"The term acceleration, used in physics, is a vector quantity. This means that acceleration contains both a number (its magnitude) and a specific direction. An object is said to be accelerating if its rate of change of velocity is increasing or decreasing over a period of time and/or if its direction of motion is changing. The units for acceleration include a distance unit and square of time unit. Linear acceleration: an object that is moving in a straight line is accelerating if its velocity (sometimes incorrectly referred to as speed) is increasing or decreasing during a given period of time. Acceleration (a) can be either positive or negative depending on whether the velocity is increasing (+a) or decreasing (-a). Circular acceleration In circular motion, the velocity may remain constant but the direction of motion change. Physics relate directly Force to acceleration with mass. Another expression putting force between space diffrenciated mass distribution separed or not by a solution of continuity (discontinuity)". A similar introduction can apply to concept of inertia.
In the fundamental physics' thinking there plenty of details that are missed during our common education but farily essential and that could help to understand how analogies could be wiser. For example representation not just as lone points (gravity center) summarizing everything but, instead volumic mass of points ( formal mathematical object: Hamiltonians) sets of points each with different speeds (not the same if not solids systems), space of multiple bodies (not just as 2 first and then linearity); but heterogeneous interactive space, etc. You may understand better proper formulation to ground physical-material levels and less simple analogies, to use them almost directly as concepts inscribed like in models of economical geography, for logistics planning, and so on.
Starting from more complex reality, including simplifying assumptions and reductions properly managed, you ought to, as we suggest reach a general complex models, enough realistic conditions and study the some marginal (?) more simplifications as criteria since which practice optimization calculus, care with 'saddle-bridge relative optimum, do not pretend to absolute extremums (to close to cracks and breaks) , have a program, may be linear if considering many hidden or not fully known constraints (produced by substitute to natural non linearity, assume by the way that all possible legitime actors are involved in the process, like of development of a regional economy that will not work to immobilize or fail your investment, not disqualify you machinery, not discare your maintenance, and so on. A carefull investigation, open involving, will give you some understanding of your ground, calibrate the matrix or vector of weights for your "higher integrated" economic level and cost calculii. Not to get out the umbrella of physical probabilities. Proceed both down(democratically) - top (scientifically) - relative top (approachable controllability) - relative down (attainable sustainability).
Threshold launching Acceleration to the Limits
Threshold effects are produced from some critical values, and also commonly with some characteristic amount: critical mass or critical value, like allowed self-reproducing agent, required to multiplicate and complete its life cycle. At the reverse, but with an eye on the redefinition of maximum reached unit, a somewhere on a scale we often imagine of complexity; a phenomenon decaying and disappearing alone or above some value (saturating or crushing effects). Buffers in chemistry are related to 'giiven' windows of value of a parameter (for example acidity and called pH), making the buffer. Out the borders or limits parameters change fast (like turning fast very acid or very basic - according, in this example the concentration of H+ - hydrogen ion). This (these) breaking point, may by analogy appliable to ideas.
For an example with turbulence: "Landau associated turbulent chaos to the existence of a very large degree of liberty, put into play after an equivalent number of bifurcations, accountable in Navier-Stokes general equations on fluids motions. Lorenz then Ruelle and Takens introduced radically new conceptions on the nature and mechanisms of turbulence emergence extending widely the field of application:"2-species models have either stable steady states where small perturbations die out, or unstable steady states where perturbations, from them grow unboundedly or result in limit cycle periodic solutions. Associated with an intrinsic chaotic motion of dissipative system characterized by a strange attractor in the space of phases".
Thresholds in Biology, Ecology, Epidemics
The analogy, a bit questionned in social sciences of complex issues, is like observing a rapid change up or down, and the difficulty to consider the process as feeded by itself; say like a curve of transformation slow - fast - slow of a logistic curve (simple formulation), or depending on environment as a break-throught, break of some environment processes of containment. To observe that these effects may not be only fast changing and destructive but constructive. See like with liquid water turning suddenly collectively to solid (freezing abruptly), so changing from turbulent to very ordered. Observe too that domino's effect has, at least, some common reason. Thus thresholds are sort of phenomena where minimum values once crossed, makes changes happens faster than expected or massive problem extending "spontaneously".
In biology or ecology of population there are "interesting models which have a nonzero stable state such that if the perturbation from it is sufficiently large or of the right kind, the population densities undergo large variations, before returning to the steady state. Such models are said to exhibit a threshold effect. A threshold perturbation is more a threshold curve or a domain and such is that, if the perturbation results in the trajectory reach the maximum". This threshold behaviour commonly arises in biochemical contexts, which are formally similar to equations for reaction kinetics and mathematically of the same type, as those for the dynamics of interacting populations.
Study of these concepts care, for example, the "displacement of equilibrium", with the exploration of limits. Compare the posivity of change with the explosive change of definitions. Consider that in a material (physics) world, things cannot go too far, but are not necessarilly of our scale, and may be one homogeneity ahead. See that a forest fire will extend more if unlimited by homogeneity of good conditions of propagation and slower if limited by heterogeneity. May be butterfly's effect need the support of a catastrophic, unadvert, disposal of Hadley's cell. "The interaction details between reactants and those for interacting populations are, of course, quite different, both in forms and motivation. With biological systems there is more complexity regarding the necessary order a mode of differential equations. However, this is often compensated by enzymes or catalysts and thus a biological justification for reducing the order considerably".
"The concept of threshold deals directly with the notion of discontinuities in process relationships in the environment and discontinuities in economic and social continuous variables. In ecology, there is a large body of literature discussing thresholds, also called discontinuities, where the simplest definition is: a rapid state change occurring as a consequence of smooth and continuous change in an independent variable". "Reaction kinetics give rise to mushrooms and isolas, even more baroque dynamic, threshold and limit cycle behaviour is possible. Biological switches, not only those exhibiting hysteresis or more exotic behaviour, are of considerable importance in biology". Relevant also to humans' economy, as epidemics, many processes of diffusion, multiplication, growth or information.
In continuous deterministic dynamical systems, all possible time series make up the vector field, which is represented by the system’s phase portrait, an idea first proposed by Poincaré. Analogous questions can be asked about discrete dynamical systems, such as random boolean networks and cellular automata. Where analytical solutions cannot be found, repeated simulations can be analyzed for their statistical properties. The initial exploration of these systems has been rewarded by the discovery of unsuspected patterns of simplicity and order, from Feigenbaum’s number to Langton’s edge of chaos, Wolfram’s Class 4 cellular automata and Bak’s self-organized criticality.
What Else ? in Dynamic of Economics and Social Change ?
In their quest for completeness of their logical system, modern sciences specialized too much. Specialists try to extend their “corpus of specialized intelligence” to explain everything, including general concepts in their specific register and in their own terms. But when exposed to difficulties, they just defer with other specialists, like wanting to ignore crossed contributions and common essence of methods. This, systematically practiced, often ignore most interesting skills of specialists, wanting them to predict according wanted. So their limited knowledge or care on limits, practical methodological tips, and so on. Too concerned and too dedicated as they are to their academism trying to make their discipline theoretically overcomprehensive, meanwhile extraordinarily deficient in simple methdological evidence. With artifices they try to extend the margins of their science, confuse details and/or too sophisticated models. These reveal with the shortness of their prediction, the time wasted on formal demonstrations of their models, the degree of logical abstractions reached by their explanations; to pretend to be more sure than other registers,other schools or other collegues; meanwhile missing the most important of problems where are with communities not so abstract as operate.
On one side developed societies look like oversimplifying and, on the other side, provide more and more sophisticated explainations. At the end of all their self-prescription. Delivered analysis ask for more specialists and more studies, for their discipline and more spendings on short solutions, inflate their services, prevent people's involvement. Meanwhile, socially working groups stay needing to resolve an increasing variety of problems, unhelped by comprehension and biased by inappropriateness of inflated perspectives, not allowing them selfsense of wholeness. Then the reason why many try to find other systems of explanation come from the need for diverse heterogeneous pieces of explanation. Imported looking scientific theories are hardly well shared neither are free of prejudgment. If cultures often apply unconscious shortcuts that can prevent flexible explorations of democratic solutions, extend to much. Reviews of appropriation should also avoid loopholes, meanwhile reach some social acceptance. Simple ideas do not determine equal behaviors. Social unity, like national or regional (subnational) ones can help good dynamics but they are often with subjective ambitions rather consciously well operating ones.
Definitions are exposed to confusion, even when well diffused and known. Especially when carried by poor intellectual intermediations (too self-interested) and always constrained by games of influence or power. Specialists are keen to provide conclusions, but carry more self-interest than real science as well as too often about things or policies; beyond their area of practice. Formal sciences useful to any other applied sciences, should not confuse real difficulties, when seeking more people willing to play their games instead of coping with their problems. Modern society’s applied exact sciences nowadays coincide enough with their utility, but still face many limits in their social extensions. In a way, that comprehension allowed by formal sciences is no longer humanely (nor theoretically) possible.
Disciplines easy to engineer can be checked by controlled experiments. But in many applications they often lack the intent to be comprehensive or to provide comprehensive devices. "Getting in times of greater uncertainties but with more surprises to come. Strictly speaking, "a surprise is an unanticipated outcome; by definition it is an unexpected event. Mathematically defined as rapid, non-linear responses; forcing system,, such as a collapse or the abrupt amplification of a small even (in a large scale frame of diffusibility?). Most global systems are inherently complex. Consisting of multiple interacting sub-units. Scientists frequently attempt to model complex systems alones, for a small audience of academics or pretending to be specialists only along strict disciplinary lines. Producing internally to their speculations stable and predictable behaviors; which increasingly have very distant links with realities. However, when studying scenarii on Real-world management coupling sub-systems; programs can cause sets of interacting systems to exhibit new collective behaviours, called “emergent properties”. Meanwhile responses of the coupled systems to external forcing can also become quite complicated.
Once demolished our exceeded ambitions on systems of perfect formal idealism (like the "I shall maintain" of captains at the top of their sinking boats) and requalified the common sense of "hope it will go on". We may see our efforts as the pathways for sweet slopes, prevented from the adverse effects; hazards and dangers produced by our activities on enough good conditions to face all difficulties and cope with adversities of our way. This can have the mathematical form of a saddle-line, be it a trail in the jungle, a suspended bridge of ropes or a bicycle side-walk in the streets of a big city. Be big changes or 'great leap forward' not at the costs of large ups, followed by steep downs. For finding sort of cautious inputs which - for not being too quantitativelly matter consumming neither energy wasting - may come from understanding of natural information provided by skills, attentions and wisdom, in management of knowledge. By caring not to take all our speculations for definitive knowledge.
The economic approaches of discontinuities are more contrasted. Indeed, economic theories are driven by different fields or schools that develop different aspects of comprehension of economic processes: macroeconomics which considers the economy as a whole vs. micro-economics which deals with individual agents, such as households and business; standard (neoclassical) approach vs. heterodox ones; environmental and ecological economics, urban or spatial economics (underlined here) … or others; theoretical models or empirical analysis. “The use and abuse of computer simulations bears watching-especially in situations where there is a notable power differential between those putting together the simulation and those whose lives are the subjects and objects of these simulations.” Only some of them like, ecological economists, standard economic growth models or classical theory of localisation, deal with the idea of discontinuities in evolution of variables (in time) or discontinuities in the co-evolution of two variables. Ecological economics also introduce the concept the notion of level of sustainability between natural capital and man-made capital in the definition of these thresholds limits. In sociology the term threshold is rarely used. It does however feature in some sociological models, like critical mass models. These discontinuities are linked to equilibrium disturbance, breakpoints or areas of rapid change in a system"
Now, since our brain can do better than what we forced it to do ( financial speculations) or lazily allowed (society of fat consumption), it would be to extract do-able informative evidences. That could solve mispecified runned programs and care some non comeasurable aspects. Sort of complicated effects, "weird patterns" if they can help to conceive forms of knowledgeable transformations. Since we have yet no overviewed sorts of infrastructures programs, because too reductionist or cartesian approaches or too executive financial management of "social sciences" have prevailed in recent paradigmas. And since it is hard to conceive good strange social building phenomena. Many words of the management of globalization are speechfull tautologies, more eye-catching abstractions than being practically applied. Being also hard to know with sure science, what will happen, with what we do and, what to prepare then. Observing that Nature itself have shape and hide so many "black boxes" at random, where you do not see much and even ignore where you are. Observe too confusing "white boxes" where we are dazzled by too much and too many lights. Conception can use simulation with some complex mechanisms mathematicaly already formulated and discovered in physics. Say like irreversibility in evolving systems. Those boxes complicate, but also allow to imagine mechanisms of maintenance and reproduction. Be them like for setting cycles of renewal, with plenty of different scales of time and space. For such sort of mechanisms to be used as models, enhance: imitation, cooperation, congregation, reproduction of consistent information, differenciate democratic treatments, etc.
By side of what can be managed, if management (of complexity) is nevertheless 'necessary', for not staying like passively expecting that the environment will spontaneously recover and set empty the tables of humans; there are a increasingly big toolbox of concepts for expressing our concern about a World better arranged. There are also already (few) hundreds years of systemic investigation discussion on how a 'better civilized World'. If we should be still questionning large scale adverse effects that are driven modernity into inhumane pathways it exist now principles of precaution, sense that sustainability is needed, resilience or fair respect byside of haunted overgrazzed battlefields of "socially fighting individual utilitarianisms", "geopolitic-sized ideological conflicts" and "absurdly well leadered misspecified generosity". Either: "In cascading pyramides of uncertainties, ranges are multiplied to encompass a comprehensive range of future consequences; including physical, economic social and political impacts and policy responses. Is the only policy response implicit on this figure is adaptation? since the processes have shown stops at impacts - in reality, perceptions of “unacceptable” risks can create policies for restorate, that would narrow the range of starting scenarios. Thus reducing the final impacts range. In that case, awareness of the large range of impacts, might feedback on policies alter the emission scenarios so the cascade would be less 'explosive'.
The Risks of Welfare Theory
"1) If we were to accept only operational definitions of a social welfare function, as Samuelson and Arrow seem to require, then we must conclude that the construction of such a welfare theory of economic choice is impossible. If Samuelson and Arrow are correct, we can never explain (within economics at least) why one Pareto optimum will be chosen over another. Those who argue this way conclude that beyond the Pareto criteria, welfare analysis is irrelevant.
2) The problem which welfare economics seems to be solving (when we allow that social welfare functions are possible) is one of choosing between allocations of resources within the constraints of existing production technology and institutions. In other words, the problem of choice is necessarily a ‘static’ problem and welfare analysis is appropriately a ‘static’ solution. Clearly, the more interesting (and pressing) problem is to find the means of expanding the various possibilities frontiers."
"Natural and artificial nets display widespread feature: the presence of highly heterogeneous distributions of links, providing inertia against perturbations. Although most theories concerning the origin of these topologies use growing graphs, simple optimization process can also account for the observed regularities displayed by most complex nets. Using an evolutionary algorithm involving minimization of link density and average distance, 4 major types of networks are encountered: 1) Sparse exponential-like networks, 2) Sparse scale-free networks, 3) Star networks and 4) Highly dense networks, apparently defining 3 major phases. These constraints provide a new explanation for scaling of exponent."
Ethical systems made by professional moral philosophers are comprehensive, create logical system, exclude many sorts of imprecision but are partial, too strongly closed and often ignore other systems of explanation, natural complexities, and human plasticity of reasoning. In their “fight for influence,” experts tend to multiply contradictions, stay far outside communities concerns, waste applicability to compete in artificial sophistications. General studies do not serve more than the ideological social “apparatus of contention.” Systems mature up to impotence: people follow Peter’s principle according which, in structures many ones reach their level of self-inefficiency. They increase artificial complexity, filli it with reductions biases and fallacies, worsening the state of natural complexity, and ignore how to cope properly with that.
Ethical systems become increasingly harder to interpret, simply because their lessons have often just one system of reference, that do not fit with all the accumulated and confused complexities of the modern world. The accumulation of technology is apparently friendlier, simpler, and more efficient but carries many abusive simplifications, developments of time constraints (speeds), complicate any coherent perspective. Already, huge natural complications grow; artificial complications grow more than proportionally, the hold demographic theorema did not help much when pretended to be a 'natural law', has happened with T. R. Malthus’ (an English philosopher). Constraints of competitive management raise too absurd social barriers, to entry or run on unsustainable paths of development. Of course, sustainable development is not made of easy pathways, but the slowdown of human progress as we think to observe does not really seems to enable peripheral societies to sustain same hope for their future, so: why not share it ? where it seems established, and to immigrate where it is.
Elementary ethical principles are poorly adapted and not in a way that could make them understandable by local communities. Hence do not feel free to adopt them. Interpretations and resources of development are impregnating and distorting many socio-economical perspectives, strengthening paradigms rigidities. Theorization is not lacking, for example, even plenty of models of altruistic economics have been already done. But this has not prevented the emergence of distortions like corruption, conflicts, wars, drug addiction, well based on inequalities, etc. Sometimes, we even think it could be worse. What remains critical is the complex-applied perspective of moral values. The wrong disqualifications of popular mechanisms as well as of cultures especially of the values they manage have been rudely promoted. Building ethical systems, despite many new facilities for claiming and marketing its rhetoric, is not easy. It starts with a combination of experience and wholistic perspectives over sustainability, at intimate and local levels of resolution. .