Discovery Processes and the Kondratieff Cycle: Mathematical Principles

Author: Widdowson, Marc
Almanac: Kondratieff waves:Processes, Cycles, Triggers, and Technological Paradigms

DOI: https://doi.org/10.30884/978-5-7057-6191-3_04

‘Discovery processes’ are hypothesised as processes in which there is an interplay between innovation activity and exploitation activity. Both require societal resources, in a zero sum game, so that, while innovation is needed to make exploitation possible, exploitation takes effort away from innovation, inhibiting the maintenance let alone expansion of exploitation. Such negative feedbacks, which propagate through the economy with a certain lag, give rise to oscillatory behaviour. Hence economic expansion proceeds in cycles. The cycle duration is linked to the human ageing process, since it is those entering adulthood who are best placed to respond to changed economic opportunities, while older adults are more committed to existing occupations. Since innovation activity is always positive (things are seldom de-invented), the cumulative activity (total inventions) manifests as quasi-logistic pulses, where growth is flatter when society's focus has shifted towards exploitation and steeper when society's focus has shifted back towards innovation. ‘Complex’ discovery processes extend the logic of these ‘simple’ discovery processes with an additional dynamic whereby high value exploitation processes stimulate competition, which reduces their value, while innovation restores their value. The coupled cycles of innovation, exploitation and competition produce a fluctuation in all three activities, whose phase relationships correspond to those of the Kondratieff cycle and whose duration, given some assumptions about the turnover of generations, can be shown to match the Kondratieff period. The ideas discussed in the paper are applied to manned space exploration and are used to estimate the growth of the human presence in orbit over the next half-century.

Keywords: economic cycles, long wave, logistics, mathematical modelling.

1. Discovery Processes

1.1. Simple Discovery Processes

In 1419, the Prince Dom Henrique of Portugal, known in the English-speaking world as Prince Henry the Navigator, was appointed governor of the Algarve. He proceeded to sponsor journeys of exploration to the Atlantic islands and down the West African coast (Findlay and O'Rourke 2007: 145–147). By Henry's death in 1460, this initiative was beginning to stall. The Portuguese had reached the Senegal and Gambia rivers and were preoccupied with the rich trading opportunities they offered (Cunliffe 2017: 520–522). It was not until 1469, when the Portuguese king commissioned a Lisbon merchant to continue the exploration effort that southward progress resumed, with Bartolemeu Dias passing the Cape of Good Hope in 1488 and Vasco da Gama reaching India ten years later.

Thus, Portuguese exploration led to the discovery of commercial opportunities, and exploitation of those opportunities diverted effort away from exploration, which slowed down exploration. Once exploitation had become saturated, or was sufficiently routine as to be transferred to private interests, royal exploration took off again.

This is an example of what will here be called a simple discovery process (see Fig. 1). Exploration exerted a positive effect on exploitation that is caused exploitation to increase. On the other hand, exploitation exerted negative feedback on exploration (i.e., caused exploration to decrease).

Another example of a simple discovery process is found in the activity of the European trading companies in the Americas and the Far East during early modern times. The high prices being obtained for spices and exotic goods stimulated exploration for more supplies, and the resulting increase in supplies then brought the price down, which caused exploration to fall (Phillips 1990: 50). One can note that price caused an increase in exploration and exploration caused a decrease in price.

Students of historical cycles will likely feel a sense of recognition at the 50-year interval between Prince Henry's inauguration of an exploration programme in 1419 and its renewal in 1469. It recalls the 50- to 60-year duration of the Kondratieff cycle in economic affairs (Grinin, Devezas, and Korotayev 2012). A period roughly reminiscent of the Kondratieff cycle is also found in the fluctuations in Europe's colonial trade that resulted from the dynamic illustrated in Fig. 2 (see Fig. 3 which shows sugar imports of the Dutch Vereenigde Oostindische Compagnie [VOC]).

Marchetti (1980, 1986) has shown that this kind of ‘50-year pulsation in human affairs’ typically has a logistic (S-shaped) form, whereby the rate of discovery initially accelerates then slows down and tapers off (see Fig. 4, showing the wave of inventions centred on the year 1857). Marchetti has shown that the same pattern applies for earlier and later invention waves, as well as for a whole range of other socio-technical phenomena, such as the construction of metro systems. His work has been continued by Modis (1992, 2002, 2013).

Marchetti attributes the logistic behaviour of invention waves to the fact that they involve learning processes. Inventions initially spread through a receptive society, meeting existing needs, and organising industries and distribution networks around themselves. As society processes, absorbs, and incorporates these inventions, the capacity to accept further inventions decreases, leading to saturation. Once full uptake has been achieved and the economy has settled into a stable configuration, factors like population growth, fundamental discoveries, and the emergence of new needs can then trigger the next pulse.

We can understand Marchetti's invention waves as another kind of discovery process. In this case, innovation leads to implementation (i.e., bringing the innovation into use), whereas increased focus on implementation reducesthe effort devo ted to innovation (see Fig. 5).

1.2. Complex Discovery Processes

As we have seen (in Fig. 2), high prices for exotic goods in the European colonial trading system encouraged exploration, which increased availability and caused exploration to fall back. However, another outcome was possible. When increased competition caused revenues to fall, entrepreneurs could respond with innovations that restored their revenues, for example through reducing costs, differentiating their products, or reaching markets more quickly (Steensgaard 1990: 151–152). For example, tobacco farmers responded to falling prices by packing bales more tightly, which reduced shipment charges, or they switched production to other crops. Similarly, the innovations in the British textile industry that drove the Industrial Revolution were stimulated by competition from Indian imports.

Let us call this a complex discovery process (see Fig. 10). It is a discovery process because there is innovation. It involves two kinds of negative feedback. Increased revenue causes competition that decreases revenue, and decreased revenue causes innovation that increases revenue. Note that innovation moves in the opposite direction to revenue so the influence of revenue on innovation is shown as negative in the figure.

Table 1 suggests that we should have expected around seven people to be in space in 2021. In fact, the mean number of people in space over that year was 9.2 (see Appendix 1, Table 3). In these early years of the cycle, the precise numbers have a high margin of error, and one can conclude that the experience of 2021 was by no means incompatible with the projections of Table 1. 2021 was also notable for a number of achievements, such as the first fully private mission to the International Space Station, the first fiction film to be filmed in orbit, the largest number of people in orbit at one time, the oldest and youngest people officially to travel beyond the Kármán Line (the ‘edge of space’), and the first occupation of China's Tiangong space station. Such a proliferation of ‘firsts’ is consistent with a process that is at the beginning of an expansion phase.

5. Conclusion

This paper has shown how economic cycles can be modelled in terms of ‘discovery processes’, which involve oscillations between an innovation / exploration phase and a production / exploitation phase. In the case of the Kondratieff cycle, where the economic dynamic is accompanied by a political dynamic, the model can incorporate an additional interaction involving feedback between competition and production / exploitation, and this further drives the oscillation. This represents the beginning rather than the completion of a research programme.

It has been assumed that the fundamental relationships are between fractional changes in the quantities of interest, so that a given fractional change in one quantity produces a corresponding fractional change in another quantity. This results in equations in which the variables are logarithms of the relevant quantities, and it means that, while the variables can take on negative values over the course of the cycle, the underlying quantities are always positive. This in turn means that their cumulative totals (e.g., number of inventions) follow a logistic-like curve, which matches empirical findings.

The formalism used for the analysis has been the simple harmonic oscillator, whose behaviour is straightforward to understand. It is unlikely that the regular sinusoidal oscillations predicted by such a model are applicable in the real world, where the duration, amplitude and waveform of the oscillation typically vary from one cycle to the next. The value of the simple model is to improve intuition about the socio-economic processes that result in cycles.
To some extent deviations of real data from the model's idealised behaviour may be explained in terms of random noise or the admixture of other processes. However, it may also be that the model's match to data could be improved by basing it on other mechanisms that involve lags and negative feedbacks and thus generate oscillations. For example, the relationships between the variables might be expressed better as a set of Lotka-Volterra equations, which have been used to model predator-prey cycles.

By adopting the insight of other researchers, the duration of the oscillation has been linked to the human generation time. It was suggested that behavioural change is achieved more readily by the influencing, for example through market forces, of uncommitted youngsters as they enter the socio-economic world than by the conversion of those already enmeshed in existing socio-economic networks. Change is thus controlled by the ageing process and by the resulting turnover of populations. In this respect, the specific analysis used here adopted some simple and stylised assumptions. It is an area where further investigation of the propagation of socio-economic adjustments and of the speed at which generations replace each other could improve the model's accuracy and predictive potential.

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Appendix 1

Number of Persons in Orbit (2020–2021)

This appendix shows the calculation of the mean number of persons in orbit in 2020 and 2021.

Table 2. Persons in orbit during 2020. An arrive date of 01/01/2020 indicates someone already in orbit at the beginning of the year, while a depart date of 31/12/2020 indicates someone who was still in orbit at the end of the year

Name	Arrival	Departure	Days
Koch Christina Hammock	01/01/2020	06/02/2020	36
Skvortsov Aleksandr Aleksandrovich Jr.	01/01/2020	06/02/2020	36
Parmitano Luca Salvo	01/01/2020	06/02/2020	36
Morgan Andrew Richard	01/01/2020	17/04/2020	107
Skripochka Oleg Ivanovich	01/01/2020	17/04/2020	107
Meir Jessica Ulrika	01/01/2020	17/04/2020	107
Ivanishin Anatoli Alekseyevich	09/04/2020	22/10/2020	196
Vagner Ivan Viktorovich	09/04/2020	22/10/2020	196
Cassidy Christopher John	09/04/2020	22/10/2020	196
Behnken Robert Louis	30/05/2020	02/08/2020	64
Hurley Douglas Gerald	30/05/2020	02/08/2020	64
Ryzhikov Sergei Nikolayevich	14/10/2020	31/12/2020	78
Kud-Sverchkov Sergei Vladimirovich	14/10/2020	31/12/2020	78
Rubins Kathleen Hallisey	14/10/2020	31/12/2020	78
Hopkins Michael Scott	16/11/2020	31/12/2020	45
Glover Victor Jerome	16/11/2020	31/12/2020	45
Noguchi Soichi	16/11/2020	31/12/2020	45
Walker Shannon	16/11/2020	31/12/2020	45
TOTAL			1559
Mean number of persons in orbit over year (= TOTAL divided by 365 days)			4.3

Source: Spacefacts 2022.

Table 3. Persons in orbit during 2021. An arrive date of 01/01/2021 indicates someone already in orbit at the beginning of the year, while a depart date of 31/12/2021 indicates someone who was still in orbit at the end of the year. Note: ‘in orbit’ excludes those who entered space in brief, sub-orbital launches. ISS – International Space Station

Name	Facility	Arrive	Depart	Days
Ryzhikov Sergei Nikolayevich	ISS	14/10/2020	17/04/2021	185
Kud-Sverchkov Sergei Vladimirovich	ISS	14/10/2020	17/04/2021	185
Rubins Kathleen Hallisey	ISS	14/10/2020	17/04/2021	185
Hopkins Michael Scott	ISS	16/11/2020	02/05/2021	167
Glover Victor Jerome	ISS	16/11/2020	02/05/2021	167
Noguchi Soichi	ISS	16/11/2020	02/05/2021	167
Walker Shannon	ISS	16/11/2020	02/05/2021	167
Hopkins Michael Scott	ISS	16/11/2020	02/05/2021	167
Glover Victor Jerome	ISS	16/11/2020	02/05/2021	167
Novitsky Oleg Viktorovich	ISS	09/04/2021	17/10/2021	191
Kimbrough Robert Shane	ISS	23/04/2021	09/11/2021	200
McArthur Katherine Megan	ISS	23/04/2021	09/11/2021	200
Hoshide Akihiko	ISS	23/04/2021	09/11/2021	200
Pesquet Thomas Gautier	ISS	23/04/2021	09/11/2021	200
Dubrov Pyotr Valerievich	ISS	09/04/2021	31/12/2021	266
VandeHei Mark Thomas	ISS	09/04/2021	31/12/2021	266
Shkaplerov Anton Nikolayevich	ISS	05/10/2021	31/12/2021	87
Chari Raja Jon Vurputoor	ISS	11/11/2021	31/12/2021	50
Marshburn Thomas Henry	ISS	11/11/2021	31/12/2021	50
Maurer Matthias Josef	ISS	11/11/2021	31/12/2021	50
Barron Kayla Sax	ISS	11/11/2021	31/12/2021	50
Nie Haisheng	Tiangong	17/06/2021	17/09/2021	92
Liu Boming	Tiangong	17/06/2021	17/09/2021	92
Tang Hongbo	Tiangong	17/06/2021	17/09/2021	92
Zhai Zhigang	Tiangong	15/10/2021	31/12/2021	77
Wang Yaping	Tiangong	15/10/2021	31/12/2021	77
Ye Guangfu	Tiangong	15/10/2021	31/12/2021	77
TOTAL				3874
Mean number of persons in orbit over year (= TOTAL divided by 365 days)				10.6

Source: Spacefacts 2022.

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