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Creating a simulation and generating results is relatively straightforward, mathematically speaking. Yet an important part of validating the principles behind a simulation are a favorable fit with actual historical data. Sometimes data is sparse. Sometimes it is plentiful, but not in a form that facilitates an easy comparison. Authorities the validity, relevance or accuracy of the data itself is in doubt and must be carefully evaluated.

 

Quantitative Challenges

What can be more difficult than identifying a regime is to identify its beginning and endpoints as well as quantifying the regime. For example, the Bourbon dynasty was disrupted by the French revolution in 1791, yet there were three more Bourbon kings up to the year 1848. Further, the movements behind many regimes begin well before the official birth date of the regime. For example, the family that become rulers of the Carolingian had ruled France in all but name since 700, which would have given it a duration of 287 years (see Table).

General Approach

For modeling, one can adjust the constants involved to produce the best fit for the data. The ways to do so could fill whole volumes in themselves, and are better covered in mathematical texts devoted to that subject. For purposes of this text, adjusting the parameters of the proposed function to provide the best visual fit provides a method that anyone who knows how to use a graphing program can utilize. Although this method is easy to implement, make sure to use the proper units for the constants!

If you do not have any data, this method cannot be used. Also, if you only a small amount of data, or data for only a short time period, be warned that the model could be less accurate.

If you have data that appears to contain a great deal of noise (random variations), is quite inconsistent from period to period or contains a cyclic variation (such as an annual cycle or a regular seven year weather pattern), you may need to smooth out the data. To reduce noise, you can use a moving average smoothing technique. For purposes of this text, you could average the each value with the value immediately before and after it. For cyclical data, you can average over half a cycle before and afterwards. There are much more sophisticated smoothing techniques that can be found in textbooks on various types of forecasting.

Derivative Approach

Full quantitative data for a historical regime is often unavailable, or is only available at great expense of time or money. Yet, historians frequently come across information that is anecdotal or qualitative rather than quantitative. Fortunately it is often possible to convert qualitative data into quantitative data using a trick from calculus. It is nearly always possible to attach somedate to anecdotal information. Often the date assigned can be quite precise.

Major trends can often be identified anecdotally, and numerical dates can be matched to anecdotal data. Therefore, a series of date-trend pairs can be created for whether the regime is growing, reaching a plateau or declining. A table such as that below can be created.

Anecdotal information indicating an increase or a decrease represents a positive or negative slope of an underlying function. Such a slope can be seen as the derivative of that underlying function.  Such slopes can typically be crudely plotted on a meta-velocity versus time graph. Then an underlying function can be proposed that is consistent with the meta-velocity graph. A change in slope indicates meta-acceleration that further indicates the presence of a net meta-force. Hence, even anecdotal or qualitative data can frequently be used to generate a meta-mechanical function.

TABLE: Date-Anecdote Data Pairs for a Hypothetical Regime

An exponential function can be created, whose first derivative function matches the anecdotal date-trend data. This is certainly rough approach, but it can give a first approximation of the quantitative rise and fall of the regime. If the potential and other characteristics can be identified, then a better quantitative characterization can be achieved.

Of course, there may be shorter term upward and downward trends. These can be modeled with a secondary function. Minor victories and setbacks should not be included in trend data for the major regime characterization.

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