Experiential learning -
Systemic learning - Quantum mechanics -
Double-entry accounting - Geometrical
- Systemic learning
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.
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
- 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
- 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
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
One can so visualize
that - for only surviving reasons - an organization or a population
does own limited resources to embrace the outwards uncertain exploration
- 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
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
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.
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
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.
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.
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.
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.
compliance and uncertainty led to high controversies and non
(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
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
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
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.
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.
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.
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
References of quantum
effect in the macro world:
- Measurable Systems and
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)
- 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
Atmanspacher,* Thomas Filk,*, and Hartmann Römer**
*Institute for Frontier Areas of Psychology and Mental Health -
**Institute of Physics, University of Freiburg - Freiburg, Germany
Weak Quantum Theory and
the Emergence of Time
Department of Physics University of Freiburg, Germany
parallelisms between quantum logic and double-entry accounting:
- Synergy, Quantum
Probabilities, and Cost of Control - John Fellingham &
- 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
Braun has written a suite of papers demonstrating the usage of
Feynman graphs in financial accounting - accessible from in the web
The words "observation
spaces" do not own here any philosophical meaning neither refer to a
proposition for eventually modeling natural or organizational
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
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