Patterns in war dynamics signalled collapse in 1939

This study shows that during the period 1495-1945 the International System produced a finite-time singularity dynamic that was accompanied by four accelerating cycles; each cycle consisting of a relatively stable period, followed by a systemic war ( a critical period). See below figure.


This figure shows the finite-time singularity dynamic accompanied by four accelerating cycles that unfolded in the International System during the period 1495-1945 (Data from Levy, see downloadable study on this website for more details).

Wars can be considered tension (energy) releases of the System; efforts of the System to maintain a functional balance.

Until 1939, Europe was the core of the anarchistic System, but at that point in time collapsed because of its (increasing) inability to regulate the accelerating build-up of tensions in the System.

This study shows that the collapse of the System in 1939 (resulting in the fourth systemic war, the Second World War, 1939-1945) was ‘announced’ by a number of patterns in the war dynamics of the System (1495-1945). In this article I discuss these patterns.

Synchronised increase of the frequency and amplitudes of successive systemic wars (cycles)

During the unfolding of the finite-time singularity dynamic (1495-1945) the frequency of the (accelerating) cycles and their amplitudes (that is the severity/intensity of systemic wars) simultaneous developed towards ‘infinity’. ‘Infinity’ would (theoretically) mean ‘perpetual’ systemic war, and the release of infinite amounts of tensions and destructive energy (assuming the System could produce these levels of tensions and energy). This study shows that the frequencies and amplitudes of the four cycles accelerated with the same factor towards infinity. This was an unsustainable dynamic that would result in the collective self-destruction of the System, and was avoided through a ‘phase transition’. The fourth systemic war (the Second World War, 1939-1945) constituted this phase transition ( I discuss later in this article).


This figure shows the development of a number of properties of successive relatively stable periods (cycles) of the finite-time singularity dynamic (1495-1945). Remarkable, but no coincidence, is that all properties regularly developed towards ‘nil’ during the fourth relatively stable period (1918-1939), shortly before the collapse of the anarchistic System (Europe) in 1939.

Increasing robustness

During the four successive relatively stable periods (international orders), that typically preceded (four) systemic wars, the number of non-systemic wars (orange line) as well as the non-systemic war frequencies (grey line), ‘at the same time’ decreased about linearly to almost ‘nil’ during the fourth relatively stable period (1918-1939).

This development shows – I argue – that the System was increasingly unable to release tensions through non-systemic wars: The System became in other words increasingly robust to disturbances (incidents and events) during relatively stable periods.

However, despite the increasing robustness of successive international orders, the System kept producing tensions at an accelerating rate. As a consequence more tensions were ‘necessarily’ released during systemic wars (as discussed above), an effect that also negatively affected the life spans of successive relatively stable periods (international orders).

Increasing fragility: ‘robust yet fragile’

The decreasing life spans of successive relatively stable periods is closely related to their increasing robustness, as just mentioned. Except for the life span of the second relatively stable period (cycle), the life spans of successive relatively stable periods decreased regularly to about ‘nil’ during the fourth relatively stable period (1918-1939). I argue that the life span of the second relatively period was temporarily distorted, a subject I will discuss in another article.

The decreasing life spans of successive relatively stable periods point to the increasing fragility of successive international orders; to their decreasing ability to maintain them selfs in a particular stability domain (that is a particular international order).

This study shows – as is also the case with certain ecosystems – that increasing robustness and fragility (a phenomenon also referred to as ‘robust yet fragile’) go hand in hand, and in fact are two sides of the same coin.
Increasing organisational and ‘physical’ stability

There are yet two other remarkable properties of the System that developed very regularly during the unfolding of the four accelerating cycles (1495-1945): (1) the linear increase of the organisational stability of successive international orders, and (2) the increase in the stability of the ‘physical’ structures (the shape and sizes) of states. These properties concern respectively the (increasing) permanence of Great Powers in the System, and of the shape and sizes of states in the System (Europe).

First I will elaborate on the linear increase of the organisational stability of the System.

Organisational stability

International orders are the outcome of systemic wars, and contain a set of rules (and accompanying institutions) that are designed to regulate the interactions between states in the System. However, International Orders are also designed to maintain the status quo of the System (the international order that is in place) in the interest of the great powers that used their powerful and influential positions to impose the new order, and its rules and institutions. The maxim ‘the winner takes it all’ – at least a number of privileges – applies to anarchistic systems. These privileges – that are embedded in international orders – produce – what I name – a ‘powerful-become-more-powerful effect’. Great Powers use their influential and powerful positions during systemic wars – if they win – to ensure the implementation of favourable international orders that (especially) promote their interests. By doing so, these states can further increase their powerful positions, and push their ‘agendas’.

Great Britain became the most influential Great Power during the four successive cycles (1495-1945) through this effect; Great Britain emerged as a ‘winner’ from all four systemic wars, and was able – by means of the powerful-become-more-powerful effect – to implement international orders that (in particular) promoted British interests. Capitalism, democracy, and free trade are (to a high degree at least) British ‘inventions’ and interests, and ultimately became the foundations of the European Union. From a system-dynamics perspective these type of dynamics are also referred to as ‘path dependence’ and ‘lock in’.

The ‘ultimate’ position of power and influence Great Britain step-by-step, systemic war  by systemic war, achieved in the International System (in 1939), also explains Britain’s reluctance to join the European Economic Community (eventually in 1973), and decision to leave the European Union in 2016 (Brexit): Great Britain became a victim of its own success, and was ‘never’ really prepared and able to adjust itself to a subordinate role (to supranational institutions) and accept other European states on equal terms.

Britain’s answer to Europe’s struggles – Brexit – is to leave the European Union, and to try to re-establish itself as an autonomous Great Power. This particular subject I will discuss in another article in more detail.

The point now is that during four successive international orders – by means of the powerful-become-more-powerful effect – the number of Great Power status changes in the System decreased about linearly as weel  (yellow line). A Great Power status change is a change in status from non- Great Power to Great Power or vice versa (see Levy).

The Great Power status dynamics decreased to ‘nil’ shortly before the collapse of the System in 1939.

‘Physical’ stability

At the same time as the Great Power status dynamics decreased to nil during the period 1495-1945, the number of states in Europe decreased from circa 300 diverse and loosely ‘units’ in 1495, to about circa 25 highly connected and highly standardised states in 1939.

Preceding the fourth systemic war (the Second World War, 1939-1945) Europe (and states in Europe) achieved their final structures: significant adjustments to the sizes and shapes of states was accomplished.

Ultimately – shortly before the Systems collapsed in 1939 –  the size distribution of states could be best described with a power-law; a power-law distribution implies fractal structures.
Fractals are self-similar structures. Fractals often point to optimisation of distribution processes.

I argue that the fractal size distribution of states is no coincidence and also the result of the application of physical laws. Ultimately – by means of these fractal structures – the production of tensions in the System (Europe) could be minimised (as far as that was possible), and their release be optimised.

Various fractal structures in the System are closely related

During the period 1495-1939 ‘fractal’ state-structures were carved out during (especially) three systemic wars, by means of the deployment (distribution) of destructive energy. Systemic wars are manifestations of criticality of the International System, I argue. Typically, systems at critical points have fractal structures.

Furthermore, during the period 1495-1939 – and that also is a related phenomenon – states developed military organisations with fractal structures, that were optimised to deploy destructive energy.

In short: Systemic wars (implying criticality), fractal state structures in Europe (carved out by means of systemic wars) and fractal military organisations (‘doing the fighting’, the distribution of tensions through the deployment of destructive energy), are closely related phenomenon, and not more (and not less) than the application of physical laws.

Collapse of the System had become unavoidable in 1939

In 1939 the anarchistic System (more precisely: its core, Europe) reached a singularity in finite time (1939), and a number of variables – properties – simultaneously reached ‘infinite’ – and impossible – values: (1) the frequency of systemic wars, (2) the destructive energy (tensions) that had to be released during systemic wars, (3) the robustness and (4) fragility of relatively stable periods, and (5) organisational and (6) ‘physical’ stability of the System.

At that point -1939 – energy (tensions) in the System could no longer be put to work to implement an upgraded anarchistic order, without causing collective destruction. The only option was further integration of states, requiring a phase transition to non-anarchistic structures.

The fourth systemic war (the Second World War, 1939-1945), was instrumental in this phase transition, including in the simultaneous implementation of a first global international order, and the merging of core (Europe) and non-core of the System.

The properties of the four accelerating cycles that accompanied the first finite-time singularity dynamic clearly signalled the collapse of the anarchistic System in 1939.