## CTS: The Complex System of Stuff

We now need to consider the stuff as a complex system and we can do so by describing it using the abstract first derivative constructs that we use to describe all complex systems regardless of their nature. It is also assumed that specific types of behaviour that are seen in all types of complex system will also be evident in the system of stuff.

A complex system is comprised of interacting parts or components. The interactions cause a change in the component’s’ level of stability or instability. The sensitivity of a component to the neighbouring influences is dependent upon its level of stability and it is this that causes complex behaviour.

We have to assume that the stuff in some manner may be seen as being composed of components and that there is a recursive nature to such components in that there are components within components. Whether this recursion is infinite and continuous, or finite and discrete is unknown. It should be noted that we do not have the constructs to fully analyse a system that is truly continuous as our methods require an analytical continuity or treat the system as truly discrete. For these reasons the analysis of the stuff will be to treat it as either analytically continuous or truly discrete.

The true nature of the components of stuff cannot be known. We will consider that to the stuff we can assigned the concept of pure properties and that to each component we can also assign one or more of these pure properties.

I will use the suffix of ‘pure’ to indicate that the specific characteristic is fundamental to the nature of the stuff as opposed to a characteristic that we assign due to a measurement interaction from within it. In essence we can never know the nature of pure characteristics of the stuff. This will be discussed in more detail later, but to give some context, charge and mass are not pure properties they are in fact representations of specific sets or classes of interactions within the stuff to which we codify numeric value and an abstract intellectual construct.

We can consider that to each pure property we can assign one or more pure interactions. To this end we can define different types of interaction:

For a pure property within a bounded component and in the absence of any coincident patterns there will be interactions between the sub-components (down to the unitary component scale). These natural property interactions are similar to the interactions within the neighbourhood of a cellular automaton. Such interactions will cause change of pattern including scale increase or decrease of the component with respect to stuff-space. This is similar to the propagation of a single CA rule.

When components interact they do so with two specific types of interaction.

There are intra-property interactions that occur between components of the same pure property. This is similar to two CAs with the same rule interacting with each other.

There are inter-property interactions that occur between different pure properties associated with each interacting component. This is similar to two CAs with different rules interacting with each other.

Each of these interaction types has a different neighbourhood topology within stuff-space.

Within the stuff it is envisaged that the resulting complex behaviour is due to the interplay of all three of these base interaction types (see diagram).

How these interactions are mediated and generate dynamics cannot be known but in some way it is these interactions that cause instabilities that begat further interaction and instability (feedback). The constructs I have described so far are abstractions but in some manner these constructs exist within the stuff to make it a complex dynamic system.

There is no reason to assume that inter-property interactions are symmetric. However it makes logical sense for all intra-property interactions to have a mutual influence on each component.

NEED TO DISCUSS NON-LINEARITY. There is non-linearity everywhere in a complex system. Its origins may be a resultant effect of influences or the nature of the interactions may in themselves be non-linear as well as the nature of the components that cause a non-linear response.

For all of this to work we need the structure of recursive components to bear a relationship to each other that leads to specific level of influence and identifiable neighbourhoods. In our universe we view this as space. However we cannot assume that the true relationship between components of the stuff is the same as our construct of space. This is neither surprising or a conceptual problem as we can already construct mathematical spaces and ordered sets that have no relationship to our construct of space, other than as a specific encoding method to make such constructs manifest to our consciousness. I will call this specific relationship within the stuff, ‘stuff-space’. There may be several facets to stuff-space (some may be emergent whilst others are pure- properties) and we may only be able to indirectly measure or infer a mapping to a proportion of these.

The relationship between components and their properties in stuff space may well translate into spatial coincidence in our construct of space. The encoding of a pattern in relation to stuff space is different to that of an encoding in our space.

At this point we can now state that our concept of a component requires in some manner a region of stuff space to be bounded such that the behaviour within the boundary is significantly different to that outside of the boundary. For this to be the case the influence of the interactions must vary over stuff space otherwise the stuff would be a homogeneous mess in which it would be difficult to define any components.

It is important to realise that we cannot assign value or concept to pure characteristics and therefore the meaning of state and pattern are un-defined. However for descriptive purposes I will assume that to each scale of component we can assign a pure state that is directly related to the pure properties associated with that component. We can also assign the idea of pure pattern, which is an encoding of the relationship between the pure properties of a component at a given scale.

I will assume that there is a unitary component which has no internal pattern of component but only a property. In practice the unitary component is at a scale at which we can no longer take meaningful measurement or apply any meaningful intellectual construct. Such a unitary scale accords with our idea of the Plank scale or smaller.

Although all change occurs at the unitary level we must assume that the stuff is a natural system and hence there is a great deal of localised (in terms of stuff space) concurrency.  By this I mean that regions of stuff are influenced ‘en masse’ and at larger scales one can attribute the change in pattern is due to larger scale neighbouring structures. This means that the resulting behaviour of larger scale structures are reliant upon the dynamics of neighbouring larger scale structures as opposed to viewing all causes at the unitary scale. One cannot attribute large scale effects to individual microscopic causes and hence it is more sensible to consider the behaviour of the larger scale patterns as the influencing factor.

However as stated all seed interactions occur at the unitary scale and the question is how important is the propagation of these micro influences through a region, compared to the concurrent influences caused by larger region interaction. As we expand the region of interaction we are increasing scale and pattern.

There are two aspects to these interactions. The inter-property interaction may be spread across a large region and be at the micro scales concurrent. However these influences also may cause intra-property perturbations that propagate and create a level of latency in terms of different scales.

It may also be that through the interactions both within and between pure properties associated with components that the dynamics of each pure property both within and across components display different characteristics, for example some pure properties may have transited to become highly stable fractal patterns, whilst others may be simple, periodic or highly complex and even chaotic.

Given the definition of the stuff this would lead to the stuff being an ideal closed system and this lends itself to the idea that the dynamics of the stuff could be perpetual.