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Parallelism : Classical mechanics - Quantum mechanics -
Automation
Classical mechanics - Quantum mechanics -
Automation
In a sense, a bit-stock is
nothing but the maximum available positions that a given
configuration may fulfill. This maximum allows to sort systems in
two classes:
Class 1: when a system owns less or the same number of
available
position than
the configuration space, a classical solution may hold.
Class 2: when a system owns
more achievable positions than the maximum bit-stock available, it
can not fulfill all its positions but only a subset of them. The
system has to "make a choice" of which positions it fills and of
which positions it leaves empty. It has so the choice between
several subsets permutations.
This recall in an accurate
sense to the different configurations that a system may achieved
as introduce in the
previous page
in the parallelism with thermodynamics.
In this second class, if the
system has no rules to make its choice, it may appear random, it
may "innovate" any time or it
may respond - either comply - to an external contextualization that will render some
subsets more probable than some other ones.
An accurate parallelism can be
made between [class 1 - class 2] and [classical mechanics -
statistical and quantum mechanics].
This parallelism between the
different domains of mechanics echoes very well what has been
exposed at the
page 5.4 in the sense that the class 1 would correspond to a
system that can be described describe only real parts - say [1] -
while the statistical domains - i.e. quantum mechanics and
thermodynamics - must infer descriptions based on the closed base
[ ] - [1] - [i].
The same parallelisms extend
to engineering domains that based upon mechanical foundations. An
illustration can be automation where the class 1 is
referred as holonomic - say a system which degrees of control is
at least equal to its degrees of freedom - and the class 2 is referred as
non-holonomic - say a system which degrees of control are less
than its degrees of freedom.
Classical system dynamics hold
for the holonomic cases - i.e. an automated production chain -
while it does not for the non-holonomic ones - i.e. a humanoid
robot participating at the
Robocup.
Care must be taken that in
that general formalization [q] x [p] x [t] may embed an imaginary
part so that in general a bit-stock may not be conservative.
In a classical and
conservative system, the pair ([q], [p] x [t]) would reflect to
the total system energy - say like ([potential energy], [kinetic
energy]) - or the Hamiltonian of the system.
(note: it has been mentioned -
in the parallelism at the bottom of the
page 2.2 -
that the bit-stock may provide quantified zeros for the Riemann
Zeta function).
As said in the
page 5.4
there isn't any reason that a classical - say a conservative
system - may not also own a description in the general
formalization [ ] - [1] - [i], the only point being that handling
the complete holotomial formalization might not be an advantage in all the
instances over the algebraic - or arithmetic - usual existing
formalizations. Care must only be taken that algebraic - or
arithmetic formalizations do usually not embed the complete
characteristics of the holotomic vision so that mathematical
artifacts may drive at deriving sense not embedded in a similar
manner by the holotomial analysis.
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The bit is nothing but like a
total quantity of energy. In its real part, it may be taken as a
given value in many problems but in general it is not a constant -
at least because the imaginary stock may not be bounded per se.
does it liaise to the
uncertain bit ?
in fact this uncertain bit has
no cost - like no mass ? and it is available every where any time
.. it as no sense ? yes it has the one to "tell" when a tranfert
is done: it gives an informatio at its reification !!!
hamiltoonien - system
conservatif et non conservatif
several form of the "Hamiltonina"
condition:
[T] =
[Q] x [P]
[T] x [T] =
[Q] x [P]
[T] - [Q] = [P]
which is refer by a
non conservative system.
Interesting is to
remember that they can only distribute between [q] and [p] that
correspond respectively to rest and working days.
Obviously like shown
in the figure, the sum of the actors at rest and at working is
always a constant.
In a general
formalization that utilizes the bit metrics, we will write
[T] =
[Q] x [P]
A case that is
frequently considered is a configuration that exhibits an
invariable [T] and that is said conservative - i.e. like in the
above figure where the system only exhibits real bits.
The example of
the working day is quite suugestive to the question ... Once we have
define our basic sequence, we can characterize their availability in a
gieven configuration. A configuration that
includes a time frame and objects-actors collections defines a
bit-stock.
If we stick on the
working day analogy, it is easy to understand that the B-Stock
refers to the available stock of resources in [bits].
this global relataions
stands valid for any motions any ... any ;
when observing a system,
by letting the system being non-conservative, it will be free to show
up both conservetive and non
In the general case of
observing a system, the complete description requirements imposes to
let at [T] the possibilty to be influenced by the T-inversion.
conservative
a system is said
conservativeIn the general case while it will be name non
conservative when [T]
collections so that
boundedconfiguration the number of working days are
If we stick on the
working day analogy, it is clear that at a given numbers of actors
corresponds a given number of working days.
When we use the
common metric of a bit, it comes that a configuration is
globaly caracterized by the relation
The adjacent figure
illustrates the real part of this relation for an eleven days
projects at which 100 bits where given
project where the
we have the accept that to a given configuration defining a fibit
available i.e. in a company, in an
economy ...
mvt "continu" instablité
unification (la grande ;-)
vortex
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