Mathematical model

How do different conditions and processes in your society interact to influence peace?

How would you describe your society?


This mathematical model is a computer-based visualization tool used to display how different levels of distinct factors interact over time to produce attractor patterns of peacefulness – or high degrees of positive reciprocity between groups – as well as patterns of destructive conflict and violence – or high degrees of negative reciprocity between groups.

To begin, click next below to answer a series of questions about the society you are interested in.

Alternatively, you can click the blue settings button on the top left, to simply adjust the levels of different factors in this society.

Then click “Calculate”.

Based on your responses to the questions (or settings), this mathematical model will display how the levels of different elements in the system change over time. It will display these increases and decreases in the values of each element by changes in the sizes of the fonts for the different factors – some will be very small elements (a decrease), and others larger elements (an increase).

If the text for Positive Intergroup Reciprocity is large, and the text for Negative Intergroup Reciprocity is small, it suggests your society will fall in a relatively peaceful place. If the opposite is true, you might expect a more destructive pattern.

Feel free to experiment with changing the levels of different variables to play with the effects that adjusting the strength of different factors might have on the overall levels of peacefulness of the community!

In physical science, mathematical models can be used to determine how micro-scale individual interactions between parts of a system produce the macro-scale system properties of the entire system. In this mathematical model, each peace factor has a quantitative value determined by its own properties and its interactions with all the other peace factors. Thus, the interactions of all the peace factors can be computed together at once.

Please note that this is a prototype of only one of many versions of our mathematical model. Other versions lead the system to end up in a different final state. The purpose here is to give users an idea of how such mathematical models can contribute to the conversation. In this particular model the strengths of the influences between the factors are fixed. They can be changed in our more complete model available as a Python 3 GUI (tkinter) program on GitHub

By running different mathematical models of sustaining peace, it was found that, over long periods of time, this system reaches only two stable configurations called "attractors": either the positive peace factors (such as Positive Intergroup Reciprocity or Positive Intergroup Goals and Expectations) have high values and the negative factors (such as Negative Intergroup Reciprocity or Negative Intergroup Goals Expectations) are zero, or vice versa.

Theoretical and trial and error studies of mathematical models have told us that the stronger and longer lasting effects of the negative peace factors can be restrained either by including the influence of many additional positive peace factors in the system, or by strengthening "gateway" positive peace factors that play crucial roles in how interactions spread through the whole system. Since there are different ways to achieve a successful peace system this also implies that the best choice of an intervention may be situationally dependent.

Watch this video for more information on operating and interpreting to visualization:

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