4.2.1. What is in an issue?

In everyday life, wherever we are, we are led to speak of time as an essential variable for measuring the course of things. If we limit our study to the application field of economy and industry, we will speak in terms of:

• – target dates, to designate at what time a production system must provide a “deliverable”;
• – planning, to define a successive set of operations, a chronological sequence of assemblies, or a time positioning of various commands and orders in a factory;
• – duration and simultaneity of several events in synchronization operations. This has also relevance to scheduling problems to organize the actions in remote production sites;
• – ranking, sorting and classifying events with respect to a criteria or a reference value. In a process, we have to identify which needs are to be done before, after or during a present time.

This is why the concepts of scheduling, sequencing and planning are widely used either in production management (in the broad sense) or decision-making, to express relations of anteriority, simultaneity or posteriority.

These notions of time can thus “highlight” or express chronologies in the actions and events that occur during an evolution: they separate what belongs to the past, present and future. Time is a concept that identifies, classifies and categorizes a batch of discontinuous facts yet inseparable in their occurrences.

Thus, in the consciousness of individuals (or of the company involved), time is a concept for integrating phenomena and to better measure, evaluate and interpret events we are trying to better control.

For convenience and to better visualize the evolution and flow of events around us, “time” is modeled as a variable (or dimension, in a common language): a continuous and homogeneous variable. This allows us to represent phenomena as diverse as animal aggressiveness, strikes, triggering riots in prison, stock market depression or crashes, the extension of a pandemic, the heart beat or the propagation of nerve impulses. Most of these systems are based on the use of differential equations.

On another subject, living in our society requires, both in economy and culture, considering a new fundamental concept that could be called “perception of interrelated variables in an n-dimension space”. For example, in a fairly conventional system within a four-dimensional space, we will consider the three geometric space coordinates, plus time. But these variables, as we will see, have no absolute value.

Now we can say that the perception of each variable is very subjective. Indeed, perception in the broadest sense (a better term is perhaps sensation) is a biophysical capability: the sensors which are specific to each human being, the psychological analysis and interpretation (with its individual and collective ideologies), the culture and societal constraints, all connect us to the environment. Moreover, perception is related to the mechanisms of cognition and thought. Thus perception is a subjective capability which may be conscious or unconscious.

In summary, the perception of a situation involves both sensorial organs, the mind, the ideas, feelings and time. This observation is very important because these factors determine our behavior, actions and reactions in the decision-making field, and whatever the sector of activity involved.

One question arises: are the notions of perception about time and space the same at micro, meso-and macro-scale level of organisms or organizations? To answer this question, we will hereafter attempt to explain some of these phenomena and consider some simple examples.

4.2.2. Notions relative to the perception of time: a static point of view

We all have sensory organs (the five senses) which nature has given us, but there is no sensor dedicated to a specific perception of time.

Time is able to measure the movement of an object, in the broadest sense of the term. Time is a concept, a mental construct, which enables a human being to detect and perceive a change or evolution in our environment. The passage of time (flowing time) is a very subjective feeling; as already mentioned, the perception of time depends on the psychological aspects of each individual and parameters such as age, culture, philosophical concerns and economic constraints:

1. For a young person, the perception of time is different from that of an adult: a young person is always in a hurry because he/she discovers the world and embraces new ways of life for him; an old person, meanwhile, has not the same challenges: he/she is peacefully awaiting some recoveries or even death at will, according to the surrounding environment.
2. In South America, the “cowboy” (gaucho) is more living to the rhythm of nature: what cannot be done tonight will be awaiting for tomorrow. In other places, say within a large computer manufacturing plant, we are immersed in a fast-paced world: typically, the delivery of a computer to a customer should be made mandatorily before say the next day, at 5:00 am. Thus, everyone will work very hard all night to deliver the computer on time.
3. Perception of the time of an event duration is different depending on the context, e.g. under stress conditions. In a plane cabin going through a storm, some passengers may continue going about their usual business (such a disturbance for them seems to last only a few seconds) while some others will experience great anxiety and forward it too (they have the feeling of having been shaken for several minutes).

Rhythms and speeds at which changes are sensed are different depending on each person, the global context and the location of the event in question. This also explains the fact that it remains uneasy to coordinate and synchronize business schedules or production planning in a global way: when working in a network of manufacturing plants, we can easily understand that it is difficult to attune the activities if we are working either in India, China, South Africa or England.

This may also explain why conventional ERP’s used in western countries are poorly or not integrated into the operations of some large companies in, for example, Maghreb. The given reason refers to the lack of “temporal flexibility”; indeed, the way of appraising the surrounding world can be different either in different countries or cultures. This is why we can observe the development of many ad hoc production management systems.

This variability and relativity in perceiving time is first related to our (relatively poor) understanding of the brain functioning and our knowledge of circadian rhythms and activities lifecycles in worldwide companies. In terms of time perception, there is no unique point of view: it is a normal fact depending on emergencies, priorities, etc.

Within this context, the temporal perception of life leads us to link the concept of time to different types of events whose underlying mechanisms and characteristics are quite distinctive:

• – the perception of time duration;
• – the perception and production of rhythm, and “takt” times;
• – the perception of a temporal order (chronology) and simultaneity.

Consequently, we recommended to describe our world and situations without using “time” as a variable, an issue that will be addressed later.

4.2.3. Digital time: a dynamic point of view

In our modern societies, the perception of time evolves continuously. This is partly due to Moore’s law, that is to say, to the complexification of nature over time. In one word, time perception is accelerating.

If we take a step back, by analyzing how time usefulness has been sensed so far, we realize that time has helped in dating or identifying the birth of some objects or events (e.g. the manufacturing date of the first Ford car).

Similarly, time enables us to set a chronology of evolution and a timeline in the emergence of main events, even if nothing is indicated about their end. Time, target dates or time duration, are unforeseeable because the world is complex, chaotic and unpredictable: there are unexpected bifurcations (disruptive events), either continuous or discontinuous, associated with both contingency and chance.

It is now important to see how time is considered within the Web framework. As we entered a new phase in information technology, time perception changed dramatically. During the related technological evolution, the response time and access to information, as experienced and felt by a person, has declined dramatically:

• – in 1970, during a training session in economy, we used a business strategy game (running on an IBM 7010); students were amazed to get their results within two hours;
• – in 1990, running applications developed on IBM 390 computers, then on an IBM Z series, allowed to have a response time of about 2 s to get an answer to our queries;
• – in 2008, the response time of some applications through a MID was about 20 ms (in the field of video games, the response time scale related to displays/monitors, although a joint notion, is around 2 ms). Beyond 20 s, for complex applications, people estimated the application was “lost”;
• – in 2012, considering the multimedia and technology evolution, we were expecting a so-called “immediate” response time (we could therefore evaluate it as 2 ms).

This shows that the perception of time changed considerably during this last half century: now, the question never arises as of whether information obtained from the cloud is relevant or inconsistent (in the sense of unique, complete, contradictory or redundant) because this is integrated in our brain. We are flooded by information and emerging ideas are generated continuously; moreover, we proceed by trial and error, and there is no time to correctly evaluate the content of information; it is becoming a natural or normal thing to do the best with what we have.

4.2.4. More about time with the Web

For physicists, the Internet network represents a change of scaling:

1. The number of items involved is very important.
2. There is a huge volume of data available.
3. Swarming (in terms of software applications) is of key importance for the emergence of innovative solutions that are robustness-oriented and with a lower global vulnerability.

People working within highly interconnected enterprises through the Web feel the Web impacts with new social paradigms, problem solving technologies, swarming, ways to better control causality factors, etc.

If we study the underpinning properties of a network, it requires some time to understand one important characteristic: within any system, we always have the habit of linking the notions of space and time to ongoing activities in the world around us; for instance, in terms of communication, we can refer to the number of “clicks” needed to access information on the web.

Apparently, the Web system seems to be very complicated. In Figure 4.1. [POU 10] we can see the relationships and interactions that exist between the various servers in the Internet (a network of 35,000 computers that manage the entire network): a spontaneous homogeneous structure and fractal tree-like, with scale invariance and a relatively dense core (i.e. based on many strong interactions). This indicates that access to information (40 billions of pages) from a given entry point, is possible but can take a “long” time.

In an actual information network, less than 20 “clicks” are required to access, from page to page, any node in the network. Similarly, in 80% of cases, the exchange of information (through libraries, social networks, etc.) takes less than 2 clicks. This shows that the Internet is relatively fragmented with a lot of relevant information grouped around few clusters in neighboring sites. There is therefore a high granularity at the leaf level of the network. Consequently, in most cases, the average access time is low.

Moreover, and this is important [KLE 09], aggregation phenomena are by nature concentrated in most visited and active areas (as for growth phenomena in crystals, or the birth of stars in densest regions of cosmic space, i.e. galaxies), then, distance between nodes, including distant remote information (in terms of number of clicks to access), remains unchanged at around 20 clicks. Consequently, global access time to distant information does not increase. Given the evolution of network technologies, the global access time can only continue to decline.

This explains why and how we tend to live: except for the computational time of our applications, and despite appearances related to the steady growth of the Web, in a smaller planet with reduced in space and time, we can understand how the clusters of nodes are generated, how structures can emerge, and how knowledge and functions are emerging and growing.

This therefore leads us to study, later in more detail, the relationship between time and entropy.

The world is getting smaller and smaller over time. It is consistent with Moore’s law which inexorably applies to the evolution in nature. Indeed, we are subject to an increasing temporal density of events: it is steadily increasing and our pace of life cannot follow closer and closer changes; that is a question of tempo. For that reason, the notion of time, we presently know and practice, could soon become obsolete in a number of conventional situations (e.g. the emergence of catastrophes).

Another important factor in this same area is what we call “immediacy”. For example we may be seduced by a new computer model, recently announced on the Web. However, rushing to the dealer to buy is not a good approach: we can get it, but it will be expensive and require a substantial time delay. By waiting more than 6 months, it is then possible to benefit from promotional advertising where a product can be acquired at lower (even low) cost, and with a great pleasure (involvement of the emotional brain). In this case, two kinds of consciousness are involved: the “reptilian” brain (devoted to immediate needs) and the limbic brain (which covers the emotional part of our mental activities). Here, the perception of time gets a relative importance: it is faded behind “reason” as offset by a “reward”. It is therefore clear that here, as elsewhere, the notion of immediacy can also evolve and adapt to any type of product, service and population, according to our culture and needs.

4.2.5. Time is not a continuous variable

Continuous time flow does not exist. All the devices used to represent time are discrete; rhythms are given by clocks which operate discontinuously: clock-work comprises an anchor, a digital display system, an atomic device of quantum variables involving fundamental physics, etc. Indeed, according to current theories, down to infinitesimal level, i.e. at quantum level, the smallest possible time length considered in our universe is “Planck time” (10-43 s). Hence, time would flow by quantum jumps corresponding to this unit time duration.

4.3.1. What is in an issue?

As for time duration, the distance between objects can be subject to a perception that varies depending on the environment. Similarly, the distance existing between a person and some observed objects changes the (perceived) size of these objects. This is also true about the ranking, or clustering, of objects which remain based on comparisons: it is a non-formal “relative” concept according to the measurement scale, the mode of observation, the metrics and geometric reference system, etc.

Hereafter are some examples to illustrate this:

• – when a young person is observing an adult, this adult seems to be a giant. Later, when gaining a normal size, the person will be able to better estimate the real size of the surrounding objects and to size down the giant of yesteryear. The same applies for our house or garden in which we lived as a child: many years later, the size of the garden will decrease and it is no more an adventure to walk inside it;
• – in a car trip, we can observe many obstacles (trees, signs, etc.) along the roadside; they have a normal size. If we happen to doze off and to suddenly wake up following a noise, our eyes are immediately opened and so we feel to be faced with very large impediments: our fear is extreme, and we step on the brakes causing big swerves;
• – the same goes with the notion of disorder: when we observe the tangled cables behind our computers, or the physical layout of an intranet network in our company, we can see a large number of equipments or computers, interconnected through power cables, intermixed interface and communication wires, all giving the feeling of a big chaos. As we would get into space in a rocket, we would progressively loose the track of details as going upwards; finally, we can see an emerging pattern, or figure, similar to the above Figure 4.1, showing the lay out of the global network of servers around the world: finally, we catch the sight of a large ordered structure.

Thus, it is possible to say either that such or such object is closer to us than another, or that such object is greater than another object, or that such classification or ranking is better than another, or even to determine that an inventory is proportionally higher in such company rather than within another.

Of course, the perception of space, and the notion of geometric dimension as well, depends on how static physiological senses (vision, hearing, smell, taste, touch, etc.) are developed and learned. Moreover, they are also based on the fact that spatial information extracted from a given environment is supra-modal: several tracking methods and pattern recognition techniques are involved; multidimensional variables are parameters preprocessed at a same time in complex sensor systems. But we also have to consider the context and status of our brain processing centers: in the brain, the limbic area and the parietal lobe are heavily involved in these phenomena of perception and their functioning is different for each human being.

4.3.2. On the perception of a disturbance

Another comment is related to the way the information can be processed in an enterprise. As we know, any decision is a mix of rationality and emotionality. Here, focus brings about the level of perception related to the emotional aspect, stress or asymmetry resulting from a specific decision process.

To illustrate this, let us take a quite common example in industry (as highlighted in the 1980s and 1990s at IBM). More specifically, let us consider the production control system of a conventional computers production plant. Periodically, e.g. on a daily basis, the Orders & Schedule Department defines what the computer production program must be. These data are the input of a Manufacturing Cost and Control Program (an ERP-like system). Thus, a Components, Parts and Sub-assemblies procurement program can be established. Before running the Planning and Scheduling module of the Computer production line, a consistency checking of the input data is performed by an operator/agent. Since this operator is either kept informed about external facts (as per Gödel theory) or influenced by the environment, he/she will be able to interpret the input date, anticipate future events and adjust data and assumptions. The analysis of this process highlights a quite common disturbance, in the matter of system “resilience” – now extended to the notion of sustainability – as follows:

1. As soon as the final product demand is decreased, the negative trend observed in the production program can be amplified by a given parameter: it seems consistent to anticipate an increase of the parts inventories (e.g. electronic components), just because their ordering and procurement takes a long time.

2. As soon as the final product demand is increased, for the same reason, a similar action is taken to anticipate a new market trend and to strongly increase the parts procurement in order to avoid future back orders.

Here again, it is a question of “disturbance” perception. It is often an emotional and reactive answer to a disturbance. As a result of such amplified variations, the Planning and Scheduling of a production plant becomes difficult to control, is quickly obsolete and requires a lot of ERP’s runs and re-runs.

In some cases, the dynamic modeling of such production systems has been done and a deterministic chaos was put in evidence at the inventory level, or in some areas of the production assembly line, etc. This result is very important and could be taken into consideration by changing several planning and control mechanisms and strategies in order to drastically improve the inventories evolution.

4.4.1. The increasing reach of media

Harold Innis is one of the first economists (born in Canada) who introduced the concept of spatial and temporal bias to describe how multimedia individuals are processing the exploitation of information in a society. Two distinctive categories of media people are mentioned:

• – media staff assigned with “temporal” biases: they are more subject to collect and store information and knowledge over a large period of time. Here, a recent information has a much more important content than the old information;
• – media staff subject to “spatial” biases: they are more involved in knowledge wide spreading around the world. Here, information holds a different interest level according to the nature and the culture of the reader.

The selection and interpretation of data, the choice of communication modes, and the decisions, are always quite subjective and partial. They directly impact the information control by the media. Thus the organization and governance of a society too are always influenced by the media. This influence is becoming critical since we are increasingly subject to information networks, modern communication technologies, social networking, etc.

A question we can ask is: who holds and control information asymmetry? Is it the media? The decision-maker ? “Dark matter” or the mental substance in a population? The mode of governance? The organization of the exchanges within a network? This explain why information and knowledge are such important and key strategic assets.

Indeed, we always have to keep in mind that a crucial advantage in decision-making comes from the fact that information is asymmetric. In a true and full peer-to-peer system, too much interconnected information is available, and under such conditions, we are unable to discriminate, rank or classify pertinent information, thus making it difficult to elaborate a decision.

Another question could be: how do we explain the emergence of asymmetry in information processing? This is similar to what is existing in nature, when physicists seek hidden symmetries that have been broken in the cold universe in which we live. They assume this is due to the high temperatures of the universe that existed shortly after the Big Bang, more precisely after Planck time. Homogeneity or initial “harmony” progressively disappeared: in nature everything is asymmetrically made with ambivalent components; similarly, each information (as we will see later with entropy) is diversified and asymmetrically distributed: information modifies our perception of the world.

In an enterprise, a lot of managers know these anomalies: for instance, an employee is provided with reduced and biased information on a given subject matter while the manager is kept better informed. This confers a big advantage during negotiations and decision-making: when information is asymmetric (a problem of winner and loser), decision-making is distorted and does not fit the peer-to-peer principles based on equity.

This reinforces that information and knowledge are key strategic assets, and also explains the actual importance of the Internet, and the associated Web applications that shake information usage. Every day we can observe how a common and wide spread source of information can influence political decisions and change the meta-governance of the world.

The next step will be related to the raising power of networked information within an enterprise or organization: who will be the real decision-maker? The manager, the employee, or the customer? Is the manager a leader or just a facilitator?

4.4.2. Knowledge management and the shrinking of the space-time system

In this section, we recall that the way to access information depends on the number of mouse “clicks” we must operate (which was described above). This “facility” can be defined as a “distance”. What is the evolution of this concept? Formerly, this distance was considered as very large: it depended on the availability of the information content (therefore its scarcity) and its price or procurement cost (usually it was only available in quite expensive books). Nowadays, this context has dramatically changed because of Internet usage and the development of wiki applications. The principle of this approach, called “wiki-management”, is as follows:

The wiki-management is a term coined in 2006 by the Net Literacy. It consists of elaborating a collective work due to the contributions from interconnected people who were not, initially, directly related. The objective is to assemble all the energies and skills involved or interested in a collective project: each internet user can directly edit, modify and complete the information available on specific web pages on a subject matter. Thus, everybody brings his own piece or snippet to build a collective scale project.

At the level of implementation, we mention Wikipedia, a free, universal and multilingual encyclopedia, written by volunteers and based on a website that uses the wiki technology. The Wikipedia project began in January 2001; it currently has over 2 million items (web pages) written by more than 200,000 regular contributors.

The basic features of the wiki-management technology are quite general:

1. The project must gain enough height, with a limited span, to be correctly envisioned by all the participants. Thus, it gains unquestionable social value.
2. The project’s purpose is often far from the individual concerns of each participant.

3. The project brings together interests, knowledge and skills; it may create cultural, disruptive and productive shocks.
4. The collective interest is greater than the sum of individual interests.
5. The project involves at least several thousand interconnected people.

Leadership is one resulting advantageous feature of the Wiki World: the challenge consisting of mastering modern ways of management (based on motivation, acceptance and integration of diversity) and managing complex changes in our unprecedented times. The proper management of smart, associated people benefitting from fast access to think tanks and huge collective knowledge databases will create a high performing company.

But we have to keep in mind that, through such a process:

• – the smartest organizations are those building smart people communities and bridging quickest collective knowledge facilities;
• – the emergence of an innovative product, service or solution is of key importance.

Here again, as seen concerning the media influence, it is important to note that wiki-management technology has a great impact on enterprises and governments management and governance. Indeed, wiki-management is a collaborative and synergistic manner of creative and evolving management strategies and tactics through the input and influence of hundreds or thousands of “Netizens” contributions (Netizen standing for Networked and Citizen people). It is a means of reinventing management and control systems, to focus on an unchanging mission in a changing world, to foster the development of new products and services, etc.

Within this framework, according to the raise of a kind of “hedonism”, the wiki-management phenomenon will become much more powerful, invasive and pervasive than what we have seen with conventional media.

4.4.3. On the rationality of our world

In our actual world, we are faced with a large inconsistency: economy, as described by the models and handled by most economists, does not integrate human feelings and, more specifically, strong emotions such as hate, fear, love and anger.

Actually, economy is an avatar of the human being, subject to deviances, reductionism and inconsistencies in its modeling and analysis. Indeed, as stated before, the common approaches in economy are contradictory with what we have in nature: nothing is rational. Everything is highly subject to relativity and subjectivity either at the physical dimension or at emotional levels. Unlike the Cartesian approach, which is the route often taken by most scientists, it is necessary to highlight some global rules, as follows:

• – first, our systems are not ordered according to a world of logic and conventional physical laws, but through a chaotic and fractal world, where networking and nonlinear dynamics become predominant;
• – second, we are living in a world where consciousness is both based on reflexive actions, reasoning and emotional considerations (as structured in our brain). So, our decisions are based on dreams but also on nightmares, on beliefs and not only on facts, etc;
• – finally, humans are subjective, shared or not shared, towards others; which leads to develop our adaptive capabilities to a world that is largely irrational, often imaginary and even ghostly. This world is an imaginary world with regard to every individual.

All these concepts are mainly related to the perception and interpretation of facts and events, network dynamics, etc.; it is a world essentially unpredictable and not objectified. Ours is a world populated by emotional fantasies, fears, and false pretenses; it is the world of passion and seduction, the mysterious world of affinities, of glories and defeats.

Nothing is ever accurate, standardized, predictable and rational. We are living in a “cloud”: everything is cloudy. Within this context, how reliable are our present theories and decisions? No decision-making can be done without asymmetry since no Nash equilibria can be reached. No decision-making can be done without antagonisms, which is to say without ambivalences and diversity: indeed, opposite feedback loops are always necessary to converge towards attractors.

4.4.4. Are time and space essential parameters and variables?

Here, we refer to the fact that time and space concepts are just necessary to express some relationships. Within this framework, we will first quote Michel Balard [BAL 06] when he says “you cannot give a judgment about the actions performed in the 11th and 12th centuries by the crusaders, according to the mentality, culture and thoughts existing in the 21st century”.

Truly, everything changes overtime. Records show that massacres were performed both by Christians, Arabs and others populations, but today, the notion of death, associated with a level of sensitivity, is not the same at all. Moreover, side by side relationships between different civilizations have allowed crusaders to transfer significant economic, scientific and cultural contributions, which they could import into Europe. The influence in the arts were not negligible; changes in management systems, governance and authority practices were important several centuries ago. The retrospective and an overall approach of problem analysis still allows us to better evaluate a situation and to have a more accurate view of things.

Another comment is related to the scientific innovations imported from Arabian countries by the crusaders: these included astronomical instruments (astrolabes), maps, concepts related to algebra and geometry, some concepts of optics, advances in health and medicine, experimental chemistry and some elements in philosophy.

As we are interested in knowing what the situation was in the 10th Century, what are the benefits after the crusades, etc., we still do not care about how things were happening during the elapse of the time flow.

Moreover, nothing regarding time and space concepts were imported into the Western world (the Occident) by the crusaders. The notion of time which traduces a change in equilibrium (from a state to another) was not an essential concept. This was studied and formalized by Galileo Galilei around the year 1650, and the first clock, with a pendulum as we still have today, which was designed and developed by him in 1637.

In a different area, we can explain how a technological defect is analyzed and processed in the electronic industry. The problem is related to the assembly and testing of large computers. When an electronic failure occurs, e.g. a chemical migration in highly integrated electronic components, the difficulty consists of defining a diagnosis, the causes of the problem, determining how many machines could evidence reliability problems, how many machines produced will be affected by the issue and which strategy has to be set up to recover from the situation (parts replaced, computer duplicated, etc.). In this case, everything has to be done as soon as possible but time is never considered an essential parameter. For instance, we do not care about when will such or such failure appear at an upper assembly level.

When studying interacting populations, as they do in society or in enterprises, time is not necessary. This parameter can be used in an implicit way in the continuous mathematical models to formulate increasing or decreasing rates, but time is not used in an explicit way to measure the evolution of each population. Indeed for a given population (#i):

Analyzing the evolution of one population compared to another does not require time as a main variable. In the following [MUR 02], we will detail three behavioral situations, well known in the companies and societies we are living in.

Situation #1: competition, exclusion and coexistence

Here, two species, the quantities of which are n1 and n2, compete for a same limited quantity of food or resources and, in some way, inhibit each other’s growth. It is a fairly general principle which is observed in nature, in business, etc.

The set of differential equations representing this dynamic system are expressed hereafter; they are of Lotka–Volterra type and include logistic growth features:

This model allows us to follow the evolution of the two populations n1 and n2, in a phase diagram. Their evolution follows phase trajectories, conducting them either to zero or to a steady state, according to the competitivity conditions and the level of resources. In Figure 4.2, from left to right, we have:

• – n₁ = 0 and n₂ = S₂; N & has been progressively eliminated;
• – n₁ = 0 and n₂ = S₂ or n₂ = 0 and n₁ = S₁;
• – n₁ = n₂ = S.

Situation #2: predator–prey populations

Here, there are two kinds of animals or humans. The first group is considered to be populated with preys, while the second group contains predators, living on the preys (e.g. master–slave systems, competitive domination game between two companies, etc.). The basic Lotka–Volterra differential equations are defined as follows:

As observed in the following phase diagram (Figure 4.3), when predators become too numerous, the preys are eliminated very quickly. Thus the resources supply of the predators decreases and its population decreases accordingly. This allows us to increase the development of the preys so that a greater supply becomes available for the predators whose number now increases again, and so on. When a serious difficulty arises, however, both populations may die out.

Situation #3: symbiosis and mutualism modeling

In nature, there are many examples where a species benefits from another one through a common cooperation. This facilitates their living and survival (e.g. trees and bees, the Kanban management system, etc.). The cooperation can be modeled in the following way:

In such a model, for initial values of n1 and n2 which are large enough, an exponential explosion of the population may occur. Otherwise, the common attractor is the stable steady state S which shows an initial and greater benefit, compared to the (1,0) and (0,1) states, when no interaction is present.

COMMENTS.–

Models of the above three types are widely used in ecology and provide a global view of the behaviors and fundamental patterns we may have, as a result of their nonlinearity: they are independent from time.

It is the same with the approaches used in statistics, probabilities and multivariate data analysis: these descriptive methods are based on statistical distributions involving factorial diagrams (the selected factors are depending on their significance, or inertia, that is to say their associated eigen values). Time is not an essential and main variable.

Additional effects can be taken into account (such as time-lag effects, seasons, death rates depending on age, behavioral reactions, different levels of needs and resources according to the evolution level of the population under study, etc.) with short-range activations and long-range inhibition as we have, for instance, in biological morphogenesis. An important comment is this: there is a great similarity between business, economic and physical models. They are always far from a thermal equilibrium, and they are able to explain how the systems elaborated by human beings can work. There is a difference, however, if we compare them to biological models. In our first models category, they lose their structure when the energy flow, or the flux of matter, is switched off or almost nil. However, biological systems, which are better adapted to survival and resilience, are more oriented toward morphogenesis and homeostasis; their structure is preserved for a significant, much higher, period of time.

This explains why economists, politicians and industry strategists are so often wrong in their predictions. Of course, the nonlinear dynamic systems which they use are not predictable and can diverge rapidly. In addition, they do not faithfully reproduce the reality of our world, as stated in the previous paragraph. In nature, morphogenesis and homeostasis are complementary properties: they help ensure a consistent evolution of our complex systems. Ignoring them, as we are doing within chaos and fractal theories, leads to the fact that our time horizon becomes very short. This is why so many errors are repeatedly observed among forecasters. The label “guru” is sometimes assigned to someone who is able to explain some events (in retrospect); yet is this ability sometimes simply down to luck?

In a different field, let us consider the governance issue in a country. Let us consider industry: we can consider that active workers represent an N prey population at a given time (N representing the quantity of human agents). When an economy evolves positively, growth happens at a given rate; then, an increased activity follows and leads to the hiring of new workers after a few months delay. As soon an economic crisis happens, the decreasing activity of enterprises requires to reduce the human resources level: an N reduction that is done within a given time delay.

However, a P predator population always exists: it is formed partly of administrative people working in non-added value tasks or organizations.

When N starts to decrease, P will continue to increase for a while (about 3% of the total human resources) just to better control the economic phenomenon, to perform a so-called “economic straightening” and to try to help the companies or the workers in trouble. Here, a fraction of prey energy is assimilated or wasted by predators and turned into new predators.

As soon the economic situation becomes unbearable, the P population will decrease following a given predator mortality rate.

As a consequence, the evolution of N and P populations can be described by the equations of a Lotka–Volterra dynamic model: contrarily to what is expected, the representative graph is time independent. Also, we can say that some disruptive events (in terms of activity, or P increase rates) may introduce instabilities and may even lead to extinction of the global system (convergence to the (0,0) attractor).

4.4.5. How are antagonisms linked to time?

In many circumstances, nonlinear dynamics (NLD) and basic or fundamental physics modeling is applied to describe the behaviors of living organisms in nature. The human species consists of nonlinear and dynamical agents: its mental thoughts, its creations and emerging organizations are also NLD. As a consequence, the behavior of a community of individuals, and their resulting systems, can converge to stable attractors, due to positive and negative feedback loops, thus based on antagonisms (ambivalence principle).

The magnitude of the different antagonisms is always expressed as a variation in time. Like pulses, antagonisms may synchronously or asynchronously evolve overtime. In this case, feedback loops are never applied with the same density function. Indeed, nature is continuously evolving so as to give advantage to one global interest according to the context: depending on the circumstances, sometimes it will favor one of the two components of a given ambivalence; sometimes it will benefit more the other one in order to provide the best possible overall adaptation.

Thus, the best-for-fit ratio of an ambivalence, which controls the influence of each opposite components, will be changing overtime; the objective will be either to monitor the neutrality of one or several causes or effects, or to find an optimal balance. To summarize, the underlying effects of an ambivalence are always linked to time or system changes. It is a dynamic process which is necessary for a solution or a globally optimal organization to emerge.

This is the reason why in any system, it is of key importance to identify, localize and appraise the asymmetries, ambivalences and nonlinearities (power laws, etc.), then to model the interactions (detection of positive and negative feedbacks, etc.), for the sake of determining whether the system is reactive and adaptive.

4.5.1. What is in a notion?

How often do we regret decisions taken previously? Over his professional life, a decision-maker may ask “if something could have been done again, I would have acted differently. Could we go back? How?” In other situations, some people say it is possible to go back in time, in a diagnosis decision-making process, for example.

These remarks raise the question of the reversibility of time, not in the sense of physics (invariance of a phenomenon whatever the sign of time) but in the sense of a complex process that can be traced back in time in order to change its course.

Such an approach is based on the concepts of regret and is mainly based on the difficulty of making a well-balanced decision rather than an optimal decision. In any management and control system, it is easier not to take a decision rather than to decide: in some cases, the risk of committing an error is almost zero; in others, energy consumption can be minimal. Any decision is always associated with a significant risk of error, and a high cost, especially if we do not implement a holistic and comprehensive approach. In fact, our decisional universe is rarely “regular” and we often converge to a local and suboptimal attractor.

The problem of reversibility arises as follows, stated in a well-known (Wikipedia) definition:

In a system, a reversible transformation is an opposite transform following a gradual and quasistatic modification of external constraints, that is to say very slow, so that the we can consider the transformation as consisting of a sequence of very close equilibrium states while the system recovers its previous successive states. It is therefore an ideal model of transformation.

Reversibility is mainly valid when addressing very small-scale or very large-scale systems. However, in nature, where most real system changes are made at our macro-level scale, any transformation is irreversible and characterized by dissipative (sometimes non-dissipative) phenomena. But other causes of irreversibility can be put forth, for instance:

• – inhomogeneity of the environment, or of the broadcasting source, expressed in terms of molecular density, temperature, pressure, consistency, etc.;
• – dissipative phenomenon, such as friction at fluid and solid levels, social restraint, reaction to technological changes, etc.;
• – spontaneous reorganization of matter: chemical reaction with feedback loops, implementation of fractal propagations and growth principles.

The situation also applies to systems characterized either by fractal geometry or by the non-differentiability of key variables. We observe such irreversible behaviors, whatever the scale, in turbulent or chaotic systems, and in most biological systems. Here, the relative nature of time and spatial resolution intervals counts: only the ratios related to interval or time lengths can be defined and used. Except for the seven basic constants defined in fundamental physics, no absolute value will be used, as an example the need to always use variable units. This satisfies a main principle related to the relativity of scales, according to which the fundamental laws of nature should apply regardless of the scale level considered in the reference system.

4.5.2. Example 1: the study of an inverse function

In order to better understand what we mean by reversibility, we discuss here (Figure 4.5) a well-known example related to the pendulum equilibrium.

1. A perfect pendulum, having no friction, can be modeled by a very simple differential equation. The motion period T of a mass attached to a string of length ℓ with a gravitational acceleration g is given by:

   

   This shows that the oscillation period is independent of the amplitude, the pendulum mass and time. In this case, the resulting solutions remain unchanged when the time variable is replaced by its inversed value. The oscillations, however, are depending on the acceleration due to gravity (g); therefore, a pendulum of the same length on the moon would swing more slowly due to the moon’s lower gravitational acceleration.

2. When the pendulum is subject to friction or external influences, reversing the time variable leads to different solutions, as seen in the formula. Here, the system under study is not considered as a reversible system.

In the first example, a technologically feasible one today, we can see that the often referred assumption of scale is not valid: in our environment, we may have a reversible or steady state system at macro-scale. Reversibility is not addressed at micro features level only.

4.5.3. Examples 2: losing one’s key, wasting or forgetting an idea

Large gaps commonly exist between theory, implementation and practice. About the reversibility of time, most people with common sense and practical intentions have always argued that the process of searching for a failure in a system or an object lost somewhere is reversible over time.

Indeed, when we lose the keys of our car in a house, we first explore an area (e.g. the lobby of an apartment), then if that fails, another room (office), etc. Therefore the search is based on the exploration of the most plausible and likely prior presence areas. If memory fails and we cannot find anything, we try to remember a number of indices which occurred during the recent past. Then, by association of ideas, and due to several facts and events interacting, we are able to remember that when entering the house, we had sore feet; therefore we went into the bathroom to remove our shoes and put on slippers. We are led to look on the side stand, on the table where keys were put above and left the night before.

4.5.4. Consequences for practical life: time’s arrow

The phenomena we are faced with in nature are taking place in what is called an arrow of time: they are assumed to be held only one way. Hence, we consider that time is irreversible and sometimes invoke the “asymmetry” of time. By contrast and according to theory, if there is no arrow of time, a phenomenon can evolve and take place in both directions of time; then time is reversible.

COMMENT 4.1.– Common experiences

There is no way, in our everyday life, to fantasize and think that we can go back in time: we do not live at the microscopic scale level (the quantum level) or cosmic level (the galactical scale). However, when talking about evolution over time, we simply say that there is a concatenation of many causes and effects in a certain order and chronology. Such organization follows a given time flow, which is irreversible.

Under this condition, the weather, as a whole, is reversible in terms of alternation between nice and bad weather, but at mesoscopic levels (emergence of a storm), time is irreversible, while at microscopic levels (molecular transformation) it is reversible again. Yet at quasi-macroscopic levels, it often appears that this is not the case: there is an obvious direction (or flow) of time. Live evolution is such in the human body. We fantasize in our everyday life that we will go back in time to benefit from some imaginary advantage: we live neither at quantum, microscopic scales nor at cosmic, galaxy levels.

On the contrary, when talking about “over time”, we most often say that there is a chaining between cause and effect in a given sequence. Actually, in our common environment and for any event, cause precedes effect, a chronology which represents what is, for instance, called in an enterprise a “time ordering”. In other words, the order of passage of time – which is irreversible – is like a flow of water, and is perceived through a sequence of events.

The same happens with life: birth is commonly considered as a causal event which occurs before life (the event) and life is the result of a successful conception, not the reverse. Thus the usual sense of causality is intimately bound to the time arrow.

COMMENT 4.2.– Organization and logistics in industry

In the assembly line of a computer, we carry out a lot of complex operations such as components manufacturing, components assembly, final product assembly, test in a given order, etc. Some components can also be removed to change or modify an optional feature, or the full system can be dismantled or disassembled to retrieve and reuse all components, and so on. There is not an arrow of time here since assembly consists of a set of reversible operations, using the same operating instructions in an upside down way. Yet, this is done during the normal course of time, which is flowing in such a way that life becomes the track of many successive present times and events.

In the above paragraph, we assume that we are in almost perfect conditions as we can neglect the energy losses related to various friction or counterproductive tasks, to our physical effort, even the energy consumption for tools and equipment. The assumption arises for a didactic example intended to explain how assembly operations – and by extension, time – are reversible.

In the same vein, methodologies based on simulated annealing (a specific variant of genetic algorithms) can be considered as reversible in decision support systems. They represent regenerative approaches that allow repositioning of the state of the problem on an uneven and curved surface in the decision space, then converging toward a new attractor.

COMMENT 4.3.– On time flow

Now, a few comments on the notion of time flow and its impact on human beings. Often time is linked to evolution and ageing issues, a negative concept since antagonistic effects are always associated with any event. For instance:

• – to exist, a living being has to have some consciousness about time;

• – we often talk about calendar time, but within ourselves we signify a psychological time; note that everybody has their own time clock and rhythm;
• – calendar time is always associated with an external “social time” concept having its own social parameters, which depends on a so-called “social clock”: a way used to measure global values related, for instance, to corporate social responsibility (CSR);
• – internal psychological time is a sort of dynamic between fullness, finitude, and perception feelings related to the nature of time. A living being psychological time perception goes faster with aging for several reasons: the overall reference period considered, the relative share of the past, stress during work, the management of priorities, our internal clock depending on health condition; and the ones related to circadian are continuously changing;
• – inner experience is also a strong factor for time perception.

The above considerations show that time is not straightforwardly linked to aging: it is a function of skill, past living and context. This is of key importance since we spend 30% of our life working in an organization and given that well-being is directly related to quality performance and the performance of an economy. As a conclusion, to represent situations, it is advisable to simply replace time by another parameter or to discuss it in terms of phase diagram graphs.

4.5.5. On decision support systems, reversibility and sustainability

In a decision-making process, reversibility is interesting for several reasons and in different areas:

• – resilience and sustainability: resilience is the precursor of sustainability. It is of key importance to develop steady stable processes and sustainable solutions, including in risk management where people try to develop processes so they can control the situations they want to avoid. What happened with the Fukushima Daiichi nuclear plant disaster in March 2011 is a good illustration of such care: the necessity to move forward in recreating, regenerating, and self-organizing a new and better system, as compared to the simple notion of resilience for instance to secure present assets or react against some disturbances so to preserve an actual system;

• – industry, logistics, administration, organization, etc one objective is first to determine what could happen, then avoid a wrong choice and determine what to do. Here, information technologies (ITs) are customarily called for elaborating better decisions or reassessing a process, etc. The IT discipline is conventionally associated with different technologies such as mathematics, economy, computer sciences and life sciences. One main objective in complex systems is to first determine what could happen (and not to plan what will happen), then to avoid a wrong choice and, consequently, to determine what to do;
• – any time it is necessary to appraise a situation, to go back and forth in order to optimize the decisions to be taken. Which explains why answers to strategic questions are necessary (Figure 4.6).

We could include these capabilities when designing a decision support systems (DSS), although some issues arise in the approaches. In a DSS, two main techniques can be used to analyze a problem and elaborate a decision: operation research and simulation. It is generally said that simulation is not reversible, while a mathematical formula is reversible but this statement, however, requires some more explanations, as it is often unclear in a decision-maker mind:

• – in conventional computing, the algorithms coded in a DSS are generally irreversible. But a mathematical algorithm can be modeled in a different way so that its usage can be reversed;
• – in DSS, reformulative methods based on simulated annealing (a specific application of genetic algorithm with limited cross over) are reversible: they allow for repositioning of a problem status on the uneven multidimensional surface of the decision space and continuing converging toward a new attractor. It is a direct application of the so-called bio-inspired approach, or again bio-mimicry;
• – over any system evolution, like a cellular automata, the underlying rule for the system tells how to proceed to the system’s next evolution step. All current evidence suggests that the underlying laws of physics, the laws of life, the same in economy or in assembly processes, show this kind of reversibility. Here, time is encoded as a succession of evolutive steps, while space is encoded as a network of nodes structured in a specific way. Physics is able to provide many more opportunities in terms of solutioning problems and this is more detailed elsewhere in this book;
• – causal networks corresponding to well-established rules (to determine the evolution of the interconnected nodes) are reversible, whatever their feedback loops, much like many cellular automata;
• – the same happens with memory-based application (e.g. based on folding mechanisms) or with discrete event simulation in manufacturing processes: it is possible to deduce not only what the system will do in the future, but also what it did in the past. Reversibility only depends on the possibility to keep track, or to get the list of past events, the precision of quantitative and qualitative data and knowledge of the previous state, at present time.

Reversible computation and simulation have a growing number of application in areas such as low power design, coding/decoding, program debugging, testing, database recovery, discrete event simulation, reversible algorithms, reversible specification formalisms, reversible programming languages, planning and scheduling, and also the modeling of biochemical or bio-ecological systems. In other areas, many paradigm changes may happen with the development of new technologies: reversible logic that provides a basis for quantum computation with its applications; the development of highly efficient algorithms in cryptography, etc.

Here, we can highlight some technological advances: in a quantum computer, it is possible to measure the state of Qu-bits at their entering and exiting an electronic gate, but not inside the quantum circuit given that observing a Qu-bit is sufficient to change its previous state. More specifically, the evolution from the initial to final Qu-bits is done through a reversible process: all quantum gates are reversible and quantum computation is done without the loss of information, thus without energy dissipation.

Some reversible circuits and quantum circuits have already been implemented and could become a complementary alternative to conventional CMOS technology, since the limits of the miniaturization of computing devices – therefore the speed of computation – are constrained by the increasing density of the switching elements in the device.

4.7.1. Generalities

The intimate structure of the brain is now better known, even if this complex structure does not necessarily explain the interactions between mental and neuronal activities. As for the concepts of time and space as perceived in the real world, and the concept of arrow of time, we would like to quote philosopher Eddington:

1. The arrow of time is vividly part of our consciousness.
2. It is required by our reasoning faculty, which tells us that a reversal of the arrow would make the external world senseless.
3. It makes no appearance in physical science except in organization studies related to a large number of people.

Accordingly, the arrow of time indicates the direction of progressive increase in a random element or agent. But, according to thermodynamics principles, insofar as physics is concerned, the arrow of time is a property of entropy, and this necessitates a specific chapter.

Given that it is generally agreed that time is a pure construction of thought, we can add Karl Popper’s comment which assumes that thought can be considered as “a field of consciousness” without mass or energy, but nevertheless exerts an influence on the reading transmission of nerve impulses by activating some basic biological particles present in the nerve synapses.

The problem to be solved is how to make the action of an intangible event (such as thinking, or the perception of space-time) on material organs (neurons) and daily actions compatible with the current laws of physics. Thus, according to the intuitive perception of time and the concept of reversibility, time is difficult to define, assess and handle, depending on the application field and the contexts considered. However, our cultures and vision of the business world are such that time became a “natural” variable, very conveniently grasped to monitor and control events around us.

To illustrate this fact, music, fashion, industry, etc., are each punctuated differently by time. Similarly, time is a useful variable to model and for explaining many physical, chemical, economic laws. Nonlinear dynamics has developed to better analyze the evolution of population trends or the behavior of living beings and helped to achieve many progresses in understanding our society better.

Today, we can observe that time itself inevitably follows a famous Moore’s law: evolution, in nature, is accelerating over time; events are rushing and increasingly submit our society to more frequent and sharper so-called “catastrophes” or disruptive events, before moving toward new paradigms.

Another problem was highlighted that concerns the approach that we must have in implementing a new governance of states and companies. Today, and more than ever, we need to think or act globally and system analysis and dynamic approaches should solely be considered. Insofar as the perception of time is different in each domain and knowing that many subjective and psychological aspects at each individual level are involved, it becomes difficult to conduct new governance approaches only based on the systemic: it is necessary to review our reengineering methodologies. This has already been called to mind either with business intelligence or project management.

On another level, time is often considered as a temporal dimension, within the space-time dimension, and is seen in a simplified manner whereby time flows so as to track a transition from past to future. In the case of time reversibility, we can consider a passage from the future to the past, and then to go forward again and reach new targets. As noticed in this chapter, this requires some specific conditions; moreover, it is not easy since time may have a nonlinear dimension or defined in a multidimensional space.

As time is not a fixed concept, it will be used in any process to organize and track planning and scheduling tasks that affect our environment. Time also allows:

• – highlighting the concepts of cause and effect, following a well-established chronology;
• – when an anomaly or abnormal event occurs, the time flow regulates a process in which were are immersed, through defect analysis, diagnosis, plan of action, correction, validation, prognosis, etc., which are all processings linked together with time;
• – the information processing performed by the media or sometimes politicians is always conducted in a chronological order, starting from analysis, biased interpretation, speculation and pervasive rumors, etc.;
• – failing to go back in time, the only alternative is to provide a very tight adjustment of the operating conditions and to proceed to immediate reactivity. This is one way to counteract the effects of unpredictable divergences coming from very sensitive dependence to initial deviation (SDID).

As already known in the theory of relativity, time is considered as a structural dimension of space through the space-time concept: space turns moving in time, and measure of time changes depending on the speed of movement of the objects in space). But, in some cases, time can be masked and replaced by another variable. For example, speaking of the evolution of the different moon phases day-by-day, we introduce the notion of flow of time. It is not necessary to go this way: we could simply refer to the position of the moon relatively to the Earth and the sun. Time would be replaced by the immediacy of some facts (e.g. a location), perhaps a less convenient approach, but a possible one.

As seen before, we can transpose these thoughts in any field of activity. For instance, in monitoring, control or process management, it is sometimes easier to explain and handle complex systems based on the notions of states, the presence or absence of disruptions, the segmentation and clustering of behaviors. This approach is more suited to work with cellular systems where interactions are becoming the main, unless it remains the only way to manage them.

The findings, however, require further studies of what the concept of entropy, state evolution, can bring to provide more abilities and a consistency in the area of sustainability. Thus, the complexity of the studied systems will no longer carry a technological barrier.

4.7.2. About decision-making

Let us recall a pragmatic statement expressed by Henri Bloch Lainé:

“Every decision is issued from the conjunction between information and competence”.

Skill is not different from the result of experience, learned or experimented, after the assimilation of information over time. There is a direct relationship between time and experience as it relates to a direct relationship between time and organization.

As we developed in [MAS 08] concerning the dynamic management of economic crisis, the introduction of advanced information systems technologies several decades ago surprisingly did not change the methodologies and practices used in finance. As in a striking example, the so-called 2008 subprime crisis was just fostered and amplified by the new capabilities provided with automation. Over time, fundamental theories and best practices did not change. Today, fast trading techniques have been introduced (as enabled by ever faster IT) but basic underlying mechanisms remain the same.

As a result, this is not because of a time reason that a problem will or will not be resolved well. The economic development and evolution goes on forward, and toward more complexity. Again some control techniques associated with still more complex approaches have been implemented, and this is consistent with the basic rule of evolution.

To satisfy some worried observers, economical time-based indicators were set up recently. Now, a lot of resilience groups are set up in many companies, etc.; not that it is the best approach, however, given that the most important parameter is not time. After a crisis what is expected is related to:

(1) creation of richness, (2) creation of employment and (3) development of new activities.

What is important in solving a problem is not to know what will happen in time, but to think about possible events associated with the required responses they engender, taking into account a global objective, rather than the satisfaction of some “happy few”. As follows an old adage: “there are no right or wrong answers but, simply, correctly or incorrectly modeled problems”.

We conclude by saying that failures and crises are not the result of lack of time or the presence of time-irreversible problems, but the result of either lack of skills, even ignorance or greed attitude of decision-makers, or societal evolution [MAS 10].