Complex Emergencies and Natural Disasters:

The Call of Turbulence.

 

Abstract: We achieve a characterization of some recent historical events. These events are

primarily chosen by the criteria of their impact on the welfare of populations throughout the

world. Great care is taken, in aligning reasons for the establishment of a common language,

where to rigorously express the concept of complexity, in the dynamics that lead to such events.

We argue for the definition of an equivalence class, under isomorphism (with respect to the

underlying structures that are responsible for the analogies found in the various dynamics that

we observe), where to include all systems that are involved in this events. Moral issues are

unequivocally raised, but we proceed to develop the thesis that turbulence is the key concept,

in the future, effective understanding of these events.

 

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checked, many of our current practices put at serious risk the future that we wish for human

society and the plant and animal kingdoms, and may so alter the living world that it will be

unable to sustain life in the manner that we know. Fundamental changes are urgent if we are

to avoid the collision our present course will bring about. »[ 1]

«Where is the science, we have asked ourselves, that will correctly analyse, explain and

predict phenomena as complex and multivariate as global change? Where and when will the

next human famine strike, and how can directions to avert it be set years or decades in

advance? »[2]

    The statements transcribed above were made in 1992, and so, they should perhaps

constitute no surprise, by now. But, as to the changes whose urgency was recognized, what

have we seen since then?

    And what about those two questions that they, somehow, motivated? Who was there,

to take a stand in giving them a definite answer?

    Undoubtedly, we have witnessed some progress, namely, on the sciences of

complexity, but is it enough for the politicians to make their options and to deliver their power

to the implementation of those fundamental changes, ecological, physical and economical that

we globally urge?

    Let us take a close look at this.

    It is a matter of fact that, nowadays, throughout the world, countless many people all

share a common fate. Their lives have been fundamentally disrupted and in most instances

immediately threatened by the perverse interaction of politics and poverty. They are victims of

what we now call 'complex emergencies'; a dreadful set of circumstances that are seen to

occur more and more as a result of the breakdown of traditional state structures and the

upsurge of ethnicity: trapped between conflicting factions, they have been thrown out of their

traditional homelands and they have had to flee for their very survival (source: DHA NEWS,

1993 [3] ).

    Complex emergencies are concurrent with some extreme ambiental processes like

windstorms, earthquakes, floods and other calamities of natural origin, in that the spatial

interaction between populations highly sensitive as, for instance, refugees are and an hazardous

environmental process, like one of these, is prone to result in severe losses, be they merely

economical, or human. We call this sort of spatial interaction a 'natural disaster', although, we

emphasize, the vulnerability of these populations to such losses is essentially determined by

poverty [3-4].

    It is also a matter of fact that a global analysis of recent trends of growth, and of

sustainable development, reveal us that, while the later is being somewhat achieved, at least

among some of the richest nations of the world, still, the former remains prevalent and scarcely

controlled in most developing countries, with the consequence of bringing countless people to

an increase in exposure to hazards (consider, for example, urbanization tendencies). It is

important to acknowledge that such an increase goes coupled with an escalating potential for

catastrophic loss [4].

These considerations enable us to comprehend the special attention given to the least

Reduction'. Let us proceed, then, in this way, by focusing our concern upon what can be

thought of as a common denominator, both to complex emergencies and to natural disasters:

the phenomenon of human famine. In fact, both sequences of processes and events can be

viewed to reduce food availability and to cause widespread and substantially increased

mortality [3]. Again, as it could be anticipated, it is usually only certain more vulnerable groups

within communities that experience these effects in a significant way.

    The strike of human famine can be interpreted as a critical point in one, or both of these

parameterize the distribution of primary goods in a community, show some serious fluctuation.

Surely, this can only happen at the expense of a scandalous violation of a pillar of justice,

namely, the Difference Principle, according to which inequalities are tolerable only if they

somehow benefit, or improve the expectations of the least advantaged members of society [5].

    As human beings, we feel that a situation like this is an offence to our dignity, and we

think that it calls to the immediate setting of a joint responsibility concerning the global effects

of our economical, social and technological activities [6-7]. This is so because the kind of

fluctuations that we denounce, in those systems that are the stage for complex emergencies or

natural disasters to occur, these fluctuations are themselves the testimony of what we know as

cooperative phenomena. Take, for instance, the case of the causal relation between economic

recessions and consumer confidence (about the state of that economy in which they occur), as

studies of the United States of America' s economy, during the last thirty years, reveal to be

possible to reject the hypothesis that the later does not affect Gross National Product in the

former [8].

    Just as we declared above to be offended with this state of affairs, so we, thereby,

manifest ourselves willing to grow up human. Turning to the communities where we belong,

their receptiveness to the call that we make will, in turn, testify their disposition to grow up, in

humanity. This growth is not an optional matter, to be decided at one's wish! [9].

    What is that we must do?

    The serious situations that we have denounced above are complex. They arise, or

emerge during an evolution of their physical or social support systems that seems oriented

toward critical regions in their, respective, phase spaces. We would like to be precise about the

sense of this likeness, but we have no acceptation concerning the terms on which to

parameterize such an evolution.

    However, it is possible to clearly identify some general characteristics, common to all

these mentioned processes and systems, the most obvious being, perhaps, that they all demand

the setting of infinite dimensional phase spaces in order for the parameterization that we ask for

to take place. This is indeed the case with the atmosphere, the earth' s crust, the global

economy, or with the various ecosystems.

    Another property, also common to these systems, but whose formulation raises delicate

questions, is that they all turn turbulent sometimes, somehow; they all have the power to

realize turbulence. But, what is turbulence? We don't have no rigorous theory available and, in

fact, we don't even dispose of a definition, gathering universal consensus, for its concept.

Nevertheless, let us proceed with a provisory one, as a working hypothesis: we shall

understand turbulence as that dynamical regime that is typical of systems whose effective

degrees of freedom are not limited above and change in time.

    Note that this tentative definition is general enough to include so-called fully developed

turbulence, in that experimental evidence for the emergence of coherent structures (another

not-so-well defined concept), in flows that attain this last, extreme regime make proof that the

effective degrees of freedom (of the support systems involved) do change in time, at least

locally.

    The awareness of the emergent complexity in systems like the global economy, or

human social networks, can be seen as an outcome of the trends toward global communication

systems, but it is not new [10]. In general, the novelty, if any, goes to the recognition that it is

becoming urgent to develop know-how to consistently manage the challenges thereby raised.

    Meanwhile, as we stand, we acknowledge that all systems of our concern interact with

each other on a variety of scales of space and time. We recognize that financial speculation can

induce some erratic economic fluctuations which, in turn, change patterns of land and energy

use in a given ecosystem [11]; we recognize that a peak in seismic activity in Japan (Kobe) can

cause such a disturbance to futures markets that a financial institution in Great Britain

(Barings) is compelled to declare bankruptcy; and we recognize that injection of waste fluids

underground at high pressure may cause the onset of seismic activity (Denver, 1966) [12-13].

    Such coupling multiplicity does not make our problem intractable, but it do invites

prudence and humbleness in dealing with it. Accordingly, we shall adopt the strategy to ignore

it, at least for start: we shall isolate one of this systems and we shall try to emulate it with a

model whose usefulness may be extended to the others. Observe that this setting apart does

not reduce the complexity of the problem, as the system keeps its power to develop

turbulence.

    Consider, then, the flow of those stress fields whose drainage along fault systems is

induced by the ongoing plate tectonics. The seismic activity thus sustained amounts to a regime

of brittle fracture of rock material that can be interpreted as turbulence of solids [14-15], but it

has also been described as self-organized criticality. [16-18].

    This last concept is another ill-defined one, just like turbulence: everybody knows what

it is, as long as one is not asked to give a rigorous definition. Notwithstanding, it is used here

to acknowledge that stress fields obeying the rupture criterion almost everywhere are attracting

states for plate tectonics, and that it happens to be so without the need of no external tuning

of parameters: the system that exhibits such a dynamics evolves spontaneously to the

neighbourhood of a critical point in its phase space [19].

    Consequently, we must assume the earth's crust, as a whole, to be an infinite

dimensional dynamical system, but we wish to combine this with the reported evidence that,

locally, some fault systems have been observed to produce time series with deterministic chaos

characteristics (in California, Greece, Japan and Ireland) [20-22].

    At the global scale, the complexity of our system can thus be thought as resulting,

either from the coupling that plate tectonics induces between local, chaotic dynamics, or from

the interaction that the propagation of seismic waves induces between fault systems [23-24]. It

is important to note that the physical support for this network of communications, so

established, can be considered as a nonlinear active medium containing internal sources of

accumulated elastic energy whose release can be triggered by small, external stimulation,

natural or man made [25-26].

    Now, if, considering plate tectonics, one has to deal with a time scale such that it is

reasonable to model the coupling induced as a constant, at least during one life's span,

nevertheless, the same is not true when it comes to modelling the interaction, either between

fault systems, or between fault systems and human activities such as mining, oil or gas

extraction, and reservoir water impoundment [27-30]. One has, then, to admit that the relevant

channels, for communication between these diverse systems to occur, are not always activated.

    Consequently, the emergence of those cooperative effects that concern us here, arising as

spatial-temporal coherent structures in the form of intelligible changes in seismic activity, and

that are, somehow, modulated in accordance with the kind of information that flows in those

channels, such emergence, one has to recognize, is rather erratic in time. But the point is that

this is the same as saying that, at least locally, the effective degrees of freedom of the systems

involved do change in time.

    Such a wealth of phenomena can be classified by yet another fundamental concept,

namely, that of spatial-temporal chaos [31]. Concerning the objectives that we prosecute, the

importance of this new concept relies on the fact that it has been used with reference to the

behaviour of globally coupled map lattices ( more properly, networks, whose elements follow

some specific deterministic chaos dynamics and share an all-to-all coupling).

    These models have been intensively studied in the last few years, both numerically and

analytically. Among the results thereby obtained, we want to emphasize the discovery that, in

their so-called partially ordered phase, they develop a regime denoted as chaotic itinerancy,

whose features match, in an essential way, those of the complex systems upon which we

centred our attention. In fact, when this phase is attained, these lattices exhibit an intermittent

evolution between stages of high dimensional chaos and a multiplicity of low dimensional

attractor ruins. It is reported that the switching among these ruins (crisis phenomena), although

spontaneous, can also be induced externally by means of small local inputs which have,

nonetheless, some remote or global effects (as jumps between phase subspaces with different

dimensions are) [32-33].

    Thus, we can infer that both the earth' s crust and globally coupled map lattices are

included in a same equivalence class, with respect to their common properties of having the

dimension of their phase spaces as a dynamic variable, and of being accessible to global

modulation by means of small, local perturbations [23-26,34-35]. This is a first step toward an

engineering of complex systems. Next, we must determine the modalities for these local inputs

to be made, in order that some specific phase trajectories be induced, through particular phase

subspaces, by opposition to others that we may classify as inconvenient or even disastrous.

This is much like a chaos control problem.

    Meanwhile, and because the dynamic regime modulation strategy that we are

anticipating is meant to be effective in relaxing certain undesirable, critical fluctuations in

complex systems other than the earth's crust, let us now argue on the relevance that the ideas

exposed until now may have on them.

    Concentrating on the global economy, we acknowledge that the task we propose

ourselves has been facilitated to the extent of the effectiveness with which economists have

been promoting the migration of concepts, from statistical physics and nonlinear dynamic

systems theory onto their own fields of research.

    Subsequently, it was reported that the time series generated by economies and financial

markets exhibit nonlinearities and deterministic chaos [36-37]. Of course that, with respect to

nonlinearities, this is no surprise at all, but as to deterministic chaos, the case is different. In

fact, the announcement of evidence for chaos in these time series has been received with

caution, as there is no general agreement on its conclusiveness [38-39].

    There are two reasons to justify such reserve. First, the scarcity of experimental data

available, which makes it hard, if not impossible to apply the proper inversion algorithms [40].

Second, the fact that, for deterministic chaos to be safely detected, in economic or financial

time series, it must be associated with a process in some phase space with dimension, say,

lesser then ten. If this is not the case, then, it is generally undecidable whether the data at hand

was generated by some stochastic process or by higher dimensional chaos [39,41].

    It is quite reasonable, however, that, independently of the final result of such a dispute

(if any), one assumes the global economy to be a complex, spatially distributed system. Then,

besides the erratic fluctuations exhibited, the fact that it manifests itself capable of endogenous

phase changes, altering its own dynamics qualitatively, invites the recognition that it develops

itself, or that it flows through phase subspaces with not necessarily constant dimension.

Observe that such transitions between subspaces can be the result of some new technology

penetrating a local market, for example, and turning dominant (and global) afterwards [39,42].

But, if this is so, then, it follows that only from time to time can we expect to witness the

emergence of a determined, low dimensional chaotic behaviour. Still, the potential remains for

this to occur.

    We also realize that these last considerations could have been the logical step to infer

from numerical studies with a panoply of models, irrespective of the type, or the aspect of the

economy being simulated (socialist versus market, for example, or the diverse macroeconomic

modes) [43-47]. Consequently, we feel authorized to include our complex system 'global

economy' in that same equivalence class that we established first, with the earth's crust and the

globally coupled map lattice (such equivalence, we conceive, under isomorphism that is relative

to the species of structure that are responsible for the common dynamic phenomenology

observed) [48-49].

    So far, so good, we next concentrate on the diversity of ecosystems around the world.

Their inclusion in this equivalence class can be motivated by the following considerations:

Take Internet, as an example of a computational network that turned out global. It is

possible to think the multiplicity of computer programs running on it as a community of agents

operating in an economy. Then, the problem of resource allocation (time in central processing

unit) translates to a problem of assignment of resources to production, which is to say that,

somehow, the global computational network can be thought of as a market economy.

    Alternatively, one can think of Internet as a community of concurrent processes, thereby

giving it the configuration of a true computational ecosystem [50-52].

    Whatever should turn out to be the case, the important point is that both computational

ecosystems and computational markets demonstrate the ability to generate oscillatory and

chaotic dynamics. Moreover, specifically, in the Internet, it was already reported [53], one

measures so-called l/f noise, which is to say that one observes one of the hallmarks of self

organized criticality. Conspicuously, the same can be said about some simple ecosystem

models [54-55].

    Certainly, as we argue by analogy, we do not make proof of the possibility to include

ecosystems in our equivalence class. But we do manage to accept as natural that many

independent studies can be invoked to point in this direction.

    Ecosystems are, indeed, complex systems that spontaneously evolve toward critical

points, in their phase space, and that somehow manage to maintain themselves in their

respective neighbourhoods. Moreover, this is accomplished without loss of potential for them to

switch between high and low dimensional phase subspaces, respectively, either undergoing

evolutionary branching, or collapsing through extinction of species [54-61].

    Note that our argument on computational networks could have been used, instead,

mutatis mutandis, to motivate what we said earlier, concerning the global economy: each

argument corroborates the other, as both the economy and the ecosystem stand in the same

analogy with computational networks.

    We now recall the situation that was our starting point. Our reflections were triggered

by an acute consciousness of some pervasive human suffering caused by phenomena that we

called complex emergencies. Subsequently, the remark that such disastrous events have the

fingerprint of generic, collective phenomena lead us to call for the setting of a joint

responsibility concerning the global effects of our participant observation of these processes.

Because we do act like participant observers, and, as such, we do have the power to control

the degree, the quality and the intentionality of our participation [62] .

    We have just made plausible the construction of an equivalence class of complex

systems. Now, assume this as a working hypothesis and let a certain globally coupled map

lattice be the representative of the class.

    Assume a community of participant observers and let them be connected to the lattice

by as many communication channels as convenient.

    The information that flows through these channels (coming from the lattice) can be

classified as symbolic dynamics [63-64]. Consequently, the observers do possess an inversion

algorithm that enables them to recover the abstract thermodynamics of the local maps that are

responsible for each such flow [65]. Indeed, they can even so detect any eventual switch made

by one of them (and consequently, by the lattice) between different phase subspaces [66] .

Finally, assume that the existent communication channels allow information to flow in

both directions, and thereby, that they permit the participant observers to stimulate, at their

wish, the local dynamics in the lattice. Thus, it becomes feasible to determine the phase

trajectory of the lattice, and to do it in a selective way. In fact, the techniques for the control of

chaos, developed since 1990, are by now validated by an enormous amount of evidence, both

numerical and experimental [67]. As to the theoretical work that drove their development,

some consequences are worth to be mentioned: the effectiveness of control (whether in the

suppression or in the maintenance of chaos) does not depend, neither on the strength of chaos,

nor on the dimension of the underlying attractors. Moreover, it is robust against external noise

impinging on the local map to be controlled [68-72].

    It may well happen to be the case that, by studying the time series generated by some

number of local maps, one of the observers detects the slow development of a symbolic

dynamics associated with the setting of a huge fluctuation in the underlying abstract

thermodynamics. Such a detection amounts to the recognition of the emergence of a coherent

structure, thus, to the occurrence of a localized reduction of the number of effective degrees of

freedom, and thereby, to a switch between different phase subspaces.

    Our team of observers may be interested in such an emergence, or it may be not.

    Suppose it is not. Suppose that, instead, they would rather prefer the switch to a different

phase subspace, in that, this way, the fluctuation whose growth was detected may relax and its

eventual inconvenient effects be cancelled. To drive the local maps in a phase trajectory that

best suits their preference amounts, then, to the induction of those symbolic orbits whose

underlying thermodynamical process drives the relaxation of the initial fluctuation. Now, the

feasibility of such fine control of chaos is already established and supported by experimental

evidence [73-75].

    Proceeding, let us now see the incidence that our discussion can have upon still another

complex system, namely, the human social network.

    In this case, also, we are pleased to acknowledge an important migration of concepts

and ideas, imported from nonlinear systems theory and statistical physics. The progress that,

subsequently, was made, has driven us to a reasonable comprehension of the mechanisms for the

social impact that politicians may have on society. These mechanisms are the same ones that

underlie the emergence of collective processes, like self-organization and chaos in social

networks, whenever adaptive decision sequences run by leaders, or leading coalitions, result in

a continuous change of the coupling between forecast adjustment and policy implementation

[76- 79].

    From this point of view, one recognizes that a new light is shed upon the way that polls

to public opinion may be conducted, as some sort of driven input to the underlying social

network, slowly altering the image of those institutional frames that give the reference for an

electorate to express its sentiment toward different politics. Afterwards, such a smooth

transformation will result in a change of the relevant preference profile, in policy space, with

the due consequences on the outcome of an eventual election, or referendum [80]. Indeed,

such an induction of an agenda path can proceed under rather general conditions and have, as a

consequence, that the configuration of voter preferences emerge as a chaotic dynamic variable,

exhibiting sensitivity to small changes and the potential for outcomes anywhere in the policy

space [81].

    Thus, the variety of behaviour accessible to a chaotic system acts as a guaranty that all

sets of alternatives in policy space, which is to say, all policy subspaces, will eventually be

visited, as different options will be favoured by the voters sentiment. Once that this state of

affairs is realized, we are faced with a system to which the techniques for the control of chaos

can be applied. It will be possible to make it wander through the different sets of alternatives in

the policy space, and it will also be possible to make it explore systematically the outcomes of

each such set (by phase locking it to the relevant subspace).

    But, is it really so? Who knows? Maybe not.

    Maybe these scientific developments that we reported here still have not arose the

greed of politicians and financials. Concerning this particular question, we reserve ourselves

from judging, although we feel conscious of the multiple technical (and conceptual) problems

yet to be solved in order that some consistent strategy for the control of complex systems may

be implemented (consider, for instance, the extreme sensitive dependence on parameters that

they exhibit [82]).

    Be as it may, we firmly assert that these problems are minor, when confronted with the

seriousness of the situations that motivated our call.

    We think that their solution will be the corollary of the theoretical establishment of

those laws that govern the dynamics of species of structure in our equivalence class (the

composition of morphisms in a category having such species of structure as objects [83]),

throughout their respective scales of space and time, but this is conjectural in character, as it

corresponds to a step that we do not want to make here, and now.

    Let us reflect.

    The disposition of spirit that drove us, from the beginning, along the lines of this essay,

prevails unshaken.

    Suppose that the aforementioned problems are solved. Then, our relation to the

complex adaptive system that we are part of is a relation with a world whose trajectory of

phase we can control. But, in what direction should we manage to implement that control?

    Such wisdom is not to be found on these lines whose writing we now put to an end.

From these lines, what we get is just the frame that lead us to a call. Yet, we do believe that

the value of the answer that we seek-for shall be calibrated by the generosity we put in our

response to such an appeal.

                                    Lisboa, 15 de Setembro de 1997

                                            Luís Calvão Borges

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