Related discussions:
SMN related discussions coving many aspects from mathematical definition, software design, software implementation and so on.

Metaphysical Context: some discussions that help contextualise SMN within an information system theoretic metaphysics.
Notice to Software Developers: describing the implications mainly in terms of information technology.
Notice to Scientists: describing the implications mainly in terms of Physics and Cosmology.

Below I have collected together a range of descriptive quotes from my notes related to SMN.

In the course of some research into the implications of a system theoretic metaphysics I developed a mathematical formalism called System Matrix Notation (SMN) which is a system representation, analysis and simulation framework. It is a fusion of concepts from system theory, linear algebra, probability theory, information theory, computer science, metaphysics, and quantum physics. It is a general method for completely specifying systems, both their structural and dynamical properties, it can represent systems whilst not omitting any detail and not introducing any false assumptions.

The mathematical formalism provides a low level metaphysically coherent information space within which systems can exist and interact. When implemented in software it produces a system modeling paradigm that has potential applications in any field of interest that involves systems; from the development of software systems, mechanical, electronic and computer systems, business systems, communication systems, transport systems etc to the analysis of physical systems, biological systems, social systems, economic systems and so on.

With SMN there is no explicit space-time within which you model, it is a dynamic state space or process space based upon states and iterations, and manifesting system theoretic metaphysical properties. There is no built in geometric space, only state space and process time are fundamental. There is a state vector and a matrix of causal inter-connections that combine to implement each iteration moment, in which the current state information flows through the causal network to produce the next state thus producing a state space that evolves over time.

System Matrix Notation (SMN) arose out of an attempt to model systems without the introduction of any metaphysically spurious concepts such as always seemed to occur when I had tried to used Object Oriented methods to model conceptual and physical structures. The models were always classical and always defined from a particular perpective, in trying to overcome this limitation I developed SMN which provides a quantum representation of the system that is independent of perspective. From this representation one can derive classical models and particular perspectives.

The models have a coherent matrix algebraic form so they are amenable to algebraic analysis and manipulation; allowing for the simulation of systems. In one sense this is an Interaction Event Manager that causes information to flow along the right chanels at the right time and thereby animates the system.

The state vector represents all existential information or the state of the universe in a single moment, whilst the system matrix is a transformation matrix that determines all state transformations. When the two are multiplied together the present moment state data flows through the transformation matrix and produces the next moments state data, hence the SMN algorithm simulates a universe.

A system is a pattern of information:A system is a persistent coherent group or pattern of state data (SV elements). This information can flow through an information space (SM) where the topology of the space defines the nature of the connectivity between systems, this corresponds to the concept of the system's interfaces. There are many levels of systems (nested matrices or relational constructs). The low level system connectivity and interaction determines the behaviour and properties of higher level systems.

The invention is a method and system for causing a computing device to behave in a particular manner which produces an information space within which generalised systems may exist and interact. These systems may be assigned characteristics, relations and symbolic meanings within some modeling or simulation context and thereby used to construct models of arbitrary systems. These systems may be used for countless system engineering purposes; much like the phenomenon of software systems, these SMN systems may be used in countless ways.

SMN can coherently represent systems whose complexity is presently prohibitive, opening up new avenues of growth for System Science. It is a low level enabling technology that will form the foundation of a new systems industry and spur the development of System Science, revolutionising the fields of General System Representation, Design, Analysis and Engineering.

SMN uses matrices and vectors to represent system hierarchies, relational networks, system behaviour and interface state. This is the core of SMN, however it has higher levels where it is essentially a graphical or object oriented modeling paradigm which can be integrated with existing modeling methods such as UML, C++, etc. So SMN may provide a unified mathematical foundation to all such modeling frameworks.

The simplest formulation of SMN is well understood and is called Classical Empirical SMN, this provides similar functionality to the object oriented paradigm but it arises from a unified mathematical foundation that allows for advanced simulation and analysis techniques. It is a mathematical implementation of a UML like modeling language. More advanced formalisms are in development, such as Transcendent SMN, which provides a lower level representational framework allowing for phenomena such as spatio-temporal non-locality and a quantum multiverse. These advanced formalisms may provide leads as to a method for the general programming of a quantum computer and also to a deeper understanding of the nature of space, time and matter.

In its most basic form System Matrix Notation is a mathematically based system modeling language which may flexibly represent the complete state of a system to any degree of detail on any scale. This includes:
1. hierarchical structures of systems with many subsystems within subsystems nested to any depth,
2. relational structures with complex networks of relations or information channels weaving these systems together,
3. state space structures or topologies, which define how the system migrates through its state space, transforming inputs to outputs and changing its state over time thereby producing behaviour,
4. system interface states or the exact data that is being received or transmitted in any particular instance.

The software implementation allows one to simulate or create systems in a metaphysically correct manner. These systems may evolve in time and manifest different behaviours depending upon the structure of the system. Therefore arbitrary systems may be constructed within an information space and connected via interfaces with other systems and the outside world, thereby providing a metaphysically correct way of performing system engineering.

By representing the entire system model within a single unified mathematical framework, this allows for advanced simulation and system analysis techniques to be developed, thereby providing a coherent foundation for system science. And given that anything may be conceptualised as a system this may conceivably lead to a unified mathematically based metaphysical foundation for the whole of science and any conceptual frameworks that attempt to comprehend reality.

SMN is an extremely flexible modeling language with countless variations, extensions, optimisations and ways of integrating with other systems to form complex hybrids of methods and systems of all kinds. One can develop purely SMN systems of several types, embed SMN systems within other systems, or embed other systems within SMN systems. Any system that can represent itself digitally or can be represented digitally or that can comprehend digital information in some form can be assimilated into the SMN paradigm.

I have developed a working prototype of the core simulation engine that allows for the representation and simulation of classical systems. The first goal is to develop this into a software application that is a graphical, intuitive and metaphysically coherent system design and analysis suite.

The initial product will be a generic SMN system modeling application. It is like a generic computational putty that can be formed into countless different manifestations, each variation giving rise to a whole range of potential products.

One possible early application of the product would be the creation of an XML based graphical document paradigm then SMN based system modelling and analysis then engineering applications such as a Universal Control System. SMN can be used to develop conceptual networks as a high level communication medium and to build knowledge spaces. Also to conduct research into complex dynamical systems, model organisational systems and coordinate and integrate information of all kinds. And also to develop a system enginering paradigm that gives us unprecedented understanding and mastery over the process of creating and integrating with systems.

SMN is simply a method of manipulating information, it is infinitely adaptable, just like a computer is.

Ascii, Unicode, tex, html, etc are technologies that allow for the representation of text and have been a low level enabling technology for all electronic texts and a vast industry based on this. SMN is a technology that allows for the representation of systems and will be a low level enabling technology for all electronic system engineering and a vast industry based on this.

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