The biological determinants of long-wave behavior in socioeconomic growth and development

The biological determinants of long-wave behavior in

socioeconomic growth and development

Tessaleno C. Devezasa,*, James T. Corredineb,1

aFaculty of Engineering, University of Beira Interior, 6200-001 Covilha, Portugalb24 Bailey Court, Middle Island, NY 11953, USA

Received 29 June 2000; received in revised form 28 December 2000; accepted 12 February 2001

Abstract

In this paper, it is claimed that the effective causality of long-term macroeconomic rhythms, most

commonly referred to as long waves or Kondratieff waves, is founded in our biological realm. The

observed patterns of regularity in human affairs, manifest as socioeconomic rhythms and recurrent

phenomena, are constrained and codetermined by our natural human biological clocks, themselves the

result of instructions impressed in the human genome and human cognitive capacity by the physical

regularity of fixed cosmic cycles. Considering that a long wave can be conceived as an evolving

learning dissipative structure consisting of two successive logistic structural cycles, an innovation

cycle and a consolidation cycle, and applying considerations from population dynamics, chaos theory

and logistic growth dynamics, a Generational-Learning Model is proposed that permits comprehension

of the unfolding and time duration of the phenomenon. The proposed model is based on two kinds of

biological constraints that impose the rhythm of collective human behavior — generational and

cognitive. The generational consist of biologically based rhythms, namely, the Aggregate Virtual

Working Life Tenure and the Aggregate Female Fecundity Interval, both subsets of the normative

human life span or human life cycle. The cognitive consist of a limiting learning growth rate, manifest

in the alternating sequence of two succeeding learning phases, a new knowledge phase and a

consolidation phase. It is proposed that the syncopated beats of succeeding effective generational

waves and the dynamics of the learning processes determine the long-wave behavior of socioeconomic

growth and development. From the relationship between the differential and the discrete logistic

equations, it is demonstrated that the unfolding of each structural cycle of a long wave is controlled by

0040-1625/01/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved.

PII: S0040 -1625 (01 )00136 -6

* Corresponding author.

E-mail addresses: [email protected] (T.C. Devezas), [email protected] (J.T. Corredine).1 An independent marketing and communications entrepreneur with a lifetime interest in The History of

Economic Thought.

Technological Forecasting & Social Change

68 (2001) 1–57

two parameters: the diffusion-learning rate d and the aggregate effective generation tG, whose product

maintained in the interval 3 < dtG < 4 (deterministic chaos) grants the evolution and performance of

social systems. Moreover, it is speculated that the triggering mechanism of this long-term swinging

behavior may result from the cohesion loss of a given technoeconomic system in consequence of

reaching a threshold value of informational entropy production. D 2001 Elsevier Science Inc. All

rights reserved.

Keywords: Long waves; Kondratieff waves; Socioeconomic growth; Logistic growth; Chaos theory; Population

dynamics; Systems science

1. Cycles and human perception

Cycles are in essence and at their very heart defined by time. Within this logic, cycles

began with time itself — the kick off of all cycles was the flash of the Big Bang some 15

billion years ago, yielding an expanding universe, that perhaps will fall together in the Big

Crunch, closing its own life cycle. The ultimate expression of the universe has always been,

as it is now, that of nonequilibrium, with bubbling activity, differences and potentials that

drove the formation of complexity and the emergence of life. It is a universe of stunningly

abundant free energy available for performing work. The life we know is the natural

consequence of the coupling of that free energy to forms of matter in nonequilibrium

systems [1]. Life is not an incalculably improbable accident, but the emergence of an

expected fulfillment of the natural order that includes the inexorable arrow of time, driving

living systems irreversibly but not linearly — cycles have been in relentless motion ever since

the beginning within the constraints and boundaries of time.

All living systems — cells, organisms, economies and societies — evolved under these

constraints and boundaries of time, experiencing random mutations and opportunistic

selections, but all exhibiting law-like properties. Gravity is one important source of cyclical

behavior in the universe, and all life on our planet emerged under the influence of the

regularities presented by the relative movement of this part of the universe, the three body

system — Sun, Moon and Earth.

Regarding the human being, after all, the object of the present analysis, there are two very

important aspects to consider under this analytical framework:

1. His biological structure was developed under the circumstances of the cyclical nature

determined by the three-body system.

2. His perception of time was deeply impressed by this ‘‘heaven’s harmony’’ — cycles

were always an inseparable component of the human sensibility about time.

In this way, the very regular alternation of light and darkness, of warm and cold, of

blossom and fall, as well as the wonderful regularity of the dance of the celestial bodies, are

thoroughly rooted in the human genome and in the human cognitive capacity. This work is an

attempt to show that the observed patterns of regularity in human affairs, manifest as

T.C. Devezas, J.T. Corredine / Technological Forecasting & Social Change 68 (2001) 1–572

socioeconomic rhythms and recurrent phenomena, are constrained and codetermined by our

natural human biological clocks, themselves the result of instructions impressed in the human

genome by the physical regularity of fixed cosmic cycles. With this purpose in mind, a

recapitulation of the existing theories/models on socioeconomic long waves is presented with

commentary (as summarized in Table 1) and a Generational-Learning Model using

approaches from population dynamics and logistic-based growth dynamics is proposed.

2. The ubiquity of the cycle

Human beings inevitably think about time, it is one of our burdens and opportunities as

intelligent species. We are aware of the passage of time in our own lives, and our societies gain

awareness of the passage of time in their existence as well. Aware of time and also eager to find

meaning, most cultures tried to think about how to reckon time, not just over years but also over

longer spans. This granted, the first point to stress on talking about reckoning time, is the

inevitable human tendency to mark time using cycles. One of the most beautiful chapters of the

human record, the struggle for a useful calendar, translates the basic human necessity of

establishing a table to describe the cycles of nature for both technical and social purposes. This

embodied a very difficult task that remains until our day, because of the inherent difficulty of

reconciling the nonsynchronous periodicity of the three bodies — Earth, Moon and Sun [2].

But reckoning time in a linear way, counting years cumulatively and establishing a linear

chronology, is a very recent human achievement [3]. In antiquity, even among highly

developed cultures, chronology was organized in defined cycles, taking into account a dynasty

or a collection of events, or simply counting years since the birth or death of a emperor or king,

and so on, but returning to the starting point for another political or religious leader. This

inclination to cycles gave rise not only to the idea of setting up years in closed loops, but also to

the conception of the return to the initial conditions — and we saw the birth of millennialism,

apocalypses, the principle of the eternal return, the mood called ‘‘fin de siecle’’ and many other

similar concepts linking time cycles with destruction and new beginning.

At this point, it is useful to take a closer look at the science of history. Historians have

organized the human record in Ages or Eras with fixed dates for beginning and ending, like

the Stone Age, Bronze Age, Middle Age, Dark Age, Modern Age, etc. The same is also true

in Paleontology. But this systematization has embodied the notion of a continuous evolution

or progress (technological or cultural) throughout succeeding epochs, and not necessarily the

notion of recurrence, or repetition of similar events. However, the old dictum ‘‘history repeats

itself’’ is common sense among people and a cyclical theory of history has evolved since

ancient times, taking many different descriptions and interpretations. From Plato to Spengler,

covering more than 2000 years of evolution of the methodology used for historical analysis

and accumulation of empirical evidence, many different types of cycles emerged, with

periods ranging from decades to millennia.

This tendency was not only restricted to the historical analysis. By the end of the 19th

century and the beginning of the 20th century, a vast sociological and economic literature on

periodic fluctuations or waves in socioeconomic systems surfaced, opening the way to new

T.C. Devezas, J.T. Corredine / Technological Forecasting & Social Change 68 (2001) 1–57 3

Table

1

Theoreticalexplanationsforlongwaves

insocioeconomic

development


fields of scientific analysis, such as societal dynamics and business cycles. In the remainder

of the 20th century, a plethora of publications on cycles proliferated, mainly in economics,

most lacking any scientific rigor, contributing seriously to the devaluation of this kind of

analysis and to the stubborn rejection of the concept of long-term fluctuations in society.

Cycles became an unfriendly arena for scientific discussion.

The fact of the matter is that cycles can be seen everywhere, and any number of superficial

‘‘explanations’’ can be advanced by anyone, amounting to a trivial theory of everything. As

stressed in Section 1, however, the real explanation is found in our biological heritage, we are

the stuff of cycles and cycles are ingrained in our cognitive capacity. It is indisputable and

unquestionable that cycles are a very powerful forecasting tool and understanding the nature

of their reality in human affairs will be a valuable scientific achievement. The important task

then is gathering the best historical thinking on this subject, to take the cream off, subtracting

the irrelevant and adding some new worthy stuff, in order to recover the very necessary

credibility of the topic.

3. The cream of the crop

Viewed on the most general level, living systems, from cells to societies, exhibit common

properties, with some attending intrinsic fundamental invariants. Recognition of this fact in

last decades is leading firmly to a new scientific paradigm, a complex bio-socioeconomics,

whose embryo emerged with Synergetics and Chaos Theory, and is blossoming now with

Complexity Theory and Systems Science. One of the purposes of this new scientific paradigm

is to understand the uncanny order that is being discovered in complex and apparently

random systems, and this includes social systems.

The existence of cycles implies a subjacent order. Recognizing cyclical patterns in human

affairs means to acknowledge the existence of an underlying order in social systems whose

real understanding is yet at its very beginning.

Among the plethora of cycles and related social phenomena actually known, there is a

category that has gained some respectability and the support of many hardcore scientists

in last two decades: the Kondratieff waves or, as superbly designated by Marchetti [4], the

50-year pulsation in human affairs.

The original work of the Russian marxist economist Nikolai Kondratieff [5] surfaced in the

middle 1920s, a period of very intense research activity in cycles, that extended with equal

vigor until the end of the 1930s, not only in economics (Joseph Kitchin, 1923; Simon Kuznets,

1926; Wesley Mitchell, 1928; Joseph Schumpeter, 1939), but also in population dynamics

(Raymond Pearl, 1926; August Losch, 1936) and societal dynamics (Pitirin Sorokin, 1937).

The intention here is not to send the reader to references (are all classical works), but just to

mention the years when these classical works were published, then reinforcing the idea that

the 1920’s and 1930’s was a period of very intense research activity in cycles. Kondratieff

was not the first to sustain the idea of long-term economic cycles of about half-century

duration (see Appendix A), but was the first to organize substantial empirical evidence for the

idea and spark a sustainable debate on the topic.


Kondratieff, accumulating data on a variety of economic variables from different countries,

could show that capitalist economies follow an approximately 50-year cycle of crisis,

recovery, prosperity and stagnation. His methodology included the examination of long-term

moving averages of commodity prices, wages, interest rates and materials production (coal,

pig iron and lead). Although Kondratieff’s main interest in long waves was empirical, he

advanced some hypotheses centered on capital investments and innovations [5,6]. The

Kondratieff theory has the predictive power necessary for good scientific theory — he

forecasted the 1929 crash of the capitalist system and the following deep recession of the

western economies in the 1930’s. The most pure scientific methodology was embodied in his

theory: observation, prediction and verification.

Unfortunately, however, Kondratieff could not complete the third element of the triptych:

arrested and killed by Stalin in 1938 he could not verify the real extent of his ideas [6]. Like

Galileo, his predictions were related to observations through a theory resting on some

hypotheses, without advancing a good explanation for the phenomenon. But Kondratieff

never refuted his own ideas, as did Galileo, and died in consequence. The explanation

remained to be resolved.

Besides the power of the scientific methodology used by Kondratieff, two other realities

contribute to give the phenomenon of long waves in socioeconomic systems the preeminence

to be taken as the cream off the subject of cycles in human affairs: historical evidence in the

past and strong factual and empirical evidence in the present.

Regarding the first point, as already recounted by other authors [7–10], is the fact that in

different historical epochs and different regions of the planet, very different cultures have

used the timespan of 50–60 years to organize their social life in the long term. Hebrews

(1000 BC), Sung China (900–1100 AD) and Mesoamerican cultures (1000–1500 AD)

developed socio-anthropological traditions based on some sort of roughly half-century

economic related cycles. For these three cultures, this kind of conceptualization was not a

simple matter of religious attitude, but rather a concrete and practical posture necessary to

organize socioeconomic life; a posture that acknowledged that there are forces acting on the

economy that if left unchecked could lead to a severe depression and financial collapse. There

is a clear outline of economic theory embodied in the Book of Leviticus 25: 8–55 articulated

perhaps over 3000 years ago. The Jubilee, celebrated every 50 years, with the remission of

debts, release of slaves, discount of prices, etc., was a means to prevent the build-up of

inefficient and dangerous imbalances in daily economic life — especially debt, over-

production and high prices. Modelski and Thompson [11] have found strong evidence for

Kondratieff waves in Sung China starting ca. 930 AD. Sung China marks the first thrust

toward modern organization and market economy on a large scale, with globally significant

innovations (mainly related to printing and paper), and the Eurasian Silk Roads serving as the

backbone of the world’s first systems network. Mayas and Aztecs organized their agricultural

cycles and other significant social events according to a 52-year cycle. Despite the religious

background underlying the Xiuhmolpilli (the complete turn of the years), it is interesting to

observe the practice among the Aztecs of performing a ritual in which pottery, clothes and

other objects were voluntary destroyed, and debts forgiven, announcing the beginning of a

new cycle, in essence the same attitude regarding a necessary renewal of economic life.


As to the second point, the missing verification that Kondratieff was unable to complete

occurred naturally with passing years. The instabilities and stagnation of the 1970s, followed

by the stock-market crash of 1987, and the persistent worldwide economic crisis of the 1990s,

recalled the same pattern of the early decades of this century, and have triggered a comeback

for Kondratieff’s wave. Although not yet accepted by many mainstream economists, as

exemplified by Paul Samuelson’s assertion that ‘‘Long Waves are Science Fiction’’ [12] and

not yet recorded by the National Bureau of Economic Research (NBER), Kondratieff’s cycles

have been intensively discussed in the last two decades. An abundance of books and articles

on the theme was published, international congresses and symposia were realized, Kondra-

tieff was rehabilitated in Russia, and the International Kondratieff Foundation was created in

Moscow in 1991. Kondratieff’s theory has gained due respectability and emergent bodies of

theory have surfaced with good and persuasive explanations for the phenomenon.

4. Limbo and revival

As pointed out in Section 3, Kondratieff did not advance a good explanation for the

phenomenon. His work was essentially based on observations about important characteristics

common to the unfolding of succeeding long waves, as for example the fact that during the

downswing of the wave a concentration of innovations and inventions is observed that can

trigger the upswing of the next wave, with a very high probability of the largest number of

great social upheavals, both revolutionary and military (i.e., hegemonic wars) occurring

during these upswings. Theoretical explanations for the long wave started earnestly in the late

1930s at Harvard with Joseph Schumpeter [13], who put forth a socioeconomic theory based

on the clustering of technological innovations during the depression phase, originating new

activities and new industrial branches (leading sectors) that pull the economic expansion of

the following wave, until wear and tear, overproduction and saturation become manifest

causing a new depression. Schumpeter, who first called Kondratieff the 50–60-year

long-wave pattern, introduced the concept of gales of creative destruction, borrowing an

image from biology, and proposed a causality based not in economic facts, but rather in social

reality, the entrepreneurial motivation of new men.

For almost three decades, the issue of the Kondratieff long wave in economics remained in

a kind of limbo, probably obfuscated, ironically, by the grand economic expansion and

ebullience of the 1950s and 1960s forecast by the self same Kondratieff wave. It was not until

the 1970s that a revival of long waves emerged, mainly due the systematic works of Gerhard

Mensch [14], Jay Forrester [15] and a research team at IIASA (International Institute of

Applied Systems Analysis, Laxenburg) led by the physicist Cesare Marchetti.

Kondratieff’s analysis concentrated on value-dominated statistical series, that is, money,

production, trade and wages. These do not move necessarily with the same periodicity as

other driving factors of the economy, but they provide a thermometer to measure the ‘‘heat’’

of economy (prices), which move in phase with other series and essentially reflect the

underlying forces in a capitalist economy, rising and falling with supply and demand. Among


these other factors underlying the dynamics of economy are, as already pointed out by

Kondratieff himself, the basic technological and process innovations.

The German economist Gerhard Mensch [14] has proven exhaustively that a real cluster of

basic innovations is evident at each downswing phase, and proposed a metamorphosis model,

whose key concept is that of a technology stalemate out of which an economy is ultimately

eased by clusters of innovations taken from a reservoir of investment opportunities formed by

a continuous flow of scientific discoveries. As old activities are disused and replaced by

revolutionary new ones, a structural metamorphosis takes place that has taken different

names, such as Successive Industrial Revolutions [13], Change of Technological Regime

[16], Oscillations of Technological and Social Moods [17] or Technoeconomic Paradigms

[18,19]. Devezas [20] recently proposed the name of Succeeding Technospheres for the

phenomenon, taking into account that at the start of each wave there is observed a dramatic

shift toward a meso-scale technological transformation. This transformation, pulsating

regularly each half-century, is characterized by the synergistic combination of new tech-

nologies, the creation of new economic activities and industrial branches and a deep

transformation of society as a whole — in summary, a new technological environment

emerges, grows and diffuses in the body of society, killing or reviving previous technologies,

until a leveling off is reached. Today’s youthful, growing global information and commu-

nication system is a living testimony to this argument.

Mensch [14] put forth the concept that the economy has evolved through a series of

intermittent innovative impulses that take the form of successive S-shaped life cycles, in

phase with the succession of long-term fluctuations in economy, or Kondratieff waves,

following a bell-shaped pattern.

Jay Forrester [15] at MIT using computer simulation was able to reproduce the 50-year

pattern for the US economy from his sophisticated System Dynamics National Model

(NM-model), which is based on 15 sectors that cause major shifts in investment and capital

plant formation. The theory underlying the NM-model sees long waves as primarily a

consequence of capital overexpansion and decline, that is, the time span of the wave

codetermined by the ‘‘self-ordering’’ of capital and the life cycles of capital plants. Although

the model focuses primarily on economic forces, it is not monocausal: it relates capital

investment, employment and wages, inflation and interest rates, aggregate demand, monetary

and fiscal policy, innovation and productivity and even political values. Accordingly, the long

wave is seen as a syndrome consisting of interrelated symptoms and springing from the

interactions of many factors. It is important to point out that innovation, while not central in

this model, plays an important role. Forrester used the concept of a leading sector, reasoning

that each major expansion of the long wave grows around a highly integrated and mutually

supporting combination of technologies.

Probably the most decisive contribution to the revival of Kondratieff waves was that of

Cesare Marchetti and his coworkers at IIASA. The great merit of Marchetti was to

conceptualize Kondratieff waves objectively via the study of physical rather than econometric

variables. He could show [4,17,21,22] that almost anything, innovations, social moods,

infrastructures, energy consumption, etc., pulsates with a periodicity of about 55 years.

Marchetti introduced very ingenious mathematical methodology to analyze long waves,


putting forth the concept of society operating like a learning system governed by logistic

(Volterra-Lotka and Verhulst) equations, demonstrating that invention, innovation and

entrepreneurship, generally perceived as the most free of human activities, are actually

governed by natural rules. This approach, raising the logistic function to the status of a

natural law of technological progress, has raised a flaming discussion, with enthusiastic

followers, such as Modis [9,23], opposed against analysts such as Ayres [24], who, while not

rejecting the hypothesis, recently qualified it as idee fixe.

5. The recent arena

During the 1990s, a handful of very interesting books on long waves and related issues

were published [8–11,23,25–30], some even becoming best sellers in the field, ranging from

texts of simple popular appeal to more scientific-minded discussions. The most recent one

[30] consists of a two-volume set with a comprehensive collection of historical and

contemporary articles highlighting the theoretical foundations, models and methods of

long-wave analysis, and also includes critiques of long-wave theory.

As pointed out previously, emergent bodies of theory have surfaced with good and

persuasive explanations for the phenomenon. But, under close examination, these interpre-

tations almost all refer mainly to explaining the unfolding of the wave, that is, the

mechanisms and events acting at each phase and not properly the underlying causes.

In discussing long waves of socioeconomic development, causality must be understood in

context of two categories: first, the triggers of the swinging behavior of the world economy

and, second, the determinants of the 50–60-year periodicity.

The existing theoretical explanations for long waves in socioeconomic development are

summarized in Table 1 [4,9–11,14,15,17,21–23,31–50]. This table is not intended as a

complete survey of the field and abstracts only the most important thinking that has appeared

in the last three decades. There are some authors and works not included in this table, for

various reasons, because they have not proposed a concrete model or theory to explain the

phenomenon or because their approach is not meaningful to the background of the discussion

here intended. For example, not included is the Elliot Wave Principle [25], developed by

people who believed they were able to discern long waves in the stock market, but as shown

by Berry [10], had merely imposed 55-year long waves on the data, developing a numerology

capable of fitting preformed ideas.

In some areas of science, where really accurate measurements or repeatable experiments

are not possible, people tend to speak of ‘‘models’’ rather than ‘‘laws.’’ To get the status of

‘‘law,’’ the model must be spectacularly successful and very simple, and that has not been the

case until now in explaining periodical recurrences and related phenomena in the social

sciences. The important thing to consider is that, even though we cannot be certain that what

we think of as ‘‘laws of nature’’ are actually true, we do see in social systems a lot of patterns

that very effectively bring certain aspects of the world under our control. Control means

forecast feasibility — that is the power of science. But getting effective control is only

possible by having knowledge of the laws governing the phenomenon, and the simpler a law,


the more fundamental it is and wider its range of applications. Long-wave research is still

toddling in the search for laws. In its present early form, our proposed Biological

Determinants Model has not the exactitude to be considered a law-like model, but is a firm

step in this search.

As can be inferred from Table 1, until the end of the 1980s, the discussion on long waves

was data rich and theory poor. Nowadays, this may no longer be the case, since several

explanations have been published, but it remains rhetoric rich and principle poor.

Marchetti and Modis were included in this table, even though they have not properly

proposed a theory for the explanation of long waves, nor explicit causalities, but because both

have made a giant contribution in providing the most important insight into the general

conceptualization of Kondratieff waves — the already mentioned concept of society

operating as a learning system governed by the fundamental law of logistic growth. As

physicists, they captured enough from today’s deficient existing knowledge to propose a

defining causality for the phenomenon and have not avoided, at least, making suggestions for

the half-century periodicity.

Marchetti explicitly chose not to propose a causality and that is the reason that none is

written under his name in the Origination Paradigm row of Table 1. His followers at IIASA,

notably Grubler and Nakicenovic [51], keep the same outlook, performing extensive

phenomenological analysis on technology diffusion while eschewing discussions to establish

causality. In 1993, Marchetti [21] wrote: ‘‘At this point the question about the origin of this

stop-and-go process comes out automatically. The answers are numerous, but none has

passed my stringent tests. One thing is sure, people slow down buying even when they need

the product and they have money. The situation points then to an oscillation of social moods,

at world level. Daimos pops up again. But why 56 years? Theodore Modis, who wrote a book

on my work in this area (‘Predictions’), observes that the three-body system — Earth, Moon

and Sun — has a periodicity of 56 years. It is not the worst hypothesis. After all, we are

already slaves of the day, of the month and of the seasons of the year. Perhaps our finer

sensors can perceive also the 56-year cycle. Or, perhaps, Gaia perceives it, with her great

antennas and fine sensors and we react in her womb.’’

These words conform with our point of view expressed earlier that our biological structure

was developed under the circumstances of the cyclical nature determined by the three-body

system and that our cognitive capacity is deeply impressed by this ‘‘heaven’s harmony.’’ If

there is a beat in human affairs, the rhythm must be given by our biological clocks acting at

the aggregate level, and not by economic or exogenous factors.

Modis [9] is bolder and in the chapter ‘‘A Cosmic Heartbeat’’of his book mentioned by

Marchetti considers two hypothesis, one related to celestial configurations and periodic

changes of climate, and the other (suggested by the physicist and Nobel laureate Simon van

der Meer) linked to the length of time an individual actively influences the environment.

It is important to stress the role played by Berry in this recent arena. His 1991 book [10] is

not only an excellent survey of the field, but his nonlinear dynamics approach using Chaos

Theory has brought sound evidence to the real existence of rhythmic upswings and down-

turns in economic growth. His charts are clear and genuinely helpful, and his discussion

raises questions cutting across economy, society and politics. Working with changes in the


rate of change and turning points marking shifts in direction of economic growth, Berry

pioneered the important observation that Kondratieff waves are not growth cycles, but

structural cycles. He pointed out that technology transitions do occur with 55-year

periodicity, but growth accelerates and decelerates with 25–30-year periodicity. Embedded

in each Kondratieff wave, there is two growth Kuznets-type cycles. This approach, however,

offered no convincing clue to the causality of long waves, even when he spoke [42,43] of

endogenous processes that result in successive technological revolutions. Moreover, in a

recent publication [50], proposing a pacemaker for long waves, there are strong contra-

dictions in his results and conclusions when compared with his previous ones [10,42,43,56], a

matter that will be discussed in a later section (endogenous vs. exogenous).

Another point worthy of mention, also emerging from the recent discussion, is the fact that

the long wave is not a phenomenon of modern times [4,7,8,10,11,17,29,37,47]. Long-term

oscillations of societal processes have most probably existed since human societies came into

being, but can only be inferred using measurable parameters. For some countries, this is only

possible (but rather imprecise) around the 15th or 16th centuries: really trustworthy data are

available only after the end of the 18th century, coinciding with the advent of the Industrial

Revolution and invention of the statistical sciences. It is important to consider also that,

whereas the half-century beat may be in action since ancient times, its effect on human

activities may have been very weak to perceive, until recent times, when radically new

production means and measurable activities were introduced. This discussion is closely

related to the existence of hegemonic cycles in history, and in this way relies on more overtly

inductive historical interpretation. For the theoretical analysis of long waves and hegemonic

cycles and their history in the European-centered world system, the reader is referred to the

excellent books of Modelski and Thompson [11] and Goldstein [29].

Summing-up, all theory/models identified in Table 1 have contributed significant insights

to the general discussion of long waves, but none have given a definitive answer to the very

causality of the phenomenon. The question of causality can be rephrased as follows — why

does a given technosphere reach a ceiling and then a new one emerge encompassing two

growth periods, each one growing at a rate conducing to a time span of 25–30 years, all this

in an ever repetitive fashion?

1998 marked a turning point in the discussion of long waves, when publications objectively

oriented to explain the 50–60-year periodicity emerged, bringing new life to the arena. Pure

rhetoric gave way to valuation principles expressed as mathematical formulations.

6. Where did the clock come from?

In the opening address of the session on ‘‘Socioeconomic Long Waves and Future

Scenarios,’’ held on July 30, 1998 at the 14th World Congress of Sociology in Montreal

[52], Devezas (Chairman of the session) presented the above question as one of the principal

remaining open questions to be answered in order to definitively explain the nature of the

phenomenon, and summarized briefly the existing speculations about possible causes of the

50–60-year periodicity. During the discussion that followed the session, a consensus emerged


among the participants that the ultimate cause of this periodicity was to be found in our human

biological dynamics with different possible explanations offered, such as the diffusion-

learning rate among two successive generations proposed by Devezas [53] or the historical-

societal generation propounded by Mallman and Lemarchand [7], or the tenure waves and

female fertility generational waves put forth by Corredine [54]. This general agreement of a

biological thesis, however, met the sole objection of session participant Berry. In both his

prepared delivery [55] and in the ending discussion, Berry presented the idea that endogenous

technoeconomic transformations drive long wave rhythms in prices and inflation that move in

lock-step with American politics as a result of an overall mode-locking phenomenon [55,56].

Then, under questioning during the ending discussion, Berry alternatively speculated that

the 18.6-year Saros or lunisolar cycle might be an exogenous timekeeper and noted that the

18.6-year cycle was one of the four periodicities that showed up in his spectral analysis of price

and inflation data and stated that these cycles are among the dominant cycles in most of the

prehistoric megalithic monuments across the world. Berry insisted that one had to examine the

possibility of an exogenous timekeeper, conceding however that it could be internal but that

these were alternative hypotheses and had to be addressed seriously as competing hypotheses:

both might be true by virtue of the mode-locking phenomenon.

Two months previous to the Montreal session, at the Third International Kondratieff

Conference held in Kostroma, Russia, Devezas [57] presented for the first time the same

question and its possible explanations, but to a very different audience. In corridor discussions,

some economists, mainly followers of the Marxist–Trotskyite school, who believe themselves

convinced of the causation of the Kondratieff waves, but who also acknowledge that their

explanations do not explain the half century periodicity, agreed that some biological or even

exogenous (Sun–Moon dynamics) determinant could act as the metronome of the process.

For these people, bound to their blind devotion of econometric parameters, the real

‘‘cause’’ of long waves is an endogenous long-term oscillation in rates of profit inherent to

the capitalist process, as established by the Belgian Trotskyite economist Ernst Mandel

[31,32], a thesis that has found numerous adepts, mainly among economists and social

scientists in the Netherlands and Germany (for a good survey on this line of thought, see Ref.

[27]). It was a very difficult dialogue trying to demonstrate to them that to consider the falling

rate of profit as the cause of long waves is similar to considering the varying velocity of a

pendulum as the ‘‘cause’’ of its swinging. In interesting contradistinction was the intervention

of Boris Loginov, a researcher at the Institute of History of Science and Technology of the

Russian Academy of Sciences, who after Devezas’ presentation of his interpretation of a

diffusion-learning rate as a determinant of the � 25 years necessary to develop a new

technosphere and another � 25 years to consolidate and to exhaust it, reacted affirming that

this explanation met his own findings in studying the diffusion of fundamental scientific

theories throughout the scientific community. Loginov presented his own spectral graphs on

intensity rates and a histogram from the famous Friedrich Hund’s book ‘‘Geschichte der

Physikal Begriffe,’’ published in 1972, showing that more than 90% of all publications (from

25 high-ranked physicists) that created the foundation of quantum theory, were published

between 1900 and 1927, implying that from the original works of Lorentz, Wien, Thomson

and Planck, Quantum Mechanics took a quarter century to affirm itself as a scientific


discipline as we know it today. Similar findings were also discovered in the diffusion of other

scientific theories, such as electromagnetism, relativity, fracture mechanics and genetics

despite differences in epochs and means of communication.

As will be further discussed in Section 13, the time span of about 25 years is closely related

to two very important phases of the life-cycle of human beings. The first � 25-year phase is

the time required to raise humans, that is, the time necessary to nurture and teach a person to

be fully productive and active in society. This timing has been constant over the entire human

record and can be seen as a constraint in the evolution of society. A second � 25-year phase

arises as the time span during which an individual effectively acts in society, mastering his

vocation or profession with progressive vigor until reaching his maximum vitality expendi-

ture. Again, this timing has been historically constant and consists in another constraint

controlling the unfolding of socioeconomic phenomena. As will be shown, both these

biological constraints play an unquestionable role in the origination of long waves.

On this point, the question can arise that average or mean life spans were much shorter in

centuries past (about � 30 years or so), that even today in parts of Africa and elsewhere life

spans are significantly shorter (around � 40 years) than the world average leading to the

incorrect supposition that average duration would mitigate the impact of the life phases.

However, average life span does not mean much with high infant mortality pulling down the

average. Moreover, it is the aggregate limits of the life span and life phases that control

the biological determination, not the mean times or averages. The normative life span of the

individual at the limit has always been about � 79 years, both in preceding centuries and

today. It is limits that control.

As to the first � 25-year phase, it is primarily a learning time, a contingent generational

learning stage, corresponding to the first stage of an individual’s life-cycle, and is also from a

purely biological point of view a maturing time, during which the human body reaches its full

maturity (appearance of the third molars, very properly named as wisdom teeth, in late teens

or early twenties, full growth and extension of the mandible, closing the temporal bones, etc.;

this full growth by the early twenties creates the platform from which humans embark on

adult pursuits). Although reproduction is possible at an earlier age, it is at about age 25 that

human beings are really prone to reproduction and, in this way, 25 years is the effective lapse

of time separating two generations.

From Grecian antiquity, with Plato, to the birth of Sociology with August Comte, to

modern History with Toynbee and Ortega y Gasset, the concept of generation has been

recognized as a fundamental element in the tempo of human evolution, and constitutes a

regular element in reasoning about long-term societal processes. So then, in the search for a

clock giving the rhythm to long waves in human affairs, we are obliged to look at the

generational process as a codeterminant of the phenomenon, and this has been done by some

of the authors included in Table 1.

Modelski [11,36,37] has been an advocate of this point of view and in his numerous

publications has developed the notion of the generational learning process as the instigator of

variety in social evolution every 20–30 years. He has pointed out also that, in evolutionary

terms, the generational process is the closest link between biology and society, between

biological and social evolution. Thus, the generational cycle has embodied both processes, a


biological process, that of reproduction, by which one generation reproduces itself and is

replaced, and a social process, by which one generation transmits its accumulated cultural

heritage to the generation it raises. The question that remains to be answered is how this

generational process actually imposes its rhythm on the whole process? Which process gives

the pace of evolution, the biological one, constrained by the reproduction capability of human

beings, or the learning process, constrained by the human capability of assimilating knowl-

edge? Or the coupling of both?

Modelski’s explanation of a replacement interval acting as a fixed delay is not enough. His

evolutionary model lacks the necessary overall engulfing meta-systemic approach. His

argumentation offers a very good insight in understanding the mechanism, but cannot resolve

the problem of distinguishing the aspects of a continuous supply of generations from that of

discrete generations. Modelski classifies generations as an exogenous factor in economic and

political processes, each with its own endogenous mode of operation. This separation, a

common practice in the social sciences, is conceptually unsuitable for the analysis of long

waves, since in the human evolutionary process the humans themselves are the constituents of

the system under analysis, that is, society. In setting the system for the present analysis, we

must consider that the human beings are the members that compose its substance, their

relationships form its structure, and their activities determine its operation.

The long wave phenomenon is not simply a manifestation of the world economy, but rather

of the complex whole substance-structure-operation. Under this conceptual framework, any

biological constraint is an internal property of the system and thus represents an endogenous

origination paradigm.

7. Endogenous vs. exogenous

Human civilization is a single organism, a great information-processing machine. In

physical terms, society is an open complex learning system living on spaceship Earth, fueled

by the Sun’s energy and consuming the natural resources there existing. Like any other

system in the universe, it must obey some iron rules of nature, the constraints that govern

what can and what cannot be done. The codified human genome contains the necessary

instructions dictating the rules for human reproduction and human cognitive behavior. These

rules form then the endogenous body of commandments dictating the irreversible human

trajectory. Physical actions from outside, like cosmic rays, sunspots or the gravitational forces

from the surrounding universe, can influence this trajectory, by chance (for instance, the

impact of moving bodies) or in a regular (periodical) way. These externalities represent

possible exogenous origination paradigms. But it is worth to point out that, as already

considered in Section 1, the former (endogenous) was formed under the influence of the

second (exogenous).

As mentioned before and depicted in Table 1, the last triennium marked a new dawn in

discussing the causality of long waves. Three different theories have emerged using very

distinct approaches, consolidating the confrontation between endogenous and exogenous

origination paradigms.


The 1998 publication of Mallman and Lemarchand [7] pioneered the attempt of explaining

the timing of long waves through the formulation of a general law, and has triggered a very

interesting discussion with commentaries from Berry [58], Modis [59] and Modelski [60],

and a reply from the authors [61], all published in the same issue of Technological

Forecasting and Social Change. In this paper, Mallman and Lemarchand proposed a

mathematical model for the dynamics of socio-motivational concerns (SMCs), represented

by a normalized function M(t) carried by the entelechy of succeeding Societal Historical

Generations (SHG) with a fixed time span t of 39.2 ± 11% years. To describe the temporal

behavior of M(t), the authors use a Malthusian type difference–differential equation

originally proposed by Wierzbicki [62]:

dM

dt¼ �k½Mðt � tÞ �M0� ð1Þ

where M0 is taken as the value of M(t) when dM(t)/dt = 0 and k is a proportionality constant

with the dimension of (time)� 1, such that k> 0 means negative feedback (resistance to

change) and k< 0 means positive feedback (support for change).

This approach although insightful in its explanation of the concept of an evolving SMC

shaping the societal response in regular intervals, each interval corresponding to a distinct

generation, falls short on some aspects of conceptual integrity. The analytical framework is

not new and resembles a vague interpretation of Schumpeter’s entrepreneurial motivation of

new men. The weak points lie in the following.

1. Trying to be extremely broad, without defining spatial or temporal boundaries to the

applicability of the SMC concept; it sounds like a ‘‘theory of everything’’ via a ‘‘cyclical

theory of history,’’ as pointed out by Modelski [60].

2. The variable M(t) is nebulous and lacks precision and, as Berry [58] pointed out, cannot

be operationalized and/or measured.

3. The proposed Malthusian type difference–differential Eq. (1) appears to ‘‘just

happen,’’ there is no foundation (theoretical or empirical) to use it as a universal law

of evolving societal paradigms, neither in Mallmann and Lemarchand’s paper nor

from the view of the original proponent [62]. Because spurts of logistic growth are so

clearly seen in the dynamics of social and technological evolution, why not instead

use the simple and powerful logistic equations, rather than seek the assistance of

invented equations, with retarded arguments, variable coefficients, time delays, etc.?

Bank’s book [63] on Growth and Diffusion Phenomena referenced by the authors is

very rich in mathematical models based on real world problems, but these models are

intended as useful tools for forecasting, planning and designing these problems, and

not as laws governing them. Natural phenomena are complex, not the laws underlying

their unfolding.

4. There is no reason to believe that all recurrent societal processes listed in Table 6 of

Mallman and Lemarchand’s paper might be described by this intangible time dependent

SMC. Furthermore, there are many others not listed in Table 6, as pointed out by Berry

[58] and Modelski [60]. This list points to those coincident (allowing for good will) with


the first three oscillatory modes resulting from the solutions for each k>0 (156 ± 16,

31 ± 3, 17 ± 2) and k< 0 (52 ± 5, 22 ± 2, 14 ± 1).

5. Last but not least, the solution of Eq. (1) depends fundamentally on the input value

given to the generational time lag or SHG, finally not convincingly demonstrated by the

authors as being � 39 years, unusually long and arbitrary. As shown in Table 2 of the

article, many other oscillatory solutions can be delivered with different input values of

t, not to mention the infinite number of possible solutions resulting from different

k values. The problem with this approach is then, the value of t can be manipulated to

match the looked for oscillatory modes.

The attempt to embrace different basic societal processes under one mathematically based

model is very suggestive and valid and, in this respect, we must give Mallmann and

Lemarchand their due merit. But the necessary theoretical groundwork for this purpose must

yet be attained.

Although not precisely proposed as a model or theory to explain long waves, Duncan’s

1999 publication [49] also appearing in Technological Forecasting and Social Change was

included in Table 1 due to the very significant insight delivered demonstrating that

Kondratieff waves, as well as many other logistic diffusion curves, obey some natural rules

that control the interactions of the entities involved, which might be people, business,

macroeconomic variables, environmental–physical features or chemical compounds. Long-

wave periodicity emerges clearly from the time constants determined by Duncan, who uses an

approach based on classic Eyring rate theory coupled with chain reaction theory commonly

applied to chemical kinetics, regarding individuals (in a broad sense) as discrete entities like

molecules, whose basic properties are statistically averaged and function as compact

descriptors of the complex system.

The philosophical criticism and objections, which can be raised from this fundamental

presumption, are well defeated by the author using the same line of thought already advanced

by Devezas in a previous publication [64]. The functioning of a social system can be

understood as the transfer of information, money, services and goods among individuals in a

way analogous to that in which energy is transferred from gas molecule to gas molecule by

collisions, in a chaotic movement. Individuals are all different in the same way, as molecules

are all different. Human differences (basically capacities) like intelligence, impetus, leader-

ship, etc., find analogies in molecular mechanical properties like vibrational modes,

momentum, configuration, etc. In both systems, minimizing the free energy is the driving

force for any phase transition, entropy grows if the system is isolated, energy input assures

negentropy and self-organization. In handling the differences among the entities for both

systems, we are concerned with average properties, rather than individual details. Kauffman

[1] catches this very well in the introductory chapter of his recent best-seller, showing how

statistical mechanics (that uses average properties like temperature and pressure) is successful

in demonstrating that we can build theories to describe complex systems that are insensitive

to the detailed behavior of the entities involved. In his words: ‘‘Discovering the existence of

key biological properties of complex living systems that do not depend on all the details lie at

the center of a hope to build a deep theory of biological order’’ (italics added).


Kauffman goes further asserting: ‘‘Economic and social phenomena are to be explained

in terms of human behavior. In turn, that behavior is to be explained in terms of biological

processes, which are in turn to be explained by chemical processes, and they in turn by

physical ones.’’ Duncan’s model moves in this context. The fundamental interaction

considered in his model is the transfer of information (knowledge and ideas) from

individuals of type A to individuals of type B so that, with respect to knowledge, B

becomes like A via a transition state ABz (overcoming a energy barrier), which may be

written (Eq. (2)):

Aþ B () ABz ! 2A ð2Þ

Denoting NA and NB as the number of A and B individuals at any given time and N0 the

total number of individual entities in the system under consideration, and reasoning with the

molar fractions fA and fB, translated by (Eq. (3)):

fA ¼ NA=ðNA þ NBÞ ¼ NA=N0 and fB ¼ 1� fA ¼ NB=ðNA þ NBÞ ¼ NB=N0 ð3Þ

the rate at which B is changed to A may be expressed by:

�dfB=dt ¼ dfA=dt ¼ kfAð1� fAÞ ð4Þ

a logistic differential equation, where k is the rate constant, which by the Eyring rate theory

may be envisioned as:

k ¼ Aexp½�Ez=RT � ð5Þ

the well-known Arrhenius equation, where Ez is the activation energy required to

overcome the energy barrier, R an universal constant and T the temperature. The

exponential part of Eq. (5) represents the physical probability of overcoming the potential

barrier, which is a function of the temperature. Here lies a weak point in Duncan’s

chemistry of social interactions.

In chemistry, the activation energy is normally estimated by determining the rate constant

at different temperatures and then plotting log k against 1/T. When analyzing social

phenomena, this is not possible because the temperature cannot be varied. To by-pass this

point, Duncan writes for the rate constant (Eq. (6)):

k ¼ Ap ð6Þ

assigning to the parameters A and p meanings closely related to the social sciences, A being

the frequency factor with which encounters between A and B occur and p the probability that

the information or idea is accepted by B. The frequency factor A is related to the time t, thetime between two encounters between A and B, through the relation A= 1/t. The criticism to

be raised can be summarized in the following questions.

1. Where is the validity in using a physical approach to the social sciences whose main

active parameter cannot be applied? Chemical reactions and phase transitions are


phenomena that fundamentally depend on temperature, and so too the encounter rate

k between molecules.

2. What is the social analog for temperature, or perhaps in other words, what is the

parameter controlling the probability of acceptance p?

3. Is it reasonable to really speak of probability in this context or does there exist another

factor controlling the rate constant k?

Regarding this third point, it is worthwhile to point out that the concept of probability

makes sense when speaking of A trying to convince B of a new idea. But in the case of a

absolutely new technology or basic innovation (the real drivers of long waves), the

probability of acceptance is irrelevant, the factor controlling its diffusion has to do with

the capacity of B to assimilate the novelty, that is, has to do with learning. What is the sense

in speaking of a probability of acceptance of electric lamps, automobiles, television or using a

modern example, the Internet? In this way, k in Eq. (4) may be interpreted as a learning rate.

There is an interesting common point between the Mallmann and Lemarchand and Duncan

approaches. In the former, the rate constant k in Eq. (1), translating the spread of the

motivational concern in the system, may assume positive or negative values (k>0 meaning

negative feedback, resistance to change, and k < 0 meaning positive feedback, support for

change), that results in different modes of oscillation. In Duncan’s Eq. (4), the rate constant k

is essentially positive and accounts for the capacity of B to becoming as A, that is, for the

declining rate of the ‘‘ignorant’’ population B, that is the same as the increasing rate of

knowing individuals A. The common in both is that k has to do with the diffusion of

knowledge or, in other words, with the rate of learning. Both are in essence endogenous.

As a whole, Duncan’s approach stands to reason. In applying the model to very different

chemical, physical, biological and social examples, he shows that different systems present

common and universal features. The fitting to the logistic curve is universal, and the constants

calculated, although subject to minor variations, emerge as roughly the same over all cases

analyzed. His final result, summarized as a perfect straight line in a graph plotting log Dt vs.

log t is meaningful, since it shows that all kinds of phenomena analyzed, seen as the result of

interacting entities, undergo the same general principle. Dt in the mathematics of sigmoid

curves represents the ‘‘take-over time,’’ the time the system takes to progress from 10% to

90% of its ceiling value. The close relationship found between Dt and the time t (a basic time

constant of the system) may have a very deep significance not properly explored by Duncan.

When drawing his final conclusion, Duncan resonates with Marchetti [17], who asserted

that ‘‘. . .the concept of a learning society is the heuristic path to a microscopic description in

the spirit of the statistic mechanics’’ (italics added). The present approach, to be developed in

the next sections, will further explore this concept and its universal significance.

Before continuing with the development of an endogenous biological origination con-

ception, let us examine the possibility of an exogenous causality, socioeconomic long-wave

behavior as a consequence of external physical actions from outside the social system, such as

geophysical cycles, sunspot activity, etc. Considerations of this sort abound in the literature of

business cycles, mainly related to harvest and meteorological phenomena, and suggestions

about their correlation with Kondratieff waves emerged in the 1980s, with, for example,


Zahorchak [39] and Noble [40], thereafter also considered by Berry [10] and Modis [9] in

their books published in 1991 and 1992, respectively. The staunchest defender of this idea is

now Berry, whose concept of an exogenous timekeeper, introduced at the Montreal

discussions and commented on in Section 6, was recently published [50] as a ‘‘Pacemaker

for the Long Wave.’’

In this article, Berry asks whether long-wave rhythms have been entrained by an impelling

natural cycle. He first makes mention of human endogenous clock-timed biorhythms, such as

circadian rhythms that are entrained by the exogenous cycle of day and night, and

circamensual reproductive cycles tied to moon phases. This is followed by a survey of the

recent literature on geophysical cycles, recently substantiated by spectral analysis techniques.

He then narrows his focus to the 18.61-year lunisolar cycle, periods of maximum lunisolar

forcing, and its triple multiple 55.83 years, the time it takes for the longitude of the eclipse to

be repeated and to occur at the same location, a timespan the Greeks called the exeligmos

period. Referring to extensive literature, he mentions that 18.61-year periods in epochs of

maxima tidal forcing have been associated with precipitation minima and drought maxima,

and � 50-year periodicity has been identified for catastrophic harvest failures.

He concludes that the shorter period geophysical rhythms appear to drive fluctuations in

global and regional climates, and asks: ‘‘Do similar rhythms appear in macroeconomic data?’’

To answer this question, Berry selects two macroeconomic series, the inflation rate and the

rate of growth of real per capita GNP, observed annually for the USA from 1790 to 1995, and

applies a spectral technique based on eigenanalysis of an autocorrelation matrix. The inflation

series yield cycles of 9, 18–19 and 54–57 years. The growth series yield cycles of 3, 6, 9,

18–19 and 54 years.

Then, Berry presents a table (Table 2, Ref. [50]) correlating years of 18.61-year maximum

lunisolar forcing with troughs in cycles of transport building, immigration and real estate

construction, as well as with long wave troughs and stagflation crises for the USA. In light of

these results, Berry asserts that there were three 18–19-year infrastructure-development

(Kuznets) cycles per (Kondratieff) long wave, and concludes: ‘‘The pacemaker appears to be

a lunisolar cycle that nudges economic cycles. . . every 18–19 years, during periods of

maximum lunisolar forcing. . . .Entrainment of long-wave crises produces mode-locked

building cycles nested within 50–60-year cycles of infrastructure building, economic growth

and inflation. The stability of peak-to-peak and trough-to-trough long-wave timing does

indeed appear to be consequence of forcing by a geophysical pacemaker.’’

As Berry characterized Mallman and Lemarchand’s claim [58] ‘‘too good to be true,’’ so

we may characterize Berry’s recent claim as too rich in contradictions as to be understood.

These contradictions mainly concern the very poor connection Berry makes in the ‘‘Pace-

maker’’ with his own previous conclusions and affirmations in all his publications

[10,42,43,56,65] prior to this, and can be summed-up by just one question: were there two

or three infrastructure (Kuznets) cycles per Kondratieff wave?

In response to the above expressed criticism, Berry presents a new paper published in this

issue (Low Frequency Waves of Inflation and Economic Growth: a Digital Spectral Analysis),

with which he simply extends the confusion. In this paper, he presents additional results using

another digital spectral technique and added to the results presented in the Pacemaker he now


has found a low frequency rhythm of � 28 years in the inflation rate series, giving it the name

of ‘‘half-Kondratiev generational cycle,’’ associating it with ‘‘Kuznets cycles of changes in

social and political development.’’ There is no explanation why these cycles did not appear

with the technique used in the ‘‘Pacemaker.’’ For him, ‘‘calling the half-Kondratievs Kuznets

cycles has been a source of confusion’’ (his footnote 2).

In the ‘‘Pacemaker,’’ the only mention Berry makes of his previous publications is a

sentence in the first paragraph affirming that ‘‘The endogenous bases of the phased behaviors

[of the long waves] now are well known’’ (brackets added), after which he cites his two books

[10,56] and his 1993 article [42]. Then he writes: ‘‘The question to be addressed here is

whether the stability of through-to-trough and peak-to-peak long-wave timing that has been

reported for the last five centuries is forced by an exogenous pacemaker, specifically a

pacemaker with geophysical origins.’’ Putting the questioning in this way, Berry tries to

distinguish two different aspects of the same phenomenon, the endogenous mechanisms and

the exogenous zeitgeber. Mode-locking, for him, serves as an entrainment agent, fulfilling the

necessary and sufficient role of adjusting and accommodating both aspects. Summarizing:

there are internal mechanisms provoking the phased system behavior, but also the timing of

the phases is mode-locked with the 18.61-year periods of maximum lunisolar forcing.

The controversial in all this is that, to fit the action (nudging) of this geophysical

pacemaker (with its periodicity of 18.61 years) into his framework, Berry speaks of three

infrastructure-development cycles (giving the name Kuznets cycles to them) with a time span

of 18–19 years, in clear contradiction with his previous finding that ‘‘Technology transitions

do occur with 55-year Kondratiev-wave frequency, but growth accelerates and decelerates

with 25-to-30 year periodicity’’ (Ref. [10], p. 79). Even more puzzling is the fact that, in

describing the unfolding of these three Kuznets cycles, Berry sends the reader to a footnote:

‘‘For further exposition of long-wave phasing, see Berry et al. [3].’’ This reference is to his

last book [56], where he asserts that ‘‘Mode-locking ensures that there will be two Kuznets

cycles per Kondratiev cycle’’ (p. 25, italics added), and ‘‘These growth cycles, averaging

some 25 years, are named for Simon Kuznets, who was the first to identify them’’ (p. 23).

In this book and in ‘‘The Leadership Generations’’ [43], Berry speaks explicitly of similar

generational and infrastructure rhythms, both with the same ‘‘quarter-century’’ periodicity.

We can find (Ref. [43], p. 6): ‘‘The quarter-century cycles of generational leadership shown in

Fig. 1, like Kuznets growth cycles, occur two to a long 50-year (Kondratiev) wave, . . .,mirroring the Kuznets rhythms.’’ It is clear then that Kuznets growth (infrastructure) cycles

and generational cycles are associated and exhibit the same � 25-year periodicity. Now, in

the paper published in this issue, Berry tries to differentiate between quarter-century

generational Kuznets cycles and � 18-year (no longer called Kuznets) growth cycles.

His 1993 publications [42,43] are oriented in advancing the elements of a economic theory

accounting for the observed phenomenon of ‘‘two cycles of economic growth nested within a

Kondratieff long wave of prices, averaging each 27 years’’ [42]. He himself claims (p. 104,

Ref. [10]) to be a pioneer in the observation of pairs of growth cycles embedded within each

long wave. Berry’s argumentation is founded in numerous graphs using moving averages and

chaos phase diagrams applied to the same historical records of real per capita GNP he uses

now, through which the paired behavior is clearly visible.


If there is then a source of confusion in characterizing Kuznets cycles, this confusion has

been caused by Berry himself when drawing conclusions with his findings in the ‘‘Pace-

maker.’’ The criticism raised here lies not in the name to be given to the cycles of economic

growth (as differentiated from Kondratieff waves of economic development), but rather in the

fact that these cycles associated with infrastructure-development were two in number in all his

previous publications, and appear as three in the light of the new results using the digital

spectral technique. The paired behavior underlying long waves, previously interpreted as

infrastructure building cycles [10,42,43,56,65] (under the name of Kuznets cycles), dis-

appeared in the ‘‘Pacemaker’’ (replaced by a ‘‘triplet’’ behavior), but appears again in the

following paper in this issue (under the name of Kuznets, but now associated with genera-

tional cycles). In trying to trace a summary of all his previous long-wave publications in this

last article, there is no attempt to explain this two–three paradox, and we can read: ‘‘Finally,

‘Pacemaker’ [18] suggested that mode-locked endogenous processes might not be sufficient

to produce the observable regularities of timing of business, building and generational cycles

within the long wave’’ (italics added). The problem here is that nowhere in the ‘‘Pacemaker’’

has he mentioned the existence of generational cycles.

Indeed, the duration of Kuznets cycles is a controversial matter, as can be seen in the

analysis of Abramovitz [66], Rostow [33] and Van Duijn [67]. However, despite the different

timings attributed to Kuznets cycles since his 1930 original publication [68], it is worthwhile

to point out that 25 years was the number obtained by Kuznets himself in applying moving

averages to time series of wholesale prices, resulting from summing up two swerves

(secondary trends) of about 12 years each.

Entrainment of the 18.61-year cycle or of its triple multiple 55.83-year cycle is absolutely

unnecessary to describe some regularities observed in human affairs. Human beings have

ingrained in their genome this heavenly periodicity. No mystery about this: individual and

collective human actions are biologically driven, in synchronization with these ingrained

biological clocks. Rephrasing the question addressed in Section 6, what remains to be

answered is how these biological clocks actually impose their rhythm on the whole process.

Reproduction capability constrains and gives the pace to the succession of generations.

Knowledge assimilation at the aggregate level constrains and gives the pace to the diffusion

of a new technoeconomic system. Modelski has already pointed the way: generational

learning is the clue [36,37].

8. 25 years again

Looking at Table 1, an interesting point jumps to mind: 25 years has passed since the

revival of the discussion on Kondratieff waves, corresponding to the downswing of the

fourth K-wave (or 19th in conformity with Modelski). Previous discussion started in the

first decade of the 20th century and clustered during the 1920s (including the writings of

Kondratieff) and 1930s (a period of very intense research activity in cycles as already

pointed out in Section 3), corresponding to the downswing of the third wave. Schumpeter’s

work surfaced at the trough between third and fourth waves. The discussion rested then in


a limbo during the next upswing. Both clusters around two successive Kondratieff

downswings can be described by logistic curves with characteristic duration in the range

25-28 years, whose middle points are separated by � 59 years, as can be seen in

Appendix A. Now, we are witnessing a new level of discussions, perhaps heading toward

a ceiling in which a reasonable understanding of the phenomenon will probably be

reached. What then? A new limbo? Maybe. Berry’s opening statement in a following paper

in this issue that it is ‘‘the final paper of our long wave series’’ is perhaps a symptom of

this ceiling.

Significant is the observation that Kondratieff discussion clusters meet again with the

findings of Boris Loginov: � 25 years as the time for diffusion of a scientific theory. The

first cluster corresponded to the finding and the diffusion of the long-wave concept. The

second cluster is corresponding to the modeling and the diffusion of the theories based on

the succession of technoeconomic systems. Further reinforcement supporting the thesis of a

25-year time span for the introduction and diffusion of a new science is the finding of

Linstone [70] that the science of Technological Forecasting has followed a logistic path

(measured as the cumulative level of TF capability), with a take-over time extending from

soon after World War II (Cold War) until the 1970s, characterizing a consolidation phase of

the Technological Forecasting methodology. Linstone perceives the trend since then as an

innovation phase in methods of Technological Forecasting, which will probably consist in a

second logistic growth phase, following a pattern similar to the configuration shown in

Appendix A for long-wave research. What is at work? Some kind of entrainment coming

from the heavens? Clearly not. Just the spread of knowledge constrained by the aggregate

learning rate.

9. The universality of learning and self-organization

Emergence of order in the universe, and consequently of life, follows the paradigmatic self-

organization process. In order to reach equilibrium any evolving system in the universe is

faced in overcoming the inertial resistance of the system, the constraints of space and time.

Neither the ultimate goal nor the best path to follow is predetermined. Progress takes place

stochastically through trial and error, random nonaverage fluctuations. In this process, the

system self-organizes and learns configuring and reconfiguring itself toward greater and

greater efficiency and in this manner with each iteration it performs some activity better. Each

stage corresponds to a given structure that encompasses previous self-organization, learning

and the current limitations. This is to say that self-organization and learning are embodied in

the system’s structure and the learning rate is an overall system’s property.

Linstone et al. [71] have depicted this evolutionary process as a series of alternating phases

of separation and combination, fragmentation and integration, or decentralization and

centralization, that evolves in a spiral of increasing complexity proceeding by periodic

restructuring involving swings between differentiation and integration. Moreover, they

pointed out the fascinating recognition of the learning programmed (and not goal pro-

grammed) nature of biological systems.


Marchetti [72] recently observed: ‘‘Every living thing has or is a machine for learning,

remembering and forecasting. The objective is to provide anticipatory reactions to the

interactions with the external world.’’ Civilization, here seen as the highest degree of order

achieved by living systems, is the latest result of the universe’s self-organizing learning

process. Goerner’s [73] deep insight that ‘‘Society centers its identity around being a learning

system’’ epitomizes that view. Long waves are modernly interpreted as structural cycles, a

point of view shared by several authors, including Modis, Marchetti, Berry, Perez, Modelski,

Grubler, De Greene and others. At each wave, a new structure (a new technoeconomic

system) experiences a beginning, a phase of growth, maturity, a phase of declining and an

end. This is a self-organizing learning process in which learning accumulates as the system

extends over time and over higher degrees of complexity. What is ultimately learned is how to

restructure the environment itself [73].

To learn takes time. How long? The rate of learning gives the timing. The point to stress

here is the fact that relatively little attention has been given to the role played by learning

processes in the unfolding of long waves, with perhaps the exceptions of Marchetti [4,17],

Modis [9,23] and Grubler [51,74]. Modis, inspired by Marchetti, has shown how collective

learning following the pattern of logistic curves can be found in a group of people following

a common goal, be that of manufacturing and selling products, discovering scientific

elements or pursuing exploration. Grubler [74] focused on the learning dynamics of the

diffusion of pervasive technoeconomic systems that are at the heart of all changes in society

and its material structures.

The concept of the learning curve appears in the scientific literature in at least two

apparently different utilizations. One, regarding individual learning, is the classical example

of the evolution of an infant’s vocabulary, first explored by Marchetti [17] and further

analyzed by Modis [9]. The words most used by the parents and the most necessary for

communication are learned first and the amount of words learned grows almost exponentially

at this beginning, corresponding to the first 40 months of a child’s life. The rate of learning

then slows down because there are progressively fewer words left to learn and, by the end of

the sixth year (72 months), this process reaches a plateau of approximately 2500 words, the

normal vocabulary of a child entering schooling. The fitting of a logistic or sigmoid curve

(also named learning curve) is perfect and, as shown by Marchetti and Modis in the

abovementioned references, this pattern of learning is not restricted to individuals, it is also

encountered with a group of people, be they a company, a country or humanity as a whole.

Duncan [49] also used this example of the child’s vocabulary in a more quantitative way,

fixing the limits of some involved parameters such as the rate of learning, in an attempt at

finding empirical support for his social interactions model. The basic equation describing this

process is the classical logistic differential equation or Verhulst equation:

dN

dt¼ dNðM � NÞ ð7Þ

where N(t) is the measured growing quantity, M is the upper limit of N(t) and d is a rate

parameter, which translates the system’s growth capacity. Due to the universality of

applications of this equation, the quantities N and M as well as the rate parameter d can be


envisioned in many different ways. For instance, N can be seen as the number of entities

(population or words in the previous example) at instant t, d the reproduction rate (or

assimilation rate) at the initial stage of growth and M is often referred to as the niche capacity

or carrying capacity, the ceiling of N(t) at the end of growth. Eq. (7) expresses then that the

rate of population growth is proportional to the size of the population and to the size of the

niche remaining empty.

Eq. (4) presented when discussing Duncan’s model is the same in a normalized form, using

f =N/M, as originally proposed by Fisher and Pry in their classic 1971 paper [75], analyzing

the diffusion of 17 technological innovations as a simple substitution process, measuring their

relative market shares f. Eq. (7) can then be rewritten as:

df

dt¼ df ð1� f Þ ð8Þ

The solution of Eq. (8) yields:

f ðtÞ ¼ 1

1þ e�dðt�t0Þð9Þ

where t0 is a constant locating the process in time, normally taken as the inflection point

when f(t) = 1/2, corresponding then to the half of the complete growth process. The

graphic representation of Eq. (9) displays as the elegant sigmoid or S-shaped curve

depicted in Fig. 1.

A second use of the learning curve concept regards the idea of economies of scale, by

which the performance and productivity of technologies typically increase as organizations

and individuals gain experience with them, that in economics is frequently referenced as

‘‘learning by doing’’ or ‘‘learning by using.’’ Learning depends on the actual accumulation of

experience and not just on the passage of time, and in the case of business is generally

described in the form of a power function where unit costs depend on cumulative experience,

usually measured as cumulative output:

Y ¼ KX�n ð10Þ

where Y is the cost of the Xth unit, K the cost associated with the first unit and n is the

parameter measuring the extent of learning or, in other words, the cost reductions for each

doubling of cumulative output. The curve of Eq. (10) looks like a decaying exponential, since

over time cost reductions become smaller and smaller, reaching a minimum final value when

the cost can be reduced no further. This ‘‘diminishing return’’ means that each doubling

requires more production volume, and the potential for cost reductions becomes increasingly

exhausted as the experience or technology matures. This approach of a production learning

curve surfaced in the 1930s in the aircraft industry and experienced an enormous progress

during and soon after World War II, being used today for a very broad range of applications.

For a good review and examples on this matter, see Yelle [76].

The most important point to be stressed here is the fact that both the above-described

learning patterns are essentially the same and, as Modis [9,23] has pointed out, production


learning curves or volume curves are the sigmoid curves ‘‘in disguise.’’ Representing costs

per unity is nothing else than the inverse of the S-shaped learning curve, representing units

per price indicator. In his words (Ref. [9], p. 48): ‘‘Business persons using volume curves

for decades have been dealing with S-curves without realizing it. The fundamental process

is learning. . . In either case, the law that governs its evolution is natural growth under

competition.’’ For him, the ultimate reason for the slowdown is some form of competition,

be it for the use of one’s time, energy or physical capabilities. This principle seems to be

universal; it acts just as well at the individual or at the aggregate level.

The universality of the learning curve pattern is striking. We are witnessing the

burgeoning not of a mere idee fixe, but rather the convergence of different fields of

science toward what may be the clue to understand the modus operandi of evolution per se.

As Grubler [74] recently observed, the world of technology is full of biological metaphors,

as for instance, evolution, mutation, selection and growth. Survival of the fittest is a

common place in the business jargon. As a physicist now active in the business world,

Modis wrote: ‘‘Companies resemble living organisms. They are born, mature, get married,

have offspring, become aggressive, sleepy or exhausted, grow old and eventually die or fall

victim to voracious predators’’ (Ref. [23], p. 28). The very appeal of learning curves or the

life cycle model lies in its considerable success as an empirically descriptive and forecasting

tool, as well as a heuristic device capturing the essential changing nature of technologies,

products, markets and industries.

Fig. 1. Normalized logistic or S-shaped curve [ f(t) =N(t)/M].


It is interesting to observe the overwhelming usage of biological concepts in describing

and understanding technological and social systems. Kauffman [1], a theoretical biologist

working at Santa Fe Institute, recently developed a powerful evolutionary model (the NK

landscape model), whose underlying assumption is nothing else than the learning curve

pattern. His model posits human artifacts and organisms at the same level, and hints to the

fact that technological coevolution may be guided by the same laws driving biological

coevolution. Fundamental innovations followed by dramatic and rapid improvements in a

variety of very different directions, followed by successive improvements that are less and

less dramatic, mirror the Cambrian explosion.

Kauffman (Ref. [1], p. 204) argues that, despite the ubiquity of learning curves no

underlying theory seems to account for their existence until now. Notwithstanding this, it

can be counterpoised that Darwin’s theory, expressed as ‘‘the survival of the fittest,’’ is the

underlying theory. But this is not a sufficient response to the universality of the logistic curves.

The assertion explaining Eq. (7) that ‘‘the rate of population growth is proportional to the size

of the population and to the size of the niche remaining empty’’ encompasses Darwin, but does

not give an answer about the why and the ubiquity of the logistic curves, not only in biological

matters, but also in pure physical phenomena. It is not evident to envision ‘‘the survival of the

fittest’’ operating in the dispersion strengthening of metals by phase transformation, where the

nucleation and growth of particles follow S-shaped curves. The same applies to the growth of

polymer chains. All this points to a more universal law underlying biological and physical

phenomena. Selection alone cannot explain the source of order in the universe.

The powerful and simple logistic equation is not an explanatory model; it does not

recognize the deep drivers of many different growth phenomena, it does not explain why

things evolve following S-shaped trajectories. But poor explanation does not imply poor

forecast, why is not how. The learning curve pattern, although not allowing the why, enables

us to look at how things evolve and to get answers about the timing of technological

transitions and/or technological trajectories.

10. An innocent-looking equation

Gleick [77] in his now famous world bestseller ‘‘Chaos — Making a New Science’’

referring to the logistic equation observed (p. 167): ‘‘In the brief history of chaos, this

innocent-looking equation provides the most succinct example of how different sorts of

scientists looked at one problem in many different ways.’’ This observation resembles that of

Modis mentioned previously about the use of learning curves by business people as being the

same curve used by biologists for over more than a century.

Really fascinating is the fact that the logistic differential Eq. (8), whose solution expressed

by Eq. (9) enables the ubiquitous sigmoid curves, when transformed in its discrete recursive

form leads to the bewitching world of chaos and fractals. The logistic discrete equation of

chaos scientists is expressed as:

xnþ1 ¼ kxnð1� xnÞ ð11Þ


where k is the rate parameter, or better, the gain-determining constant that influences the

degree of nonlinearity of the system. Depending on the value of k and on the initial value

x1(xn< 1), Eq. (11) may exhibit four different behaviors, namely, stability, oscillation, chaos

and unstable divergence [77]. For further reference on applied chaos theory, the reader is

referred to the excellent and didactic book of Cambel [78], and for applications in the social

sciences to the book already referred in Ref. [65], as well as to the series of articles published

by Gordon in Technological Forecasting and Social Change [79–82].

The apparently conflicting distinction and similarity between the two forms of the logistic

equation (differential and discrete) is more than academic and has far-reaching implications in

understanding real-life problems, such as the succession of technoeconomic systems and long

waves, after all the aim of the present work. Real-life systems are not properly continuous,

but consist of discrete elements like molecules in a gas, cells in an organism, individuals in

society or even in a more intangible level, inputs and outputs such as bits of information.

Another reason why the discrete logistic equation recommends itself is the fact that real

complex systems involve discontinuities and chance events.

A fact to be stressed here, which will be further explored in the diffusion-learning

dynamics to be developed in a section ahead, is that the relationship between the differential

(continuous) and discrete logistic equations has not received its due attention when analyzing

learning processes and their role in socioeconomic systems. It will be shown that the

relationship between the rate parameter d of Eqs. (7)–(9), hereafter named as the diffusion-

learning rate, and the gain-determining constant k of Eq. (11) should contain the hidden

cause explaining the timing of long waves.

It is worthwhile here to point out the linkage between the Kondratieff wave and the logistic

function. The first to adduce the relationship between long economic waves and logistic

growth was Mensch [14], who as previously discussed, put forth the concept that the world

technoeconomic system has evolved through a series of intermittent innovative pulses that

take the form of successive S-shaped life cycles (Ref. [14], p. 73). The concept of life cycle is

another metaphor that has been borrowed from biology to the world of technology, and

describes the growth of a process, the coming into and out of existence. Its pictorial

representation is a ‘‘bell-shaped’’ curve (see, for instance, Ref. [9], p. 33), that describes

the unfolding of the rate of growth over time, crossing the successive stages of birth, growth,

maturity (maximum rate of growth), decline and death (or saturation and ceiling). This

template is translated mathematically by the Verhulst first order differential Eq. (7), whose

solution in normalized form is the logistic Eq. (9), which represents the cumulative growth

(the S-shaped curve) of the system under observation.

Mensch developed then the motif that each economic long wave is the result of a swarming

of innovations which forms an organic technoeconomic system, whose unfolding is well

described by the life cycle template. Economic indicators like prices, inflation, interest rates,

production, etc. consist in a manifestation of this deeper underlying cyclical innovative

behavior, which evolves over time following the same ‘‘bell-shaped’’ life cycle pattern.

The linkage can be then mathematically summarized by asserting that the bell-shaped

wavy form of Kondratieff cycles is the first derivative of the logistic pulses of the human

innovative behavior. If we want to find the answer to the question ‘‘why the 50-year beat,’’


we must narrow our focus to the human constraints driving the dynamics of the logistic

curve underlying the long wave phenomenon. In the next sections, it will be shown that

these deep drivers are related with the human learning capacity and with the very human

generational succession.

11. The simple logistic and the logit transform

The Verhulst Eq. (7), or simple logistic, consists of a simplification of the most general and

celebrated Volterra-Lotka equations accounting for the behavior of species (a differential

equation for each species) under Darwinian competition in the same niche. In the business

world and technology assessment the Volterra-Lotka equations have found numerous

applications in analyzing the competition between innovations or simply among new

products struggling for a bigger market share [9,23,83,84]. In contrast, basic innovations

leading an emerging technoeconomic structure (leading technologies) do not properly

compete with existing technologies. These are already exhausted and the only competition

is for resources in a Malthusian way. Fisher and Pry [75] pioneered the demonstration of the

validity of the normalized Verhulst equation (Eq. (8)) in accounting for simple technological

substitution processes.

Several attempts have been made in modifying the Verhulst equation to account for the

cases of varying carrying capacity [63,85] or time lags [63]. These approaches, however, are

unnecessary in describing the learning processes involving the diffusion of basic innovations

and pervasive technoeconomic systems. The reason for this lies in the expression of

generation that will be the central reference point in the present approach: since the

complete diffusion of the new structure is a learning process within the same generation,

to consider a varying upper limit or a time lag accounting for noninstantaneous renewing of

resources is unnecessary. The resource is the flow of human energy, and the numerical

increase of the world population does not influence the normativeness of the biological

constraints acting upon the rate at which the process unfolds within the same generation. In

this way, the Verhulst differential equation as expressed by Eq. (8) and its solution Eq. (9)

are sufficient and self-consistent for describing the dynamics of the diffusion-learning

process of a new technosphere. In addition, as previously stressed in this paper and as

Marchetti et al. [86] already pointed out, the simple logistic often outperforms more

complicated parameterizations, which have the disadvantage of losing physical interpreta-

tions for their parameters.

For practical purposes, it is common to mathematically manipulate the logistic Eq. (9) in

order to put it in the logarithm form (Eq. (12)):

lnf

1� f¼ dðt � t0Þ ð12Þ

whose graphic representation is a straight line with a steepness d. This linearization, or logittransform, allows the determination of the timespan Dt between any interval of growth (from

fi to fj) as a function of the rate parameter d. Very often Dt is referred to as the ‘‘characteristic


duration’’ [85] or ‘‘take-over time’’ [75], representing the time for the diffusion process to

grow from 10% to 90% of saturation, in which case we have:

Dt ¼ t0:9 � t0:1 ¼ln81

dð13Þ

It is important to stress that considering the interval between 10% and 90% of the complete

growth as a ‘‘characteristic duration’’ is arbitrary, there is no practical or theoretical basis for

this choice, it is just a matter of reference. Other authors [88] prefer to consider the slope of

the sigmoid curve at its turning point (t = t0), which corresponds approximately to the linear

portion of the curve and to 76% of complete growth (roughly between 12% and 88%). This

consideration allows writing for this characteristic time span simply:

Dt ¼ 4=d ð14ÞAn important property of the logistic curve is the relationship between this ‘‘characteristic

duration’’ and the duration of the entire (complete) diffusion process Dtc, that is, between 1%

and 99% of complete growth. Eq. (13) yields:

Dtc ¼2ln99

d! Dtc

Dt¼ 2ln99

ln81! Dtc ¼ 2:09Dt ð15Þ

and Eq. (14):

Dtc

Dt¼ 2ln99

4! Dtc ¼ 2:2975Dt ð16Þ

12. The diffusion-learning dynamics

The first question to be addressed is how long is the ‘‘characteristic duration’’ of the

diffusion of basic innovations? It is evidently clear that because the long-wave phenom-

enon is essentially the result of the worldwide diffusion of a new technoeconomic

paradigm, its timing (duration) should be determined by the aggregate diffusion-learning

rate of the leading technological innovations in the whole society. Previous studies

[4,14,17,19,51,74,75] on technological basic innovations that have characterized each of

the preceding Kondratieff waves point to a mean timespan of 25–30 years for the leading

innovations. Grubler and Nakicenovik [51] analyzing a sample of 265 diffusion processes

(117 case studies performed at IIASA and 148 case studies taken from literature,

encompassing a universe of different kinds of innovations, not only technological

processes, but also product innovations and social diffusion processes) have shown that

over 30% of the analyzed cases, corresponding to the leading technical and process

innovations within the same innovation cluster, last on the order of between 15 and 30

years, a timespan with a length similar to that of a generation.

In a recent study, Santos and Devezas [87] analyzed the growth of the Internet, quantifying

its growth by the number of hosts attached to the web, whose semestral statistics are available


since its beginning. The Internet is a typical basic innovation that, together with personal

computers, protocol communications (TCP/IP), optical fibers, communications satellites, etc.,

is leading the diffusion bandwagon that is triggering the already observable trend toward

the upswing of the fifth Kondratieff wave. The results show a characteristic duration of

� 27 years of the whole information–communication (I&C) technologies, extending from

1980 until ceiling by 2007, corresponding to the recession phase of the present wave. This

� 27-year phase carried out the swarming of innovations related with the new worldwide I&C

system, which will be consolidated in the following � 25-year phase (until � 2030), when

the new technoeconomic structure will reach its saturation.

Using then Eqs. (13) and (14), and fixing a time span of 25 years for the characteristic

duration of basic innovations we obtain a diffusion-learning rate in the range of 0.16–0.175

per year. Two questions may then be raised: what is the meaning of this rate? Is there some

support allowing us to recognize this number as a constraint on collective human behavior?

In the following, it will be shown that some empirical and theoretical evidence seems to

support the concept of a biologically rooted constraint acting on human actions (learning) at

the aggregate level.

Danielmeyer, a German physicist, vice-president of the European Science and Technology

Assembly and former member of the board of Siemens, recently developed a new economic

growth theory [88,89] accounting for the growth trajectory and gross fixed capital formation

of industrial society. For him, growth is driven by the gap in relevant knowledge compared

with the state-of-the-art, and he advanced that there is a maximum sustainable real per capita

growth rate of 0.16 per year constrained by a time span that can not exceed 25 years. This

time span corresponds first to the generation succession time (physical generation gap)

during which relevant knowledge is transferred to the following generation. The argument is

that ‘‘when social order changes faster, the relevant knowledge of the parents becomes

essentially useless for the performance of their children, the society breaks down and

sustainable development is not possible.’’ A second candidate for imposing a limit to growth

is the finite physical (not fiscal) lifetime of capital stock, which is the inverse of its average

physical depreciation rate of 0.04 per year [88,89], which also happens to be 25 years. This

approach has embodied the concept that mankind builds its strategic infrastructure to last, on

average, just through the generation gap, understanding this in terms of relevant knowledge

and the capital stock per capita. Danielmeyer concludes: ‘‘It is very important to see that the

economy is principally ruled by a basic (biological) human factor rather than by monetary,

fiscal or tax policy,’’ and that ‘‘the generation gap is the most important economic constant’’

(Ref. [89], p. 16).

Danielmeyer’s approach resembles the one of a ‘‘learning society’’ developed by Marchetti

and strongly meets the present approach of a biologically driven limit to growth, constrained

by two (human) control parameters: the rate of learning and a timing of � 25 years, which

corresponds to the generational interval.

Another hint pointing to a typical value of 16–17% for the diffusion-learning rate can be

found in Grubler [74]. His histogram (Ref. [74], p. 84) of the distribution of learning rates

(unit cost reduction for each doubling of cumulative output) has a mode of distribution of

about 20%, as the result of the largest contribution of 17% for mass production. We have seen


that industry learning curves are nothing else than the inverse of the S-shaped learning curve,

representing units per price indicator.

Looking at the human capacity for learning, it is interesting to focus on the already

mentioned example of the evolution of children’s vocabulary. Duncan [49], using the data

available in the literature [9,18], determined for this case a rate of 22.34 10� 9 s � 1 or

0.7045 per year. Children’s vocabulary achievement constitutes a first phase of the human

learning, lasting for 6 years, at home. Human learning can be seen as a four-phased process:

the first phase at home, a second phase corresponding to the primary school (5–6 years), a

third phase corresponding to the secondary school (5–6 years) and a fourth phase

corresponding to professionalization or university (4–6 years), totaling 20–24 years.

Considering these phases as four successive learning processes following S-shaped curves

with approximately equal growth rates, it is possible to trace a composite logistic (super-

logistic, determined by the midpoints of the four component logistics) with a resulting

learning rate of � 0.16 per year. Again, we have the coupling of a rate parameter of � 0.16

per year and a time span corresponding to that of a generation.

To highlight the meaning of this coupling, one must look at the relationship between the

differential and the discrete logistic curves, making use of a geometric approximation, as

depicted in Fig. 2. The recursive Eq. (11) is the result of making discrete the logistic

differential equation, as (Eq. (17)):

dx

dttn ffi

Dxn

Dtn¼ dxnð1� xnÞ

��

ð17Þ

where xn is a descretized normalized function of the time t. The required geometric

approximation consists in considering the linear segment of the sigmoid curve, which, as

previously mentioned, corresponds roughly to the portion between 12% and 88% of the

complete growth. From Fig. 2, we see:

tana ¼ DX

tG) DX ¼ tGtana ð18Þ

where tG represents the ‘‘characteristic duration’’ of the process and DX its ‘‘characteristic

length.’’ Since for tan a in this characteristic interval, we have also (Eq. (19)):

tana ¼ DXn

Dtn¼ dxnð1� xnÞ ð19Þ

Eq. (18) can be rewritten:

DX ¼ dtGxnð1� xnÞ ¼ kxnð1� xnÞ ð20Þ

where k = dtG is nothing else than the steepness of the parabolas depicted in Fig. 3, which are

the geometrical place of all transitions xn! xn + 1of the recursive Eq. (11).

In this way, k= dtG represents the link between the differential and the discrete logistic

equations, and consists in an intrinsic property of the logistic growth dynamics. Considering

then that the diffusion of basic technological innovations, characterizing each new techno-


economic structure, follows the path of a simple logistic curve, we must look at the possible

values of k to finding a possible explanation for the timing (duration) of the phenomenon.

From chaos theory [77–82], we know that for k< 1 there is no growth (xn converges to

zero), and for 1 < k < 3 the graphic interactions converge to a fixed or stable point (xs in

Fig. 3a), i.e., a nonzero equilibrium value is achieved. However, when 3 < k < 4, the fixed

point becomes unstable, as represented in Fig. 3b. It is the range where one has the onset of

bifurcations, indeed, there may be more than one fixed point, one high and one low, for xn, the

function oscillates between these limit cycles. As k becomes larger and approaches 4, more

and more fixed points arise and xn wanders all over the parabola in an apparently random

manner, suggesting chaos. For k>4 the solutions of Eq. (11) lose their reality, the value of the

iterate can become >1, and lead the next iterate to < 0, sparking an explosion toward �1.

Then, the range 1 < k< 3 means endurance, stable equilibrium, and k > 4 means breakdown,

uncontrolled behavior. The range 3 < k< 4 means chaotic behavior, i.e., the behavior appears

to be random, but is, despite its bizarre appearance, deterministic, that means, its past and

future course are constrained by its dynamic nonlinear properties.

By definition, deterministic chaos means the presence of randomness, which is a stochastic

issue. In stochastic processes, the parameters of the system evolve with time, not deterministi-

cally, but probabilistically. This leads to uncertainty in forecasting, and consequently

theoretical models must include probability distributions and other statistical factors. Before

chaos theory scientists were restricted to two kinds of models: deterministic models to solve

Fig. 2. Discretization of the logistic curve. Considering the linear segment of the sigmoid curve, it is possible to

show that DX= dtGxn(1� xn).


physical problems or stochastic models to solve social problems. The advent of chaos theory

changed this, and the coexistence of the two approaches is now possible.

Social systems have all characteristics of chaotic systems, since the requisites of

discreteness, nonlinearity and feedback are attained, as shown by Gordon [81]. Social

phenomena are exceedingly sensitive to the initial conditions (large effects from small

Fig. 3. Parabolas representing the geometrical place of all transitions xn! xn + 1 of the recursive equation

xn + 1 = kxn(1� xn). (a) k = 2.7, convergence to a fixed point xS. (b) k = 3.7, oscillation between limit cycles

(chaotic behavior).


causes). The long-wave phenomenon, being a natural manifestation of social systems since

ancient times as previously discussed, must then be assessed from this framework.

Using then the approximation of Eq. (20) and considering that the typical timespan of

the generational interval (and that of the diffusion of leading technologies) is about 25

years, we have that d, the diffusion-learning rate, must not exceed a typical threshold value

of 0.16 per year, in order to avoid the breakdown of the system (dtG� 4). This value

matches the ‘‘maximum sustainable growth rate’’ stated by Danielmeyer [88,89], as well as

the rate of ‘‘diffusion-learning’’ found by Grubler [74]. It is important to see that man does

not control this rate parameter. Attaining this threshold value is a matter of survival, what

otherwise is a biological issue. Both parameters of the product dtG are the determinants

giving the pace of the technoeconomic development and essentially originate from

biological nature.

The diffusion-learning rate d is the cognitive biological determinant, the rate at which

humankind learns to deal with new environments, and as shown before, this learning is

embodied in the system’s structure, and the learning rate is an overall system’s property. The

characteristic time tG is the effective generational determinant, consisting of biologically

based rhythms, a point to be analyzed in Section 13.

An important point to stress is that, following this approach, it is not so relevant to consider

the exact values of d and tG. They consist in apparently flexible parameters, possibly varying

slightly among different social systems, as well as varying for different epochs of the human

record, depending too on the complexity of the environment. It is the environment that

determines the exact values of d and of tG; changing the environment means to change the

constant k= dtG. Drastic or radical environmental changes (chance events for instance) can

lead to the collapse of the system, either by vanishing (k< 1) or by paralyzing equilibrium

(1 < k < 3) or even by unsustainable growth and breakdown (k > 4). Rise and fall of

civilizations can be better understood under this framework.

Sustainable growth and evolution requires 3 < dtG < 4, granting the necessary oscillations

or chaotic behavior. The system is said to be chaotic within predicable boundaries. This rule

may not produce exact reproductions of the past for the system under consideration or yield

accurate forecasts of its future unfolding, but certainly helps to highlight our comprehension

about the aggregate behavior of human beings. Social systems are complex adaptive systems

exhibiting manifold stability, and [d,tG] are the biological control parameters of the long-

wave behavior.

The value of the aggregate diffusion-learning rate d might be very difficult to assess

theoretically; all we have are the few empirical evidences presented at the beginning of this

section. Some further research, mainly from cognitive neurobiology, could give a hand here.

Apparently, since the evidence points to a typical value of 0.16 per year, this means that

probably the social process of aggregate learning within a generation operates near the

threshold limit, in the region of manifold bifurcations and wider oscillations. But this is the

driving force for mutation (innovation), selection and diffusion or, in other words, for

evolution. The present result via chaos theory leads to a comprehension of the suggestion of

Danielmeyer of a maximum sustainable growth rate in order to grant the balanced transfer of

relevant knowledge from generation to generation.


Modis and Debecker [90] have shown that putting the solution of the logistic differential

equation (instead of the equation itself) into discrete form, chaotic behavior appears at both

ends of the sigmoid curve. They demonstrated that the solution of the logistic equation could

be written in the following recursive form:

Xn

M � Xn

¼ KXn�1

M � Xn�1

ð21Þ

where M is the niche size and K is a constant linked to the rate constant d through the

relationship2 K= edDt. The authors show that oscillations occur for K< 0, which imply

complex values for d. Then, the modulus of K is related to the steepness of the growth, while

its argument determines the frequency of the oscillations. This modeling, although not

establishing a threshold value for K, is compatible with the presented result of instabilities

linked to the value for d, since as d becomes bigger, the parameter K will then become bigger

impacting the oscillation period and oscillation amplitude. The stability of the growth phase

during the ‘‘take-over’’ process (characteristic length) is then ‘‘apparent,’’ it results from the

capacity of the system in maintaining 3 < dtG < 4. The present modeling accounts for the fact

that a small disturbance may have disastrous consequences.

Another result reinforcing the here suggested limit to growth was that obtained by Gordon

[81] and Gordon and Greenspan [82]. These authors developed a simple model of a social

system (Educational Model), a teacher giving lessons periodically to a student, the length of

the lesson being determined on the basis of the score of a test given just before the lesson. The

percentage of learned stuff retained is a function of the time elapsed between lessons. Writing

a recursive equation for these interactions the authors showed the bizarre (chaotic behavior)

consequences of giving lessons at closer intervals in trying to enhance the performance of the

student. They conclude then ‘‘speeding things up tends to move nonlinear systems toward

chaos’’ [82]. When drawing suggestions for the management of social systems the authors

hint to ‘‘slow things down, . . ., slowing down tends to move systems toward stability’’[82].

Most probably, society operates naturally allowing itself to be driven into chaos, without

losing control, granting in this way its own evolution and higher performance. The range

3 < dtG < 4 must be kept.

13. The aggregate effective generation

If from one side the theoretical considerations concerning the aggregate learning rate d ofthe product dtG consist in a difficult topic requiring specialized training and knowledge to

permit an understanding of the complexities involved in order to develop meaningful

parameterizations, the same is not true for the control parameter tG, which permits analysis

from a practical and theoretical biological framework. The characteristic duration or genera-

tional interval tG may be described as the Aggregate Effective Generation. This typical

2 Probably due to a typing error, it appears as K = eaM (a is our d) in their original work [88].


duration of � 25–30 years is ultimately the product of the interaction of two fundamental

biological time constraints recently proposed by Corredine as ‘‘The Aggregate Virtual

Working Life Tenure’’ [54] or ‘‘AVWLT’’ and the ‘‘Aggregate Female Fecundity Interval’’

[91] or ‘‘AFFI,’’ both subsets of the normative human life span or human life cycle, ‘‘the

basis of all social cycles’’ as expressed by Modelski [11,37].

The first constraint, a typical � 54-year Aggregate Virtual Working Life Tenure (AVWLT)

or tenure wave functions as a naturally forming, limiting and controlling biological clock, a

control cycle that contains within sets of social, political and hierarchical relationships, that is,

a regime that creates an aggregate periodicity displaying, and driven by, the expenditure of

relative human energy or relative intensity of vitality over its span, an approximate � 54-year

period from ages � 25 to � 79 in which aggregated constituent individuals obtain, gain and

diffuse economic power and influence.

An approximate � 54-year typical periodicity for long waves has been suggested by a

number of authors, including Kondratieff himself. In 1847, Dr. Hyde Clark described long

cycles of a 54-year duration [28,92]. Lord William Henry Beveridge’s analysis of agricultural

prices in the 1920s pointed to cycles of 50–60 years averaging 54 years [28]. In Chapter 9 of

his book The Kondratieff Waves [28], Mager devotes a section to answering the question

WHY 54 YEARS? Probably the most vocal proponent of idea of a 54-year long wave

periodicity is Snyder [93]. In his introduction to Guy Daniels’ translation of Kondratieff’s The

Long Wave Cycle, Snyder specifies the idea of 54-year cycles pointing out US Kondratieff

peaks in 1812, 1866, 1920 and 1974, that is, 54-year intervals. The first three peaks are

supported by Kondratieff’s chart ‘‘Indices of Commodity Prices’’ (the 1812 peak may be a

fudge, Kondratieff had 1814), the fourth peak in 1974 is from Snyder’s contemporary data.

On page 37 of this translation (Chapter V) in a discussion of the change in the average

level of commodity prices, Kondratieff himself says ‘‘The rising wave of the first cycle takes

in the period from 1789 to 1814; that is, 25 years. The downward wave of the first cycle

begins in 1814 and ends in 1849; that is, lasts 35 years. The entire cycle in the movement of

prices is completed in 60 years. The rising wave of the second cycle begins in 1849 and ends

in 1873; that is, lasts 24 years. True for the United States the prices peak in 1866. But this

upswing is due to the Civil War; and the observed lack of coincidence between the turning

point for prices in the United States, on the one hand, and for England and France on the

other, does not invalidate the general picture of the cycle’s development. The downward wave

of the second cycle begins in 1873 and ends in 1896; that is, lasts 23 years. The entire cycle is

completed in 47 years. The rising wave of the third cycle begins in 1896 and ends in 1920;

that is, it lasts 24 years. According to all available data, the downward wave of the third cycle

began in 1920’’ (italics added).

Kondratieff specifies that what will be named here the ‘‘Intensity Upslope’’ lasts for 25,

24 and 24 years, 24 years in two out of three cases. He also states that the entire first cycle

lasts 60 years and that the entire second cycle lasts 47 years, allowing a mean value of

(60 + 47)/2 = 53.5 years or � 54 years. What emerges is a seemingly typical average wave

of about � 54 years duration, with a seemingly typical upslope of � 24 years and a

downslope that averages � 30 years, as applies to the change in the average level of

commodity prices. It is significant to note that Marchetti [4,17,21,22], working with physical


parameters (like energy consumption for instance) instead of economic ones (prices), has

found sound evidence of 55-year secular fluctuations. Malthus [94] in his discussion of

demand and supply in his Principles of Political Economy synthesizes his original idea of

‘‘intensity of demand.’’ With rare insight he pinpoints the fundamental cause of price

fluctuations — the ability to make sacrifices and increase exertion, that is, the concentrated

expenditure of human energy. The increase or diminution of ‘‘intensity of demand’’ that

drives the increase or decrease in prices is a function of the increase or diminution in the

number, wants and means of the demanders. The ability of demanders to make sacrifices or

increase exertion to satisfy their wants drives prices up. The inability of demanders to make

sacrifices or increase exertion will drive prices down. Malthus concludes emphatically: ‘‘It is

in the nature of things absolutely impossible that any demand, in regard to extent, should raise

prices, unaccompanied by a will and power on the part of the demanders to make a greater

sacrifice, in order to satisfy their wants.’’

From Kondratieff’s own work, it appears that prices over the � 54-year long wave

increase for approximately � 24 years and then decrease for an approximate average of � 30

years. Taking our instruction from Malthus as pertains to prices, it can only be increasing

intensity, that is, the power to increase exertion and make sacrifices, that drives the ‘‘Intensity

Upslope’’ and decreasing intensity that drives the ‘‘Disintensity Downslope.’’

Dent [95] provides contemporary support for the � 24 +� 30 =� 54-year Intensity/Dis-

intensity template. In a chart from the US Bureau of Labor Statistics, annual Consumer

Expenditures Survey, entitled Average Family Spending by Age, reproduced here as Fig. 4, one

can plainly see the increase and decrease in ‘‘intensity of demand’’ according to family aging

spread over a � 54-year wave. Major increases in family spending begin at age � 25 and

plateau at age � 49, a � 24-year ‘‘Intensity Upslope,’’ thereafter, family spending decreases in

a major decline or ‘‘Disintensity Downslope’’ that lasts � 30 years ending at age � 79.

So then, the force that drives the approximate � 54-year Kondratieff Long Economic

Wave in prices is founded in our humanity, that is, our human biological energy. It is the

relative intensity of human vitality as distributed over and constrained by the limits of The

Aggregate Virtual Working Life Tenure that creates the long-wave ‘‘Intensity Upslope’’ and

‘‘Disintensity Downslope.’’ The � 54-year economic long wave is just the manifestation of

the underlying relative aggregate ‘‘intensity’’ of human vitality over the � 54-year AVWLT.

In this view, the long wave is seen in its conventional cresting wave depiction, from trough

to trough, to reflect the general rise and fall in prices over the wave as originally described by

Kondratieff. The Intensity Upslope, from trough to peak, consists of economic growth and

rising prices related to the consolidation, progress and success of a new technoeconomic

environment and the incorporation, empowerment and entrenchment of a vast new young

leadership cadre and work force with the progressive vigorous vitality or ‘‘intensity’’ required

to ‘‘get the job done.’’ For Malthus, the ‘‘intensity’’ required to raise prices was the ability to

make sacrifices and increase exertion, the same intensity required for the success of the new

technosphere. The Disintensity Downslope, from peak to trough, consists of economic decline

and falling prices related to the saturation of the new technosphere and the onset of declining

vigor in the now entrenched but aging cadre and labor force, who continue to hold positions

of economic power by simple virtue of their working life tenure but become progressively


less able to make sacrifices and increase exertion, that is, progressively disintense. This

progressive disintensity continues until finally diminished to torpor at the end of the

Aggregate Virtual Working Life Tenure.

Kondratieff waves were discovered looking at the secular up and down trend of prices, but

such econometric parameters are just ‘‘surface manifestations’’ of underlying biologically

driven dynamics. These ‘‘surface manifestations’’ are simply quantitative indicators that

express the relative dynamic connection of human endeavor (manifest as innovations and

technospheres) to their deeper biological determinants.

The second constraint, a normative 35-year Aggregate Female Fecundity Interval (AFFI)

is the biological temporal foundation for generational fertility cycles and birth waves [91].

The AFFI is the aggregate form of the female fecundity interval, the 35-year time interval

between age 15, the approximate age of first ovulation, and age 50, the average age of

menopause, the extreme age limits to the range of time when a human female is able to

produce children. Fecundity is the ability to produce children as differentiated from fertility,

which describes reproductive performance. It is the discreteness of the fecundity interval in

relation to the normative life span that initially sets up the conditions and limits for the

aggregation and repetition of fertility and birth waves, which, in consequence, create the

Fig. 4. Average family spending by age, chart from the US Bureau of Labor Statistics, Annual Consumer

Expenditures Survey, Copyright. The H.S. Dent Foundation (hsdent.com), reproduced with permission from Harry

Dent’s book ‘‘The Roaring 2000s’’ [94].


changing age distribution dynamics of populations. Not only must mothers give birth

sometime during this 35-year interval, if they are to give birth at all, but because fecundity

is not uniformly spread over the aggregate reproductive years and is rather stacked up in the

earlier years when libido is more intense (and because many women become sterile before

age 50) the average age of childbearing usually occurs naturally in the earlier years of the

interval. This age, which demographers call the ‘‘mean length of generation’’ or ‘‘mean

reproductive age of females,’’ came to 26.79 years for the US in 1995 as calculated by Weeks

[96]. Losch [69,97] in his work in the 1930s on population and business cycles based his

projections on a 33-year cycle or ‘‘length of generation.’’ Excerpted from Population Cycles

as a Cause of Business Cycles (Ref. [97], p. 650): ‘‘We find quite clearly great [centennial]

waves, the main cause of which are the great wars. The deficit of births during a war and the

surplus of births in the immediate postwar period repeat themselves about 33 years later,

when the new generations are at their time of highest fertility. For the same reason 33 years

later, a third wave occurs. Of course, these subsequent waves become broader and broader,

flatter and flatter, and after a hundred years entirely interfere with each other, . . .’’ (italics andbrackets added).

Losch did not describe in this paper the origin of this axiomatic 33-year periodicity. The

basis of the axiom is found in a footnote on the first page of Bevolkerungswellen und

Wechsellagen [69] and most closely translates into English as: ‘‘The average age of mothers

giving birth in Sweden during the years 1750–1900 was approximately 32 years, the

husbands were approximately 3 years older, the average age of parents amounted therefore

to 33.5 years. For Germany, the number may have to be reduced somewhat because of earlier

marriages. However, of all age groups, it is without question the 30–35-year-old wives who

give most births’’ (authors’ translation).

Losch simply added 32 and 35 then divided by 2 to yield 33.5 years as the average

periodicity on which to make projections. Significant here is the fact that Losch considered

not only the age of the mother but the father as well in deriving his axiomatic ‘‘time of

highest fertility.’’

Malthus [98] in his classic ‘‘An Essay on the Principle of Population’’ wrote: ‘‘In the

United States of America, where the means of subsistence have been more ample, the

manners of the people more pure, and consequently the checks to early marriages fewer, than

in any of the modern states of Europe, the population has been found to double itself in 25

years. This ratio of increase, though short of the utmost power of population, yet, as the result

of actual experience, we will take as our rule, and say that population, when unchecked, goes

on doubling itself every 25 years or increases in a geometrical ratio’’ (italics added).

For Malthus then, the axiomatic natural ‘‘length of generation’’ is a 25-year interval. Lee

[99] notes: ‘‘a tendency for human populations to move in cycles of one generation or 25–33

years; we will call these ‘generational cycles’ or ‘echoes.’’’

Dent [95] in a chart titled US Births Per Year, reproduced here as Fig. 5, gives an idea of

recent birth activity in the US showing succeeding peaks in 1921, 1957 and 1990, successive

intervals of 36 and 33 years averaging 34.5 years.

One can see from the foregoing that the ‘‘length of a generation’’ or ‘‘generational

cycle’’ may range from � 25- to a � 34.5-year average, varying from time to time and


place to place according to these different authors, and that of course they must have their

origin in the 35-year AFFI biological time constant. The scope of the present work

precludes an extensive discussion of generational waves based on the AFFI. Corredine [91]

has suggested renaming the demographer’s ‘‘mean reproductive age of females’’ or ‘‘mean

length of generation’’ as the Aggregate Female Fertility Wave and has proposed two new

concepts to help clear up thinking in this area: the Aggregate Male Virility Wave and the

Mean Reproductive Age of Parents or Parental Mean Length of Generation, which can be

simply called the Parental Wave.

For present purposes, it is enough to show that even though the exact length of a

generation can and may vary, as a practical matter an effective generation consists in a

characteristic duration of � 24–30 years. It will be shown in the following lines that this is

because the controlling power of the � 54-year Aggregate Virtual Working Life Tenure

(AVWLT) subsumes imprecise generational lengths and makes them a ‘‘characteristic

duration.’’ In the vigorous, booming � 24-year Intensity Upslope of a long wave, opportunity

abounds. As will be analyzed in Section 14, this is a Knowledge Consolidation Phase

triggered by the need for ‘‘Lucky Generations’’ to ‘‘not rock the boat and just follow the

program’’ in order to maximize chances for wealth, prestige and privilege. Achievement of

innovative knowledge decelerates and is displaced by amassing knowledge of how to best

Fig. 5. US births per year, reflecting the recent birth activity in the US, showing succeeding peaks in 1921, 1957

and 1990, successive intervals of 36 and 33 years averaging 34.5 years. Copyright #. The H.S. Dent Foundation

(hsdent.com), reproduced with permission from Harry Dent’s book ‘‘The Roaring 2000s’’ [94].


consolidate, institute and apply the innovative basic knowledge learned in the Disintensity

Downslope of the previous long wave. Individuals who begin their serious careers at age

� 25 in the trough of a long wave are ‘‘Lucky Generations’’ because they will ride the long

wave for their entire lives and have the greatest chances at success. ‘‘Unlucky Generations’’

who begin their serious careers at age � 25 during the long-wave first crisis live in a much

different world, at the start of the � 30-year Disintensity Downslope and hard economic

times. This is a basic innovation knowledge achievement phase, where a form of time-based

competitive behavior develops, triggered by the long-wave first crisis and driven by the need

for the more enterprising members of the ‘‘Unlucky Generations’’ to achieve and create

innovative knowledge and opportunities for themselves in a world where the tenure holders

enjoy the wealth, prestige and privilege denied to them.3

Except for Malthus’ ‘‘natural’’ early USA frontier demographic dynamics, known

historical birth wave patterns (� 33-year waves in Germany and Sweden in the 19th century

and average � 34.5-year waves in the US in the 20th) do not fit the generational timing

required by the AVWLT control cycle for painless progression. Births do not take place at a

steady or constant rate, but occur in waves that do not match the AVWLT generational

requirements. This offset polar dynamic further mitigates the virtual ‘‘Lucky/Unlucky

Generation’’ phenomenon. ‘‘Lucky’’ or ‘‘Unlucky’’ generations are not discrete but virtual,

that is, their memberships consist of interchangeable constituent individuals absorbed and

included by the system as needed as to relative degree of ‘‘Luckiness.’’ For example, those

who graduated in the late 1940s at the inception of the fourth Kondratieff, were most lucky.

Those who graduated in the 1970s, at the first long-wave crisis of the fourth Kondratieff and

the beginning of hard economic times were least lucky. Along the continuum from 1940s to

1970s, graduates progressed from most lucky to least lucky, and were absorbed accordingly.

Also remaining to be well understood is the deeper relationship between birth wave

intensities and their closer correlation to Kondratieff wave turning points. The upslope of the

fourth Kondratieff appears associated with the family formations of what is generally called

the Post-War baby boom and the now emerging upslope of the fifth Kondratieff appears

associated with the baby-boom echo family formations.

Under Darwinian logic and from our own real life experience, we know that people seek and

hold on to power for as long as they can. Power is rarely given up voluntarily. Individuals in

the mighty AVWLT leadership cadre who especially cherish power will hold it to the bitter end.

Because as young men many started their aggregate careers in or near the long wave trough, a

sizeable enough remaining number can retain and influence economic and social power, that

is, hold tenure until their own physical intensity diminishes to certain ineffectiveness at about

age � 79 or so, the limit of a normative life span. (As already commented in the earlier section

Where Did the Clock Come From?, it is life-phase limits that control, not mean times or

3 The Disintensity Downslope is a time of great opportunity for those few entrepreneurs on the leading edge. In

the 1920s and 1930s, great fortunes were made in such new industries as Automobiles, Aviation, Motion Pictures,

Radio and Broadcasting, Electrical Appliances and Chemicals. In the 1980s and 1990s, new industries and

products such as cable television, VCRs, CDs, cell phones, personal computers, computer-related technology and

software, the Internet, etc. again created great entrepreneurial fortunes.


averages.) The result is the creation of a � 54-year limiting time periodicity or control cycle

that programs the Disintensity Downslope. When at the onset of the Disintensity Downslope,

about � 24 years into the AVWLT, it becomes apparent that the established power regime, for

its own survival, will allow few new entrants, competition from outside by the bolder members

of the ‘‘Unlucky Generations’’ is one of the few ways to acquire the denied wealth, prestige,

privilege and power. This is the trigger for the creation of an effective generation of innovators,

as suggested by Schumpeter [13] — the entrepreneurial motivation of new men.

The Disintensity Downslope is the time of creative destruction when the entrenched

dominant AVWLT regime, motivated by keeping and guarding their wealth and power, that is,

protecting their established ways of profit-making, insure their own destruction. Simply

because they are preoccupied with running their empires and holding power, they neither

have nor develop the skills or incentive to innovate. A concentration of new men,

entrepreneurs, from outside the established regime, with little to lose and the world to gain,

seize this opportunity, learn, create and internalize new abilities, innovate new products,

services and ways of doing business to compete with and replace the old regime and their old

ways. Noteworthy is the idea that the entrepreneurial motivation of new men is limited to just

a few of the ‘‘Unlucky Generations’’ who may go on to achieve great wealth and prestige.

Because they are locked out of the dominant AVWLT regime their contribution is antipodal

and a weak beat in the general scheme of the unfolding. Most others in their ‘‘Unlucky

Generation’’ who are not innovators are just victims trapped in the disintensity downslope.

The natural rhythm that appears to emerge is the syncopation of two effective aggregate

normative life cycles both with a characteristic duration of � 79 years each segmented into

three stages. For simplicity of demonstration, a schematic straight-line representation (i.e., not

technically derived from actual data) of the succession of these aggregate life cycles and their

superposition originating a long wave is depicted in Fig. 6.

The first � 79-year cycle, represented in Fig. 6a as the intensity of human vitality over

time corresponding to the dominant Aggregate Virtual Working Life Tenure-AVWLTC — of

knowledge consolidators, and the strong beat in the unfolding, consists in stages of � 25,

� 24 and � 30 years duration. The first � 25-year stage, coincides with Malthus’ natural

‘‘length of generation,’’ the time it takes to develop a human being to full maturity and the

time in a mother’s life that she can devote to nurturing her children to maturity. This is a

contingent knowledge generation phase. The second � 24-year stage coincides with career

building in a knowledge consolidation phase of a progressive Intensity Upslope, which

corresponds to an effective generation time tGC. The third � 30-year stage consists of tenure

holding and progressive disintensity.

The second � 79-year cycle, represented in Fig. 6b (also as the intensity of human vitality

over time), corresponding to an emergent antipodal Aggregate Virtual Working Life Tenure—

AVWLTI and to the rise of the new knowledge innovators — the weak beat in the unfolding,

consists in stages of � 25, � 25–30 and � 25–30-year duration. The first � 25-year stage is

again the contingent knowledge generation phase. The second � 25–30-year stage coincides

with the entrepreneurial motivation of new men in the innovation knowledge achievement

phase of a dominant disintensity downslope, with progressive intensity in antipode to the

general progressive AVWLT disintensity. This corresponds to an effective generation time tGI.


Fig. 6. Schematic of a long wave (c) as the result of the syncopation of two successive effective aggregate

normative life cycles. The durations tGC and tGI act as codeterminants of the timing of the long-wave phenomenon.

The dominant strong beat AVWLTC generation carries both the ‘‘Intensity Upslope’’ and ‘‘Disintensity

Downslope.’’ The AVWLTI generation carries an antipodal weak beat ‘‘Intensity Upslope’’ within the general long

wave ‘‘Disintensity Downslope,’’ which creates the basis for the next long wave.


The third � 25–30-year stage consists of tenure holding and progressive disintensity in

antipode to the rise of newdominant AVWLT Intensity. Fig. 6c shows the unfolding of a long

wave as the conjuncture of two successive AVWLTs, that is, increasing and decreasing levels

of economic activity as a product of the syncopated beats of economic activity originated by

the two successive effective generations — dominant effective generation tGC and antipodal

effective generation tGI.

In summary, the biological determinant tG, the time span of the Aggregate Effective

Generation, arises from the interaction of the Aggregate Virtual Working Life Tenure and the

Aggregate Female Fecundity Interval. The AFFI biological time constant is the mother of

‘‘generational’’ cycles that vary within approximate limits of 25– � 34.5 years. The AVWLT

is a ‘‘control’’ cycle that descretizes these imprecise ‘‘generational’’ cycles into a ‘‘character-

istic duration’’ of � 24–30 years as triggered by the onset of either the AVWLT Intensity

Upslope and the need for an effective consolidating generation (duration tGC) ‘‘to get the job

done’’ or the onset of the AVWLT Disintensity Downslope and the emergence of an effective

innovating generation (duration tGI) to bring about evolution and change.

14. The generational-learning model of long waves

The schematic depiction shown in Fig. 6c portrays the conventional cresting representation

of the long wave, using as a template the widely referenced graph (see, for instance, Ref. [25],

p. 21, and Ref. [28], p. 451) of Media General Financial Services, reproduced here as Fig. 7.

As seen in Section 13, this graph translates the succession of an ‘‘Intensity Upslope’’ and a

‘‘Disintensity Downslope’’ resulting from the relative intensity and phased behavior of

human vitality as distributed over and constrained by the limits of the Aggregate Virtual

Working Life Tenure.

Fig. 7. Graph of four Kondratieff waves originally published by Media General Financial Services in 1974 and

reproduced in some books [25,28]. Reproduced here with permission of Media General Financial Services.


It remains however to join to this ‘‘Intensity–Disintensity’’ description the diffusion-

learning dynamics inherent to the structural nature of an evolving technoeconomic system,

that is to consider the underlying dynamics of innovations and their diffusion throughout the

socioeconomic system, giving rise to the phenomenon named here as succeeding techno-

spheres. As seen previously, and also pointed out by De Greene [45,46], each long wave can

also be conceived as an evolving learning dissipative structure bounded by instabilities. At

each long wave, a new technoeconomic environment is created, used and exhausted,

following the path of an overall logistic curve, dragging within it not only new technologies

and industries, but new ways of life, new occupations, new forms of organization, not only in

business but also in politics and social order. This overall logistic growth is the envelope

curve encompassing two logistic structural cycles, whose unfolding is depicted in Fig. 8. The

upper part of this figure is again a schematic straight-line representation of the ‘‘Disintensity

Downslope’’ and ‘‘Intensity Upslope’’ phases, also using as a template the graph of Fig. 7.

The first logistic structural growth curve, corresponding to the ‘‘Disintensity Downslope’’

or downswing of the long wave, is triggered during the ceiling (saturation) of the previous

technoeconomic system, a period of high instability, economic stagnation and recession,

soon followed by a deep economic depression. It corresponds to a phase of renovation,

mutation and selection, during which basic innovations accumulate and interact synergisti-

cally, and new ideas emerge apparently out of nowhere. Through the action of an effective

generation of innovators and new entrepreneurs society begins to deal with a new

technological environment, while old structures collapse and give place to the emergence

of new ones. This process takes time and the endogenous mode of operation is the rate of

achievement of innovative knowledge, a rate of learning characteristic of the first structural

cycle of the new technosphere.

Once the necessary knowledge is established and accumulated, and the new technological

environment is reasonably entrenched, the economic expansion starts again. It is the

‘‘Intensity Upslope’’ phase or upswing of the long wave, corresponding to the second

logistic structural growth curve, a phase of consolidation and maturing, carried by the

effective generation of consolidators. Now the endogenous mode of operation is the rate of

consolidation of knowledge, again a rate of learning, but now corresponding to the transfer of

relevant knowledge to the following leading generation.

In this description, the long wave is now seen from peak to peak, comprising two logistic

growths, carried out by two successive effective generations. During the first one, from peak

to trough (Disintensity Downslope), the bases of the new technological environment are

established by the ‘‘unlucky’’ innovators generation. Then follows the second one, from

trough to peak (Intensity Upslope), carried out by the ‘‘lucky’’ consolidators generation,

during which the new environment and its strategic infrastructure consolidate throughout

society. Each logistic structural cycle corresponds to an effective generation time or

characteristic time tG, which can take slightly different values at each structural cycle, since

different learning processes are at stake.

These characteristic tG (tGI for the innovation structural cycle and tGC for the consolidating

structural cycle) coupled with the maximum growth rate d (consisting for each cycle in an

aggregate learning rate), determine the unfolding of the process, within the range 3 < dtG < 4



(deterministic chaos), the necessary requirement to grant the system’s enduring evolution and

survival. It is interesting to observe that using Eqs. (15) and (16) for the determination of the

entire diffusion process Dtc for each structural cycle, and considering a typical timespan Dt of

� 25 years, periods are obtained ranging from 52.25 to 57.44 years, corresponding to the

range of durations of Kondratieff waves, in principle approximately equal to tGI + tGC.

The present Generational-Learning Model opens the way for further research aiming to

clarify some other open questions about the long wave phenomenon, a theme of ongoing

research being conducted by the present authors. For instance, there has been a controversial

discussion about whether the long-wave duration may be shrinking or extending [100] or if

the pattern will change or not in the next century [45]. Opinions abound about these issues.

Since the pattern of the unfolding of the long wave is a function of the product of the

biological control parameters dtG, that ultimately are also responsible for its stability or not, as

well as for the timing (duration) of the phenomenon, the presented framework may offer a

good help in finding answers. As pointed out above, the values of d and tG are not necessarily

equal at each structural cycle, and thus their product may take different values at each cycle.

Each structural cycle at each long wave may have their own characteristic values relevant to

their control parameters, that is, each structural cycle at each long wave may have its own

chaotic behavior.

Some criticism of the present model has been raised with regard to how the social

environment influences the unfolding of the long wave. It may be argued that the social

environment is at least as much of a determinant of the long wave as biology. Our answer is

that the action or influence of the social environment may be seen in two ways.

� First, by affecting the control parameters d and tG, modifying slightly the product dtG,but keeping it in the chaotic (but deterministic) range 3 < dtG < 4.

� Second, by drastically disturbing the product, bringing it outside that range, threatening

the system’s survival, either by vanishing (dtG < 1), by paralyzing equilibrium

(1 < dtG < 3), or even by unsustainable growth and breakdown (dtG > 4). This would

be the case for unforeseeable chance events.

These points were already considered in our analysis in the section ‘‘Diffusion-Learning

Dynamics.’’ Added to these considerations is the fact that the social environment undoubtedly

influences human decisions and attitudes — different environments imply different reactions.

But the rhythm of these reactions, the human response to these influences, as dictated by the

constraints of the human biological clocks, is always approximately the same (or varies

within a certain limited range). Chance events can eventually destroy the system, but if not,

Fig. 8. The generational-learning model of long waves. The overall logistic growth curve of a new

technoeconomic system encompasses two successive logistic structural cycles: an innovation structural cycle

with characteristic duration tGI triggered during the ‘‘Disintensity Downslope’’ of the previous technosphere, and a

consolidating structural cycle with characteristic duration tGC which marks the definitive entrenching of the new

technosphere and the vigorous ‘‘Intensity Upslope’’ of the long wave. At each structural cycle, the product dtG(d = diffusion learning rate, tG = aggregate effective generation time span), maintained in the interval 3 < dtG < 4controls the unfolding of the process.


the consequence will be the temporal displacement of the long wave, but keeping the same

period (or frequency) and the same dynamics.

There are yet a lot of things to consider within this new proposed model, considerations

that will not change the basic assumptions of the model, but will instead bring deeper

understanding of the unfolding of the phenomenon and even the possibility of determining its

exact timing. The proposed model is presented in the spirit of exploring a new approach to the

understanding of Kondratieff waves, generally not yet accepted by economists. On this basis

alone, it is enough for this paper that the biological approach will be perceived by both social

scientists and economists as the unifying reality that underlies the phenomenon.

15. The time being and final considerations

It has been widely anticipated that a new economic boom corresponding to the upwave of the

fifth Kondratieff long wave will open the new century. For the present authors, one an academic

the other an entrepreneur, both interested in the phenomenon of long waves for almost two

decades, it is really gratifying to observe that much of what has been forecast about their

unfolding has happened and is happening, if not in the details, then in its whole appearance and

timing. There were two decades marked by an incontestable worldwide economic depression,

during which it was possible to observe a succession of events characteristic of the downwave

or ‘‘disintensity’’ phase, in many aspects very similar to preceding long waves. These events

are related to the diminution and end of established political and industrial structures that

supported the previous upswing, an overall clean-up process that includes the burgeoning of a

new worldwide order, political and technoeconomical.

The facts of the past dozen years are striking. The disintegration of the Soviet Union, the

fall of the Berlin Wall, the end of the Cold War, the transition to capitalism in China, the

end of the East Asian economic miracle exemplify the twilight of the previous established

order. A new way of conducting wars (Gulf War and the Balkans War), the growing

concept of globalism (globalization), the new information and communication system, just

to mention a few, are signs of the dawn of the new international order. Now stock markets

worldwide speak of a new economy in an attempt to differentiate new stock valuations

from conventional stock values. Much has been said also about the incapacity of people in

forecasting each of these shaking events, including the arrival of the Internet [101]. Failure

of prognostications? Uncertainty about the future? Maybe. But this would not be the case if

due attention to the phenomenon of long waves and the pattern of their unfolding had been

applied in a massive effort. The collapsed structures were founded on a political and

technoeconomic order that, following previous examples, must come to an end after

enduring by one or two generations. The emergence of the new order was already on the

way by the middle of the 1980s, coinciding with the downslope of the fourth long wave,

conduced by a new effective generation. The lack was not in precision, but in completeness

of observation.

We are undoubtedly witnessing the emergence of a new technoeconomic structure that is

coming with overwhelming force. The new and pervasive information and communication


global system is transforming the everyday life of people, companies and nations, as well as

positively impacting the global economy. During the last dozen years, a huge number of

absolutely new enterprises in the domain of personal computers, software, communications

and Internet business emerged, bringing onto the scene a new entrepreneurial generation and

new fortune holders. More recently, scientists are developing new breakthroughs in genetic

related technologies, with the stock market values of small and unnoted enterprises rocketing

in just 1 day. The way the present work was accomplished is perhaps one of the best examples

of the revolution in the way of doing things: two persons on two continents, separated by an

ocean and 3500 miles, changing ideas, opinions, texts and images in a few seconds, are using

a set of equipment, concepts, source of data and technologies not existent (and even

unthinkable) some 15 years ago. Research teams are no longer restricted to one institution

or nation, and the perspective this opens to the scientific community is enormous.

The Kondratieff or long-wave concept provides a very important and accessible operating

principle bridging science and history [45], and its understanding would fill the existing need

for accuracy and completeness in forecasting, as recently voiced by Gordon [102]. Reasoning

with this author, we can say that ‘‘uncertainty can never be eliminated, but generally

diminishes as the time horizon shortens, as the dimensionality of the system decreases and

as the availability of pertinent and accurate data increases.’’ The long-wave approach fulfils

all these three conditions, forcing the development of future scenarios within the reasonable

time span of one or two generations, bounded by well-defined dimensions and based on

objective collection of data.

It seems a contradiction to speak of ‘‘predictable long waves’’ and ‘‘chaotic (apparently

random) behavior.’’ There is no contradiction at all, but the action of some kind of

Heisenberg’s uncertainty relation, limiting our capacity to simultaneously evaluate the state

and progression of the system. The predictability allowed by the present approach considers

only some general aspects of the long wave, for instance, that some structures will collapse,

new structures will emerge and that within the time span of a generation the now blossoming

technoeconomic order will reach its apogee, carrying with it a period of great economic

expansion. We can go further affirming that another stagnation and depression will follow,

supported by another generation. Details and exact prospects are difficult, if not impossible to

foretell since a characteristic of chaotic systems is the unpredictability of the particular

trajectories, due to their extreme sensitivity to initial conditions.

But we cannot forget that we are facing a dissipative system exhibiting a ‘‘limit cycle’’

regime with very definite boundaries, and hence a predictable overall behavior. Further

improvement of the model is possible (for instance, for the exact evaluations of the control

parameters d and tG as a function of environmental influences) that will enhance its forecast

performance, allowing more detailed prospects.

16. Conclusions

To operationalize the long-wave approach as a useful forecasting tool, it is necessary to

understand its causality in the way addressed in the beginning of this paper, that is, the


causality of long waves of socioeconomic development must be understood in the context of

two categories: first, the triggers of the swinging behavior and, second, the determinants of

the 50–60-year periodicity.

The claim of the present work in understanding both categories is that long-wave behavior

in socioeconomic growth and development is essentially biologically driven. The swinging

behavior is a natural manifestation of social systems as a response to their survival and

improvement capability, that is, for their evolution in the most pure Darwinian logic. Social

systems, like all other living systems, consist of a hierarchy of oscillating structures, and the

behavior at one level is constrained by the control parameters of the level above, in a chain of

causalities [45]. The immediate ones acting upon the aggregate behavior of human beings are

the control parameters d and tG, and following the causality chain we come to the last one, the

geophysical system, where lies the source for the timing of all phenomena in the ecological

sphere. Consequently, the cyclicity of social phenomena is embodied or better, ingrained, in

our biological structure. No entrainment via mode-locking process is necessary, the clock is

embedded within us.

In terms of the biology of population growth, each new technoeconomic environment is a

new stage in the development and growth of the means of subsistence or carrying capacity

needed to sustain an increasing population. As long as there is space, population will grow,

provided a diffusing technoeconomic infrastructure develops in support. However, this

infrastructure does not grow continuously but instead discontinuously over time as pro-

grammed by the limits of the rate of learning, the limits of the AVWLT stages, the relative

intensity of human activity, vigor or energy contained within the stages and the resulting

timing triggers.

Recent research published by Kiel and Elliott [103] on the evolution of public admin-

istration, points to a corresponding two-phased learning behavior (innovation + consolidation),

as presented here in Fig. 8 (Generational-Learning Model). Organizational ‘‘reform initiation’’

accompanies technological and knowledge innovation during the long wave downswing, and

‘‘reform confirmation’’ corresponds to knowledge consolidation during the upswing.

Linstone et al. [71] in ‘‘The Challenge of the 21st Century’’ included a brief discussion of

logistic curves and cyclical patterns as related to forecasting long-term trends, in which they

put forth a very important observation. They noted that 56-year cycles are a common pattern

(and a basis for T-type forecasts) underlying Kondratieff waves, American wars, technology

cycles, overarching technologies, energy sources reaching peak, process innovations and

corporate organization, and summarized all these regularities in a single figure (Ref. [71],

Fig. 7.3, p. 151). Commenting on this figure they state: ‘‘The ubiquity and the repetition of

the patterns considered here at many different levels of human behavior underscore the

self-organizing nature of complex systems,’’ but that ‘‘the reason for the 56-year periodicity

lies beyond our comprehension at this time. One suspects that there is a biological driving

force, a deep rhythm, that extends beyond the natural and human biological sphere to societal

systems’’ (italics added).

These statements firmly resound with the conceptualizations presented in this work

favoring the biological determinants explanation for the long wave. All evidence points to

a cyclical pattern of human affairs, and since human involvement itself is the common feature


in many different observed patterns, this strongly suggests that the rhythm is biologically

given, that is, constrained by our biological clocks.

In ongoing private discussion with the authors during the review of the present paper

Linstone [104] further observed: ‘‘Your hypothesis is that biology is decisive or overriding in

determining the economic and technological rhythm described by the long wave. Thus, the

determinant for the collective entity appears to be of a purer nature than that for the individual.

This would be interesting, suggesting that the biological determinant operates at a metasystem

level, swamping all other perturbation-creating factors which operate at lower levels.’’ This

statement fittingly summarizes the essence of the message intended with the present work.

Yet, this understanding is not final. What remains to be understood first and foremost is the

important question about the ultimate cause of the first category, the trigger (or triggers) of the

swinging behavior. We could not resist suggesting a way to find the explanation, anticipating

some not yet published results.4 We must turn to the conception of a long wave as being an

evolving dissipative structure bounded by instabilities, and use the chaos science framework

to look to the characteristics of its dynamics. Nonlinearity is a necessary, but not sufficient,

condition for chaotic behavior, which in turn is due neither to external noise nor to an infinite

number of degrees of freedom. The source of irregularity is the nonlinear system’s property of

separating initially closed trajectories exponentially fast [105]. Chaos scientists developed a

set of criteria to characterize the dynamics of chaotic systems, which allow separating the

predictable from the unpredictable in their behavior. These criteria are the fractal structure of

the attractors, the Komolgorov–Sinai entropy or simply the metric K entropy and the

Lyapunov characteristic exponent l.Gaining knowledge of the application of these criteria to social systems and their subsystems

is yet at its very beginning, but is the necessary way to overcome the present difficulty in finding

a definitive explanation for the long wave phenomenon. K entropy is linked to the decrease in

the information about the system over time when measured against the initial state, and the lexponent is linked to the information available about the system. Both parameters might

embody the hidden cause of why a given dissipative structure ceases its growth, triggering a

profound transformation through a clean-up process, opening the way to a new and necessary

beginning. The larger the Lyapunov exponent, the greater the information loss about the system.

The gain or loss of information reflects the amount of uncertainty in the dynamical process. For

instance, with the loss of information, the amount of predictability decreases, the certainty in the

future is diminished and the system losses cohesion. Thus, it is very reasonable to expect that, as

a given techoeconomic system evolves with time, some threshold value of K or l is reached,

translating a limit value of loss of information and uncertainty, that in turnmitigates its cohesion

and determines the end of growth and the necessity of a complete restructuring. Thenwe can say

that the duration of a technoeconomic system (technosphere) is biologically programmed, but

the necessity of its substitution and renewing is physical and related to the informational

entropy of the given technoeconomic system.

4 Some of these results will appear in a forthcoming article of the present authors—‘‘The nonlinear dynamics

of technoeconomic systems: an informational interpretation’’, to be published in Technological Forecasting &

Social Change, v. 70/1.


Edward Gibbon5 wrote in 1780: ‘‘There are few observers who possess a clear and

comprehensive view of the revolutions of society, and who are capable of discovering the nice

and secret springs of actionwhich impel, in the same uniform direction, the blind and capricious

passions of a multitude of individuals.’’ Pearl [106] noted in 1925: ‘‘. . .plainly all growth,

including that of population, is fundamentally a biological matter. . .’’ and ‘‘Growth occurs in

cycles.’’ The secret is that we are the stuff of cycles. Man is a clock, society is a clock, a

biological, sociological and economic clockwork propelled by the deterministic cosmic lottery.

Acknowledgments

Author Tessaleno Devezas wishes to thank the Portuguese Fundacao de Ciencia e

Tecnologia which partially supported (through the Unity of R&D #202) the present

investigation, as well as Engineers Humberto Santos and Carlos Duarte for their assistance in

designing the figures and Table 1, respectively. Author James Corredine wishes to thank

physicist Nick LaRocca for his sacrifice of many hours in face to face discussion, his earnest

help, wise counsel and first-class suggestions. Both authors especially thank Prof. Harold

Linstone for his recognition of the importance of the long-wave phenomenon and his

determination to maintain TFSC as a forum for the long wave discussion.

Appendix A. Long wave on long waves

Kleinknecht [107,108] writing in the middle of the 1980s pointed out that theorizing on

long waves seems itself to move along a long wave path, noting at that time, as in the 1920s, a

concentration of long wave research was observable. And, in fact, by observing the history of

the publications on long waves, we can see clearly the formation of two clusters separated by

� 59 years, each following a logistic trajectory as depicted in Fig. 9.

The first cluster corresponding to the finding and diffusion of the long-wave concept

peaked in the late 1920s, coinciding with the apogee and downswing of the third Kondratieff

wave. A total of 17 publications were counted, considering just those strictly related with

long waves, and not considering the huge amount of publications on business cycles that

surfaced at this same time. Authors such as Kitchin, Juglar, Mitchell and even Kuznets were

not considered, as also the very frequently cited work of Dewey and Dakin (Cycles: The

Science of Prediction, 1947). The counting for the first cluster starts with Parvus (1901) and

includes the works of Van Gelderen (1), De Wolff (3), Kondratieff (4), Beveridge (2),

Woytinski (1), Von Ciriacy-Wantrup (1), Spiethoff (1), Schumpeter (1), Garvy (1) and

Dupriez (1), using as sources Mager [28], Kleinknecht [107,108] and Barr [109]. Nineteenth

century authors such as Hyde Clark (1847) and Jevons (1865) were also not considered.

5 Edward Gibbon in ‘‘The Decline and Fall of the Roman Empire’’ (Chapter 27 — The Death of Theodosius)

— 1780.


The second cluster corresponding to a typical phase of proofing the existence, modeling

and theorization on economic long waves peaks in the middle 1980s coinciding with the

downswing of the fourth Kondratieff wave. Our count starts in 1964 (U. Weinstock, as

mentioned in Ref. [106]) and considered 118 books and papers (only periodicals) appearing

until the first quartile of the year 2000. Again, the publications on business cycles were not

considered, as also the papers appearing in proceedings of conferences (very difficult to trace

in totality), which could most likely lead to a doubling of this number. The unfolding of the

second logistic reveals that we are witnessing the ceiling of publications on long waves,

probably heading to a reasonable understanding of the phenomenon.

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