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Parallelisms : Management - Mechanics - Physics - Astrophysics
- Quantum mechanics - Programming language - Holotomography
Management
The concept of a closed space
to project observation mapping is not
new neither difficult to capture.
As already mentioned at the
page 2.2,
Stephen Covey - in his
book "The Seven Habits of Effective People" - proposes to
represent your world by two concentric circles where everything
you can effectively influence will be recorded inside the central
circle while everything that you can not influence will be set in
between the two circles. This is a close space where you can set
any observation and information that you would own about the
world.
Mechanics - Physics -
Astrophysics
The spacetime - as initially
presented by Einstein - was also a closed space.
The idea is in a sense to say
that the universe must be a whole, in so included the time. Hence it must a close space that embeds bodies
(see coordinates x,y,z) and the time (t) so the spacetime being
define by (x, y,
z, t).
Concepts like the big bang and
the relativity of Einstein are consequences of this assumption of
a closed - hence curved- space (Einstein is quoted to have joked
that if we could see very far in the future, we would see our
bag).
However our motivations to
work within a closed space are only related at creating an
observation space - and not at providing a model of physical
phenomena - one can anticipate that our decision to
also utilize a close space will
naturally infer parallelisms with questions that are investigated
in physics and associated disciplines.
Worth is to shortly remind
some of those questions because they will be encountered as a consequence of
the similar initiating visions so that several parallelisms that
have been mentioned in the previous section are not strange
coincidences but will be better enlighten as in relationship with
our choice of handling our records within closed spaces.
In example, we can mention
that one of the difficulty of physicists - say also
astrophysicists - has been that when you consider that a closed
space is embedding the universe and owns a constant volume, the
problem of solving the "equations" of the universe will in some
sort resume alike finding how to enter like an infinite time-wire
within a finite space - only because the time unfold itself
continuously and never will "cross twice the same place".
This is one of the reasons why
mathematics paid attention at the development of unusual concepts
that may respond at this strange requirement of infinity within
"finity" - i.e. concepts like what they named manifolds
of which one of the most popularly renown is the Möbius strip, or
other novel mathematical species like the Mandelbrot fractals
which are said to come at studying economic systems where
uncertainty cumulates without resuming within classically
distributed variances.
If we already mention the
recognition of some self-similarity potentials - see the
parallelisms of the
page 1.5 - it is because this noticeable
properties has been famously highlighted by the Mandelbrot
fractals. This observation is so possibly indicating a link with
already known underlying systemic characteristics that are related
with a closed space representation.
Quantum mechanics -
Programming language
As presented in the previous
comments, the configuration we choose induces a fair amount of
similitude with previously investigated problems - i.e. in
mechanics and in physics.
The next page will show that
this choice also complies with fundamental characteristics of
contemporary programming languages - i.e. like in object oriented
programming.
Those approaches usually infer
interconnections and inheritances between system components and
agents - i.e. state properties in physics and inherited classes in
object oriented programming.
Our concern has been that
those options frequently
lead to high degrees of complexity and/or to methods that hardly infer operational results.
As we owned the advantage not
be linked at physical observation or postulated constrains but
that we remain at playing with only geometrical properties in an
observation space, we utilized this position to freely adopt
convenient choices that lead to an operational simplicity at
providing the ability to represent any situation.
Diverse options have been
investigated and - at the opposite of the above mentioned domains
- the choice of "no overlap and no inheritance" has
been retained because of the great simplifications it inferred
further on.
We will first exemplified the application
of this "no overlap and no inheritance" choice and next we will anticipatively explain the resulting
simplifications that we have recognized.
The "no overlap" rule means
that no label can overlap neither any line crosses any other like
shown in the adjacent figure that illustrates permitted and non
permitted instances.
"No inheritance" means that
any label - even resulting of labels combining - is an
individualized label and that a label or a cluster within a
cluster does is not with filiations to the surrounding but only
geometrically included - say it may move out as a free
individualized entity.
To illustrate the difference
with physics, say that an electron is known to have a spin and
that a spin may take the value of +1/2 and -1/2.
In physics, all those are
properties that are linked to an electron while with us an
electron, a spin, a value of +1/2 and of -1/2 are separated and
individualized properties as well as an "an electron having a
spin", "an electron having a spin of +1/2" and an "electron having
a spin of -1/2" are also three independent and individualized
entities.
Noticeable also that in
physics, because the time is seen unfolding continuously, a period
of time follows a previous one and precedes a next one. In here,
any period of time is also seen as an individualized and
independent entity.
Our conventions may looks to
possibly infer non necessary complexities because we intuitively
feel like we will need to handle and display an enormous number of
entities collections. In practice we won't and we will see that it
is mainly an conventional artifact that allows us to build a
method which ends with very accessible tools where this feeling of
possible complexity become irrelevant.
In particular, those
conventions will lead at the fact that our manifold of reference
will not be obliged to own a high complexity because the above
conventions will allow the usage of the surface of a sphere.
From there, we will mainly
make usage of the known properties of this surface so that an
explicit care at our conventions will rarely be needed. The sphere
and our conventions being equivalent, we will only utilized the
more convenient which in the case we investigated has been the
geometrical format.
Holotomography
Noticeable is that with our
conventions, a "multiple holotomy" - says an holotomy
embedding
several item-clusters - can always be grouped into a "single
holotomy" - say an holotomy with only one item cluster.
Conversely, a "single
holotomy" may always be associated with other "single or multiple
holotomies" within a "multiple holotomy".
This says in short that an
holotomy is always a "whole" and can also always be a part of a "whole".
We mention that the above reminds the notion
of "holon" that is known in philosophy -
Wikipedia: "a holon is a system that is a whole in itself as well as a part of a larger
system".
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