Keith Devlin:	So, there's been a project ... there's actually three books involved. Well, there were several books, but three books, I have written two of and I'm writing a third one. All about Fibonacci. I didn't set out to write three books, I set out to write maybe one book, and this is around 2002. I sort of had this idea around 1999, 2000 that period, that I wanted to write a book about Fibonacci. Why? Because as I've just been mentioned, I spent a lot of my career doing mathematical outreach. Trying to take deep ideas and make them accessible. 
	Very few mathematicians try to do that, but one of the ones who did very successfully was Leonardo. Leonardo of Pisa, now called Fibonacci. With a series of books, he had an incredible impact on the development of the modern world, and it was partly because he had the mathematical ability, the mathematical chops to just do deep mathematics, and deep mathematics in basic was arithmetic and the beginnings of Algebra, but he had the capacity to do that well ahead of his era, but he also had, not only the ability to write about it in a moderately accessible way- I say moderately accessible cause the audience he was going for- but he also had incredible marketing sense. As every good teacher knows, it's marketing, marketing, marketing. It's not just technology that he's marketing. You have to market, and you have to make that person want to know what you're talking about. That is marketing. That's basically one of the things we do. It's the same in K through 12 as well. It's marketing and creating excitement. 
	Around 2002, I actually started to do this work. These images were all taken ... this is Pisa in around 2002. It was my first ... not my first visit to Italy, but the first of what was going to be very many visits to ... particularly to the Tuscan area, Siena, Florence, that general area of Pisa, because Leonardo was born and grew up and spent most of his life in Pisa, so I wanted to go there. 
	No one had written a history of Leonardo. I'm going to call him Leonardo because in my mind, he's a friend of mine, and I don't want to call him by his vulgar nickname, so he was Leonardo. He was lived through his life as Leonardo of Pisa because he was a respected gentleman, so I'm going to call him Leonardo. Not only did he live in Pisa, but many of the buildings that were around him when he was ... He was living in the time when the Leaning Tower was built and started to lean, and the [inaudible 00:02:21] beginning of the 13th century. 
	Many of the buildings in Pisa, which is Italy, they don't knock buildings down. In California, they knock a building down every twenty years. You put it down to the ground and rebuild it. In Pisa, you leave them up until they actually fall down, and most of them down. You walk around Pisa today, and you're walking streets looking at things that Leonardo would have looked at. Part of the reason people didn't write a history was there was nothing known about him. For an astounded historian, no one could write a history of Leonardo. There just isn't any, because there's really nothing to go on. 
	I'm not at all a historian. I found [inaudible 00:02:57] pretend historian. I've spent a lot of time in the archives on this project, but what I am is a mathematician that was able to get into his mind. Through his writings, get a sense of him, and by going to Italy many times, wandering around and trying to imagine what it was like in the 13th century, reading his own words in the original Latin, one of the few benefits of my English school experience was I was forced to learn Latin. Of course, I said for years, "What a waste of time! I will never need that." Well, now I do need it, so I actually got benefit out of it.
	It's like Steve Jobs taking a course on Fonts. Why does someone take a course on fonts? What do you end up designing the graphic user interface computer web [inaudible 00:03:41]? It's a classic liberal arts thing. Learn it, file it away, you'll probably use it one day or another. I did use my Latin on this project.
	I went to write this book by trying to get at Leonardo through his writing, because after all, his impact ... I'll say a little bit about what his impact was. It's much bigger than you could possibly imagine. Bigger than I imagined at the beginning. His impact on the world was so great, but that impact was [still 00:04:06] his mathematics. In a sense, the minutiae of Leonardo's life doesn't matter, because the impact was Leonardo the mathematician. Leonardo the citizen of Pisa. 
	Those things we have access too. We a lot of story. We have a lot of history about 13th century Italy and Pisa. There's a lot of information in the [account 00:04:24] about what it was like then. What it was like to live then. What we're missing is just the details of his social activity. I did find one thing that wasn't generally known, that he actually had a brother. That was new. I didn't discover that. Someone who did discover that told me that, because if you learn Latin, you can pick up Italian, and I started talking to some Italian scholars. Medieval scholars, and they told me all sorts of things that's only been published in Italian, which means American scholars never read about it. Well, I did.
	Okay. This is the river Arno. This is what Pisa looks like today. Back in the 13th century, that was one of the most important ports in the world. There was Florence. There was Pisa. Later on there was [Genoa 00:05:08]. These were the big ports dealing across the Mediterranean. The basic trademark was the silk route from North Africa down into the [Oriens 00:05:18], and so you have all the stuff coming from the [orien 00:05:21] north of the silk route covered by the muslim traders on camels. Put into ships on the north ports of Buja and so forth. Sent across to Europe. 
	This was the beginning of international trade, in a global sense. The Mediterranean was one of the hubs. One of the biggest hubs in this network was Pisa. Now, Pisa, if you've been to it, Pisa is miles from the coast. About 15 miles from the coast. Beautiful bike ride. If you're a cyclist, there's nothing better than doing research in Tuscany. Take your bike with you, and the mornings you're in the outside, and in the afternoon you're riding through vineyards and in the evening, you're drinking the wine that was grown in the vineyards. It doesn't get much better than that. I used to hate going back. Although going back to California was kind of nice, but it was hard to live Tuscany. Pace of life is very nice there. 
	Okay. It's miles from the coast, and that's not a deep river. How did it work? These are flat bottom boats. What happened was there was a thing called a Porto Pisano, Port of Pisa, which is where Livorno, the big sea going port is now. It was a big sea port on the Mediterranean, and things were brought across the Mediterranean in the same boats. They were off loaded and then put into shallow barges and taken up to Pisa and then Florence. 
	That was where the hub was. Pisa was particularly one of the hubs of international trade. Leonardo was born in a family where his father was a trader on a government official, so he grew up in this world. This is how we can start to put together a picture of Leonardo. I simply ... what I did, was I would go there and say, "Imagine I'm Leonardo. I'm a math- I understand his mathematics. I've read his works. What would it feel like? If I had seen this, what would I have thought?" Then recreate this individual. 
	Okay. Let's go a little bit further back in time in 2002. If you went to Pisa in 1944, towards the end of the second world war, when you got to the river Arno, looking across, what used to be the central bridge, its in ruins there, you will see that there had been one incredible battle there. This was a battle between the Germans and the Italians on one side, and the allies, the Americans and the Brits so forth on the other side, and they basically, you know, just knocked whatever out of this thing. They completely destroyed all sorts of things to try and get across up river, and just advance. 
	Huge battle. Destroyed almost everything. It's sense been rebuilt. That building there, it's obviously ... when you look at what's going on, the Allies were certainly trying to avoid destroyed very beautiful buildings, so they didn't completely destroy that, but it got knocked about quite a bit. The buildings to the side got completely demolished as did the bridge. I took that photo when I went there in 2002 or 2003. 
	It's been nicely restored to it's original, but focus now on that, because in the middle of all this destruction carnage, a marble statue about eight foot tall remained virtually in tact. Nothing hit that thing. Either by good luck or fortune or whatever, that marble statue remained undamaged. If you see it today ... if you want to see it today, you'll have to go to the [Campo santo 00:08:43], which is in the [inaudible 00:08:46], where the leaning tower and the cathedral are. There's sort of a big building at the bottom of Camposanto, the monumental cemetery and in the building, you will find that statue beautifully repolished and put on display right at the end of a long corridor in a very, very spectacular location. 
	That's a statue, a 19th century statue. I think it was created in about 1863. Something like that, by Florence [Scotter 00:09:12]. That is one of two images we have of quotation marks, Leonardo of Pisa, because no one knows what he looked like. No drawings were made in his time, or if they were, they didn't survive. We have no knowledge of what he looked like but a 19th century Italian sculptor created an image of Leonardo. That's the image we have. It's the image I used in my work. Solid image. I can't imagine myself inside that body walking around Pisa, which is sort of what you think ... it sounds kind of [inaudible 00:09:44] history, but when you think about it, most history is kind of [inaudible 00:09:47], because you're recreating stuff. However you do it, you use the best tools you have to recreate it.
	That statue survived. If you look at it actually though, he's holding a book. Important to realize he's holding a book. This was representing the fact that he wrote a very influential book. There are some tips of fingers missing. However, they are missing in a very clean fashion and the suspicion is allied troops took them as souvenirs afterwards, so probably in houses across Ohio and Illinois, you find on a mantle shelf somewhere the end of a finger, and people will say, "Oh, that's from my grandfather. He brought that back from Italy." Maybe one day it will get reunited with the original. Other than that, there was no damage to this thing. 
	It's a statue of Leonardo. It's one of two images we have. The other one is taken from a woodcutter, which is a little bit earlier, to which color has been added by some person with Photoshop to try and create a sense of this person, appropriately under the present  [inaudible 00:10:48]. Lived from around 1170 to around 1250 as far as we know. Spent most of his life in Pisa. The dates are iffy. The Pisa part is known. His father was an international businessman.
	We know some of this because Leonardo left a brief record of his life. If he hadn't, we'd have no knowledge whatsoever, but what little we have, comes from Leonardo himself. Okay. He then traveled to Buja when he was a teenager. He learned arithmetic in the schools. People did learn basic arithmetic. He learned it. He had a flair for it. He had a good mathematical mind. When his father went across to North Africa to the port of Buja to represent the Pisan traders, acting as sort of a trading representative customs official, he invited his son to join him a few years later when he was old enough to help with that work. 
	When he did so, Leonardo takes a boat and goes across ... actually travels by boat to the Port of Pisa, gets on a ship. Typically ships didn't cross the Mediterranean. They went all the way around the edge of the Mediterranean. They hugged the shores, both for navigation and to avoid storms. These were long journeys of several weeks. 
	So this teenager on his own goes to north Africa. When he's there, he sees the muslim traders in the cafes on the sea front there. The trading was on the front of the Mediterranean, on the shore there. He saw them using this method of calculation using these ten represent, these digits zero through nine, and using the traditional methods that are still being taught today. 
	Now, many people were using those of the world, and many people would have come from Pisa, including Leonardo's father, and seen that, and they would have thought, "Oh, that's kind of cute." Well, Leonardo did not. He thought, not only ... we know this by looking at the way he wrote his book. He looked at that and said, this is not just cute. This is huge. This is absolutely huge. This is a way of giving people, anybody, the ability to do arithmetic, which is the essential ingredient you need to set up in commerce and trade. 
	This is a world where there was trade, commerce, and engineering. There's one thing you need for trade, commerce, and engineering. You need arithmetic, and you need to be able to do it, or you need to be able to hire people to do it. So Leonardo clearly realized that this was a way of democratizing arithmetic. That you could give it to everybody. The weird thing is, the people who'd been using it for several hundred years, the muslim traders, picked it up, but didn't sort of ... they used it. They recognized it's utility, but no one seems to have realized that it could carry you further. It wasn't that they were stupid, it's just that the world wasn't ready for it. 
	The circumstances in the 13th century were such that when someone reflects on the power of arithmetic, it could have a big impact. It's like the personal computer revolution in the 60s. It was only when microchips became cheap and widely available that you could put a computer in everyone's homes. It turns out, and I'll talk about this later, that Silicon Valley in the 1960s, 70s, 80s, in particular, it all happened in 13th century Tuscany, down to the most refined detail. It's remarkable how that was history [inaudible 00:14:21].
Male:	Buja is not [inaudible 00:14:24]. Is the city still there?
Keith Devlin:	Yes, but it's called ... it's got several names. That's one of the old Latin names.
Male:	What country is it in?
Keith Devlin:	It's probably now ... well, it's hard to say now because I think it's now called Libya, but who knows what country that is. That part of the world. The north Libya to Italy sort of area. It's got three names. If I gave this talk seven or eight years ago when the book was new, it would have been fresh in my mind, but Buja is one-
Male:	Go on.
Keith Devlin:	Easily found. Okay. That system had been ... it was a system that the Indian, the Hindu mathematicians had developed in the first several centuries of the common era. It was picked up by these traders. The muslim traders traveling up and down. They recognized it's utility, and they started using it. They knew a couple of things were really important for trade. Prior to that system becoming available, there were various ways of doing arithmetic. First of all, and certainly in Europe, a lot of the numbers were recorded by Roman Numerals. Book keeping people in Florence, for example, all of the records were done in roman numerals. 
	Now, roman numerals is fine for recording numbers. It makes addition and subtraction trivial but it's not well suited for multiplication and division, which are the key operations you need for doing trade and commerce. So, prior to this system becoming available, there were two methods that traders and people in commerce would use to do arithmetic. One, they used an abacus board. Just a board with lines and pebbles, and you moved pebbles around. There was a Chinese version of this [inaudible 00:16:09], where you put the beads on wires and you change the algorithm a little bit, but it's the same idea. You just move things on a board, and you have the different columns that do different things. 
	When you learned the rule to that thing, you don't need to think about it. You just move the things and, you know ... you can find videos on youtube of people doing it very fast. One of the methods was using some form of mechanical device like an abacus board or a wired abacus. The other method was finger counting. Now, that isn't just one, two, three. A system was developed over many hundred years of finger reckoning, which was good for numbers up to ten thousand, and the traders became extremely good at counting with numbers with a limit of around ten thousand, using the fingers in various positions and combinations of the fingers. Anyone who's tried to program a Japanese wrist watch knows that you can get a lot of complexity, but it's very confusing [inaudible 00:17:03], or the Rubik's cube is an example, just by using combinations people were able to do the arithmetic.
	Those were the methods. Finger arithmetic or abacus boards. Both of them require quite a lot of training. I mean, to become quite facile, especially with finger arithmetic. It was extremely complicated. Books written in the 12th, 13th century showed you how to do it, including books written by Leonardo, but it was complicated and took a lot of practice. Hindu arithmetic, on the other hand, is so simple that you could teach it to a five year old child, and we've been doing that ever since. You just have to write the numbers in columns with the lined up on the right, and just do things in the columns and carry and things. You could just learn the rules and carry on that computation.
	One thing that happens with the ... you need sort of paper to do this. You couldn't do this in the days when people were writing on the sand. It wasn't the best way of doing it. So, this was when there was enough paper available. When paper or something with writing materials were cheap. Something had to be in place. Then, people start using this thing. There's another advantage to the Hindu arithmetic system, which is incredibly important for commerce. Your calculation keeps a record of every step. It's its own [inaudible 00:18:19]. 
	If you're in business, and you're in business in a society, which is more than two people trading. Most of the muslim trades, it was people on camels trading one to one, but the moment you got to the point where some person had a trading empire or trading company where you sent people to negotiate for you, you wanted to be able to keep track of where the money went. It wasn't enough that someone went out and did a calculation. You needed a record of that calculation. Hindu arithmetic keeps its own record. Someone does the calculation in the company book, you can track the calculation. You can see what was going on.
	This was a system that anyone could learn. You could practice it a little bit and become good at it, and it kept its own record. It kept its own trail. This was an incredibly powerful method for doing arithmetic. So much so that when Leonardo was clearly completely smitten by it. When he was finished working with his father, he traveled around a bit in the muslim empire. Talked to traders, found out a little bit more about this. 
	Then, this new thing called algebra, which had been invented in 9th century Baghdad, the name coming from the word [Algabra 00:19:32], which is a technique for solving an equation, and one of the things that happened when the Arabic speaking, Persian speaking traders and scholars in that part of the world, when they picked up this method, they generalized it, they beefed it up, and they figured out a way of doing arithmetic at scale. They scaled it up by providing standard methods. That gave us modern algebra.
	Leonardo sees all of this and learns more about it. When he goes back to Pisa, he ends up writing a book, which means you're sitting up and you're writing long hand in Latin, in his case, and you write what an incredibly large book. He writes [inaudible 00:20:12] when he goes back to Pisa. At least, he finishes it when he goes back to Pisa. By the way, he did spell abacus with two Bs. I like to think that he realized that in the days of early search engines, you want to misspell the word so yours comes up at the top if people look for it. It's one of things that we get-
Male:	Fire alarm? 
Keith Devlin:	It's something kind of strange, but anyway. 
Female:	[crosstalk 00:20:40] Weather alert. 
Keith Devlin:	Maybe it's- [crosstalk 00:20:42]. Oh, there it comes. [inaudible 00:20:46]. It's one of those days. 
Keith Devlin:	He deliberately misspelled this to ... interesting, because scholars have often tried to correct the spelling, but he knew what he was doing. He wanted it to be different. My agent actually tells me that one word in the title has to be a word you make up or misspell deliberately, especially in a search engine. Okay, but it was a book of calculation. It was a book of doing the arithmetic without the abacus, if you like. It makes no sense to all it the book of the abacus. It was the book of the non-abacus. It was finished in 1202. That book has generally been credited with bringing the Hindu Arabic system and it's arithmetic to Europe. It certainly wasn't the first thing that brought the Hindu Arabic numerals to Europe. They had been coming in for the last 100 years or so before that. 150 years. However, what this did was bring in a very accessible way arithmetic using Hindu Arabic arithmetic, and that was new. It was generally credited to Leonardo through this book Liber Abaci of launching the modern commercial world. 
	I'm opening up a lot of threads now that I will eventually tie together. The discovered story is this. This is the story we tell all the time at the beginning of math classes to graduates or whatever. This number system began in the first six or seven centuries of the common era. It was formulated in a book by [inaudible 00:22:19] around 7th century time where all of these things were written down, including zero and all of the rules of arithmetic. 
	It was then taken by the muslim traders, carried north on the silk route, until the 9th century when [inaudible 00:22:34], whose name ... he gives us the name algebra. He also gives us the name algorithm. He wrote two books. One book describing the algorithms for doing arithmetic, and then another book describing the algorithms for doing arithmetic at scale. In the title of that second book, he uses the phrase 'Algabra' and so we now call that stuff algebra, which actually means ... could be dangerous getting on an airplane with an algebra textbook these days. Be careful. Look a week ago in the news in California, if you think I'm joking. It's getting really scary on the airplanes these days. Not because of terrorists, because of TSA and all the other going on. The least risk we fear in the United States is terrorism. Right? Do the math. 
	Then we see [inaudible 00:23:21] wrote this in two books. This is a story of books. In those days, books tended to be very influential. If a book became a leading book, that sort of sent the thing on its way. We go a book in the 7th century. A book in the 9th century, then another book in the 13th century, Leonardo of Pisa's book, and that was supposed to have taken this Hindu arabic arithmetic, brought it to Europe ... it certainly did that, but the other claim was that it then led to everything that people did with arithmetic. 
	The question, however, was, "Was that part true?" This is what happened. Within a few decades of the appearance of Liber Abaci, we have coming out of that one little part of the world, banking, using from the original word banker. Basically bankers traveled around, and they would set up on a tree stump or a bank, and that's where they would do the money work. That's where banking began. You have banking began. You have insurance coming out of that part of the world. You have the beginning of genuine international trading empires, stretching north through Germany and then through Europe. You have double entry book keeping coming out of Florence. 
	All of this happens within a few decades of the appearance of this book, Liber Abaci, written by Leonardo Fibonacci. That is one incredible combination. The question, as always, is there any causation going on? There was always a question mark as to ... oops. Too fast. There was always a question mark as to whether Leonardo was actually the cause of that. Book appears, lots of stuff happens. 
Male:	What are the colored regions? Is there any significance to your story here? The colored regions on the map?
Keith Devlin:	What'd you say?
Male:	The colored regions. The blue, brown, etc. 
Keith Devlin:	Oh. This is the best map I could find of what it was like in the day of the 13th century. This is a representation of the different whatever they were ... they're bigger than the city states, but those are the regions of Italy that were significant in the Medieval period. 
Male:	Okay. 
Keith Devlin:	All right. It is worth remembering that Italy was sort of, in large regions and even smaller regions, each of which have their own currency, so doing trade in those days meant you had to constantly convert currencies. Once it had converted to trading with another, you had to do lots of ... The arithmetic was huge. Multiplication and division was absolutely central to that. You had to do it with everything. The weights and measures varied. The currencies varied. 
	In fact, those tend to be the clues to answer the question whether Leonardo was responsible, because you can put a time stamp on things, and you can put a geography stamp on things. You can follow the spread of the ideas. You can follow the girth of arithmetic by looking at the numbers that were used in the examples in the books, because when a book was copied- and all the books were copied by hand- when someone copied a book from Tuscany to Umbria, not only were they put in the local dialect, of one of the [inaudible 00:26:32] Italian dialects, they would change the currencies to the local currency. They would change the weights and measures to the local ones. 
	By looking at all of the examples in textbooks, you can put dates on when things were written. That's part of what happened in reconstructing the entire story we have about Leonardo. I wasn't doing that myself, I was the first person that came in from outside as a sort of journalist, if you like, and read all of that research, and saw what they had been doing. 
	There was always this question as to whether the appearance of Liber Abaci was the pivotal thing. Now, you might say to yourself, well, there was nobody else who [of fame 00:27:10] around at that time. He was the one with the mathematical [inaudible 00:27:13]. He spent those years learning it from the muslim traders and the scholars that he met with. He had all the knowledge. He brought it. He published a book. Who in his right mind or her right mind would object to that?
	Well, they had some iffy stories to get to that, because it turned out there was a big, big question mark in that data. That question mark wasn't resolved until 2003, a year after I started my project. [inaudible 00:27:40]. One thing I realized, there were many reasons to not start and spend several year writing a book on Leonardo, because there was nothing known, but I thought, I want to know. I just want to know for myself. I'm going to do it, and I got lucky, and then I got lucky, and then I got lucky. At least five times, I got unbelievably lucky. With the result, by 2010, I was able to sit down and write a book. In fact, I sat down and wrote two books, and I'm just writing a book to sort of summarize the whole process.
	I just got lucky. Sometimes it makes sense to just go ahead, and you'll get lucky. I'll talk a little bit about the luck later on. There were some incredible strokes of luck that allowed me to move forward with this project. We'll come back to the obstacle later. Why did people think that he might not have done it? There was a big obstacle, and I'll come back to that. 
	First I want to just say a little bit about the guy himself. Well, actually I did want to do that very briefly. All of that stuff about the financial world I just mentioned about him having an impact on trade and commerce, you don't have to just take my word for this. No less a scholar than the very distinguished finance professor at Yale [inaudible 00:28:53] roughly the same time as I was doing my research, he was doing his research. 
	By the way, the reason we did this was that in 2002, an English language translation of Liber Abaci came around. He and I both got a copy, and we both read it, and we looked at it from our own perspectives. I used it as a way to try and get inside Leonardo's mind. He was looking at it to see where did modern financial instruments arise. By looking at the book, it was a finances professor, he interpreted it in a very different way. This is fine, because you're not expected to read it, but this is just a summary of some of the things he said. Basically, everything for which people have gotten Nobel prizes in economics can be traced back to stuff that's in Liber Abaci. Leonardo would have gotten a Nobel prize in economics if there had been one, we might like to think.
	Let's talk about this guy himself. Leonardo. That's the beginning of a manuscript in Pisa. One of the versions of ... by the way, there are 14 copies of at least parts of Liber Abaci in existence. Three of them are almost complete copies. One is Siena. One of the complete ones, one of them is in Siena. One is in Pisa ... no. One is in Siena, one Florence, and one is in the Vatican library in Rome. Those are the three almost complete ones, then there are another 11 copies scattered around, some in Florence, a fragment in Siena, and one or two in Pisa. There are little bits of things, but three copies dating from roughly Leonardo's time, a little bit afterwards. Nothing in Leonardo's original hand.
	This is from the 2000  and ... well, it was one of the ones that was in ... I took this, I got this image made in 2002 on my first visit I got a digital image made. This is in the Siena Public Library, and this was written roughly in the late 13th century. What he says at the beginning ... this is the 2nd version [inaudible 00:31:02]. He says, here begins the book of calculations composed by Leonardo Pisano, family [inaudible 00:31:07] in the year 1202. 
	This is Leonardo's own hand ... I mean, it's his own words copied by a scribe. The name Fibonacci was very recent. That was ascribed to him in 1838 by a french historian here on [Libre 00:31:24]. I guess the name Libre is just coincidence. Neat. Leonardo would actually just have been known as Leonardo, or when he became distinguished, Leonardo of Pisa. That's how people would give names. That would have been his name. You can see why a historian would want to give him Fibonacci, to give his a surname, because it helps to sort of ... not least, because there was another Leonardo that came along a little bit next that was very famous, so you need to be able to distinguish Leonardo from the other Leonardo. 
	If you see Leonardo on it's own, people default to da Vinci. I'm sure that google, in your case, google will default to Leonardo da Vinci. In mine, it will default in complete to Leonardo of Pisa, but that's because I've searched on that many, many times. Fibonacci comes from looking at that phrase at the top, because in that book he [inaudible 00:32:25] which literally means, son of [Binacci 00:32:27]. You know, the were no surnames, so that really means I'm in the family that's become become known as Binacci because there was Binacci's around at some point. 
	These names got acquired and just built up. This really means from the Binacci family. That phrase composed by Leonardo, family Binacci, that's a translation done by a successful scholar who sort of interpreted it. It's not a complicated translation. That's really how we should interpret that. That's where the Fibonacci comes from. [Famiglia Binacci 00:32:59]. It's a clever way of making up a name, and it's a nice name and it sort of sounds like it's been around for a long time. You could use it to open Italian restaurants. There have been movie villains [inaudible 00:33:13] called Fibonacci. It's a nice name, and it sort of filled a hole in a history book.
	As soon as you mention the word Fibonacci, people say, "Oh, yes. Fibonacci." The person who invented or discovered the [Fibonacci 00:33:27] sequence. Well, he didn't. It had been around for generations. Hundreds of years before that. You'll find it in manuscripts going back hundreds of years. 
	What happened was, when he was writing this book Liber Abaci, Leonardo wants to put in ... its adorable. It's hundreds and hundreds, six or seven hundred detailed calculations to do with weights and measures and trading. It's a heavy duty book. Being a good marketer, understanding you need to keep people's attention, he spiced it up with these fun little problems, including one about a fictitious rabbit problem. This was one he just found somewhere. He had read many books, so he obviously come across this one. This gives you a good excuse to do lots of additions and get practice at addition. This was the problem. That's actually a statement towards the bottom. That's a direct translation from the Latin. That was how Leonardo himself posed the problem of the Fibonacci sequence, the rabbit sequence. 
	He didn't invent it. There was no indication in anything he wrote that he was interested in it. He almost certainly wasn't, because he was frying much bigger fish. He was changing the world of commerce. He wasn't interested in a fictitious rabbit population, but it was a fun problem. One of many fun problems in the book. [inaudible 00:34:50] recreational mathematics problems. If you solve it, and you interpret it correctly, you end up with the answer 377 furs. 
	All the other stuff about the Fibonacci sequence about it being related to the golden ratio and so forth, that was all much later. Almost certainly wasn't known to Leonardo da Vinci, much, much later. Most of the things you read about the golden ratio were actually invented in the 19th century by a German writer of popular books. 
	Going back to the introduction, there's two ways to write a popular book. One is you take the facts, and you try to make them interesting or bring out the interest and the other way is you just invent facts. Unfortunately, the German just invented facts. Things to do with the [inaudible 00:35:36] and the beauty of the human face and so forth. You won't find those references before the middle of the 19th century before this German book appeared with them in it. You can [inaudible 00:35:46]. Seems as we're about to decide the presidency of the United States and sent them away. There you go. It works. 
	Okay. One of the nice things about having dual citizenship, you can criticize two countries with immunity, and one of my passports is a European passport, so I can criticize the whole European union and get away with it. 
	Books Leonardo wrote. This is a little image I showed. That was just the very top part of this first page of this book in the Siena Public Library. I love this is in the public library. You can walk in off the streets and ask to see it, because you don't have ... well, if you have an Italian citizenship and you're a member of the library. You can just sit down and read it. If you're a foreigner, not from Italy, they will ask you to deposit your passport with them, but then they'll bring this book and they'll just let you sit down and read it. Kind of awesome to sit there with a 13th century book, one of three that only exist today, and sniff it and look at it and measure it and read it and turn the pages. Absolutely astounding. There was so many manuscripts in Italy that so long as they like the look of you, they'll just let you look at them as long as you want to. 
	That was from the Siena Public Library. The first edition [inaudible 00:37:06] what he did. Leonardo wrote a bunch of books. He writes this one in 1202. That was the first edition. No copies of that have been found. He completed the 2nd edition what was more than a quarter of a century later, because what happened was the first book made him famous. He became famous very quickly throughout Italy. He was a big shot in Italy. People started using it ... well, they ideas very ... perhaps a hint as to why there was a big question mark about his origins. 
	It was actually at the request of the emperor, [inaudible 00:37:43], he wrote a second edition much later in his career, of which 14 copies exist, three of them complete. He wrote a shorter account, and we know this because he refers to it in his various writings, which was ... that first book was [inaudible 00:37:59]. It was written in deep Latin. It was modeled on [inaudible 00:38:03] elements. There were [inaudible 00:38:04]. It was thick. It's heavy. It was not designed for reading by a lot of people. 
	So, he writes a simpler one. He's a good marketer. He says, I'll make a simpler version that people can read. Arithmetic for dummies, is what we would call it today. Rings that out. No copies exist, so we don't know what it looked like. He writes a book on geometry, practical geometry. Geometry for commoners and architects, also written with proofs, modeled after [inaudible 00:38:32]. He was writing for the scholars. Other than that first book, that shorter book, he's writing for scholars. 
	He has this deep book about ... he's capturing all of the known knowledge. Geometry textbook. He then does the medieval Italian version of jeopardy. He goes to the emperor's palace and he's giving a public demonstration of his mathematical prowess before an audience where they throw questions at him and he answers them, and some of the answers are so astoundingly good, that he writes that up and dedicates that book to the emperor. That's the book called [inaudible 00:39:09]. 
	Then he writes what we would regard as an elementary algebra book.[inaudible 00:39:15], the book of squares, which for 13th century, is pretty darn impressive. He writes those, sandwiched between two versions of Liber Abaci. This is a big career. He's a big shot. He travels around. He's Leonardo of Pisa. He ends up becoming a government ward in Pisa. He's an advisor. He's put on a pension. He's a really big shot. 
	Then this other stuff happens. This was the first [Persian 00:39:46] country in the revolution. 1202 the first edition comes out. Since the 1960s, we have known that within a couple of decades of that book appearing, increasing numbers of handwritten manuscripts appeared of basic arithmetic. Think about it. Books are written and you want to learn something. Once it was known that there was a method for doing arithmetic, everybody wanted to do it. This was about to become a best seller because here was how you can create your own start up company. This was [inaudible 00:40:18] back in the 13th century. Here was a method that allowed ... this is like acquiring a personal computer. You had to do it in your head, but it was the method. 
	These algorithms are powerful. People wanted them. The only way you could get them is by writing your own books, so typically what people did was they would borrow whatever copy of the book arrived in town, if it was Florence or Lucca or wherever, the book would come in. You'd get a copy, you'd write it as quickly as you could. You'd make a copy. You'd give the original back, and then you'd start to work through your copies. 
	You'd write your own book, then you'd read your own book, and then you would work on your own book in the margin. Many books, and this is one of them, looked like that. It was copied, faithfully reissued, then the person started to work through it and their diagrams and doodles ... this person liked to doodle when he or she was thinking about arithmetic, and wrote things in it. There were hundreds of these things written. Actually, probably thousands. 250 have survived. Since they were written by individuals for their own use, you've just got to make a wild guess, if 250 have survived, of books that have no other value than to the person, how many thousands must have been written in that period? 
	These were not discovered until the 1960s. Why would we discover? These were not books written by famous people. These were books written by ordinary people that somehow have managed to survive and find their way into the archives. Here, you can even see the grooves. These are the ones that have survived and have been cataloged. 
	This one was in the ... actually, the one on the top right is the one that we know from the 13 ... from 1294. Then there were eight, ten ... they went up and down, and then they reached the largest number around 1476 to 1500. You might ask yourself, what happened around 1476 that would have meant people stopped hand copying books? Well, think about it for a minute. We'll come back to it, but people did for whatever reason stopped hand copying books. 
	This was a [inaudible 00:42:19]. This was before social media. These had to carried on the backs of camels or horses or on a mule to houses, so these were individual books, but you've got a growth. You've got a huge growth. Not only was that all over Italy, you had these evening [clusters 00:42:35], these schools set up to go over the commercial arithmetic, practical arithmetic. We have records for at least 20 in Florence alone, in that period. 
	There was the growth of interest in arithmetic, fueled by, we assume, the appearance of Liber Abaci. After which, there was no more record of Leonardo. In many of those books, these hundred books, the author would say, this is arithmetic in a style presented by Leonardo of Pisa. That eventually died away, but initially people referred to the fact that this was Leonardo's style. It was definitely in his image. 
	Then all of a sudden, there's no more references in the history book. In fact, it almost disappeared from history all together. The reason was, and this is what happened around that time, we invented the printing press. Arithmetic was in such demand that after the printing press came along ... I mean, everyone knows that the Gutenburg Bible was one of the first books printed, if not the first book. 
	The second or third was a book on practical arithmetic, and then more, more, more. Among the books that were printed very quickly using the printing press was arithmetic books. [inaudible 00:43:51]. Now of course, since currencies change, these are practical [inaudible 00:43:56], the book he would put into print would be the most current one, with current weights and measures, the local common currency, well written in the most [inaudible 00:44:05] form. You would put recent manuscripts. You wouldn't go back 200 years to a book of great length, written in Latin, by this person that's been long gone. 
	No one was going to put into print Leonardo's book Liber Abaci. There's already [inaudible 00:44:22]. The dust was already gathering on that. What was brought into print were the more recent books. The first one being published just outside of Venice, shortly after the printing press came along.
	So, that basically put the nail in the coffin for Leonardo's record in the history books, with one exception. Among the books that were printed, was a book by this very distinguished mathematician, and if you google him you'll find that he was actually a pretty distinguished mathematician comes up in history of algebra and so forth, and he writes this book, Summary of Arithmetic, Geometry and Proportions for functionality. This is a printed book, and he actually, as a scholar, maintained this standard phrase that you would see in many of the early popular arithmetic books. Since we follow for the most part Leonardo Pisano, I intend to find out if any enunciation mentioned without the name of the authors is to be attributed to Leonardo. He basically said, "If I don't tell you who did it, this is Leonardo." 
	He writ a very strong statement that all of that stuff came from Leonardo, at which point you might say, "Okay. Why would anybody think that Leonardo wasn't the person who started this entire commercial revolution? The first person of computed revolution? I mean, it's just ... come on. It all happened after the book. There's just so much evidence." 
	Well, here was the problem. There's Liber Abaci, 1228. One of, essentially. Three copies still exist. Maybe only 15 or 16 copies were ever written. It was a very big book. Hard to follow, written in great detail. Then you've got these so called Abacus books, of which there were probably thousands. That was the one that came out around 1290. All of those authors copied from each other. We can tell because the way the currencies changed, you could do literally forensics, and you could figure out when they were written, where they were written. You can sequence these things. They were copying from each other all the time, sometimes with an attribution, mostly they didn't because they were just writing it for themselves. These were people's own notes. Copy, copy, copy, copy. You compare any two of those, you can see which one came first over the other. There was virtually nothing in common between any of those thousands of books and this one. The mathematics was in common, but none of the examples, none of the exposition, none of the phraseology. That book was set [inaudible 00:47:00] any of those. Something else came in between them.
	Now, the assumption was, Leonardo's book written for merchants. His little book. His arithmetic for dummies. It seems obvious, but a teeny, weeny little problem. We don't know what it looks like. Without the evidence, you get off. This is not real reasonable doubt. This will work in a civil court, but not in a criminal court. There's a preponderance of evidence, but this is not beyond reasonable doubt because there is reasonable doubt. There were scholars who actually built their careers ... I don't know what their doing now, but they built their careers on saying, "No, it wasn't the case. I'm actually gathering considerable evidence against ..." They were good scholars, because there's a lot of evidence you can put against this happening.
	The way this was resolved, and I know the time is coming on, but this is a story with a very fast ending. If you ended up looking at all of his other books, one of the things that happened with these practical arithmetic books, many of them, they often include in a chapter on geometry, but geometry is not in Liber Abaci. It's in his practical geometry book. It looks as though Liber Abaci and his book on practical geometry, the material in both of those, fit in to this book on practical ... these books on practical arithmetic, these thousands of them. 
	The assumption was absolutely that when he wrote the smaller book, it was a summary of both Liber Abaci and practical geometry, both arithmetic and geometry, and it was written in a fashion that made it accessible to people to start copying. Whether Leonardo wrote that in [Italian 00:48:40] or Latin, we don't know. Someone may have translated it, but it was written in a form that was accessible. Wouldn't it have been nice to know what it looks like, and just nail this sucker? 
	This is one of the points where I got lucky, because one of the people I got to know on my 2002 visit was a person called Rafael [inaudible 00:48:59]. In 2003, she found the copy. Wow. I did the book and ... so, the next thing, I turn it over to the library where it was found on another visit, because I couldn't get in that time. I had to leave. I've still got a day job in Stanford. So, I went to [inaudible 00:49:22]. 
	This was a missing link. This person who found it, she was a former algebraic geometer, and then algebraic geometer sort of person, and then she just tuned into history and became a ... she's now a direct [inaudible 00:49:37] of a medieval mathematics at the university of Siena. There, she's in her office, and if you walk through that door, which is about 20 meters north of the [inaudible 00:49:46] in Florence, so that street, and you go through that non script door, when you get past the guard, which you won't get past, but I do because I've got a pass. I got lucky. 
	You can't get into the archives in Italy without a pass. You can only get a pass if you're an Italian with a lot of archival history, or you get lucky and someone [inaudible 00:50:09] to get a pass, which gives me ... I actually have a pass which will get me into any archive in Italy. Over drinks, you can bribe me, and I'll tell you how you get one of those passes. It's one of the most valuable possessions I own. A Stanford library card did not get me through that door, but this pass got me through instantly. That leads you into this beautiful room, and in that beautiful room, you find this manuscript, and that is a very early copy. Probably a first edition copy of Leonardo's book for merchants, and you can look at how the ideas spread. That entire genre of thousands of books.
	So at this point, we are looking at the book that launched the modern world, at least in the first or second copy. You can see how the person had sort of written this, and then started using diagrams and working through it, and there's bits of geometry in there. 
Male:	Is it in Latin or Italian? 
Keith Devlin:	This is in Italian.
Male:	Is it in Latin or Italian?
Keith Devlin:	Yes. The answer is yes. This is Italian. This is a book in [Italian 00:51:11]. Yeah. It begins with that phrase, but then it was an early one. People did that in the early days. Leonardo was barely in his grave at this point. People did do that. That sort of tells you nothing. That only became significant when Pacioli used that phrase, but we now know that this was the [change 00:51:31]. Liber Abaci, the book for merchants, and then all of ... that actually is an abacus book that sold for about a half a million dollars in new york a few years ago. It's a common version of these things. They were [inaudible 00:51:42] at the time. 
	We now know what the thing is. We've got it's contents. Part of the reason it was important to know the contents was lots of other scholars jumped on and got collaborating evidence, so lots more linguistic forensics sort of nailed the fact that ... this is just one page. This is meant to be [inaudible 00:51:58]. A bunch of papers that show that this things all fits together. This is as good as evidence as you're going to get. 
	Now, we can go back to that question. We can remove the question mark, which is much easier to do with cleaner than it was back then. Sometimes technology is faster than the historians. Now we definitely know that that was what happened. I'm going to finish by just showing you some of these manuscripts, because they're just cool to look at. 
	If you want to see the one in Siena, you can see it. It's a public library book with a reference in the public library. In the days when I went, it had a beautiful entrance, but then they put devices to prevent you taking anything to blow it up, and so you have to go through a different door and you have to go through a security thing, but back in 2002, it was a delightful place. It looked like an old hotel, the way you might expect to see [inaudible 00:52:51] walk out or something. 
	When you walk through, you'll be given this book, and here's some of the pictures. I got images made of these things, high definition digital images. Not just of the calculations in the margins. If you're interested, I'll tell you why the calculations were in the margins and not in the text later on at the end, the Q and A. 
	I just want to show you some of these. Notice that they also tended to write with numerals in red to distinguish them. Diagrams in the margins, rather than in text. There was a good reason for that. If you go to the Florence Central Library, and you've got one of these magic cards, you can get in to see this manuscript. Same content, just looks a little bit different. Has a different feeling. Different smell. Different texture. There's nothing like having a book in your hand from the 13th century. Try to imagine how many people looked at this and learned it in several empires and things. 
	There's also some memorials you can look at. there's the statue I've already mentioned in the Campo Santo. There's various images, including images of it when it was previously in a public park where the pigeons used it as a restroom, as you can see from all of the gunk on it. That's the [inaudible 00:54:17] describing the origins of the statue. Also, this is on the banks of the Arno. Next to that bridge that we saw that had been destroyed, you go along there for a 100 meters or so and in what is a city archive, you'll find a plague on the wall, which is a commemoration in the 19th century after they rediscovered him. This was after Leonardo was rediscovered. Please realize that we've got this famous ancestor, so they moved fast to create statues and to create plagues and things to honor him. 
	There it is in [inaudible 00:54:48], in it's building. They give us a little bit of information about Leonardo. We know he was still around in 1241 because he was honored by the city, so this is evidence we have that he was recognized as a big shot in his own lifetime, and remained so until the printing press obliterated him for 300 years. 
	Pisa has a bunch of streets, or it has a street with a bunch of street signs named after him. This is the [Fibonacci 00:55:20]. I went around and took the photos of the various numbers. In Florence, they have a street in which there were no fewer than 11 signs of Leo Fibonacci. The street's only about 200 meters long. There's these signs everywhere. There's some of them, and there's the rest of them. There's also a building, which is the Association of Computing Professionals in Italy, which is appropriately at 12 Fibonacci. I guess 12 is the best they could do, not Fibonacci number, but it's a good one. I bet they tried to get it. So, there's a street with those things.
	Finally, that was the book I wrote in 2011. I published in 2011. One of the things that struck me when I was doing this research was since I was commuting back and forth between [inaudible 00:56:16] and Tuscany, I was struck by the uncanny similarity between Silicon Valley in the 80s, which was before I went there in the late 80s, when in the days when the map [inaudible 00:56:27] and personal computing took off, and I was actually in Colorado when that subject, half of that happened, it was so detailed. I actually went and got Steven Levi's book about [inaudible 00:56:41], however you want to pronounce it, his book about the creation of the [inaudible 00:56:45] and I went through the entire book, and I basically just rehearsed the words Steve Jobs by Leonardo and the book was accurate about Fibonacci. It was staggeringly accurate, and it was so accurate that I put it in the book. 
	My agent said, "Hey, this should be an E-book." You've got a written book about Leonardo, we should have an E-book about how Leonardo was just a first personal computing evolution. We brought up this E-book, Leonardo and Steve, the young genius who beat apple to market by 800 years, which he did. Exactly the same passage. 
	To finish with, here is why it's sort of uncanny. This is the beginning of why this is an uncanny composition. They both changed the world by making a very accessible book. A laptop in one case, or a computer, and a handwritten book in the first place. These have got modern dressings because that [inaudible 00:57:43]. That statue doesn't have a manuscript, it's got a bound book. That's just a modern version of the thing, but they both produced a device that makes something very accessible to ordinary people. 
	Neither invented what it was. It was an interface issue. Hidden Arabic Arithmetic is just a better interface to arithmetic than the roman numerals. That's a better interface than anything that came out of [Washington 00:58:06]. In both cases, it was all about marketing. 
	I'm going to finish by just pointing out a couple of elements about the marketing that Leonardo did. Leonardo writes Liber Abaci. That makes him a famous guy. This is a scholarly, professional. People listen to him, but he knows that no one is going to read it because it's just for the scholars. So, he spends time writing a simpler version. The book for merchants, because he knows people will read that, and by golly they did and were desperate to get it. 
	Steve Jobs goes to [park 00:58:47] in the late 1970s, sees something that allows him to build a very fancy computer, which he called Lisa after his daughter. The first thing they built at Apple on this model, with a graphic user interface, was this very expensive, difficult to use, cumbersome device called the Lisa. Very powerful. It was built on a device that had been built in [park 00:59:13]. Based on the same design principals, but he knows that that establishes his chops, but isn't going to sell. Too expensive, too difficult, so he builds a cheaper version. A smaller version for merchants. A smaller version for everybody. That's marketing. 
	The ideas established at a high level, then you take it and you don't dumb it down, you just make it accessible with really good interface and really good design. Leonardo did that back in the 13th century. Those are the cool comparisons. You can take me down two or three levels, but what Leonardo did is exactly what Steve Jobs did with apple 800 years later. We are done.