Diving deep into the
foundations of physical reality requires a deep dive into advanced mathematics.
Usually this goes together with formulas or other descriptions that are
incomprehensible to most people. The nice thing about this situation is that
the deepest foundation of reality must be rather simple and as a consequence it
can be described in a simple fashion and without any formulas. For example the
most fundamental law of physical reality can be formulated in the form of a
commandment:
“THOU SHALT CONSTRUCT IN A
MODULAR WAY”
This law is the direct
consequence of the structure of the deepest foundation. That foundation
restricts the types of relations that may play a role in physical reality. That
structure does not yet contain numbers. Therefore it does not yet contain
notions such as location and time.
Modular construction acts very
economic with its resources and the law thus includes an important lesson.
"DO NOT SPOIL RESOURCES!"
Understanding that the above
statements indeed concern the deepest foundation of physics requires deep
mathematical insight and it requests belief from those that cannot (yet)
understand this methodology. On the other hand intuition quickly leads to trust
and acceptance that the above major law must rule our existence! If you look round, then you can quickly agree to the conclusion that all discrete objects are either modules or modular systems.
Modular construction involves
the standardization of types and it involves the encapsulation of modules such
that internal relations are hidden from the outside. Thus in addition it involves the standardization of connecting interfaces. The methodology becomes
very powerful when modules can be constructed from lower level modules. The
standardization of modules enables reuse and may generate type communities. The
success of a type community may depend on other type communities.
An important category of
modules are the elementary modules. This are modulus, which are themselves not
constructed from other modules. These modules must be generated by a mechanism
that constructs these elementary modules. Each elementary module type owns a
private generation mechanism.
Another category are modular
systems. Modular systems and modular subsystems are conglomerates of connected modules.
The constituting modules are bonded. Modular subsystems can act as modules and
often they can also act as independent modular systems.
The hiding of internal relations
inside a module eases the configuration of modular (sub)systems. In complicated
systems, modular system generation can be several orders of magnitude more
efficient than the generation of equivalent monoliths.
The generation of modules and
the configuration of modular (sub)systems can be performed in a stochastic or
in an intelligent way. Stochastic (sub)system generation takes more resources
and requires more trials than intelligent (sub)system generation.
If all discrete objects are
either modules or modular systems, then intelligent (sub)system generation must
wait for the arrival of intelligent modular systems.
Intelligent species can take
care of the success of their own type. This includes the care about the welfare
of the types on which its type depends. Thus modularization also includes the
lesson “TAKE CARE OF THE TYPES ON WHICH YOU DEPEND”.
In reality the elementary
modules are generated by mechanisms that apply stochastic processes. In most
cases system configuration also occurs in a trial and error fashion. Only when
intelligent species are present that can control system configuration will
intelligent design occasionally manage the system configuration and binding process. Thus in
the first phase stochastic evolution will represent the modular system
configuration drive. Due to restricted speed of information transfer, intelligent
design will only occur at isolated locations. On those locations intelligent
species must be present.
Here comes a bit of advanced mathematics.
In a modular system relations
play a major role. The success of the described modular construction
methodology depends on a particular relational structure that characterizes
modular systems. That relational structure is known as “orthomodular lattice”.
This lattice acts as the foundation of each modular system. Orthomodular
lattices extend naturally into separable Hilbert spaces. Separable Hilbert
spaces are mathematical constructs that act as storage media for dynamic
geometric data. The set of closed subspaces of a separable Hilbert spaces has
exactly the relational structure of an orthomodular lattice. However, not every
closed subspace of a separable Hilbert space represents a module or modular
system. Elementary modules are represented by one-dimensional subspaces of the
Hilbert space, but not every one-dimensional subspace of the Hilbert space
represents an elementary module. However, if the one-dimensional subspace represents
an elementary module, then the spanning Hilbert vector is eigenvector of a normal
operator that connects an eigenvalue to the elementary module. Hilbert spaces
can only cope with number systems that are division rings. This means that
every non-zero element of that number system owns a unique inverse. Only three
suitable division rings exist. These are the real numbers, the complex numbers
and the quaternions. The quaternions form the most elaborate division ring and
comprise the other division rings. Quaternions can be interpreted as a
combination of a scalar progression value and a three dimensional spatial
location. The scalar part is the real part of the quaternion and the vector
part is the imaginary part.
Thus in this view the
elementary module is represented by a single progression value and a single
location. In reality elementary modules are characterized by a dynamic
geometric location. Thus we must extend the representation of the elementary
module such that it covers a sequence of locations that each belong to a
progression value. After ordering of the progression values the elementary
module appears to walk along a hopping path and the landing positions form a
location swarm.
From reality we know that the
hopping path is not an arbitrary path and the location swarm is not a chaotic
collection. Instead the swarm forms a coherent set of locations that can be characterized
by a rather continuous location density distribution. From physics we know that
elementary particles own a wave function and the squared modulus of that wave
function forms a continuous probability density distribution, which can be
interpreted as a location density distribution of a point-like object. The
location density distribution owns a Fourier transform and as a consequence the
swarm owns a displacement generator. This means that at first approximation the
swarm can be considered to move as one unit. Thus the swarm is a coherent
object. The fact that at every progression instant the swarm owns a Fourier
transform means that at every progression instant the swarm can be interpreted
as a wave package. Wave packages can represent interference patterns, thus they
can simulate wave behavior. The problem is that moving wave packages tend to
disperse. The swarm does not suffer that problem because at every progression
instant the wave package is regenerated. The result is that the elementary
module shows wave behavior and at the same time it shows particle behavior.
When it is detected it is caught at the precise location where it was at this
progression instant.
Those that possess sufficient
knowledge of mathematics might be interested in the paper "The Hilbert
Book Test Model"; This pure mathematical model exploits the above view.
See: http://vixra.org/abs/1603.0021
