Holotomial
Analysis

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Section 1         Foreword        *Issues        *Mapping        Usages        Extensions        Archetypes
 

1.1

 - Foreword

 

 

Holotomial analysis is a method for ordering complexity and for visualizing structural relations within intricate systems.

 

It consists at utilizing holistic (holos) complete observation spaces to slice (tomos) the reality in separated views and at superposing them within a unique observation space.

The holistic characteristic unifies the variables within a unique metric while the completeness enables to link the system states with double-entry balances akin to standard management practices. 

It generates so a geometrical group owning an equivalence with the double-entry accounting and it extends a quantum-like logic by the addition of a universal completeness.

Before the introduction of the method itself, this section exhibits shortly how the experiential motivations emerged via heuristic and operational novel solutions in various domains where they afforded an operational efficiency.

 

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Parallelisms : Experiential learning - Systemic learning - Quantum mechanics - Double-entry accounting - Geometrical spaces


Experiential learning - Systemic learning

- "Experiential learning" refers to cycles that comprise four phases: heuristic learning of new solution from operational practices, a reflection on it, a conceptual translation and a tentative of practical extension into a wider range of field cases (i.e. D. Kolb).

Those four stages may turn out into a continuous and systemic learning process: the conceptualization grounds how the extension of a knowledge can be pro-actively conducted inside or outside of an initial domain, which in turn may feedback where the limits of the knowledge may stand. Getting further requires to restart an heuristic learning phase which may reinitiate a new cycle.

Two experiential dynamic cycle archetypes can usually be distinguished:

- inwards: when done in a restricted operational domain, the dynamics lead at closing cycles inside of operational limits which may conduct to best practices enhancements and confirm specialized knowledge and formalizations.

- outwards: when extended across different domains, the dynamics may eventually cross applicability frontiers more easily. To recover applicability, heuristic knowledge has to be added to nurture conceptualization extension or reformulation. The conceptualizations that are so progressively built from fields and frontiers crossing may gain a larger ubiquity or become generic at several specialized domains - sometimes unrelated in appearance.

As illustrated in the next figure - from A. Castiaux - the first cycle (on the right in the figure) is like narrowing a knowledge field to the most efficient practices within an operational environment while the other cycle (on the left in the figure) is like possibly expending the knowledge field from the exploration of a wider environment:

Alternatively, the next figure illustrates that cycling within uncertainty may increase knowledge at usually generating exploration expenses while restricting knowledge usages cycles by operating within known procedures and certainty tends to favor revenues. 

By so the figure helps to illustrate both the inwards and outwards experiential dynamic trends which have been mentioned above: the extension of one zone tends to decrease the other one. In example, profitable operation tend to decrease the need for exploration while too much exploration may decrease revenues.

One can so visualize that - for only surviving reasons - an organization or a population does own limited resources to embrace the outwards uncertain exploration trends - however a minimum might be required for long term survival.

However this sound difficulty, the holotomial analysis is the result of cross domains extensions by having gather operational experience within various domains and having maintained the conceptual translation effort tending to validate common patterns between this diversity of contexts.

The context diversity which has been crossed at building holotomial analysis embedded several domains over a 15 years period - like natural sciences (paleogeography, diagenesis), mechanics (dynamical instability, self excited vibration control), information technology (semantic, agile programming and evolving development), business management (intangibles accounting and valorization), economy (regional economic development and relationship network management), information management (market intelligence and news publishing), phenomenological life sciences (sociology, psychology and neurosciences) and mathematics (quantum logic, geometry and group theory).


Quantum mechanics - Double-entry accounting

We do not refer here "quantum mechanics" to the popular image of electrons revolving like planets around a nucleus but to the uncertainty which infers to a system an apparent compliance at the question of an observer - say to a system management which is essentially of the result between probabilistic interaction.

Unexpectedly, the process of designing maps reflecting interconnected economic spaces exhibited progressively acquaintances with quantum mechanics - in the sense of nothing was certain and that achievements would result from probabilistic additive effects.

So we investigated more the quantum aspects in this sense and we discovered a means to ground a geometrical construction of our maps based the superposition of complete spaces - say a process very similar to quantum logic.

Surprisingly also, when we evaluated the flux balances realities and expectations between agents acting within our maps, it came that a double-entry accounting method was naturally appropriate and so we discovered intimate complementarities between methods issued from quantum logic - which based our maps constructions - and this old accounting principle that was born at the end of the 15th century.

Prior entering more details specifically related to those two aspects, an insight to this unexpected parallelism between quantum logic and double-entry accounting is simply suggested by the next figure which is similar to the previous one but where the left side has been name "Assets" and the right side has been named "Liabilities".

Both the left and the right sides of the above figure are like lattices of two exclusive cases. As shown, they can be represented like "physically" owning a mirror symmetry while the "debit-credit" recording accounts are not mirror symmetric to reflect that the assets-liabilities records are made from the view point of two different observers - i.e. the company and the bank respectively for the assets and the liabilities. 

More details on those aspects will be introduced in a progressive manner along the following sections.

The present section introduces how a solution for compliant systems has emerged from practices with some guidance based on parallelisms with quantum mechanics - the upper frame of each page shortly describe the operational evolution while the lower frame exposes the related parallelisms.

The next section starts with a translation of the concept of othocomplemented lattices (introduced by G. Birkhoff and J. von Neumann in The Logic of Quantum Mechanics) to ground links between the achieved practices and a specific geometrical space. The links with a double-entry accounting are introduced in the third section.

From there, the properties and the methods are derived to describe such a possibly compliant system - say quantum - with a coherent method - say double-entry accounting - which constantly respect a complete balance however uncertainty remains inherently present.

To our knowledge, quantum mechanics is the first noticeable reported example in (said) exact sciences where the observer has been possibly associated to the quest of an objective reality - say when it has been discovered that quantum systems may not be objectively totally apprehended and that those systems may show a compliance at the experimental conditions.

One can say that a quantum system is a bit like someone who can answer you something and answer exactly the opposite to your neighbor. It is also particular in the sense that we can not a priori predict what will be his answer when he meets you or your neighbor the first. It looks like someone who's answers looks sometimes only to please the people he meets or sometimes are completely not predictable.

When you try to anticipate what would do a system made of several such compliant components, you may anticipate that a stable solution would be a one where every component "would please" each other.

One can find solution of this type but still physics had a problem because when a component has two choices, physics could not tell which one would be the "pleasant" one. Because of this remaining uncertainty, instead of having only one stable solution for a system, the physicists may remain with collections of solutions that would in principle be all observable but not all simultaneously.

Historically, the astonishing point has been that they have been effectively observed. It turned out like the observer was having a choice of how he would like the system to be.

This unexpected compliance and uncertainty led to high controversies and non acceptances (i.e. Einstein has been the most famous enemy of this fundamental uncertainty is frequently quoted for his sentence "I, at any rate, am convinced that He [God] does not throw dice).

Even if sciences could not explain the origin of this unusual compliant nature - and can apparently still hardly explain it today - the existence of a fundamental uncertainty has been widely accepted and expressed in the Heisenberg uncertainty principle.

In short, the Heisenberg uncertainty principle states that pairs of variables are coupled and can not be observed simultaneously so that if you look "more at one variable", "you see less the other one" and vice versa.

It means in turn that the manner you look at a system may influence its answer or that the system is somewhat compliant to its environment but it turned out also that successive measurements of one variable or the other "may - or may not" - maintained previously observed correlation - like if on the top of this compliance, the measurements may also possibly modify the system itself.

A day life illustration of such situation could be to accept that one can hardly observe simultaneously the past and the future and that measuring the future - in the sense doing it - may or may not correlate with the past as well as it can change the system itself.

(note: the physicists usually separate their sciences from macro world phenomena but recent references - see the bottom of this parallelism - exhibit investigations tending to demonstrate that quantum logic may apply to day life observable "by all" situations).

It remains that the classical view point is that an observation should tend to be objective - say independent of the observer - and so unique. This belief is commonly accepted in many day life domains: a judge is required to make the truth, a journalist claim for his objectivity, the accounting balance of a business must be unique.

This later case - accounting - is particularly illustrative about the widely spread and prevalent human belief that uniqueness is a must.

Accounting is clearly an observation means which is created by human being as an attempt to reflect a business status.

The enforcement of a unique and objective accounting method looks like an increasing requirement over years while in the same time it seems that the efforts necessary to gain this unique method are increasing conversely.

I like to mention IAS and IFRS standards as a good illustration because I have been said that they came from the inability to find a "unique agreement" on the "unique method" at describing a business (the "jokes" indicate that we may soon take more time at accounting for a business that at doing it).

However we have been convinced for years that accounting may only require a reporting system which can comply with several view points, we never related this view point with quantum mechanics formalizations before it showed up a relationship from this experiential learning evolution.

Referring to the figure at top of this page, we think this relationships came naturally from the fact that we have not aimed at objective reality neither observers possible influence but from the fact that we straight on put ourselves within an observation plane space set in between both.

So it appeared like quantum mechanics was having an appropriate liaison between the real world and the observer but not the accurate accounting system, while businesses owned the accurate accounting system but did not accept the subjective liaison between the observer and real world.

Or otherwise said, like quantum mechanics was having the correct viewpoint (say a multiple nature) but not the proper accounting (say a simple entry accounting) and the double-entry accounting was having the correct method (say a double-entry method) but not the correct view point (say rejecting a multiple nature for the sake of objectivity and uniqueness).

The "in between" view point that we took heuristically revealed many comfort at enabling to gather both view points without any disadvantages or intellectual restrictions. The parallelisms and guidance which emerged along the construction of our progression came in a large diversity from numerous domains. They are all exposed for the sake of information in the lower frame of each page.

Important to us is to understand that the present work is not at all a translation or a transposition of quantum logic or quantum mechanics into economic and human related domains.

It is true that this work has been initiated from a parallelism detected with quantum mechanics - namely a mixed of Hilbert spaces as mentioned in the parallelisms of the page 1.3 - and that some further benchmarks have been performed.

But it is true also that quantum logic and quantum mechanics did not appear as such enabling to restitute accurately the practices learned from the experience which related in the present section.

The methodological development has so been made at focusing on this actual experience and at solving questions associated with it. It came a method which still owns acquaintances with quantum theories but which also owns specific differences that in turn provided us with a very different and significantly more simple set of analytical tools.

We may mention that acquaintances between the macroworld, quantum mechanics and the double-entry accounting system seems only tediously investigated by the academic world however we did find some echoes which we mentioned here below:

References of quantum effect in the macro world:

- Measurable Systems and Behavioral Sciences
V. I. Danilov† and A. Lambert-Mogiliansky‡ - February 10, 2007
†CEMI, Russion Academy of Sciences Moscow
‡PSE, Paris-Jourdan Sciences, Economiques (CNRS, EHESS, ENPC, ENS) Paris

- The Violation of Bell Inequalities in the Macroworld¤
Diederik Aerts, Sven Aerts, Jan Broekaert and Liane Gabora - 2000
Center Leo Apostel, Brussels Free University

Weak Quantum Theory: Formal Framework and Selected Applications
AIP Conf. Proc. -- January 4, 2006 -- Volume 810, pp. 34-46
Harald Atmanspacher,* Thomas Filk,*, and Hartmann Römer**
*Institute for Frontier Areas of Psychology and Mental Health - Freiburg, Germany
**Institute of Physics, University of Freiburg - Freiburg, Germany

Weak Quantum Theory and the Emergence of Time
Hartmann Romer Department of Physics University of Freiburg, Germany

References of parallelisms between quantum logic and double-entry accounting:

- 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".


Geometrical spaces

The words "observation spaces" do not own here any philosophical meaning neither refer to a proposition for eventually modeling natural or organizational processes.

They only refer to a space where observation imprints can be recorded.

More precisely, they truly refer to the 2-D physical means that one currently utilize to consign and display observations and prospective visions - namely a sheet of paper, the screen of a computer, a display board or a digital camera.

An attention needs to be paid at that aspect because it truly means that the holotomial analysis only reflect properties and constrains owned by geometry.

By such - and out the present section that shortly introduces for the sake of illustration how holotomial analysis emerged from solving operational management issues - all the further sections - namely 2 to 5 - only recall to geometrical properties and so they do not require any other proof that a correct geometrical argument.

Care must be maintained that an holotomial analysis has to be taken as a pure observation means and not as an interpretative vision of experimental perceptions.

From the observations recorded via an holotomial analysis, the reader may eventually derive process modeling - but only on his own behalf. We underline that in case the reader may do so, he will remain constrained in his modeling by the geometrical properties of the holotomial space in case his modeling process does not escape from the observation holotomial space.