Episode 407: A Mathematician, The Last Supper And The Birth Of Accounting : Planet Money Jane Gleeson-White, author of Double Entry: How the Merchants of Venice Created Modern Finance, tells us the story of how one mathematics book changed business across the planet.

Episode 407: A Mathematician, The Last Supper And The Birth Of Accounting

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Hello, and welcome to PLANET MONEY. I'm Jacob Goldstein.


I'm David Kestenbaum. Today on the show, the story of an innovation that changed the way the world works and of the man who made that possible. He was a monk, a mathematician, a magician and possibly the boyfriend of Leonardo da Vinci.


GOLDSTEIN: The man's name was Luca Pacioli. And this transformative innovation that he brought to the world is, of course, double-entry bookkeeping. Whoo, double entry.

KESTENBAUM: Jacob, when I mentioned to the PLANET MONEY team here that we were going to do a show on the birth of modern accounting, Chana Joffe-Walt said to me, really? Are you joking? I said, no, no, we are not. It is a great story.

GOLDSTEIN: It is a great story. It's one that we learned from a new book. The book is called "Double Entry: How The Merchants Of Venice Created Modern Finance."

KESTENBAUM: It's by Jane Gleeson-White. Jane has an accounting degree. And she just got obsessed with this topic. One of the first things she pointed out to us is that in order to have accounting, there really is something else that you need first. You need to have numbers. And when our story takes place - this is the 1400s - much of Europe is still using these Roman numerals.

JANE GLEESON-WHITE: You know, I thought Roman numerals must have gone out with the Roman Empire. But, no, they lasted well into the Renaissance. So the problem with Roman numerals, as any school child knows if they've tried to work with them, is you can't add or subtract with them. You have to (laughter) - they're just like a written language for recording numerals. So you cannot do anything with them. So they're these inert recording thing - I mean, you may as well carve them into rock. That's how useful they are. Well, we still do that, don't we?


KESTENBAUM: I mean, Jacob, think about it, right? Say you have 426 pounds of pepper, and you want to write that down. You would write down - and I had to look this up - CDXXVI, which is not useful. It is really just like you are writing out 426 in words, like F-O-U-R-H-U-N-D-R-E...

GOLDSTEIN: Right, I got it. I got it. And, you know, so imagine if you're writing it out in words and you want to do math with that. You know, quick, what's LXIX plus XVII?

KESTENBAUM: I have no idea.

GOLDSTEIN: I think it has an N in it.

KESTENBAUM: I mean, it was really complicated for merchants because like, if someone wants to buy a certain amount of peppercorns from you or wool, how much was that going to cost? That required some math. And Jane says that was a problem.

GLEESON-WHITE: So with the Roman numerals, they had to have what they called an abacus. But it's not the sort of abacus we think of today. The abacus was a board of sand with pebbles on it in the columns of the unit. So that was used for the adding and subtracting. So the bankers and merchants sat around the squares with their abacuses adding and subtracting prices and, you know, quantities.

But then they had to record the results of their sums in Roman numerals in a scroll. And so there was no connection between the working - the mathematical working and the results. So the two things were separated. And there was no trace of the procedures that had gone on before, you know, the addition or the subtraction or whatever the...

GOLDSTEIN: So like the way on math tests when they say show your work.


GOLDSTEIN: In Roman numerals...

GLEESON-WHITE: Yeah (laughter).

GOLDSTEIN: ...There is no way anybody can ever show their work.

GLEESON-WHITE: Yeah, that - you can't show the working, which meant that you couldn't really tell, you know, if there'd been an error or not.

KESTENBAUM: But around this time, merchants in Europe are picking up on something that's being used over in the Middle East - Arabic numerals. These are one, two, three, four, five, you know, what we all use today.

GOLDSTEIN: Jane mentions one philosopher in Europe who said, hey, these numerals, they're super powerful. Every scholar should be learning them. But the church actually accused the guy of practicing magic and sentenced him to life in prison. So this was, like, a big, controversial development.

KESTENBAUM: For the merchants though, these numerals were just super, super useful. It was this new way for them to understand and track what was going on in their businesses. And the center of business at the time in Europe was a crazy, exciting and decadent place - Venice.

GLEESON-WHITE: Venice in that day was, I think, the equivalent of Silicon Valley and New York all sort of wrapped up together because everything was happening in Venice. It was an incredibly wealthy trading center, merchants from all over the world - from England, from Germany, from Holland, from the Middle East. The merchants set the international exchange rates for the whole of Europe and Asia. So it was equivalent to Wall Street, but it also is the center of a brand-new industry which was the printing press.

KESTENBAUM: You write that it was smelly. There was malaria, plague.

GLEESON-WHITE: Oh, yeah (laughter).

KESTENBAUM: And it was known as being sexually excessive.

GLEESON-WHITE: Yeah, because of the swamps, it was excessively stinky. And they used to put incense and perfume around the canals to try and reduce the smell, which probably, I'm sure, only made it worse. It was a place of decadent excess. People had all sorts of strange illnesses, as well as malaria, which the physicians put down to sexual excess. So, you know, once more, I give you Manhattan.


GOLDSTEIN: Venice, at this time, it has become the center of this huge trading network. You know, it's no longer just, like, little merchants selling flour to the baker down the street. Things are, you know, coming on ships, and they're coming in from the Middle East and going out to England. It's really this kind of global hub.

KESTENBAUM: And trading is getting - commerce is getting much more complex. Businesses are issuing letters of credit instead of actually shipping physical gold. And merchants in Venice, to keep track of all this, they were starting to use a very sophisticated system of accounting. The origins of this are kind of obscure. It seems like the first known use of it is around 1300. But at this moment in Venice, it is really starting to take off. At the time, it was known as Venetian bookkeeping. Today, we call it double-entry bookkeeping.

GOLDSTEIN: And that phrase, double entry, that means that everything you do, it gets entered in two different places. And so to just do an example of this, say you're a spice trader and you have $100 in cash and $50 worth of pepper. And you sell, say, $10 worth of pepper. So you write one entry in your pepper account showing that now you have $10 less pepper, and then you write another entry in your cash account showing that now you have $10 more in cash.

KESTENBAUM: So this double entry thing, it basically lets you see what's going on in all of your different accounts. And at the end of the day or the month or the year, it lets you check all that. All those pluses and minuses, they should balance out.

GOLDSTEIN: That's the double entry part. But really, the key thing about double-entry bookkeeping, it's the bookkeeping part.

KESTENBAUM: (Laughter).

GOLDSTEIN: You know, it's a system, a precise system for keeping track of everything that's going on in your business. And it's hard to imagine, but Jane says that really did not exist before this.

GLEESON-WHITE: Previously, the profit was either in kind - you know, so you had three extra cows at the end of your period. You know, with double-entry bookkeeping, it was abstracted into hard numbers that you could compare with other periods and really know that you had increased your wealth by 2 percent rather than by three cows, which is, you know, a much more sort of earthy measure.

GOLDSTEIN: And you can see when you - you have, you know, currency. And you have animal skins. And you have wool. And you have whatever. I mean, if you imagine a universe where people are just keeping track of that by writing in their diary, which is...


GOLDSTEIN: ...What they were doing before. I have this. I have that. I bought this. I saw that. And they're just sort of writing notes all day. At the end of the year, what - I mean, you have your notebook. But it's sort of a nightmare to imagine trying to figure out if you made money, if you lost money, what parts of your business made or lost money.

GLEESON-WHITE: Yeah, absolutely. That was the other benefit of double-entry bookkeeping, that you could itemize the profits in each account. So you knew which account - which - as you say, which products you were doing well in and which you weren't. And then you could start to think about how you would change your business activities. I think it just became, for want of a better word, much more scientific.

KESTENBAUM: OK, so now we have the numbers. We have some people practicing what we would call modern accounting. There's one more obstacle. This big idea, it needs to get out to the rest of the world. And this is where we meet the - sort of the accidental hero of our story. His name is Luca Pacioli.

GOLDSTEIN: David, earlier this year, I was doing a story just about taxes. It was tax time. And I was interviewing an accountant. And I said who's, like, the Michael Jordan or the Muhammad Ali of accounting? You know, who is the greatest? And I'm thinking he's going to give me a partner at some big New York firm or something. And he says Luca Pacioli.

KESTENBAUM: The guy who's been dead for, like, 500...

GOLDSTEIN: Right, yeah.

KESTENBAUM: So Pacioli, he was all kinds of things. He was a monk, a magician. But his real love was numbers and math. Really, he was a math guy. Pacioli, he grows up in a small town, and he makes his way to Venice. And that is where he sees those crazy Arabic numbers. And he's totally taken with them. He's also particularly entranced with this fancy way that merchants are using them to keep their books.

GLEESON-WHITE: He was so impressed. He says it is the best of all booking systems.

KESTENBAUM: And in 1494, Luca Pacioli plays his big role in history. He writes it down. He writes down how to do this double entry thing - instructions and examples. And then he buries it inside this big, huge book he's writing. It's an encyclopedia of math.

GOLDSTEIN: Yeah, clearly, Luca Pacioli is not thinking of himself as the father of accounting, right? He's thinking of himself as this guy who's writing an encyclopedia of all math known in Europe at the time. And, yeah, there's this little section about accounting. I mean, the whole book, it's giant. It would be, like, a thousand pages or more today.

KESTENBAUM: The title is "Summa De Arithmetica, Geometria, Proportioni Et Proportionalita."

GOLDSTEIN: Well done, David. And so this book comes out. And thanks to the newly invented printing press - the great technology of its time - this giant book, it can be mass produced. And Jane, she's seen one of the original copies.

GLEESON-WHITE: Yeah, it's a beautiful leather cover. It's so heavy. You have to sort of read it in a cradle. It's - the pages are densely, densely written. There are no gaps between the letters, so each word is just run on to the next one. There are no gaps between the lines. It's almost impossible to read. But that was how it was at the time. You know, the very, very early days of printing, each - you know, each letter that starts a new page has a woodcut of Luca Pacioli entwined in it. You know, it's very, very beautiful.

GOLDSTEIN: A woodcut of Luca Pacioli. Like, you mean, like, a picture of him?

GLEESON-WHITE: Yeah, of Luca Pacioli holding his dividers. You know, those mathematical dividers, they're like - that you make circles with or that you measure circles. So he's holding a pair of dividers. Yeah, it's a very, very beautiful book.

KESTENBAUM: Jacob, I was thinking this is, like, one of the first coffee table books. I mean, you buy it just to have it around to impress people so people go, whoa, that's a big book. It had math puzzles and games in it. It had information on how painters could use math to get really three-dimensional effects, you know, how to paint with perspective. And the book was a really huge hit.

GLEESON-WHITE: One of the first readers of Luca Pacioli's encyclopedia was Leonardo da Vinci. At the time he was painting what has become his most famous painting, which was "The Last Supper."

KESTENBAUM: Does Leonardo use it to - for his painting? Or...

GLEESON-WHITE: Yeah, yeah, yeah, Leonardo reads the book and thinks it's the coolest, latest thing. It is the coolest, latest thing in mathematics. It's like the ultracool mathematics text of its day. I can't imagine what that would be today.


GLEESON-WHITE: So Leonardo da Vinci reads it, realizes that it's really, really useful for the mathematics of perspective that he needs to paint his masterpiece, which is "The Last Supper." So Luca Pacioli arrives in Milan while Leonardo da Vinci is painting "The Last Supper" to help him with the mathematics of perspective-painting.

GOLDSTEIN: So can we imagine - is it plausible that Pacioli would have, like, gone over to where da Vinci was painting "The Last Supper" and been, like, no, you need to do the math like this, you need to draw the lines like that?

GLEESON-WHITE: Oh, yeah, yeah, totally. They were hanging out together. They hung out - you know, they lived together after they left Milan. It's very possible they were lovers because they both, you know, had homosexual tendencies. They certainly spent a lot of time together. And definitely, Luca Pacioli was there in the actual church when Leonardo da Vinci was painting "The Last Supper," and he was very moved by it.

KESTENBAUM: OK, so this book, maybe it helped bring us "The Last Supper." But also of great historical significance, what Pacioli is known for today - a different little part of the book - Volume 1, Chapter 9, Part 11, the section about double-entry bookkeeping.

GLEESON-WHITE: In the Italian, it is called particularis de computis et scripturis. And it looks as if - the way that it's put into the book, it looks as if it was something he added at the last minute for his patron so that his patrons - citizens could keep their accounts properly and become wealthy merchants.

KESTENBAUM: And one of the first things he writes is, like, you have to - merchants, you have to do an inventory. You have to know what you own. And he gives this example of a typical Venetian merchant who has golden coin, cases of ginger, sacks of pepper, packages of cinnamon and cloves, sandalwood, fox and chamois skins, bank deposits. So he walks them through really the whole double entry thing.

GLEESON-WHITE: Yeah. Yeah, he shows them exactly how to do it from the beginning. So he - as you say, he walks them through the whole thing. He imagines that they have never had an account before. And so the very first thing you do when you're opening your books is to take an inventory. And that becomes your capital. So that is all your wealth. And as anyone knows, inventories are still an essential part of running a company.

KESTENBAUM: So Luca Pacioli publishes this book, and it's sort of an instant hit. It goes abroad, and people start to - people read that chapter, and they start to use double-entry bookkeeping. Is that what happens?

GLEESON-WHITE: Yeah. So what happens is not only does it go abroad and they read that chapter, but that chapter was extracted and turned into a volume of its own. So not long after Pacioli published his book, the Venetian empire crumbled, and the new center of trade was - went to Germany and then to Holland. So as the centers of trade spread, so this new technique was adopted by the merchants in the local regions. So you can see that this one tiny mechanism that was invented in Italy and codified by Luca Pacioli in 1494 spread gradually across the world. And by 1900, it had - it was the basis of business across the planet, which is pretty extraordinary.

KESTENBAUM: What do you think Luca Pacioli would think of the world today and double-entry bookkeeping everywhere, not just in every business - you know, whenever anyone buys a business, they say, show me your books, you know?

GLEESON-WHITE: (Laughter).

KESTENBAUM: If you have - you know, if your stock is sold publicly, you have to, you know, basically show your books, you know, a bunch of times a year. But also for countries - you know, countries keep track of their entire economies basically through double-entry bookkeeping.


KESTENBAUM: What would he think?

GLEESON-WHITE: I think he'd be absolutely astonished. I mean, you know, he, as an aside, codified and published this 27-page bookkeeping treatise in his beloved mathematical encyclopedia. And to think that that had gone on to become the governing system of every economy on Earth and every corporation, every business, he would be astonished, wouldn't he? He'd fall over backwards, I think.


NOAH AND THE WHALE: (Singing) Tonight's the kind of night where everything could change. Tonight's the kind of night where everything could change. The rumble strip clack...

GOLDSTEIN: Jane writes that the last record we have of Luca Pacioli is in 1514 when he took a job as a math professor at the University of Rome. He died a few years later, probably in 1517. He was 72 years old.


NOAH AND THE WHALE: (Singing) Under lamp's light glow and paradise stars an infinity of dancing white light. He says that his debt is to experience only and not to those who'd plan out his life.

KESTENBAUM: You can see a painting of Luca Pacioli and a photo of his huge, beautiful math book on our blog, npr.org/money. We'll also put up a link to Jane Gleeson-White's book. It's called "Double Entry: How The Merchants Of Venice Created Modern Finance."

GOLDSTEIN: As always, we'd like to hear from you. You can email us at planetmoney@npr.org, or find us on Facebook or Twitter. I'm Jacob Goldstein.

KESTENBAUM: I'm David Kestenbaum. Thanks for listening.


NOAH AND THE WHALE: (Singing) Tonight, he's not going to come back home. Oh, tonight, he's not going to come back home. Oh, tonight, he's not going to come back home.

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