Double Entry Bookkeeping
Double-entry bookkeeping is the predecessor of matrix calculus/algebra. It was often considered[1] to be first published in Luca Pacioli's Summa de arithmetica, geometria, proportioni et proportionalita[2]. Arthur Cayley wrote a short book[3] 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[4]:
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[5]. More recently, Jane Gleeson-White, published a book[6][7] on Double Entry Bookkeeping. To learn a bit more of the original text and how was it written, a paper[8] on the book was published in June 2008.
A partial translation of the original Pacioli book can be found in John Geijsbeek's book[9].
Double Entry bookkeeping inspired Matrix Algebra and later Quantum Physics
This historical relationship has been documented in many well known publications[10][11][12] and A Theory of Justice[13].
References
- ↑ Sangster, Alan (December 2015). "The earliest known treatise on double entry bookkeeping by Marino de Raphaeli". local page: Accounting Historians Journal.
- ↑ Pacioli, Luca (1494). Summa de Arithmetica, Geometria, Proportioni et Proportionalita: Distintio Nona, Tractus XI, Particularis de Computis et Scripturis [Pacioli on Accounting]. Translated by R.G., Brown; K.S, Johnston. local page: McGraw-Hill.
- ↑ 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
- ↑ Gleeson-White, Jane (Jan 25, 2015). Jane Gleeson-White on Monks, Maths and Magic. local page: WheelerCentre.
- ↑ Gleeson-White, Jane (2011). Double Entry: How the merchants of Venice shaped the modern world- and how their invention could make or break the planet. local page: Allen & Unwin.
- ↑ 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.
- ↑ Rawls, John (1999). A Theory of Justice (PDF) (Revised ed.). local page: Harvard University Press. ISBN 0-674-00078-1.