Starting off Fibonacci year…

The HistSci-Hulk woke up briefly from his winter slumbers to cast a bleary eye over a piece by Katie Steckles on the web site SciLogs celebrating, what some are calling the Fibonacci New Year, because it starts with 1/1/23 the first four digits of the so-called Fibonacci sequence. It doesn’t really because the sequence correctly begins with a zero and Fibonacci began it with 1, 2 not 1, 1, 2.

“I bet she doesn’t point out that old Leo wasn’t the first to elucidate this sequence,” the grumpy beast muttered as rubbed the sleep out of his eyes. 

Surprisingly he was wrong, as Steckles does actually point out that the sequence first appeared historically in Indian grammatical studies of Sanskrit prosody. However, much to the annoyance of out grumpy friend, her second paragraph is loaded historical with historical errors.

Leonardo Fibonacci, also known as Leonardo of Pisa, was an Italian mathematician born circa 1170 CE, who – like many historical mathematicians – is primarily remembered for one book he wrote. 

His name was never Leonardo Fibonacci. He was Leonardo Pisano, which translates as Leonardo of Pisa. The name Fibonacci, which unfortunately has become universal, was created in the nineteenth century by a French historian. 

In Fibonacci’s case, the book was called “Liber Abaci” – literally, “The Book of the Abacus” – although it was actually presented as an alternative to the then-common use of abaci for calculation. 

Liber Abaci, which on the title page is actually spelt Liber Abbaci, although Leonardo uses both spellings in the text, has absolutely nothing to do with the abacus or counting board. Abbaci comes from the then Italian term for calculate or reckon and the correct translation of the title is Book of Calculations.

Published in 1202, this was the first European work covering Indian and Arabian mathematics, and introduced the idea of Hindu-Arabic numerals – the standard digits 0-9 with a decimal system we use today – to Europe for the first time.

This was not the first European work covering Indian and Arabian mathematics, that honour probably goes to the Latin translations of al-Khwarizmi’s On the Calculation with Hindu Numerals, (Arabic original c. 825), Latin Algoritmi de numero Indorum, al-Kindi’s On the Use of the Hindu Numerals (Arabic original c. 830), and al-Khwarizmi’s The Compendious Book on Calculation by Completion and Balancing (Arabic original c. 820) all of which were available in Europe earlier than the Liber Abbaci.

The Liber Abbaci was the first presentation of the Hindu-Arabic number system written by a European author, and had a greater impact than the Latin translations of the Arabic works, because it was presented as commercial arithmetic, leading to the abbacus schools and abbacus books to teach commercial arithmetic to apprentice traders in a Europe, when trading was increasing exponentially.

A minor but important point is that the digits for 0-9 introduced by Leonardo looked very different to the ones we know today.

Evolution of the digits 0-9 Source: Wikimedia Commons

Another minor point is that the digits for 0-9 had already been introduced in the tenth century by Gerbert d’Aurillac (c. 946–1003) but not the number system. He used them to label the counters on his abacus.

A more detailed post on the history of the Hindu-Arabic number system can be found here


Filed under History of Mathematics

8 responses to “Starting off Fibonacci year…

  1. It took me a while to decipher ‘He took religious orders and proceeded B.D. 23 November 1615’. What an interesting turn of phrase. A google search for ‘proceeded B.D.’ does not illuminate.

  2. Curious to read that the sequence “correctly” starts with 0,1. First off, this is a matter of convention. It is true that nowadays one usually sets F_0=0, F_1=1, and then proceeds by the standard recursion. But in your post on Year Zero you’ve declared yourself strongly opposed to zero-based indexing, so I think you’d prefer the alternate convention.

    • Michael you are not just comparing but confusing apples with oranges. The Fibonacci sequence or series, as it exists in mathematics today, is an abstract mathematical structure that is conventionally defined as starting F_0=0, F_1=1, as you state. The numbers attached to the years in a calendrical system are the ordinal numbering of a sequence of real objects, solar years. A ‘zeroeth’ year would be an oxymoron, a year that by definition doesn’t exist.

      • I fear your answer suffers from some confusion.

        1 CE is not the first trip of the earth around the sun—it’s every bit as conventional, as much a product of the human mind, as the Fibonacci sequence.

        Or maybe more so. After all, there are good mathematical reasons for setting F0=0, etc. For example, if m divides n then Fm divides Fn. But it makes as much sense for the calendar years to jump from 1 BCE to 1 CE, as it would for the temperature scale to skip from −1° to 1° with no 0° in between. It’s an unfortunate artifact of history, nothing more.

        A little odd to claim that solar years are “real objects”, more physical somehow than numbers. It’s not like you can find the years stacked up like cordwood! But put that aside. The claim that if you have a sequence of real objects, then you are logically forced to index them starting with 1—that’s a non-sequitur pure and simple.

        Suppose a park ranger wants to put mile markers—real physical pieces of wood—along a hiking trail. Do you think he should label the one at the trailhead “Mile Marker 1”?

        This back-and-forth just substantiates the Stephen Jay Gould quote I included in my post Year Zero:

        A subset of these unresolvable debates—ultimately trivial, but capable of provoking great agitation, and thus the most frustrating of all—have no answers because they are about words and systems, rather than things.

  3. Faye Getz Cook

    This post makes me even more cross than I usually am and I don’t even entirely understand it. Time for lunch.

  4. jrkrideau

    Just to help keep the HistSci-Hulk raging:

    Fibonacci, also called Leonardo Pisano, English Leonardo of Pisa, original name Leonardo Fibonacci,

    Oh, happy new year.

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