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The historical significance of Double-Entry bookkeeping can not be understated. Prior to Leonardo "Fibonacci" Bonacci bringing it to Pisa from the Arabs in Algi
by notthemessiah 6y ago
The historical significance of Double-Entry bookkeeping can not be understated. Prior to Leonardo "Fibonacci" Bonacci bringing it to Pisa from the Arabs in Algiers, North Africa, there was no concept of "budget" for most merchants, each transaction was a separate affair, and consequently, finance could not scale. There were several attempts at international lending, and it bankrupted the Bardi and Paruzzi companies who lent lots of money to King Edward III, who ended up defaulting on it. The Medici family succeeded where others failed, providing a level of service in banking previously unparalleled, thanks to being able to manage complex cash flows through Double-Entry bookkeeping. (Fibonacci also introduced the Hindu-Arabic numeral system at a time where most of Europe was using Roman Numerals for arithmetic). It made the Republican city states of northern Italy on par with the political power of noble families, and as other countries caught up with Florence, one could, for the first time, seek an education outside of the Church and in their own country.
Every programmer should be familiar with one descendant of double-entry bookkeeping: the integer. Though its binary representation may be more familiar, the formal mathematical construction of the integers consists of an equivalence class of pairs of natural numbers. In the Chinese "Nine Chapters on the Mathematical Art" they describe red and black counting rods denoting gains and losses, and the equivalence class being that taking away a red and black rod at the same time leaves the "total" or normalized form unchanged. Integers took a lot of time to be accepted in mathematical practice, but they were in use for far longer.
- pbourke 6y agoIf you enjoyed this comment you might also like “Double Entry: How the Merchants of Venice Created Modern Finance” by Jane Gleeson-White
- simonebrunozzi 6y agoThanks for sharing this; I doubt I will ever buy a book just to learn about double entry and Venice (despite I love historical books and I have a special interest for Venice). Would you mind sharing a brief summary of what the book says?
- steerablesafe 6y ago> Though its binary representation may be more familiar, the formal mathematical construction of the integers consists of an equivalence class of pairs of natural numbers. That's an elegant construction. It's interesting how different number sets can derived from pairs of a "smaller" set, equivalence classes, or both. integers: equivalence classes of pairs of naturals rationals: equivalence classes of pairs of integers reals: equivalence classes of Cauchy series on rationals complex numbers: pairs of reals It's quite thought provoking to arrive at the construction of complex numbers just by counting apples.
- yesenadam 6y agos/understated/overstated/
- drieddust 6y agoIntresting facts: 1. Fibonacci didn't invent the series named after him. He was merely copying it from the Indians he came in contact. He himself admitted this 2. Hindu arabic numerals are just Hindu numerals. Arabs didn't add anything. Roman numerals reached the world due to Beitish but they aren't called British-Roman numerals.
- divyamistry 6y agoNot doubting these points, but you should always cite peer-reviewed or otherwise verified sources. It makes all the difference between a fact and an opinion. This is especially true when contradicting a widely held belief. Without a verifiable source, these are just "interesting hypotheses".
- drieddust 6y agoI am glad you asked, here are the references. 1. Please read "Liber Abaci". It is right there in the prologue section. Hard to find a free copy of this link hence posting a link to tweet[1] with screenshot of the relevent page. You can also cross verify with Italian version on archive.org[2] 2. Same story repeat itself with Indian numbers and algorithms.[3][4] [1] https://twitter.com/TIinExile/status/1198526477026807809 https://twitter.com/TIinExile/status/1198526477026807809 [2] https://archive.org/details/LiberAbaci/page/n5/mode/2up https://archive.org/details/LiberAbaci/page/n5/mode/2up [3] https://twitter.com/TIinExile/status/1180777105778307072 https://twitter.com/TIinExile/status/1180777105778307072 [4] http://kutubltd.com/book-details.aspx?CID=11&ID=30591 http://kutubltd.com/book-details.aspx?CID=11&ID=30591
- gumby 6y agoYeah, many hindu digits are ostensibly by inspection the origin of the Latin digits we use today in the west, while the Persians and Arabs adapted the system to their own writing (which you can also tell by looking at the actual arabic digit system which has different glyphs but orders the numbers the same way the Hindus did — so numbers are written little endian in Arabic but spoken big endian like everyone else). They are quite reasonably referred to as hindu-arabic simply because the Islamic scholars introduced them to Europe. Likewise we ought to refer to most of Greek philosophy, poetry, and literature as “Greek-Arabic” as without the Islamic scholars who preserved it very little would have survived.
- specialist 6y agoTerrific, thank you. I LOVE learning the history of ideas. Stuff like Burke's Connections https://en.wikipedia.org/wiki/Connections_(TV_series) https://en.wikipedia.org/wiki/Connections_(TV_series) FWIW, 5x5's Critical Path podcast has a few real gems. http://5by5.tv/criticalpath http://5by5.tv/criticalpath
- notthemessiah 6y agoJames Burke's The Day the Universe Changed (both the TV series and accompanying book) have more to say about Fibonacci, specifically in the chapter Point of View.