At the heart of the Toynbee quote (above) is the question of whether History has Purpose. Are we evolving toward some Utopian End State or is History just a Random Walk or a succession of random steps in time? Actually, both can be true and may not be the only options.
In this post, I present a selective list of countries, during different time periods, that are either a short-term Random Walk or a long-term Random Walk, meaning for the later that there is no observable Attractor Path. The question has fundamentally to do with the question of Stability in Macro-Social System. A Stable System has an End State (desirable or not--the End State could be death). A Random Walk is unstable and does not have a Stationary State.
Countries with Short-term Random Walks
A Short-term Random Walk means that, from year to year, the System State is a function of the t(-1) state plus random error, that is, S(t) = S(t-1) +E(t-1). For the System S(t) = I S(t-1) + E(t-1), the System Matrix is an Identity Matrix, I (see the System Matrix below).
- W_RE Model The World System Short-term Model for the years 0-500 was a Random Walk. You can run the model using R-Code on my Google Site here. See the Measurement Matrix and System Matrix below and the time plot:
Countries with Long-term Random Walks
Notes
- Pasdirtz, G. W. (1981) Instability and Late Nineteenth Century German Development UW-Madison Thesis.
Wikipedia Links
- History the systematic study of the past, focusing primarily on the human past. As an academic discipline, it analyses and interprets evidence to construct narratives about what happened and explain why it happened. Some theorists categorize history as a social science, while others see it as part of the humanities or consider it a hybrid discipline. Similar debates surround the purpose of history—for example, whether its main aim is theoretical, to uncover the truth, or practical, to learn lessons from the past. In a more general sense, the term history refers not to an academic field but to the past itself, times in the past, or to individual texts about the past.
- Arnold J. Toynbee (1889 – 1975) was an English historian, a philosopher of history, an author of numerous books and a research professor of international history at the London School of Economics and King's College London. From 1918 to 1950, Toynbee was considered a leading specialist on international affairs; from 1929 to 1956 he was the Director of Studies at Chatham House, in which position he also produced 34 volumes of the Survey of International Affairs, a "bible" for international specialists in Britain.
- Random Walk a stochastic process that describes a path that consists of a succession of random steps on some mathematical space.
- Attractor Path a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.
- Stability Theory the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions.
- Stationary State with all observables independent of time. It is an eigenvector of the energy operator (instead of a quantum superposition of different energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar to the concept of atomic orbital and molecular orbital in chemistry, with some slight differences.
- State-Space Representation In control engineering and system identification, a state-space representation is a mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time through first-order differential equations or difference equations. These state variables change based on their current values and inputs, while outputs depend on the states and sometimes the inputs too. The state space (also called time-domain approach and equivalent to phase space in certain dynamical systems) is a geometric space where the axes are these state variables, and the system’s state is represented by a state vector.
- R-Programming Language a programming language for statistical computing and data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science.
World (0-500) Random Walk Model
Measurement Model
System Matrix
