Holotomial
Analysis

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Section 3         Foreword        Simple-Entry        *Double-Entry        *Closures        *Metrics 
 

3.1

 - Foreword

  
 

Because our mapping came from handling a business space, when it came at utilizing it to describe actual and potential transactions via computable numbers, it naturally came that the double-entry accounting method was a natural means to liaise graphical scenarios with computable numbers.

  

We discovered that we can have a perfect analogy between a T-accounting system and a system superposing complete views as introduced in the previous section.

We will show in this section that creating a map or a balance sheet in a double-entry bookkeeping system are equivalent.

This provides with the advantage that a  mapping is on one side very accessible to most of the people - educated or not to express their cases in a graphic mode - while on the other side the maps may feed any current accounting system.

More astonishing has been that the double-entry bookkeeping drove us to re-discover expressions analog to those of quantum fields and that our maps can be seen as projections of a spherical Riemannian space. This will be shown in the next section.

  

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Parallelism : Accounting - Sciences - Quantum mechanics

Accounting - Sciences - Quantum mechanics

Noticeable is that the double bookkeeping accounting has been described for the first time in "Summa de arithmetica, geometrica, proportioni et proportionalita" by the mathematician Luca Pacioli in 1494 and that - at few exceptions like D. Ellerman - no one has ever considered it as a field of application for the mathematics.

Sciences, engineering and business are looking at balances like a current means of handling their tasks. Very astonishingly, the link with the very safe business accounting system has rarely been adopted in sciences.

We discovered that several scientific domains - and most probably quantum mechanics - may gain understanding - if not sense - at adopting the old business accounting practice that is the double-entry accounting system - seemingly introduced by a mathematician at the end of the 15th century.

Care must be taken that the double-entry accounting system is not simply built as a double writing  practice - like writing twice the same. It is in fact a system which provides naturally with a cross check via the inference of two different view points - say one internal and one external - like explained in the page 3.3.

In particular, it will be shown in the parallelisms exposed in the bottom text frame of several following pages that double-entry practices may bring new insights at questions left by quantum mechanics, in particular by G. Birkhoff and J. Von Neumann in their seminal work on Quantum Logic. 

Other scientists interested within parallelisms between double-entry accounting and quantum mechanics can be found in the following recent references:

- Synergy, Quantum Probabilities, and Cost of Control - John Fellingham & Doug Schroeder - Ohio State University - May 2005

- Quantum Information and Accounting Information: Their Salient Features and Applications -
by Joel S. Demski,* Stephen A. FitzGerald,** Yuji Ijiri,*** Yumi Ijiri,** and Haijin Lin* - August 2005
*University of Florida, Fisher School of Accounting
**Oberlin College, Department of Physics and Astronomy
***Carnegie Mellon University, Tepper School of Business

- Dieter Braun has written a suite of papers demonstrating the usage of Feynman graphs in financial accounting - accessible from in the web page "Bookkeeping Mechanics".