ZM theory I: Introduction and Lorentz covariance

We consider defining time as a function of a cyclical field, an abstraction of a clock. The definition of time corresponds to a novel interpretation of the relationship between space-time coordinates of observers at different locations in space. As a first test of the utility of this definition, we show that it leads to a Lorentz covariant description of space-time. This derivation of Lorenz covariance provides a starting point for considering more general constructions that relate to physical laws. The definition of time couples time to space, making time not orthogonal to space, and making dynamics a result of geometry, providing a vehicle for curved space-time theories that generalize general relativity.Comment: 15 pages, 2 figure

ZM theory II: Hamilton's and Lagrange's equations of motion

We show that considering time measured by an observer to be a function of a cyclical field (an abstract version of a clock) is consistent with Hamilton's and Lagrange's equations of motion for a one dimensional space manifold. The derivation may provide a simple understanding of the conventions that are used in defining the relationship between independent and dependent variables in the Lagrangian and Hamiltonian formalisms. These derivations of the underlying principles of classical mechanics are steps on the way to discussions of physical laws and interactions in ZM theory.Comment: 11 pages, 0 figure

From Big Data To Important Information

Advances in science are being sought in newly available opportunities to collect massive quantities of data about complex systems. While key advances are being made in detailed mapping of systems, how to relate this data to solving many of the challenges facing humanity is unclear. The questions we often wish to address require identifying the impact of interventions on the system and that impact is not apparent in the detailed data that is available. Here we review key concepts and motivate a general framework for building larger scale views of complex systems and for characterizing the importance of information in physical, biological and social systems. We provide examples of its application to evolutionary biology with relevance to ecology, biodiversity, pandemics, and human lifespan, and in the context of social systems with relevance to ethnic violence, global food prices, and stock market panic. Framing scientific inquiry as an effort to determine what is important and unimportant is a means for advancing our understanding and addressing many practical concerns, such as economic development or treating disease.Comment: 24 pages, 7 figures (Complexity, in press), New England Complex Systems Institute Report 04-01-201

Why are public health authorities not concerned about Ebola in the US? Part I. Fat tailed distributions

US public health authorities claim imposing quarantines on healthcare workers returning from West Africa is incorrect according to science. Their positions rely upon a set of studies and experience about outbreaks and transmission mechanisms in Africa as well as assumptions about what those studies imply about outbreaks in the US. According to this view the probability of a single infection is low and that of a major outbreak is non-existent. In a series of brief reports we will provide insight into why properties of networks of contagion that are not considered in traditional statistics suggest that risks are higher than those assumptions suggest. We begin with the difference between thin and fat tailed distributions applied to the number of infected individuals that can arise from a single one. Traditional epidemiological models consider the contagion process as described by $R_0$, the average number of new infected individuals arising from a single case. However, in a complex interdependent society it is possible for the actual number due to a single individual to dramatically differ from the average number, with severe consequences for the ability to contain an outbreak when it is just beginning. Our analysis raises doubts about the scientific validity of policy recommendations of public health authorities. We also point out that existing CDC public health policies and actions are inconsistent with their claims.Comment: 16 pages, 1 figur

The Limits of Phenomenology: From Behaviorism to Drug Testing and Engineering Design

It is widely believed that theory is useful in physics because it describes simple systems and that strictly empirical phenomenological approaches are necessary for complex biological and social systems. Here we prove based upon an analysis of the information that can be obtained from experimental observations that theory is even more essential in the understanding of complex systems. Implications of this proof revise the general understanding of how we can understand complex systems including the behaviorist approach to human behavior, problems with testing engineered systems, and medical experimentation for evaluating treatments and the FDA approval of medications. Each of these approaches are inherently limited in their ability to characterize real world systems due to the large number of conditions that can affect their behavior. Models are necessary as they can help to characterize behavior without requiring observations for all possible conditions. The testing of models by empirical observations enhances the utility of those observations. For systems for which adequate models have not been developed, or are not practical, the limitations of empirical testing lead to uncertainty in our knowledge and risks in individual, organizational and social policy decisions. These risks should be recognized and inform our decisions.Comment: 18 pages, 1 figur

ZM theory IV: Introduction to quantum concepts, Klein-Gordon and Dirac's equations

We describe a general approach to the correspondence of ZM theory with quantum electrodynamics. As a first step, we show the correspondence of helical clock-field states with plane wave states of the Dirac equation. Specifically, defining the direction of time as the gradient of the field in the combined field and space dimensions, for constant gradients, results in states that are consistent with conventional plane wave Dirac equation eigenfunctions. Particles and antiparticles, as well as up and down spins are related by axis inversions. The Dirac wavefunction represents the clock-field and the observer defined direction of time and spatial coordinate axes rotation relative to the region of observation. Additional steps showing the correspondence of ZM theory to quantum mechanics and the Dirac equation are deferred to subsequent papers.Comment: 28 pages, 0 figure

ZM theory III: Classical oscillators and semi-classical Bohr-Sommerfeld quantization

We consider the description of classical oscillatory motion in ZM theory, and explore the relationship of ZM theory to semi-classical Bohr-Sommerfeld quantization. The treatment illustrates some features of ZM theory, especially the inadequacies of classical and semi-classical treatments due to non-analyticity of the mapping of classical trajectories onto the ZM clock field. While the more complete ZM formalism is not developed here, the non-analyticities in the classical treatment resemble issues in the comparison of classical and quantum formalisms. We also show that semi-classical quantization is valid for a periodic manifold in ZM theory, though the quantum number $n=0$ is allowed, as it would be in quantum mechanics for a periodic manifold. Still, this suggests a connection to the first-order success of Bohr theory in describing the phenomenology of atomic quantum states. The approximate nature of the semi-classical treatment of three dimensional atomic orbits is, however, also apparent in relation to ZM theory. These observations are preliminary to a discussion of ZM theory in relation to quantum mechanics and quantum field theory in subsequent papers.Comment: 16 pages, 1 figur

ZM theory V: Lorentz force equation and the vector potential

In ZM theory the direction of time has a non-zero projection onto space and this projection corresponds to the local velocity relative to the observer. Classical trajectories can be obtained by following the local direction of time. The relationship of time to space enables the change in momentum over time to be related to the spatial change in energy and momentum. Previously Hamilton's equations-of-motion were derived by considering trajectories in one space and one time dimensions. Here we consider three space and one time dimension. Without any other assumptions we derive the Lorentz force law of electromagnetism with relevant definitions of the scalar and vector potentials.Comment: 13 pages, 0 figure

Power and Leadership: A Complex Systems Science Approach Part I - Representation and Dynamics

Historical narratives are dominated by actions of powerful individuals as well as competitions for power. Characterizing the origins, types and competitive strength of different kinds of power may yield a scaffolding for understanding historical processes and mechanisms for winning or avoiding conflicts. Michael Mann distinguished four types of power: political, military, economic, and ideological. We show this framework is justified by four motivations of individuals to transfer decisions to leaders: Desire to be a member of a collective, avoiding harm due to threat, gaining benefit due to payment, acquiring a value system. Constructing models of societies based upon these types of power enables distinguishing social systems and describing their dynamics. Dynamics include (a) competition between power systems, (b) competition between powerful individuals, and (c) the dynamics of values within a powerful individual. A historical trend is the progressive separation of types of power to distinct groups of individuals. In ancient empires all forms of power were concentrated in a single individual, e.g. Caesar during the Pax Romana period. In an idealized modern democratic state, the four types of power are concentrated in distinct sets of individuals. The progressive separation suggests that in some contexts this confers a "fitness" advantage in an evolutionary process similar to the selection of biological organisms. However, individual countries may not separate power completely. The influence of wealth in politics and regulatory capture is a signature of economic leader dominance, e.g. the US. Important roles of political leaders in economics and corruption are a signature of the political leader dominance, e.g. China. Ideological leaders dominate in theocracies, e.g. Iran. Military leaders dominate in dictatorships or where military leaders select leadership, e.g. Egypt.Comment: 13 pages, 3 figure

UPDATE July 2012 | The Food Crises: The US Drought

Recent droughts in the midwestern United States threaten to cause global catastrophe driven by a speculator amplified food price bubble. Here we show the effect of speculators on food prices using a validated quantitative model that accurately describes historical food prices. During the last six years, high and fluctuating food prices have lead to widespread hunger and social unrest. While a relative dip in food prices occurred during the spring of 2012, a massive drought in the American Midwest in June and July threatens to trigger another crisis. In a previous paper, we constructed a model that quantitatively agreed with food prices and demonstrated that, while the behavior could not be explained by supply and demand economics, it could be parsimoniously and accurately described by a model which included both the conversion of corn into ethanol and speculator trend following. An update to the original paper in February 2012 demonstrated that the model previously published was predictive of the ongoing price dynamics, and anticipated a new food crisis by the end of 2012 if adequate policy actions were not implemented. Here we provide a second update, evaluating the effects of the current drought on global food prices. We find that the drought may trigger the expected third food price bubble to occur sooner, before new limits to speculation are scheduled to take effect. Reducing the amount of corn that is being converted to ethanol may address the immediate crisis. Over the longer term, market stabilization requires limiting financial speculation.Comment: 6 pages, 2 figure