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Parallelisms - Sciences - Geometry
Sciences
Sciences tend usually to adopt
an objective view point - say independent of the observer - on the
assumption that it must exist a reality that does not depend upon
the observer view point.
As said, we adopt here an
other view point that is an observation plane set in between the
real world and the observer and where both an objective and a
subjective reality may co-exist.
It means in turn that we can
not constrain ourselves to knowledge assumed to be objective but
that we can only frame our process within geometrical constrains
related to view making.
In our view, the analogy of a digital camera is very good at
highlighting the difference of the present view point with the
classical quest of objectivity - i.e. like the one usually taken
by the physicist.
In example, a physicist
usually adopts the assumption that the world, the universe or an isolated system
is conservative. Say that nothing can be lost and also that
nothing can be created.
We don't argue that the
physicist does not own good reasons for this view point but that if
the universe or an isolated system would be non conservative, the
physicist will need to infer artifacts that are only the results
of his initial assumption of conservative system.
In our view point, we can not
restrict the camera at only taking the picture that we think
accurate and at forbidding pictures that are not likely to occur.
Referring to the physicist case, our camera will not decide if the
system is conservative or not and will be ready to take picture of
both cases.
Our camera must be able to
take picture of everything even though everything may not show up.
The analogy of the camera
illustrates also very well how our view point must be able to
accept opinions and imaginary view created by the observer as it
is an evidence that taking a picture depend upon the focus and
wishes of the camera owner.
On a scientific stand point,
our "camera" can be seen as gathering two scientific "philosophy":
1. human being may never
capture an objective knowledge of the world but only an "image" of
it, so lets talk about "images" and not about objective reality
2. the observer is part of the
world, so a complete observation of the world must also embed the
observer.
Sciences - Geometry
While the classical quest of
objective reality must usually be companioned by experimental
proofs, it is noticeable that the standpoint taken here relies
only upon geometrical properties.
We will only display here how
to handle an observation space - say "how to take pictures" - so
that if one agrees that the procedures have been correctly
developed, other proofs should not be required.
For this reason, the
procedures does not own an interest by themselves but only the
taken pictures may own some value - i.e. when they are useful at
something or when they serve aims of the observer.
This value point related to
the "usefulness of the images" inferred an other important aspect
of the work that is exposed here: they are several manners to
"take picture" in an observation space.
We are not about all of them
or about a best one, but we choose among a large diversity of
tests, a manner that showed inferring noticeable and useful
results. say that variations and alternatives exist, our criteria
for selection have been usefulness of the results.
In example, noticeable is the
fact that we have rejected the description processes inferring the
existence of properties or inheritances to adopt an individualized
existence for any observation - even when combining several
grouped characteristics.
The reason of this
individualization alternative over the relation with properties
has nothing to do with an internal process logic. It only reflect
an advantage perceived in the outfit of the process - say the
pictures being more sense making.
The adoption of a geometrical
view point for handling observations has of course already been
extensively developed - i.e. in classical and quantum mechanics -
such that a warning must be given: even though strong parallelisms
will appear, the two approaches remain independent by the very
fact that we are only considering our development within an
observation space.
Noticeable differences appear
so in the observation space, like in examples:
- the coordinates, the
momentum and the time will own a unique metric (as a
consequence that we impose to ourselves that anything can be
recorded within our observation space and that the observation
only own one metric)
- the "uncertainty principle"
will not be a principle but a consequence of the imposed
completeness that we like to keep at our observation views (say
that to keep a picture complete, we need always to let it own a
cluster embedding "things that we do not know")
- the "orthogonal complement"
of an experimental proposal will not be its "negative" in the
mathematical sense**, but any other experimental proposal
Those points will make such
that several questions and aspects will exhibit equivalences with
questions and aspects developed in mechanics, but their
resolutions may lead here to unexpected different conclusions because
of their embodiment within a geometrical space only.
In particular, we like to
highlight in advance the great simplifications that have been
discovered on most of those questions by the only fact to remain
within an observation space only.
This allows to expose in a
very simple fashion an accurate sense for most of the major
questions and concepts treated in system dynamics by classical and non
classical mechanics and that have not often been transferred in other
domains - i.e. economy, management or neurophenomenology -
commonly because
of an inaccessible or intractable formalism complexity.
In particular, a seminal
concept like a closed manifold to embed any world view and
analysis within a complete closed space is here simply exposed
because the simplification generated by a spherical instance.
We do not argue here to
resolve the problems of physics and mechanics but we stand to
provide a rational and accessible opening within complex systems
management like they appear in daily common life and economic
activity, and this with a unexpected coherence of vision with the
mechanical view points and not their complexity.
Of course in our case, the
reader may by himself access anytime to a verification of any
conclusions while it may require an experimental knowledge for
similar aspects developed in mechanics.
**G. Birkhoff and J. Von
Neumann in "The Logic of Quantum Mechanics" published in The
Annals of Mathematics - 2nd Ser., Vol. 37, N°4. (Oct., 1936), pp.
823-843 |
