The world’s top empire area has grown in three distinct phases, reflecting shifts in message speeds. But the millennial trend has been exponential growth. If this 5000-year trend continued, a single world state would form around 4400. The most populous state’s share of world population also has increased exponentially, pointing to a single world state around 5300. The combined date is around 5000. Projections are not predictions, but still, if some people worry that the United Nations is trying to become a world government, while some others hope for it, they need not hold their breath. If the past offers any guidance whatsoever toward the future, a single world state is highly unlikely much ahead of 3000. Empires form where people are. Hence, the top shares of world population exceed the top shares of world dry land area. They do so in a logically predictable way: the square root law of people empires. The most populous state’s share of the world population tends to be the square root of its share of world dry land area. The law does not apply to “area empires” – those that are the largest but not the most populous.

Our book was written during the COVID pandemic. As a result, it was natural to include a chapter on this topic. In line with the overall theme of our book, we highlight aspects close to the understanding and communication of risk. Topics included in more detail are the inherent danger of exponential growth and the need for adhering to the precautionary principle when faced with a new, possibly catastrophic and hence not yet widely understood, type of risk. The precautionary principle enables decision-makers to adopt measures when scientific evidence about an environmental or human health hazard is uncertain and the stakes are high. A question we address to some extent is whether this pandemic happened totally unexpectedly; was it a so-called Black Swan? We present evidence that it most certainly was not. We give examples of early warnings from scientific publications, highly visible presentations in the public domain as well as regulatory measures in force to absorb the consequences of a possible pandemic. In discussions around risk, numbers, especially large ones, and also units of measurement play an important role; we offer some guidance here.

Utilitarian conservation focuses on a few ecological processes: population regulation in resource-limited systems, succession, predation, and competition. This approach assumes that nature tends toward equilibrium. According to this balance-of-nature mindset, populations are regulated by density-dependent processes. Exponential population growth can generate high numbers quickly, but competition for limiting resources generally keeps populations near the carrying capacity of their environment. In the absence of predation, however, populations may erupt, deplete their food supply, and crash. Similarly, plant associations go through predictable sequences of seral stages culminating in stable climatic climaxes that are able to reproduce themselves indefinitely unless in the absence of disturbances such as fire. Plant associations are groups of interdependent species that all react in the same way to their environment. Utilitarian conservation focuses on keeping populations of economically valuable species such as game animals and commercially harvested trees in balance with their environment.

This is the first of five chapters on ecological modelling and presents basic homogenous (absence of spatial structure and variability among individuals) and deterministic (absence of stochasticity and randomness) population models. The first model describes unlimited exponential growth, which is followed by the introduction of intra-specific competition and density dependent growth. Two types of dynamics are considered: continuous in time and discrete in time. It is demonstrated that the time-discrete formulation can lead to chaotic population dynamics which in ecological models can be caused by scramble competiton where individuals share limited resources rather evenly so that all individuals suffer from the lack of resources. Opposed to this is contest competition where the share of the resources is uneven, so a few winners reproduce and/or survive, and the emerging population dynamics are not chaotic.