Earth System Analysis

Earth System Analysis is defined as the development of a mathematical-logical formulation of principles applicable to Earth Systems. A global overview of Earth Systems can be found on global earth systems

Scientific hypotheses and mathematical postulates must be refutable by the finding of contradictions with data or internal inconsistencies in a set of postulates. The systems principle of specification hierarchies will be used as an integrated analysis model for Earth systems Analysis.

The systems principle of specification hierarchies derives from science an intelligible understanding of our world and of our place in it, in short, a meaningful story of the world. From its inception it has had a developmental framework, beginning with origins, as the Big Bang theory for example. It features a role in the world for humans based on science, where stress should be put on the descriptors ‘intelligible and meaningful’.

Specification Hierarchies

Fig.1: An Example Specification Hierarchy

When used to model systems, higher levels (control, regulate, interpret, harness) lower levels, whose behaviors are made possible by properties generated at still lower levels. So behaviors of higher levels are initiated by lower level configurations. It is important to realize that few users of hierarchical forms would insist that particular levels exist in actuality. Levels are discerned from hierarchical analysis, aimed at constructing (discovering) Nature’s “joints” with respect to given projects.

Formal relations between Specification Hierarchy Levels

The specification hierarchy is one of classes and subclasses, as e.g., {material world {biological world {social world }}}, where {lower level(s) { highest level}}.

Style of growth of a Specification Hierarchy

In the specification hierarchy new levels can emerge. So this system can grow — but not in space. Growth here is by the accumulation of informational constraints, modeled as a process of refinement by way of adding subclasses.

Criteria for levels in Specification Hierarchies

Levels in the specification hierarchy mark the qualitative differences of different realms of being, as in ‘physical realm’ versus ‘biological realm’. It is an intensional construct, open at the top and so free to give rise to ever higher levels.

Complexity of a level in a Specification Hierarchy

The specification hierarchy embodies intensional complexity, which characterizes a system to the degree that it is susceptible to many different kinds of analyzes.

Dynamical relations between levels in a Specification Hierarchy

Dynamics in the specification hierarchy are entrained by development, which is modeled as a process of refinement of a class or category. It is important to note that this process is open-ended in the sense that there could be many coordinate subclasses of a given class. That is, the potentials arising within any class form a tree. So, {physical realm { material realm { biological realm }}}, or {mammal { primate { human }}} each follow just one branch of a tree. Evolution (unpredictable change) is one -> many, and so we can picture organic evolution.

How is its direction into new subclasses insured (giving rise to the hierarchy)? In the material world by the fact that information, once in place (or once having had an effect), marks a system irrevocably. If a system continues to exist, it must march forward if it changes.

So, development of a specification hierarchy requires a two-level basic form. Yet these hierarchies involve more than just two levels. Why do not the more general levels prevent change, as by the weight of their accumulated information? Here we are led to note another aspect of development. The amount of change required to launch a new level is ever smaller as the hierarchy develops — refinements are just that. The more general levels do exert their influence; biology is a kind of chemistry, and humans are a kind of mammal. The key to understanding this situation is that in the specification hierarchy informational relations between levels are transitive. This means that there are functionally just two levels at work anywhere in the hierarchy — and new levels may branch off anywhere in the hierarchy, potentially giving rise to collections of coordinate classes.

Informational relations and semiotics

In the specification hierarchy the lower levels also make possible the emergence of a new realm. And here too the process is top-down, but in a different sense, involving finality. Thus, as organism sociality implies biology, and biology implies chemistry, so, because this is a process of refinement, only a very narrow set of possibilities could imply organism sociality. That is, chemistry could give rise to many kinds of super systems, biology to fewer, and sociality to even fewer. Developments (in distinction from evolution) are always entrained by final causes, and approach them asymptotically with each emergence of a new realm. Involved here, as in all developments, is the process of senescence, a condition of information overload (recall that information in this hierarchy is transitive across levels), leading to overconnectivity, leading in turn to functional underconnectivity, leading in its turn to inflexibility and habit driven responses (loss of requisite variety), leading ultimately to loss of adaptability (inability to produce interpretants of novel situations).

Mathematical Framework

A method with a mathematical framework for supporting modeling and analyzing a Complex System with a hierarchy of constraints given with a specification hierarchy was presented at the 23rd International Conference on Statistical Physics of the International Union for Pure and Applied Physics, IUPAP.

Below a picture is given how the mathematical level given in fig.1 by the question mark on the top is divided in mathematical (sub)levels, resulting in the (mathematical) specification of the physical quantum and general relativity theory.

Fig 2. A Mathematical Specification Hierarchy of the Physical General Relativity and Quantum Field Theory

In the presented mathematical framework the efficiency of prediction of a System is defined as the ratio between its excess entropy and its statistical complexity. A System S derives from another System Q if and only if S = f(Q) for some measurable function f. A derived System is emergent if it has a greater predictive efficiency than the System it is derived from. A dynamically autonomous System self-organized between time t and time t+T if and only if its statistical complexity increased between t and t+T.

The mathematical framework and tools can be applied to all types of systems which can be constrained with a specification hierarchy, e.g. Information, Physical, Chemical, Biological, Ecological, Social and Economical Systems. Below some qualitative analysis examples will be given.

Earth System Analysis Examples

Mathematical Ecology

Mathematical Ecology seeks to improve the understanding of the flow of energy and materials through ecosystems and the regulation of the distribution and abundance of organisms. It covers productivity and biogeochemical cycles in ecosystems, tropic dynamics, community structure and stability, competition and predation, evolution and natural selection, population growth and ecology. In mathematical ecology, earth systems are analyzed using the {Mathematical {Physical {Chemical {Biological {Psychological {Social}}}}}} specification hierarchy. Mathematical Ecology examples can be found on mathematicalecology

Non-Renewable Energy Resource Analysis

Non-renewable fossil energy sources on earth can be regarded as stored energy. Given the earth systems specification hierarchy {Mathematical {Physical {Material {Economical}}}} we see the economical systems depend on material systems.

Non-Renewable Energy gives an analysis of the earth’s non-renewable material energy sources. It can be easily seen that the material fossil energy sources will last only for the coming decades. Given the specification hierarchy above, if the non-renewable fossil fuels remain the main energy source of the earth’s economical systems, these economical systems will be severely disrupted. Since most fossil fuels are formed on earth over million years and are currently used in several hundred years without being regenerated, it is easy to see that using these fossil fuels in a very short time causes massive disruptions in the earths systems specification hierarchy given above.

Climate Change Analysis

Given the {Mathematical {Physical {Material {Biological}}}} specification hierarchy, biological systems depend heavily on the material systems on earth. When earth’s material systems will change much more rapidly then during evolution caused by human activity many biological systems on earth will not be able to adapt in time.

Renewable Energy Resource Analysis

Given the {Mathematical {Physical {Material {Biological {Economical}}}} specification hierarchy of earth systems, we can see the earth’s specification hierarchy is in balance only if economical systems depend on renewable physical, material and biological sources and don’t use sources stored on earth which will not be regenerated again.

On Renewable Energy an analysis is given of the renewable energy resources usable on earth. On earth enough renewable energy can be generated given all current and future demand given the specification hierarchy above.

Energy System Transition Strategy Analysis

In order to analyze a transition strategy of the earths systems we can use the {Mathematical {Physical {Material {Biological {Legal {Economical }}}}}} system specification hierarchy. Given this specification hierarchy, the economical realm depends on legal policies. By using legal policies we can make investments in renewable energy technologies more economical then investments in non-renewable energy technologies. This will result in replacement of non-economical non-renewable fossil energy technologies with economical renewable energy technologies. If we analyze biofuels with the {Mathematical {Physical {Material {Biological {Social {Economical}}}}} specification hierarchy, we see economical investments in biofuels are only justified when these investments don’t increase social inbalances.

A good video which illustrates this analysis can be found on Common Wealth: Economics for a Crowded Planet.

Earth System Transition Scenario’s

Scenarios are “What if” explorations to understand the consequences of choosing a deadline to eliminate global ecological overshoot. In simple terms, Overshoot is the shortfall in earth’s biological capacity to meet the consumption demands of all humanity.

Scenario 1

Business-as-usual. By 2050 accumulated ecological debt may be irreversible.

Scenario 2

A slow-shift scenario, leading to the elimination of overshoot by the end of the century.

Scenario 3

This scenario requires greatest initial economic investment but it carries lowest ecological risk because it minmizes ecological debt the fastest.

Timeframes

The graph below compares typical lifespans for some human and physical assets with the timeframe for the growth of overshoot.