rule book on chess? It is absolutely true. And because of that, I was able to get in the other fun fact that you told us during the summer into the late proofs of my book about how checkmate is the person Charmat, the king is dead.

10:21Charmat? Yes. Can we all recall that time when I was right? about a thing. You were. You were. Not only were you right, I actually plagiarised it. I don't even acknowledge it in the footnotes. You did, did you? I don't. I should know. There is a thank you to you at the beginning, but not specifically for that point. I didn't know, but that's outrageous. But anyway, all the people who listen to Empire will know. Will know. Okay. So tell me, after the handover, does Toledo maintain its position as the seat of learning and build upon the foundation that's been left? Exactly that. So as I say, some of the promises are not honored.

10:58You do get the mosque turning into the cathedral, which still stands to this day. It's built over the mosque. But the libraries are intact and many of the scholars of Toledo are there still during this Christian period. So what happens then is fascinating. A whole series of scholar monks individually from across the Christian world make their way to Toledo, realize that this is the moment of opportunity. And you get this wonderful group of different people. And we're going to talk about some of them now. One is called Gerard of Cremona, who is from the monastery of Bobbio, which again, do you remember the movie, The Name of the Rose?

11:39I do. The Name of the Rose. Sean Connery. Exactly. in that library. That library is based on the library at Bobbio. So a monk from the name of the Rose Monastery called Gerard of Cremona turns up. There's another one from England called Adelard of Bath, who's this sort of fashionista who wears these bright capes. And he goes, first of all, to Paris, but he thinks the French are just basically full of shit. He said they build ropes of intellectual sand, which is the most lovely thing. I saw that Funnily enough, being tweeted in French, somebody that had read the book. Anyway, and then you'll be very pleased to hear, Anita, that there is a Scotsman who comes into the story.

12:23Always thrilled to hear there's a Scotsman. Always. He's not a derimple, I'm afraid to say. Okay. But you'll be glad to hear it. Somewhere. If you go back far enough, he will be. But he is from near our heartlands, and he is called Michael Scott, known in the borders as Michael Scott the Wizard. And the stories which I grew up with was that Michael Scott cleft the Eildon Hills in three. And he's in Sir Walter Scott's Lay of the Last Minstrel and Marmion. He's this sorcerer who has this book of spells that he's brought back from far away. In reality, he's a historical character who was a Scot who had learned Arabic and having taught in Rome and in Italy, finds his way at this period with all these other extraordinary scholars to the bridgehead of Toledo and begins the work of translating all these libraries full of manuscripts.

13:19I think this is amazing. So these are sort of, you know, robed and wizardy people who all come together and they're like, you know, pigeons, homing pigeons. They translate into the language that I use and then they fly away with all this stuff and spread. Can I just say my little Gerard of Cremona memory? I just remember quoting him to our very good friend Peter Frankopan when we were doing a Byzantine episode. and he went, nobody has quoted Gerard of Cremona to me for many years. And I was like, yes, Frankapan, that's right. Take that. Well, we love Peter Frankapan, as we know, but we also learn a great deal from him.

13:53We learn a great deal and he took great pleasure in telling us how we were wrong about everything in that episode. But he welcomed my Cremona quote. Okay, look, so, I mean, you've mentioned these extraordinary wizardy homing pigeons who come together. So let's do a deep dive into all of these characters. So we know where Gerard of Cremona came from, from this amazing library in Bobbio. But who was he? What's his origin story? And what does he then do? So he is a great scholar. And like all the others who collect in Toledo, he is desperate to get his hands on two things. First of all, original Arab texts that advance science and explain the movement of the stars, allow for predictions and teach about the movements of the heavens and mathematics.

14:37But he's also after, and this is very, very important, the Greek classics lost in the barbarian invasions of the West and the rise of Christianity and the death of the old learning, but preserved in the libraries of Baghdad set up by the Barmakids who we had in the last episode. so he doesn't know what's there he's heard there are these amazing libraries in Toledo so he makes his way over the Alps by foot he turns up in the middle of winter and he's given the position of canon at the newly built cathedral which is occupying the site and I think probably some of the buildings of the old Jamma Masjid and he begins to learn to read Arabic with the help of his friend who's called Ghalib the Moz Arab.

15:21And Ghalib the Moz Arab is fluent in Arabic. He's a native Christian Spaniard. And between them, they have this very sort of strange translating system whereby I think Ghalib translates the Arabic into 12th century Castilian, the language spoken in Toledo by people of both faiths, all faiths. And it's then Gerard of Cremona's job to translate from Castilian into Latin. Oh, that's two jumps. Mistakes could crawl in there, couldn't they? Absolutely, they could. And given that some of these texts originated in Persian or Sanskrit or Greek or Syriac. That's three or four jumps. That's three or four jumps, each of which could be a Chinese whisper.

16:07And yet, Gerard's translations, and I think he translates in all 88 works of Arabic learning on astronomy, mathematics, medicine, philosophy, and logic. They are regarded as foundational to later medieval thought. They are the best available translations. There's a gorgeous little observation about this because you're absolutely right. It's sort of the foundation of learning elsewhere. He has in time a student called Daniel Morley or Daniel of Morley. And it's Daniel of Morley who takes the works, the translated works, to England to what is now the University of Oxford. That's right, isn't it?

16:50Like the sort of a foundation stone of the seat of learning at Oxford University. Exactly that. He literally takes Gerard's translations after Gerard's death, five or six of them end up in the Bodleian Library. That's great. And they're still there. You can actually go and see them. I mean, it's fantastic. What do they look like? Are they bound? Are they on scrolls? They are bound. They're early books. And he carries them literally in saddlebags of donkeys over the Pyrenees, over the Channel, and makes it to the Bodleian today. And they're some of the very oldest books in the Bodleian in Latin.

17:22And so this becomes something called the 12th century Renaissance. All this new material, not only out of Arabic, but out of the Greek classics, things like Euclid on geometry, Ptolemy on geography, a lot of the major works of Roman and Greek history. All these things are available to scholars in Europe, in the Christian world, for the first time for 600 years. And this is massive excitement, but there's also all this new learning coming in from the Arab world and ultimately from India. But he's not the only one. It's not like there's just one donkey route to wisdom coming to England? Because there's also, you mentioned Adelard of Bath.

18:03And was Bath a great place of learning at that time as well? I mean, why was he headed to Bath or taking these things back to Bath? So Adelard is sometimes called the first English scientist. He's born in Bath. His mother is of Anglo-Saxon stock and his father is from the New Normans. His uncle, or I think some distant cousin is Bishop Guizzo of Wales, who came to Somerset for Lorraine. And Adelaide is this fantastic sort of dashing character. He's ambitious, adventurous, colourful. He's known for his dandiest dressing in a green cloak with a kind of lapis blue shirt and a cap striped with red and bordered with ermine.

18:47And he sports a dazzling emerald ring. He hunts with a hawk. He's known for the sweetness of his playing on the lute, probably the oud from the Arab world. And his lively prose is laced with jokes. And he writes this lovely book explaining complicated physics and mathematics in a conversational way called Questions from My Nephew. And he writes this book about having to explain to his nephew all this complicated stuff. And he's very, very well traveled. He's gone to the Crusader States, what's now Israel-Palestine. He's gone to Sicily. He's wandering around southern Turkey in 1114. We know that date because he mentions an earthquake.

19:34And he's on this bridge, which is shaken near Mamistra in Adana in southeast Turkey, where I went earlier this summer. And he says the bridge at Mises felt hardly more secure on earth than you would on water. In other words, the earthquake was making it shake all around. So we actually know the date he was there. But he, like all these others, turns up at Toledo and just dives into the library. And the detail that I love about him is that when he gets round finally in the 1120s to translating Alcharismi into Latin in Wells in Somerset, which is where he settles. So in Somerset, so not far from Bath.

20:14So it is a seat of learning or just because of him, it's a seat of learning. It's just because he takes it back to where he lives. Yeah, he takes it back home. He's been to all these exotic places, and then he comes home and does all these translations. And part of his translations are what's called the Zij tables, which are like tables of signs and cosines used in astronomy. And he finds that Al-Qarizmi is referring to the meridian that he's using on the Tropic of Cancer, which he translates from the Arabic as Arin, A-R-I-N. So you've got this Englishman sitting in Somerset in 1120, writing the letters A-R-I-N, and wondering where this place could be.

20:56And it is our old friend Ujjain in Madhya Pradesh, near Bhopal. So the translation has moved from Ujjain, Ujjain, to whatever iteration in these jumps, and it's now Arin. And it's now become Arin. And he doesn't know where this is, but we, looking at his text, can understand that it was the great centre of Gupta mathematics. And this is hand-holding over 600 years, and you've still got the truth of it. Maybe the words are morphed, but the truth is still in there. Exactly that. And so it goes from Brahmagupta to Al-Khwarizmi to Adelaide Bath, where it gets translated in Somerset. It's just a wonderful story, isn't it?

21:30It's just bonkers, isn't it? Bonkers. And when Adelaide translates them, is it the case that there will be many copies made and these will be disseminated to voracious readers? Where do his translations go? these texts end up in court because Adelaide, who's, as I said, this very dashing figure, ends up, I think, as the tutor to Henry II. And there's even an attempt, which doesn't get very far by Adelaide of Bath, to introduce what we call the Arabic numbers, the Indo-Arabic numbers that originated in India onto the English coinage when he's in London. And it doesn't work. No one else. They say no.

22:08Don't want this foreign muck. Don't want this foreign muck. On our coins. So are we overstating it when we say this is an epoch changing intelligence that comes to Britain at this time? So yes and no. Yes, because it is an astonishing moment. Suddenly access to all these Greek, Roman, Indian, the world's learning suddenly is available. And you have these guys like Daniel of Morley with his donkey bringing these incredibly valuable books to the Bodleian. But equally, it's only this small scholarly circle. The rest of the world carries on, and this attempt by Adelaide of Bath to get the Arabic numbers on the coins fails.

22:48So the whole of Europe is still using Latin numerals. And what we're going to do in the next half is tell the extraordinary story of how these numbers that originate in India have passed through the Arab world, suddenly ignite and take over Europe. And the crucial place for this is Pisa.

23:15Welcome back. Now, in this half, William teasingly told us that we are going to find out how things proliferated, things that were resisted maybe for a while with having these weird, weirdy foreign numbers on our coins to suddenly becoming the lingua franca of mathematics throughout the Western world. And the name that will come up is a name that I'm sure many of you are familiar with, and that's Fibonacci of the golden ratio of the Fibonacci number. It's an amazing man who's had an amazing contribution to mathematical learning. So, Fibonacci is 1175 to 1250. Those are his dates. How does he get access to this stuff and convert it into a palatable form that people are going to find yummy and delicious?

24:02So Fibonacci is actually a nickname. His name when he was young was just Leonardo of Pisa. And his story is that he is the son of a trader who is appointed by the commune of Pisa in Tuscany to sail to Algeria to set up a Pisan trading house and customs office on the Algerian coast. And this is the town then known as Bejaia, which is now known as Oran, which is also the place, incidentally, where Camus lived and wrote the plague and all those sort of extraordinary books before the end of French Algeria. Wow. Someone test the water there immediately. Back to Fibonacci. So his father is a trader.

24:44His father has been in this extraordinary place. And what is it his father who first crosses paths with these ideas? And does he understand them and say, son, come and look at this? How does that work? No, Fibonacci's dad is just a trader who gets on and does his stuff. But just as a matter of course, without particularly thinking about it, he puts Fibonacci in the local school. So just as some of my kids learn really quite good Hindi at their school, so Fibonacci learns Arabic, just as a matter of course, and also as a matter of course, picks up the Arab mathematics, which is being taught by this stage just to anyone who's at school.

25:19Which is the Indian mathematics. Which is the Indian mathematics, exactly. The rebranded Indian mathematics. The rebranded Indian mathematics. and it's important to say that the Arabs know that it's the Indian mathematics because Al-Qarizmi is very clear his title of his book is that it's Hindu mathematics as he calls it and Fibonacci in all his writings about this also calls it the the method of the Indians so Fibonacci just is a normal kid just goes to school studies math studies Arabic language and so by the time that he's 18 and his dad is posted back home to Pisa, he knows all this stuff.

25:54And as you said earlier about how it's often very young people who get mathematics most quickly, Fibonacci comes back to Pisa, aged I think only 18 in his case. And he writes this book called The Lieber Abiquid, because he finds all his friends back home are still doing MCVX divided by MXVV1. And he realizes they need help. So he writes this book called the Libra Abaki, or the Book of the Abacus, or the Book of Calculation, as it's usually translated. And he writes in this what he calls the modus indorum, the Indian method, which he thinks is superior even to the methods of the Greek and Pythagoras.

26:36And he makes it his life's work to bring it to his readers, all the details of the Indo-Arabic numbering system. And he writes all this, including the Fibonacci sequence, which I know many Indians say Aryabhata, I think, first came up with. So for people who don't know Fibonacci sequence, we do learn this at school, but it is where each number is the sum of the two preceding ones. There is a beautiful symmetry and progression about it. And these numbers are always attributed to him, but you're saying that he got them from India. They already existed. Yep. Aryabhata has the Fibonacci sequence and it's Fibonacci merely translates it, I think.

27:14That's certainly the view of many Indian mathematicians, as you can imagine. Is this controversial or is this just fact? You should ask your husband that because I live in India and I've always heard it as fact, but it's quite possible that Europeans dispute that. Well, that's what our lunchtime conversation will be. Yeah, I know what we're going to be talking about. Carry on. So whether that's true or not, it's certainly true that Fibonacci's whole book, Liba Abaki, is translating Al-Khwarizmi, who is translated Brahma-Gupta. So it's a relay race of mathematics. And this book is immediately regarded as a work of genius, as a game changer, but it's very theoretical.