# A Mathematical Theory of Statehood and Warfare

Standard

Consider a system S containing state s at time t. At this initial time, the state has certain attributes, call them ai, and certain loose attributes are left within system S. Due to entropy in a closed (or quasi-closed) system, it is the natural tendency of things to change. At the most basic level this means that certain attributes will undergo mutations within state s. Like the biological concept, they can be alterations (in orientation, definition, etc.), insertions or deletions. Thus, the number of changes for any given time will be more than likely positive. However, we must specify three kinds of changes: 1) Systemic changes, which occur as part of the attributes tied to the system itself, 2) Nonessential changes of state, extra ‘baggage’, additions, etc. that are tied to the state as well, and 3) Essential changes of state without which the state would not be referred to as such. These changes would be measured by a rate of change  where ∆t = t’ – t at some arbitrarily and appropriately defined interval of time. E.g. the rate of change of software would have a unit of months while a rate of change of legal system would have a unit of years or decades.

When is reform better, and when is revolution better?

We can predict the likelihood of reform being accepted by the state as the ratio of nonessential changes to essential changes. Nonessential changes are to be maximized: for this is the entire purpose of reform, while essential changes are to be minimized, otherwise that specific state would lose its character. Thus, the equation  represents this ratio and is, as a net effect, to be maximized. Thus we want . This determines how favourable and likely a reform effort is going to be.

The probability of revolution in a system depends on what can be termed the pressure elasticity; that is, the ratio of the rate of change of systemic changes to the rate of change of (total) changes of state. It is a pressure because it is essentially a tendency ‘pushing’ towards a certain point of change. As the ratio increases, the number of systemic changes becomes increasingly large so that ∆si (i.e. si’ – si) << ∆Si (i.e. Si’ – Si); that is, the state, which was established at, and in response to, certain no longer present systemic conditions represented by Si (the new conditions being Si’). Note that since the state is a subelement of the system (at the same organizational level as nonassigned systemic attributes), a systemic change implies a change of state, if the state s is to survive in the new systemic organization S’. Thus, this ratio over a given interval of time, , will determine the likelihood of revolution. A revolution occurs when a state s can no longer sustain itself within the system S’, as it was established in the system’s (relatively) initial configuration S. It can be seen then, that : the changes of state will be so insignificant that they practically amount to no visible effect, increasing the likelihood of non-response to reform and therefore a continuation of this tendency (itself of static character). Revolution is most likely to occur when the two elements of a low visible effect of reform () and  is attained. However, a revolution can be starved off by compensating for the positive systemic rate of change  by an equally large rate of change of state , thus masking the effects of systemic change.

An interesting consequence of this to be observed is that the likelihood of revolution is always positive, so long as there are changes of state (and there always will be due to the constancy of system-level entropy); thus, short outbursts of instability can be seen as a result of a natural tendency of a larger trend of ‘faultlines’ reestablishing themselves, and having a ‘cracking’ effect to let off steam, if the analogy were apt. This is because the universe is by nature homeostatic (resistant to change), since for a closed and quasi-closed system, it generally takes more energy (and therefore more effort and resources) to adapt to this change than to remain static.

Note: here, state refers not just to the traditional geopolitical entity, but also to any form of being in the sense of ‘states of matter’.