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by Valentino Piana (2019)



1. Basic distinction between logical and chronometric time, operations on logical time, and measurements
  2. Applications to economic fields  
  3. How this conceptualization of time differs from current economics  
  4. The subjective point of view of the protagonists of the stories  
  5. How to embed this concept of time into formal models  
  6. Final remarks about its use in evolutionary economics  



This paper presents a conceptualisation of time and of time structures which is very general but also particularly suitable for the new paradigm in economics and management to which EWI is devoted. We shall distinguish a logical time (hingering on time phases) from a chronometric time (where the measurement of time is of central importance). A sample of application of the concepts to key areas of economic and managerial research (including consumer choice, business cycles, the diffusion of innovations, long-term shifts of the centre of the world) is enlisted. Some remarks on how this vision differs from the neoclassical and econometric ones and on how it can enrich evolutionary economics are briefly sketched.

Then we leave the assumption of an external omniscent observer (of actions taking place over time) to explicitly consider the subjective point of view of one of the actors.

Next, we enter into the modelling domain, showing how simulations over time generate time structures in which the present is subject to "the burden of the past" and "the tension towards the future". At that point we shall emphasise that this conception of time is particularly fruitful in a perspective of evolutionary economics.

Keywords: time, logical time, phase, period, operation, chronological time, granularity.

1. Basic distinction between logical and chronometric time, operations on logical time, and measurements

As more widely discussed in this paper (in Italian language), we start from an initial distinction between a "logical" time from "chronometric" time. These terms may have been used in other context with other meanings but we want to apply them to describe two different aspects of time.

In logical time, a story is a sequence of phases with something in common, whose duration is measured by the chronometric time. Discussing logical time (e.g. its properties and the operations that can be applied to it) must be separated from the discussion of the chronometric time.

For instance, a trip in train can be seen as occurring in three phases: waiting for the train at the station, travelling with the train, descending at the final station. A graphical representation can be:


There is a sequence of three phases, each of which is an extended segment of time. A typical operation on such sequence is the possibility of collapsing one or more phases into higher order phases.

For instance, a sequence in which the agent is at home, takes the train, and arrive at work contains the previous structure (collapsed in its second phase).

This procedure can be replicated (leading to a sort of matrioschka structure of time), for instance in describing a time sequence of living in a certain house, having a certain job, then leaving the job or changing the house. This sequence contains the previous one, with the single trip "dissolving" in a higher-order structure. Obviously, life is a time sequence that contains every other sequence of the person living. History is an even higher-order structure, going beyond the life of any specific individual.

The number of phases is not fixed, so a sequence can receive additional phases at the end or being preceded by one or more phases before.

The basic operations that can be applied to the sequence in logical time are the following:

* Collapse of one or more phases into one;

* Split of a phase into two or more;

* Addition of one or more phases at the end or at the beginning;

* Swap a phase with the next (which invert the sequence);

* Shift a phase two or more places (forwards or backwards);

* Any more complex recombination of the sequence of phases.

The analogy with film editing is pretty evident.

A futher operation is providing an alternative to an existing phase, as we did before where we mentioned "leaving the job OR changing the house". It's like having phases as building block, cutting and joining sequences, including cutting a phase, putting another one at its place and reconnect the latter to the phase that was following in the original sequence.

By colouring the segment, one can show this substitution process in this way:





In parallel to the initial sequence one can put a new sequence, referred to the same agent or a different one, possibly leading to a phase where the two sequences overlaps. For instance two sequences referring to two different passengers might have the same initial station, the same train travel but a different final station.

"Fusion" can be the name of this operation of overlapping sequences.

Within this scheme, forecasting means being explicit about possible stories, identifying which story we are in, structuring its phases and detecting in which phase a certain system is currently and providing which of the phases of the sequence will follow, possibly with some alternatives and early warning signals as for which alternative is prevailing.

For instance, in a story of someone taking a train, when he is on the train we forecast that, earlier or later, he will descend at his final station. How long it will take, it's a matter of chronological time. But we are sure he will enter the next stage. As early warning we may look at his behaviour in the train: when he stands up, collects his luggage and goes towards the exit (which are three sub-phases), we can be pretty sure that the next station will descend (with some alternatives in the case he is particularly anxious, the stations are near one to each other or, conversely, if he is immersed in his thought and may not prepare to exit, which leads us to forecast that he'll have some probability of missing the correct station, etc.).

What a story has in common is primarily the agent(s) that populate it. The story can relate to an individual or to a group, be it a human being or an organization. However, one might have a story where the place is fixed and we analyse who is entering, staying, and exiting (thus the common element is the place). A story may have a piece of text (e.g. a book) or a good or a technology as common element (then we can look at how it was born, how it was copied and spread, how maybe eventually disappeared).

In other terms, what usually the story has in common is a noun, whereas the phase is qualified by a verb (for an extensive discussion about the role of verbs in economics and human activities see here). When someone eats an apple, the two stories of the man and of the apple overlap.

Stories can intersect with each other or being completely unrelated. They can share their common element, phases, and values.

In each story, each phase has a defining feature, which may be qualitative or quantitative, with potentially certain quantitative variables being common with other phases, allowing for comparison and detection based on such values. But this is not granted: it may well be that a defining variable for a phase simply is not defined in the other phases. The object to which refer might not exist or it may be impossible to compute the variable. For instance the age of a person who is not yet born is undefined.

How long each phase lasts is the domain of application of the chronological time. Its granularity may be hours, days, months, years, depending on the type of story one is considering. One does not need to assume that all phases have the same duration, or that a certain phase has the same duration across many stories. The exact moment in which a certain phase terminates to give way to the following might be fuzzy or requiring some convention. For instance the moment in which the person enters the train may be defined as 1. when the first foot is on the train 2. when the second foot is on the train 3. when all feet and luggages are on the train. Chosen a convention, when necessary, the measurement gives the answer.

2. Applications to economic fields

This concept of time is helpful to structure and address many economic issues and fields. Consumer choice can be considered a multi-phase story where the stages can be swapped in a combinatory way. You have e.g. five phases of awareness of a need, looking for a solution, checking whether the solution is feasible on a number of aspects, activating the procurement of the solution, and utilising the solution to meet the need. By swapping such phases, you get a sequence where, passing by a store, the agent's attention is attracted to a good with a price tag and both trigger to reflect if he needs, pop in and pay, trasporting back to home where one day in the future someone, not necessarily he, will utilise it. Another combination is that he is utilising a good, which however terminates or break down before the need is satisfied, so we goes looking where he can find a substitute but stops short of purchasing because it's too expensive. These stories have some insights in them, but you can also automatically recombined all phases, once you code them.

Some phases may be split (e.g. looking for a solution may involve a sequence of shops where you look for products and prices) or made in parallel (e.g. asking others to help you).

Current models of consumers are way too simple if compared with this approach: they collapse all phases in one, assume that all information has been collected, that decision is easily taken and immediately performed, both in its real and financial consequences. That choices are sequential is a key tenet of bounded rationality behavioural evolutionary economics. It is also recognized that the final outcome does depend on the sequence of steps. Accordingly, our approch seems to widen and enrich such strand of research, since in many cases only one sequence is used, without further operations on it.

A second field of application is about business processes. For instance a story may consists of phases in which a foreign innovator is noted, contacted, convinced to distribute its product through our network, including through legal means (e.g. a contract), then we include this product in our catalogue, we present the catalogue in a trade fair where many retailers are contacted, a short list of our current retailers and these additional one is given samples of the good to be shown to their customers, we collect the orders, import the good, organize the logistics and payment flows.

A third field is innovation cycle, where due to individual and group activities, including networking and active cooperation inside and outside a company, an innovation is envisaged, target performance and key technological choices made, a prototype is produced, tested, with the lessons learned leading to a second one, which is produced in a small pre-commercial series, presented to the press and to the public, collected orders, set up the factory, produced and delivered, used, commented both by professionals and final users, in turn giving rise to a social opinion on it, further modifications of the product and a strand of imitators takes off. This diffusion process may meet obstacles, go in unforseen directions and niches of utilisation, attract critics and legal actions slowing down or completely shutting down the process.

During this process, the quality of life of people and places can change, physical parametres (e.g. CO2 emissions) as well, the urban and regional development may be impacted, especially if a larger cluster of innovation is taken into account and many stories are intertwined. An international life cycle of innovation is giving rise to such stories with delays and adaptation to the local conditions and opportunities.

When collapsing a lot of intersecting stories occurring in the same national space, one gets to the macroeconomy, which is thus rising from a more complex "geometry" of stories than the usual sum from individual agents. Then, the business cycle promanates along several phases, such as expansion, boom, crash, recession, depression, recovery, but also in a recombined sequence, some of which more likely than others. Subphases and qualified phases ("alternatives", in the above wording) can occur and an analyst would better track a wide array of indicators so as to identify in which story and in which sub-sub-phase we are.

As with the diffusion of technologies, business cycles move around countries, with phases in which some countries share the same phase in the same sequeces and phases where one country precede the other (in the same sequence of phases) or lead in unchartered territories and phases that belong to different stories. In this political, financial and real connections, including trade, matter.

History follows a sequence of phases as well, with alternative pathways and stories. The centre of the world shift towards new hegemons with the quality of bilateral and triangular relations evolving, structural freedom being a temporary relief from a former dominant country but possibly entering into new subjugations. However, a different story, with a rising number of integration relations may well turn to out into being.

From the closed global system to the microlevel of individul life and activities, the logical time unites and shares, split and merge, with qualitative and quantitative parametres tracking development, whose judgement however relies on the interpersonal consensus. Societies, economies, territories co-evolve over time in a multidimensional pattern of stories.

3. How this conceptualization of time differs from current economics

Basic textbook microeconomics utilize a mathematics that simply ignore time. The equilibrium found at the crossing of two curve is time-indifferent. The sequence of changes in demand or in supply curves has no impact on the equiibrium, which is only determined by current variables (the quantity purchased at a certain price is the same, irrespective if this price is achieved after a rise or a fall of a previous price). Only verbally the process is described in time, but the applied mathematics ignore it.

In more advanced microeconomic tools, which are not shown to general students in economics and business but only to the few specialists, time becomes a symbol in an equation, maybe a differential one. But time is just a point on a curve: a dimensionless instant in which production, purchasing, and consumption occur simultaneously, negating the evidence that all these processes procede by phases, each of which takes some chronometrical time and that the coordination of phases may well be a goal of a planner but a lot of variability will almost inevitable take place.

The interest of our approach is even stronger if compared with the current status of econometrics, where issues related to the chronological time prevail, with the unrealistic expectation of a fixed delay of values in t + n due to values in t, t-1, t-2, etc. There is no reason to assume a phase will last exactly always the same amount of time. When making a forecast, econometrics utilize only past values, without a structure of logical time shaping them. To forecast what the person on the train it looks at whether the person did get out earlier. If he didn't the forecast is that he will never get out. If he already exited, the forecast is that he will get out again (although he is not on the train anymore). They drive a car looking at the backward mirror.

Evolutionary economics hinges on the creative value of time, of the importance that agents (and things) get to life, evolve and finally die. Thus it should embrace our vision, that significantly enrich any evolutionary process and explanation.

4. The subjective point of view of the protagonists of the stories

Until now, we were omniscents observer of a human being or thing that was undergoing a story - and we utilized our observation to talk about economic fields and systems. But how time enters into the experience of a human being? When a person wakes up and open his eyes in a enlighted room, he perceives it from a specific angle; by rotating his head and eyes, the perspective changes and the more so when he stands up and moves in the room. The sequence of phenomena through which the rooms and its objects present themselves to the person follows a number of laws, in terms of continuity, reversibility, increase or decrease of perceived length and heights in response to movements (such as nearing or getting more distant), in proportion to the speed of the movements, etc. The person may have the intention to go somewhere, e.g. to the breakfast, so it takes an oriented attention to what is immediately in the sequence necessary to get there (e.g. the door to be opened, the corridor, the kitchen, the fridge, the microwave oven, the table, the biscuits), with previous perceived objects and scenes (the room where he slept, the corridor, etc.) regressing into oblivion. In other words, the intentional consciousness lives in an "extended present" where protention towards the immediate future and retention of the immediate past smoothly represent emerging and fading boundaries, respectively. To carry out what the consciousness wants, it protends towards things and other human beings, putting in action gestures and sounds, both for immediate touching and for communication purposes. Action takes place in a space, with certain objects at hands, in interaction with others and with immediate consequences for the setting. The person is doing something and organises its interaction with the world accordingly.

In all this, one might sharpen or weaken the importance of certain elements. For instance, while taking a train in a busy hour, one has to care about a lot of other active people, in a condition that might contain some dangers, thus the consciousness is on alert and act quickly on whatever happens, with no much time for thinking at something else. But when he finally sits in its coach on a comfortable bench, he can close the eyes and get immersed in thoughts that may have no relationship with what has just happened or is going to happen (such as descending). He may direct his thought to memories of real events, to plans of future actions or to imagination of fictonal worlds or whatever else.

This conception, which broadly speaking takes inspiration from Husserl's phenomenology, fits well the structure of time we were presenting before, with some important qualifications. The extended present of the consciousness is in line with the "segment" as the buiding block of time. It's not just a dimensionless point.

The fall into oblivion of the past scene marks the end of the previous phase. However from a subjective point of view this is smooth and not crisp and sharp as the vertical sign we used to "cut" phases. So also in our perspective one needs to be ready to accept that such cut is fuzzy, conventional or placed in a sufficiently far away past that is for sure past and not belonging to the extended present anymore. The smoothness of the transition between a phase and the next is in itself a matter of degree which may undergo changes: when a door is closed with a clash, the room that was closed becomes a thing of the past quite abruptly; when the person is not on the train anymore but in the arrival station, the train becomes a thing of the past. So even if the exact millisecond in which this happened may require some convention (the first foot, the second foot or the luggage), if one take the two situations in which both feet were on the train or in the station one can attribute the first to a phase and the second to another. In other words, to compute the chronometric time of the duration of a logical phase, one may need conventions and measurement breaks, cutting an experience that in certain cases would rather be smoother.

Does this mean that the person is not aware that he's living a new phase? No, he could well answer a question by an external observer that could ask whether he's on the train or in the station. But the possibility that from a subjective point of view a lot of small changes were to be considered a unique phase is real (and corresponding to the operation of "fusion" were were talking about earlier).

Conversely, the actual duration of the "extended present" depends on how sharply and frequently changes the perceived scene. There is a reset phase with is feld as the beginning of a new story, when the field of thoughts and actions is unrelated with respect to what was before the reset, or taking its results as a starting point which does not need to refer back to the process that led to them.

All this calls into question the decision to separate two phases and two stories. The inner point of view may see more connections across phases and stories than an external observer, who however may have an interest in simplifying because he's usually going to put the individuals in the context of a broader number of people (e.g. the acts of purchases and consumption as component of a broader "demand").

A particularly interesting case of personal experience is the relationship with other living bodies, communication and interaction (inter-subjectivity) which lies at the intersection of different stories. Conversely, while in our approach, a thing can well be the protagonist (the common element) of a story, this is impossible from a subjective point of view because they do not have a consciousness.

It should be noted that the agent know much more than an external observer as for the intention, the perceived constraints, the background in which his actions take place. He may see connections across different phases and stories that get missed to a real external observer, who in general does not have access to such wealth of details and whose interest is in classes of explanations, actions, and consequences that can have a validity for many people and not "private reasons" which, while explaining in detail the reason for an action from the protagonist's point of view, cannot be shared by others and cannot be externally influenced. This simplification is particularly pronounced in formal models but can well occur in qualitative narratives.

5. How to embed this concept of time into formal models

As extensively covered in ch. 3 of this book of mine, the temporal structure in formal models can be based on the abovementioned perspective and be implemented through algorithms and routines, leaving back equations and systems of equation.

The extended present is mainly the moment of the action and action is taken under the burden of the past and in an ongoing tension towards the future. In the model, a phase tends to be a line of code, where a certain decision is taken and/or carried out (the reverse is not true, as they are many lines of code that are not a phase).

In particular a sequence of phases, which may well be decisions and/or modification of values, can be contained in a loop, which repeats several times (identical or with structural differences). Everytime a loop is performed a "period" of logical time can be counted and the time counter is increased by one.

The chronometric time is a random value with some rules, attributed to each phase or to each period. It can degenerate to a constant when the rule is that its variability is zero and is always equal to one (year, month, hour, or any other unit). This can be helpful when mapping which phenomena of the real world we want to include in the model (a necessary although not sufficient condition is that their time granularity is compatibile with the choice made as for the unit of the constant).

Simulation is a chain of sequentially placed algorithms. In a single phase, you start from some data and you determine a result, useful for another, serving for yet another and so on. Graphically, these steps can be represented as such:




With a simple example, given the work coefficient and wages, you get costs, which affect prices, which contribute to determining sales, so spending on R&D. If this activity is successful, the work coefficient of the next period will be smaller.
Two consecutive periods can be represented as follows:



In the second period, the same determinations (phases) are made as in the first period. Since adding a third and a fourth period becomes difficult to represent if we just add them at the end, we can also represent the situation, expanded internally to five phases, in this way:

where it is understood that the first period begins with determination 1, continues until determination 5, then begins the next period with a new determination 1. Each time a period is transferred to a subsequent period, the time counter (of the logical time) increases by one. Disregarding the internal determinations of each period and collapsing them into one, we can to represent the situation in this way:

Here, time is a potentially unlimited succession of periods. Formally, the simulation is composed of a series of algorithms in sequence with a final reference that, increased the logical time counter of a unit, brings of at the beginning of the algorithmic sequence. The time counter can only take on integer values. First there is the period one, just after period two. What's in between? Nothing. They are not moments taken at a certain distance from each other. Each period is an extended interval ending precisely where starts the next one, without leaving any gaps, exactly as it happens in the for the succession of years. There is nothing between 2012 and 2013.

In these models, the time counter cannot assume any real value, but only a natural number. This is important because, on the contrary, the metaphor of economic dynamics as a movement in a n-dimensional Cartesian space assumes the opposite. The same use of differential equations, resolved then with analytical or numerical methods, is based on a concept of time formed by instants and not by intervals. In our modelization, the continuity of time is not given by the density of the variable "t" but from the juxtaposition of extended intervals without gaps. Conversely, in an instant totally devoid of duration nothing can be produced. No production process is possible. And a succession of moments in each of which nothing can happen is "a timeless time", an expression used by of Nobel Prize winner Ilya Prigogine.

Each period determines the data for subsequent periods and, conversely, each period is based on the results of the previous periods. Accordingly, it is not possible to determine the value of a variable in a certain period knowing only its temporal location, but it is necessary to do something about it: to run through the simulation until that time. Time is not just a variable as it would be in an expression like p = 10 t + 12.

In another vein, the time horizon of the agent taken as a whole is a "sliding horizon". In every period it looks forward and tries to understand what will happen in the immediately following periods. It is not a finite horizon, as if the world lasted three periods, then two, then one and finally ended, as in the dynamic games of the "New Industrial Organization" of finite duration. It is not an infinite horizon since the agent considers, in the action-oriented forecasting phase, only a limited number of periods, even if they renew themselves over time.

In the story of a repeated investment in capital of different vintages, thus productivity, if the installed capital is of unlimited duration, the company keeps "memory" of his past for ever. The composition of capital by year and its productivity reflects all the events and investments starting from the initial period. But if, more reasonably, the physical capital has limited duration, also the "weight of the past" will be determined by the recent past and not by the more remote past, in line with the reflections on the oblivion above.

For further examples of models that implement, at least in part, the concept of logical time presented in the papers see here, here, here, here, here, here, and here.

This representation of the macro-economy at works, with this interactive graph, is assuming a chronometric time, left random and open, in line with the current paper.

These models generate time series which can be compared with this vast array of time series from the real world, possibly using this testbed for checking structural differences in emerging structures.

6. Final remarks about its use in evolutionary economics

This is particularly fruitful in an evolutionary economics perspective. There, time is irreversible and characterized by an "arrow" that goes from the past to the future. The past is a source of events and news about events. The present is the time of choices, which are taken with imperfect information, undergoing a set of selected alternatives the past, previous choices and results achieved. The choices, when carried out, often have inertia and cumulativity. The results of the actions are not foreseeable, if not with forecasting rules subject to the possibility of error. The future is uncertain because it depends on the interaction non-linear of a plurality of agents heterogeneous in objectives, means, capacity. Path-dependency and lock-in phenomena occur, thanks to which inferior technologies may prevent the development of more advanced technologies.

Agents have time to at least try to adapt to the new competitive and technological conditions. But there comes a time when their time is up and only those who have made the right choices are able to survive.

These - and other - complex dynamics can be elaborated by the time conceptualisation that we sketched above.





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