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: 


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