Double Entry Bookkeeping
Double-entry bookkeeping is the predecessor of matrix calculus/algebra. It was first published in Luca Pacioli's Summa de arithmetica, geometria, proportioni et proportionalita[1]. Arthur Cayley wrote a short book[2] on this topic.
Symmetry and Relations
To realize why Double Entry Bookkeeping is grounded in many profound ideas, one may start with Yoneda Lemma, a concept that can be summarized as Tai-Danae Bradley's statements on her blog[3]:
1. Mathematical objects are completely determined by their relationships to other objectsCite error: Invalid<ref>tag; invalid names, e.g. too many. 2. The properties of a mathematical object are more important than its definitionCite error: Invalid<ref>tag; invalid names, e.g. too many.
The two statements above show that Double-Entry Bookkeeping is a numeric version of content invariance/symmetry over time.
To find an earlier account on the history and origin of Double Entry Bookkeeping, one can read Edward Peragallo's book[4]. More recently, Jane Gleeson-White, published a book[5] on Double Entry Bookkeeping. To learn a bit more of the original text and how was it written, a paper[6] on the book was published in June 2008.
A partial translation of the original Pacioli book can be found in John Geijsbeek's book[7].
Double Entry bookkeeping inspired Matrix Algebra and later Quantum Physics
This historical relationship has been documented in many well known publications[8][9][10].
References
- ↑ Luca Pacioli, Summa de Arithmetica, Internet Archive: https://archive.org/details/A335068/page/n21/mode/2up, Last Accessed: June 2nd, 2021
- ↑ Arthur Cayley, The Principles of Book-keeping by Double Entry, Cambridge University Press, First Published in 1894, Digitized by the Internet Archive: https://archive.org/details/principlesofbook00caylrich, last accessed: June 2, 2021
- ↑ The Yoneda Perspective by Tai-Danae Bradley
- ↑ Edward Peragallo, Origin and Evolution of Double Entry Bookkeeping: As study of Italian Practice from the Fourteenth Century, American Institute Publishing Company, 1938
- ↑ Jane Gleeson-White, Double Entry: How the merchants of Venice shaped the modern world- and how their invention could make or break the planet, Allen & Unwin, New York, 2011
- ↑ Alan Sangster, Greg Stoner, ,The market for Luca Pacioli's Summa Arithmetica, Accounting Historians Journal, Vol. 35, No. 1June 2008pp. 111-134
- ↑ John Geijsbeek, Ancient Double-Entry Bookkeeping, John S. Geijsbeek, Denver Colorado, 1914
- ↑ Demski, Joel; Fitzgerald, S.; Ijiri, Yuji; Ijiri, Yumi; Lin, Haijin (2009). "Quantum information and accounting information: Exploring conceptual applications of topology". 28. local page: Journal of Accounting and Public Policy: 133–147.
- ↑ Demski, Joel; Fitzgerald, S.; Ijiri, Yuji; Ijiri, Yumi; Lin, Haijin (2006). "Quantum information and accounting information: Their salient features and conceptual applications". 28. local page: Journal of Accounting and Public Policy: 435–464.
- ↑ Demski, Joel; Fitzgerald, S.; Ijiri, Yuji; Ijiri, Yumi; Lin, Haijin (August 2006). "Quantum Information and Accounting Information: A Revolutionary Trend and the World of Topology" (PDF). local page.