#### Quantitative and Physical History

# Creating And Using Models

#### By Mark Ciotola

First published on February 27, 2019

A model is a hypothesis about how something exists or works. A model could be a small version of something large, such as a table top copy of the Notre Dame cathedral in Paris. Such a model would represent the large, most important features of the cathedral such as the towers and flying buttresses, and possibly representations of some of the more distinctive smaller features such as the stained glass windows.

A model can also be one or a set of mathematical equations that relate one quantity to another. For example, an equation could relate dynasty power to time. Such a model could be refines, such as to represent central versus regional power. We will primarily be concerned with creating quantitative models.

Creating a quantitative model is *really*easy. Just relate two quantities to one other. For example, write the following equation:

\(quantity~of~Roman~empire~soldiers = year~in~CE\).

According that his model, the number of soldiers in the Roman empire is equal to the year in current era years. So in 100 CE (AD), the number of Roman imperial soldiers would be 100. This certainly *is*a model, because it produces results that can be compared with actual data. Historians evaluate the validity of such data, which may come from literary or archeological sources, and then can compare it with the model. A range of uncertainly is estimated. If the model produces a result that *not*within the range of uncertainty for the data, the model is rejected or revised. If the model fits within the range, then it is valid, although not necessarily absolutely correct (no model ever gets proved) or representative of ultimate truth. Generally, models that fit the data the best and are consistent with other valid models tend to be more accepted.

It often requires several attempts to get a valid model, and many attempts to obtain better ones. The above example concerning Roman soldiers can be quickly rejected using commonly available data.

Models can be improved by including additional terms. and changing parameters. For example, adding a baseline number of soldiers, and then a term that might take into account the growth of mercenaries might improve the accuracy of the model.

In history, often the available or accepted data is limited, and uncertainties may be high. So initially, a more pragmatic approach may be to propose models and explore to what extent they might be valid.

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