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

Summary

Empire Episode 194: "Empire of Numbers: Fibonacci and the Birth of Modern Money"

Hosts: William Dalrymple and Anita Anand
Release Date: October 14, 2024

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Introduction

In Episode 194 of Empire, hosts William Dalrymple and Anita Anand delve into the fascinating journey of numerical systems from ancient India through the Islamic world and into Europe. Titled "Empire of Numbers: Fibonacci and the Birth of Modern Money," the episode explores how mathematical breakthroughs have shaped modern civilization.

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The Transmission of Indian Numerals through the Islamic World

The episode begins by tracing the origins of the Hindu-Arabic numeral system. William explains how these numbers traveled from India to Baghdad, thanks to scholars like the Barmakids and Al-Khwarizmi. Despite their widespread adoption in the Islamic world, Europe clung to Roman numerals well into the 12th century.

Notable Quote:

"As late as the 1100s, all calculation in Europe was still taking place with sort of MV CCM V1 times XV1 1 XV. You know, those clumsy Roman numerals..."
— William Dalrymple [03:02]

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The Role of Spain and Toledo

Anita highlights Spain as a unique melting pot where Christian, Jewish, and Arab communities coexisted, fostering a vibrant exchange of ideas. Toledo emerges as a critical intellectual hub where the transmission of knowledge took a pivotal turn.

Key Points:

• Convivencia in Spain: The coexistence of diverse cultures facilitated the blending and preservation of knowledge.
• Toledo's Significance: After the decline of Córdoba's prominence, Toledo became the new center for learning, housing vast libraries and scholars like Said Alandalusi.

Notable Quote:

"Toledo had become the main intellectual center of Spain... Said Alandalusi, who amasses all these books of Indian learning..."
— William Dalrymple [08:29]

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The Peaceful Handover of Toledo

A significant moment discussed is the peaceful transfer of Toledo from Muslim to Christian hands in 1085. King Alfonso VI, accompanied by the legendary figure El Cid, negotiated terms that preserved Toledo's intellectual heritage.

Key Points:

• No Looting: Unlike typical conquests, Toledo was spared from destruction and looting.
• Preservation of Knowledge: The libraries, especially those containing works of mathematics and astronomy, remained intact, ensuring the survival of critical texts.

Notable Quote:

"He [Alfonso VI] marches in and he declares that there will be no looting... The main mosque will remain a mosque and no one will be forced to convert to Christianity."
— William Dalrymple [08:36]

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Arrival of European Scholars in Toledo

Post-conquest, Toledo became a beacon for European scholars eager to access and translate advanced knowledge from Arabic texts.

Key Figures:

• Gerard of Cremona: Originating from the monastery of Bobbio, he translated over 80 works on astronomy, mathematics, medicine, philosophy, and logic, many of which became foundational texts in Europe.
• Adelard of Bath: Often hailed as the first English scientist, Adelard traveled extensively before settling in Somerset, where he translated Al-Khwarizmi's works and introduced Arabic numerals to England.
• Michael Scott the Wizard: A Scotsman who assisted in translating manuscripts, bridging cultural and linguistic gaps.

Notable Quote:

"Gerard's translations... are regarded as foundational to later medieval thought. They are the best available translations."
— William Dalrymple [17:15]

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Fibonacci and the Liber Abaci

The narrative culminates with the story of Fibonacci (Leonardo of Pisa), a pivotal figure in disseminating the Hindu-Arabic numeral system in Europe.

Key Points:

• Early Exposure: Raised in Algeria, Fibonacci was immersed in Arabic mathematics from a young age.
• Liber Abaci: Published in Pisa, this book introduced the Indian numeral system and the Fibonacci Sequence to Europe, advocating for its superiority over Roman numerals.
• Impact: While his initial attempts to replace Roman numerals on coins failed, Liber Abaci laid the groundwork for the mathematical renaissance in Europe.

Notable Quote:

"Fibonacci just is a normal kid, just goes to school, studies maths, studies Arabic language... And by the time that he's 18... he knows all this stuff."
— William Dalrymple [26:22]

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Legacy and Influence on the Renaissance

The adoption of the Hindu-Arabic numeral system had profound effects on European society, particularly during the Renaissance.

Key Points:

• Banking Revolution: The new numerals facilitated complex financial transactions, spurring economic growth.
• Artistic Advancements: Renaissance artists like Piero della Francesca integrated mathematical principles into their work, enhancing perspective and proportion.
• Spread of Knowledge: Translations reached institutions like the University of Oxford, embedding advanced mathematics into academia.

Notable Quote:

"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."
— William Dalrymple [24:42]

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Conclusions

Episode 194 of Empire masterfully illustrates the intricate journey of mathematical knowledge from India to modern Europe. Through the preservation and translation efforts in Toledo, scholars like Gerard of Cremona, Adelard of Bath, and Fibonacci played instrumental roles in shaping the numerical systems that underpin today's global economy and scientific understanding.

Notable Quote:

"It's an astonishing moment. Suddenly access to all these Greek, Roman, the world's learning, Indian, the world's learning suddenly is available."
— William Dalrymple [19:06]

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Final Thoughts:
The episode underscores the profound impact of cultural exchanges facilitated by empires, highlighting how the fusion of diverse intellectual traditions can lead to transformative advancements. From the serene hills of Toledo to the bustling streets of Renaissance Italy, the legacy of these numerical systems continues to influence the modern world.

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References:

• Book Mentioned: The Golden Road by William Dalrymple

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Note: Times are approximate and based on the provided transcript.

Transcript

[William Durimple]

If you want access to bonus episodes, reading lists for every series of Empire, a chat community, discounts for all the books mentioned in the week's podcast ad, free listening and a weekly newsletter. Sign up to empire [e-mail]. want to shop Walmart Black Friday deals first. Walmart plus members get early access to our hottest deals. Join now and get 50% off a one year annual membership. Shop Black Friday deals first with Walmart + seed [e-mail] the holidays are here at the Home Depot. So let's get to decorating. Find your perfect tree in our huge assortment of shapes, sizes and styles. Like the easy to assemble Jackson Noble fir with pre lit branches perfect for styling with all your favorite ornaments. Or the flock starry light Frasier fir with over 1900 pre lit memory wire branches that keep their shape so it's ready right out of the box.

[Anita Arnand]

Ooh.

[William Durimple]

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[Anita Arnand]

Hello and welcome to Empire with me, Anita Arnan 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, innit? That's quite neat, isn't it?

[William Durimple]

You came up with that all of your own.

[Anita Arnand]

Yes, and I went, 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. It's everywhere. You're bloody everywhere. I can't turn on a TV or a radio without hearing you talking about it.

[William Durimple]

I have been working hard for the last month on all this.

[Anita Arnand]

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.

[William Durimple]

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 Barma kids, then Al Khwarizmi 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, and 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 MV CCM V1 times XV1 1 XV. You know, it was those clumsy Roman numerals that you struggle to understand the date of a BBC series or something, because they're written in it and they were still being used for calculation across Europe. And 400 years after these numbers have been adopted by the Arabs and Al Khwarizmi'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.

[Anita Arnand]

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.

[William Durimple]

Exactly 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 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.

[Anita Arnand]

Ancient Persian iconography. We talked about this, you know, winged figures and things, all of that.

[William Durimple]

Exactly. 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. And 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.

[Anita Arnand]

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? At what point in time are we looking at this place?

[William Durimple]

So Spain is conquered by the Arabs in the. Is it the late 6th, early 7th century? They 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 don't know where that dates come from the back of my mind, but I think that was the date.

[Anita Arnand]

So, George, you're going all Murray Pittock on it and just remembering dates. Look.

[William Durimple]

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. But 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, funny 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. And 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?

[Anita Arnand]

I do.

[William Durimple]

And he was this character who lived in the borderlands between the Arabs and the Christ. Change 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.

[Anita Arnand]

So that's fascinating because it's normally at force of arms. So, I mean, how do they accomplish this peaceful handover?

[William Durimple]

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, you know, they pour in rape, loot, pillage, burn everything down, and everything's destroyed. What's remarkable about Toledo and why it's the center 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. And there's this particularly this amazing scholar, judge or Qazi, called Said Alandalusi, 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 copyright copies of it. He amasses the works of Al Khwarizmi 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. And 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.

[Anita Arnand]

And 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?

[William Durimple]

Yes, please.

[Anita Arnand]

Toledo.

[William Durimple]

Why?

[Anita Arnand]

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 sort of a rule book on chess?

[William Durimple]

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. About how checkmate is the person. Sharmat. The king is dead.

[Anita Arnand]

Sharmat. Yes. Can we all recall that time when I was right about.

[William Durimple]

You were. Not only were you right, I actually plagiarized it. I don't even acknowledge it in the footnotes.

[Anita Arnand]

You did, did you?

[William Durimple]

I don't. I should do. There is a thank you to you at the beginning, but not specifically to that point.

[Anita Arnand]

No, but that's outrageous. But anyway, all the people who listen to Empire will know.

[William Durimple]

Will know.

[Anita Arnand]

Okay. Okay. So tell me, after the handover, does Toledo main its position as the seat of learning and build upon the foundation that's been left?

[William Durimple]

Exactly that. So as I say, some of the promises are not honored. You 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 gonna 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?

[Anita Arnand]

I do.

[William Durimple]

The Name of the Rose, where Sean Connery. Exactly. In that library. That library is based on the library at Bobbio.

[Anita Arnand]

Okay.

[William Durimple]

So a monk from the Name of the Rose, Mon Cremino, 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. They said they build ropes of intellectual sand, which is the most lovely thing. I saw that, funny 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 who is called.

[Anita Arnand]

Thrilled to hear this. A Scotsman.

[William Durimple]

He's not a durimple, I'm afraid to say, but you'll be quite.

[Anita Arnand]

He will be somewhere if you go back far enough he will be, but.

[William Durimple]

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.

[Anita Arnand]

I 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 languages that are used, 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 Frankeban, when we were doing a Byzantine episode and he wrote, right. Nobody has quoted Gerard of Cremona to me for many years. And I was like, yes, Francopin, that's right. Take care.

[William Durimple]

Well, we love Peter Frankopan, as we know, but we also learn a great deal from him.

[Anita Arnand]

We 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?

[William Durimple]

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. But 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 Jama Masjid. And he begins to learn to read Arabic with the help of his friend, who's called Ghalib the Mozarab. And Ghalib the Mozarab 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.

[Anita Arnand]

Oh, that's two jumps. Mistakes could crawl in there, couldn't they?

[William Durimple]

Absolutely they could. And given that some of these texts originated in Persian or Sanskrit or Greek.

[Anita Arnand]

Or Syriac, that's three or four jumps.

[William Durimple]

That's three or four jumps, each of which could be a Chinese whisper. And yet Gerard's translation, 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.

[Anita Arnand]

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 like the sort of a foundation stone of the seat of learning at Oxford University.

[William Durimple]

Exactly that. He literally takes Gerard's translations. After Gerard's death, five or six of them end up in the Bodleian Library.

[Anita Arnand]

That's great.

[William Durimple]

And they're still there. You can actually go and see them. I mean, it's fantastic.

[Anita Arnand]

What do they look like? What do they look like? Are they bound? Are they on scrolls?

[William Durimple]

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. And 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.

[Anita Arnand]

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 and 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?

[William Durimple]

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 Guizot of Wells, who came to Somerset for Lorraine. And Adelard is this fantastic sort of dashing character. He's ambitious, adventurous, colorful. 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. And 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 with 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. And 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, about him is that when he gets round finally in the 1120s to translating Al Khwarizmi into Latin in Wells in Somerset, which is where he settles.

[Anita Arnand]

So in Somerset, so not so not far from Bath. So 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.

[William Durimple]

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 ZH tables, which are like tables of sines and cosines used in astronomy. And he finds that Al Khwarizmi 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. And it is our old friend Ujjain in Madhya Pradesh, near Bhopal.

[Anita Arnand]

So the translation has moved from Ujjain Ujena to whatever iteration in these jumps.

[William Durimple]

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.

[Anita Arnand]

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.

[William Durimple]

Exactly that. And so it goes from Brahmagupta to Al Khwarizmi to Adelard of Bath where it gets translated in Somerset. It's just wonderful. It's just bonkers, isn't it?

[Anita Arnand]

Isn't it bonkers? And when Adelard translates them, is it the case that there will be many copies made and these will be disseminated to voracious readers who, I mean, where do his translations go?

[William Durimple]

These texts end up in court because Adelard, who's this, 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 Adelard of Bath to, 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 can do it.

[Anita Arnand]

They say, no, don't want this foreign muck, they want this foreign muc on our coins. So are we overstating it when we say this is an epoch changing intelligence that comes to Britain at this time?

[William Durimple]

So yes and no. Yes, because it is an astonishing moment. Suddenly access to all these Greek, Roman, the world's learning, 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 Adelard of Bath to get the Arabic numbers on the coins fails. So 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. Want to shop Walmart Black Friday deals first Walmart plus members get early access to our hottest deals. Join now and get 50% off a one year annual membership shop Black Friday deals first with Walmart plus see [e-mail].

[Anita Arnand]

Welcome back. Now, in this half reading, William teasingly told us that we are going to find out how things proliferated, things that were resisted maybe for a while with, you know, having these weird, weirdy foreign numbers on our coins to suddenly becoming the lingua franca of mathematics throughout the Western world. And 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 amazing man who's had an amazing contribution to mathematical learning. So Fibonacci is 1175-1250. 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.

[William Durimple]

So 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 Bajaya, 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.

[Anita Arnand]

Wow. Someone test the water there. Immediately back to Fibonacci. So his father is a trader. His 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?

[William Durimple]

No, Fibonacci's dad is just a trader who gets on and does his stuff. But just as a matter of course, without sort of particularly thinking about it, he puts Fibonacci in the local school. So just as some of my kids learnt 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, you know who's at school, which.

[Anita Arnand]

Is the Indian mathematics.

[William Durimple]

Which is the Indian mathematics, isn't it?

[Anita Arnand]

The rebranded Indian mathematics.

[William Durimple]

The rebranded Indian mathematics. And it's important to say that the Arabs know that it's the Indian mathematics, because Al Khwarizmi 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 Method of the Indians. So Fibonacci just is a normal kid, just goes to school, studies maths, 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. And 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 Abaci, 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 Liber Abaci, or the Book of the Abacus, or the Book of Calculation, as it's usually translated. And he writes in this of what he calls the modus Indorum, the Indian Method, which he thinks is superior, even the methods of the Greek and Pythagoras. And 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 Arya butter, I think first came up with.

[Anita Arnand]

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 it's. These numbers are always attributed to him. But you're saying that he got them from India, they already existed? Yep.

[William Durimple]

Ari Bhatta has the Fibonacci Sequence and it's. Fibonacci merely translates it. I think that's certainly the view of many Indian mathematicians, as you can imagine.

[Anita Arnand]

Is this controversial or is this just fact?

[William Durimple]

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.

[Anita Arnand]

That's what our lunchtime conversation will be. Yeah, I know what we're going to be talking about. Carry on.

[William Durimple]

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 Brahmagupta. 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. And again, like the works of Jared of Cremona, it's taken in locally to the scholarly community, but it absolutely does not spread further than that. And then something very important happens. In 1225, Fibonacci is visited by no lesser figure and fanboy than Frederick ii, the Holy Roman Emperor known as Stupor Mundi.

[Anita Arnand]

That's not bad, is it? You know, the Holy Roman Emperor is reading your work and liking it.

[William Durimple]

And Frederick II is not someone to just sort of, you know, put on a pair of jeans and pop over. He arrives in Pisa with his entire menagerie. There's elephants and giraffes and camels and what have you. And his. And he also is the great aficionado of falconry. And he's written a book when he's only 18 about the art of falconry.

[Anita Arnand]

So he's another. He's another boy wonder, but he's also an intellectual. I mean, he speaks many languages. He's into, you know, philosophy. Doesn't he speak five languages? Greek, Arabic included among them? He's a different cut of Holy Roman Emperor, isn't he?

[William Durimple]

Different cut of king. Absolutely right. And he is incredibly curious. He writes these letters that we still have to all the sultans in North Africa and Egypt, asking about their cosmology, their understanding of what the world is, where heaven may or may not lie. How do we locate all these places that we read about in the Holy Scriptures? And he's asking people that the Pope would regard as terrible heathens for the answers of these great questions. So eventually he actually gets excommunicated by the population and he dies without the blessing of the Church anymore. But anyway, he turns up at Pisa and he challenges Fibonacci to a sort of. Remember that TV show Countdown?

[Anita Arnand]

It's a Maths off, is what it's a Maths Off.

[William Durimple]

Exactly. He has a sort of maths contest which your husband and son would excel in. And in this case, it's the young Fibonacci who just wipes the floor with the other.

[Anita Arnand]

With all the other contestants. That's hilarious.

[William Durimple]

And so what happens then is that Fibonacci is called to Palermo and he's taken into the palace to join Michael Scott, the Scotsman, in the astronomy room. And there's this wonderful exchange. Michael Scott is this recognizably pragmatic Scottish figure, and he reads the Lieber Abaki and he realizes that it's an astonishing work of genius, but he also realizes that it's just too theoretical and it's going over everyone's heads. And Michael Scott says, look here, Paul, this is all very well, but you're not going to have anyone understand this.

[Anita Arnand]

You're losing the audience. Fibonacci.

[William Durimple]

Yeah, you're losing the audience. And so he says what you've got to include, and he gives him a list, is accountancy, double bookkeeping, weights and measures, money conversion, and most important of all, interest rates and how to calculate them. So the second edition of the Lieber Abake, which is dedicated to Michael Scott, is produced, and it's this text that, like Al Khwarizmi goes Wildfire, is taught in every school.

[Anita Arnand]

I just bloody love this.

[William Durimple]

Isn't it great?

[Anita Arnand]

Yeah, it's the collegiate world of mathematics. It is amazing, actually. You know that I'm not going to be jealous of your. Of your accomplishments. I'm going to tell you how to make it better, even better, and do something to make more people read it. I think that's still a thing in the world of mathematics today.

[William Durimple]

Yeah, it's great. And so this goes out across Italy and there's all sorts of results. First of all, you get the Italian banking revolution, you get the Medici, and not only do you get the Medici, who patronize all the greatest painters of the Renaissance, the painters themselves are mathematicians. At this point. Today, we think of mathematics and painting as being too completely different worlds. But the painters of the Renaissance discovered perspective from Indian and Arabic mathematics.

[Anita Arnand]

And also the golden ratio then becomes a real thing, the perfection of painting.

[William Durimple]

Exactly that. So Piero della Francesca is fascinating because he known today as one of the greatest Renaissance painters. For me, the greatest. I went this summer and saw some of his great masterpieces in Tuscany, and he's an extraordinary and wonderful painter. And I went and saw for the first time the flagellation in Urbino, which Kenneth Clarke calls the greatest small painting in the world. But that is itself an essay on perspective, and it derives from the ideas of Fibonacci, which, as you say, derives from Alcharismi, which derives from Brahma Gupta. So he writes. Piero himself, the painter writes three treatises on mathematics and perspective. And after he dies, his friend. I don't know whether they were. They lived together, but they certainly lived in the same town. A friar called Luca Pacioli takes Piero della Francesca's three mathematical treatises on perspective and Fibonacci and he takes it to Milan where he shares it with his flatmate. His flatmate is Leonardo da Vinci.

[Anita Arnand]

Woo hoo.

[William Durimple]

That's very nice little. It's good, isn't it? It's a collection of very clever people, I should say. This is not in the. And I've learned it subsequently from my friend Nick Booker who I should call out just like the second edition of the Lieber Abakey contained all sorts of stuff not in the first edition. I definitely wanted to add this with Nick's Permission to the 2nd edition.

[Anita Arnand]

Feel free to credit me with the Charmorth Checkmate fact in your next edition, won't you?

[William Durimple]

A footnote will be there, Anita. Absolutely.

[Anita Arnand]

Very good, very good, good. I mean this is wonderful but also what a time where you can ask your flatmate to have a look at a book and it blows his and he's Leonardo da Vinci and he's painting.

[William Durimple]

At this moment or he's just about to paint the Last Supper and that is the result of this set of treatises. So there's an extraordinary watching these great ideas pass like a relay race from India all the way to Leonardo da Vinci. It's a wonderful story and the Leonardo and the Piero things I owe to Nick Booker isn't in the book and it will have to be in subsequent editions because it's so wonderful and is such a great part of the story Anyway, Fibonacci's work goes all around, everyone in Italy uses it, it's used by bankers and his ideas begin to spread north of the Alps and you begin to see by the 15th century, for example, Durer gets very excited by the new numerals, the Indian numerals that are still credited in Renaissance world as being Indian, they haven't yet become Arabic numbers that we know them today. So the year that Fibonacci's work, Piero della Francesca's work and Luca Caroli's work gets printed for the first time in Venice is 1498, the same year Vasco da Gama crosses the ocean from the African coast and in inverted commas discovers the sea route to India, in fact it's taught to him by an Indian. But in all the history books he's credited with this and what you can argue, I think, is that the weapons with which the East India Company ultimately subjects India accountancy, double bookkeeping are weapons that the Europeans have learned from the Indians. They use their own weapons against them.

[Anita Arnand]

Oh, the irony. Oh, the humanity. Oh, the symmetry.

[William Durimple]

So which brings us back to our old friend the East India Company again where we started the very first episode of Empire. A very nice circle.

[Anita Arnand]

What a lovely circle. Stroke. Nautilus shell spiral we followed. Listen, this has been amazing. Thank you very much for listening. That's all we've got time for on this episode of Empire. Till the next time we meet. It's goodbye from me, Anita Arnand and.

[William Durimple]

Goodbye from me, William Dripple. And I should just put out the flag again. This is all in my new book, the Gold Golden Road.

[Anita Arnand]

The Golden Road.

[William Durimple]

If you haven't bought, you should go immediately and buy.

[Anita Arnand]

Everyone's bought it already. God, you've been in the bestsellers list for weeks now. They've all got it.

[William Durimple]

Goodbye. Bye.