Foremost, ESE strives for a grounding in quantifiable, physical terms. Physical variables exhibit persistence over time, and physical processes impose firm limits on possible rates of change, leading to dynamic predictability. Physical variables also lend themselves to strict definitions, which can prevent double counting while simultaneously helping to ensure inclusivity. Much of the predictive success of natural sciences lie in their ultimate recourse to physical variables, which provide pathways to diverse insights whether starting from biology, physics, or chemistry. For example, the conservation of mass, momentum, and energy play essential roles in many branches of Earth system science, from atmospheric circulation to ice sheet motion and sea level rise. Ecosystem and biogeochemical models benefit from the understandings of living processes as molecular interactions writ large.

That said, the aim to ground the human system in physical quantities is not trivial. For some things – population demographics, cars, infrastructure, fossil fuel consumption – it is straightforward. But for many of the most fascinating and important aspects – such as behavioural motivations and subjective experience – the biophysical bases remain vaguely described. Operationally, it will always be necessary to use coarse approximations for these (and other) unresolved or poorly understood processes, a common strategy in Earth system models, such as the representation of cloud physics with empirical parameterizations. These parameterizations are always unsatisfying, but the fact that they are explicitly recognized as unsatisfactory and can ultimately be replaced by more physically grounded mechanistic understandings identifies a direction for progress. Resolutely abstract variables, on the other hand, resist connection to complementary scientific insights and reinforce disciplinary silos. Thus, the important thing is that strengthening the physical foundation is ever present as a central goal of ESE: that long-term progress can be made by improving the physical representation of all aspects of the human system through improved observations and theoretical development.

The diversity of human endeavours can be overwhelming and might appear to defy a recourse to conserved quantities in the way that the motion of fluids is linked to momentum and density through the Navier–Stokes equations. However, there is no question that the amount of time available to each human is a strictly conserved quantity. All humans engage in some form of activity for exactly 24 hd-1. The activities in which a population is engaged determine its impact on the biophysical reality and also play a major role in determining the subjective experience of its individuals. Thus, activities are employed here as the central feature of ESE.

There does not exist a universal system for classifying activities. Even the activity of a reader of a scientific article can be described in many ways, which may include reading, working, thinking, learning, sitting, or using a screen or computer. The activity may be subjectively enjoyable or unpleasant, depending on the quality of the text and disposition of the reader. The optimal strategy to classify activities would involve as little subjective interpretation as possible and be grounded as firmly as possible in physical features, a possibility that could be further developed elsewhere. For the moment, it is sufficient to consider this a difficult and incompletely resolved problem.

In the absence of a universal lexicon of activities, applicable to all humans at all times, a lexicon must be constructed for a particular purpose. An activity lexicon must identify, as unambiguously as possible, a set of mutually exclusive activities that together include all possible activities available to the population. Thus, the fractional distribution of time between the activities must sum to exactly 1. For example, a simple two-activity lexicon would be sleeping and not-sleeping. To be useful, the lexicon should align activities with the outcomes that motivate them, by considering how they modify state variables.

Humans live rich inner lives, and individuals can be either filled with joy or tormented by suffering, depending on what circumstances befall them. Improving the inner life experience of humans has pre-occupied much of society for generations and remains a central goal of global society, as exemplified by the UN Sustainable Development Goals: 11 of the 17 goals are oriented towards improving the life experience of humans, while only six are oriented toward maintaining non-human aspects of the planet. Given that subjective experience appears to be a top priority for most of humanity, it is explicitly included as an essential component of the ESE approach.

Despite its importance, the biophysical understanding of subjective experience remains rudimentary (e.g. ). It will take many years of additional research before quantifications are available to assess human experience that rival, for example, our ability to quantify the concentrations of trace gases in the atmosphere. Nonetheless, the field of subjective well-being has made great strides in providing large datasets on how people themselves evaluate their life experiences . These can be considered along two axes:

Affect: this refers to the momentary emotions felt throughout the day, sometimes assessed by asking a subject whether they felt positive or negative emotions (e.g. laughed, cried, felt angry) over some preceding time interval or by asking a candidate to rank the pleasantness or unpleasantness of different activities.

These axes of subjective well-being do not capture all that is important to human experience, and the difficulty of comparing assessments between cultures and languages cannot be taken lightly. But it appears likely that the quantitative basis for constructing population-level assessments of life experience will continue to improve as time progresses.

Many disciplines study humans, including the core social sciences of economics, anthropology, sociology, and psychology, as well as history, medicine, law, business, and education. All of these disciplines can provide useful insights on the global human system. For this reason, ESE aspires to establish common ground that is compatible with aspects of all fields of human study, by explicitly considering the physical foundations that underly them.

So why use the term “economics”? In its modern use, this term has become narrowly associated with the distribution of scarce resources, the production and consumption of goods and services by firms and households, and monetary exchanges. However, the origin of the word, from the Greek oikonomia, referred to managing the home in a rational way in order to benefit its occupants . The root oiko is also the basis of “ecology”, study of the home. The aim of the current proposal is to provide an additional means for holistic, science-based perspectives to assist in rational decision-making that can improve the management of the wealth of our common home, the Earth system, for the benefit of its inhabitants. Hence, the usage here is consistent with the original Greek term. Nonetheless, it should be born in mind that ESE is only distantly related to mainstream economics.

ESE focuses on humans at the population level as the primary interactive unit. Of course, human behaviours and experiences all actually happen at the individual level. But just as the dynamics of a fluid can be usefully described without resolving the motions of individual molecules within it, population characteristics can be usefully described without resolving individual interactions, and symmetry breaking can lead to fundamentally different behaviour across scales . What is more, these population characteristics can show greater predictability when the emergent result depends on well-behaved statistical distributions of individual behaviour, as illustrated by the dynamics of human mobility .

Focusing on the population level does not mean that variability within the population must be ignored. Variability can be incorporated as additional information that describes the variability in a parameter, such as a probability distribution function. For example, the distribution of wealth within a population can often be approximated as a power law, for which only a single parameter (the exponent) needs to be defined .

A great deal of human study is oriented towards understanding how social activities are coordinated and the means by which the cooperative activities of many individuals can be optimized. The mechanisms by which this coordination occurs underpin many fascinating aspects of culture, economics, management, and law, but are not the target of enquiry here.

Instead, ESE is characterized by a focus on the what and why of human activities. Here, “what” refers to the final net outcome of an activity, or complex of cooperative activities, in physical terms. The “why” refers to the ultimate motivations for undertaking the activity, again in relation to the final net outcome in the case of a complex of coordinated activities. For example, the final outcome of creating farming tools, tilling soil, sowing seeds, tending plants, and harvesting crops is to provide food (what). The motivation for this is a hunger-driven need for food (why). Thus, ESE aims to circumvent the complexity of immediate, individual motivations for component activities (such as whether the work is done for pay, which could itself be motivated by material consumption, which itself could be motivated by a desire to raise social standing) by considering the net outcome of any set of activities as the relevant motivating factor.

It could be easier to design a conceptual system exclusively for the present day, with which we are intimately familiar, than one which works equally well back to medieval times or the Late Pleistocene. Yet, if we aspire to consider the distant future, many decades or centuries hence, this ability must be a bare minimum requirement, since presumably the future could hold many revolutionary changes that defy the imagination today. The ESE approach strives to be applicable across the full temporal scope of human existence, enabling hindcasts to test dynamical hypotheses against historical observations as well as to explore hypothetical future projections.

Most aspects of complex systems, including the human–Earth system, are unpredictable. But within this sea of unpredictability lie islands of predictability. For example, the chaotic processes that determine daily weather can be approximated well enough to provide a very detailed forecast over the next 12 h but are almost completely unpredictable on a timescale of 1 month. Yet, on a coarser scale, seasonal and even decadal climate forecasts are now reasonably good . Similarly, societal dynamics include a vast variety of interacting, nonlinear processes that are extremely challenging to predict but within which occur more predictable aspects. Thus, ESE strives to identify the more robust, least unpredictable aspects of the system, seeking insights on the emergent results of their interactions. Societal, cultural, and economic characteristics of populations are described through the simplifying lens of how they impact physical variables and time allocation. The roles of the more unpredictable aspects can then be assessed through the quantification of structural and parameter uncertainty, the use of probability distributions, and the inclusion of tipping points if they are identified through other means.

The ESE framework is defined by state variables. Each state variable represents some physical aspect of the human–Earth system, living or non-living. Each variable could be measured and quantified over some spatial and temporal domain (at least in theory, even if impractical or impossible with current technology) and is subject to physical constraints.

The highest-level grouping of six variable classes, proposed here, is illustrated in Fig. 2 and elaborated below. The five variable classes in the outer ring include everything on the surface of the Earth and can therefore be thought of as a conceptual superstructure within which more detailed subdivisions can be resolved. The final state variable class, time allocation, is not physically embodied but is nonetheless subject to the limitation of 24 hd-1 and is unambiguously defined for a population within a given spatial–temporal domain.

Soma. This refers to the living ensemble of human bodies and their biophysical characteristics, including microbiota. The Soma determines the biogeochemical fluxes required to maintain the population, including food and water consumption as well as the production of heat and waste. It also includes properties reflecting the health status of the population (including symbiotic and pathogenic microbes) and physical fitness. Example state variables here could include the total population biomass (kg), an age-structured population description (number and age), or detailed information on body compositions (e.g. C:N ratio, Fe content).

Neural structure. It is because of the dynamical processes in our brains that we are the dominant species on the planet. Our neurons encode networks that are highly plastic, and this plasticity forms the foundation of our ability to learn as well as our responses to stimuli . The biophysical characteristics of our brains lie at the foundation of core societal traits such as knowledge and behaviours, as well as subjective experience . Thus, state variables describing the brains of humans within a population can be used to represent these essential features. One type of state variable could quantify aspects of associative links within the population connectome (the ensemble of all synaptic connections in a population, sensu ), such as the number of associations encoded by synapses. Other possibilities would be topological descriptions of the neural structure, e.g. the degree of diversity of associations within the population, the quality of the predictive capacity of associations, or links with hormonal and emotional responses. Although the processes underlying the formation of new synapses and their selective destructions remain incompletely understood, they are certain to happen at finite, biologically constrained rates, placing limits on possible rates of learning and modulating the persistence of behaviour, values, and emotional features within a population. Conceptualizing neural structures as real, persistent aspects of the Earth system prompts a novel perspective on the consequences of human time allocation and points toward the underlying physical basis of how systemic, population-level societal changes can occur.

Neural activation. Existing neural structures are activated by sensory stimulus and result in what we experience as thoughts, emotions, and feelings. The sensory stimulus includes external factors such as the landscape, music, food, mobile phone screens, and conversation, as well as interoceptive body status such as hunger and thermal comfort, and in fact both types of sources generally co-occur . This class of state variables represents manifestations of this neural activation. Because the details of the activation itself remain difficult to observe, emergent properties such as subjective well-being measures are most usable at present, though observation technologies are rapidly improving. Neural activation is also conceptually useful as the pathway by which neural structure is modified.

Things. Humans are clever, but it is not through individual cleverness alone that we have become the dominant species on the planet . Rather, we leverage our ability to think by creating entities with novel properties, constructed through shared knowledge and social coordination, that then amplify our ability to modify the physical environment. This includes the fabrication of tools, the construction of buildings and infrastructure, the making of vehicles and airplanes, and the writing of books and computer code. The Things class includes all of these and is defined as all non-living entities which are brought into existence as a desired outcome of human activity. As such, the Things class does not include livestock or genetically modified organisms, nor does it include waste. Instead, these are regarded as modifications of the remainder of the Earth system.

Remainder of the Earth system. This includes all living organisms other than humans (including agricultural plants and livestock), the atmosphere, regolith, soil, rock, the ocean, and the cryosphere. These fall within the traditional domain of Earth system science. Although the variables within this class can all be affected by the human system, and many may be very strongly modified (e.g. cows, grapefruit), they do not require human activity in order to persist and/or are living organisms, thereby differentiating them from Things.

Time allocation. The allocation of time between activities is a complex topic, which has been studied in many branches of social sciences (see , for a useful overview). In a simple form, the allocation of time can be regarded as the emergent outcome of competing motivations, expressed at the population level. As discussed above, a motivation is strictly defined as the reason to undertake an activity (the why) that relates to the set of physical outcomes caused directly by the activity (the what). The consequent population-level time allocation, which emerges from the balance of competing motivations, causes changes in state variables including subjective experience according to the context (e.g. the presence of Things, neural structures, climate). The variables in this class are simply the fraction of time (e.g. hd-1) devoted to each activity by the population.

The purpose of the model is to illustrate how linkages can be simulated among the six classes of state variables through dynamical interdependencies. The model focuses on the interaction between a human population and an ecosystem that provides food, with feedbacks mediated by state-dependent motivations that re-allocate time between the activities of collecting food (provisioning) and doing something else (other). The model generates time-varying patterns in population-level state variables, including neural structure and affect, and generalizes many societal features through their influences on motivating time allocation. This simple illustrative model is not intended to realistically capture any particular period of human history but to give an example of how the ESE conceptual framework could guide model construction.

The model is not agent-based and therefore does not simulate interactions amongst entities. Instead, the model considers dynamical changes in state variables, starting from an initial state, according to ordinary differential equations. This distinction is analogous to the distinction between what are referred to as Eulerian and Lagrangian models in fluid dynamics . The approach taken here is equivalent to the Eulerian method, modeling the human population as a field, characterized by its state, rather than trying to resolve the motions of individual particles.

The model includes state variables that fall within the six classes introduced in Fig. 2, as listed in Table 1 and shown in Fig. 3. Each state variable has a single scalar value at any point in time. The two time allocation variables are Aprovision and Aother. Each of these represents a compound activity, comprised of many unresolved component activities.

The entire planet is represented here as a single entity without any spatial resolution, for ease of illustration, similar to the seminal model by . This “zero-dimensional” spatial form is common for a proof-of-concept in Earth system modeling (e.g. ), though it is envisioned that the most useful application for this framework would be on a global grid. The model is discrete in time and is solved numerically through finite differences from a prescribed initial state using forward time steps of 1 week.

First, the population motivational factors are calculated, based on the food surplus and time allocation from the prior time step, and these motivational factors are used to calculate the time allocation for the current time step. Next, the mass flux of provisioned food is calculated as a function of the biomass variables (Efood and Smass) and the time allocation to provisioning (Aprovision), and the biomass is updated to conserve mass while accounting for metabolism. Finally, the neural characteristics are updated, and the subjective experience is recorded, according to the time allocation.

The model considers a few physical features of a global human population, tied together by a novel use of time allocation as the central dynamical variable. Two activities are defined in terms of their physical outcomes (the “what” of the activities). The allocation of available time between the two activities is determined by the relative strengths of their motivational factors within the population.

The first activity, provision, includes all activities required to extract edible organic matter from the environment and distribute it to the population in an edible form. Conceptually this could include hunting, fishing, or farming, as well as any necessary processing and transportation of food. The transfer of biomass between edible food and the human population is strictly conserved, and the model uses realistic values for human metabolic and growth rates. The second activity, other, includes all other non-essential activities in which the population is engaged.

Motivational factors are conceptualized as originating from the individual level (at which state-dependent neural activation would occur), scaled up to population-level changes in time allocation as modulated by social structures. Motivations are formulated as competing influences on time allocation, similar to the dynamics-of-action approach used by but applied here at a population level rather than an individual level. I am not aware of prior works that use the same formulation, but the precise means by which this is achieved are not the focus here. Rather, the goal is simply to simulate internally consistent dynamical links.

A simple model is used for changes in the neural structure of the population, based on two simplifying assumptions: first, that the rate of new synapse formation within the population is randomly distributed at a constant rate within individual cortexes and, second, that synapses that are being fired through activation are more likely to strengthen and persist . Under these two assumptions, the development of strong synapses, which then become important pathways for future thoughts, are dependent on engagement in relevant activities. In this way, the time allocation to activities contributes to the modification of the neural structure.

Finally, one metric of subjective well-being is used here: the affect balance associated with different activities. It is assumed that a population-average level of affect αx occurs under each activity x, as determined by many factors that are not resolved here. Basically, one of the activities is bound to be more enjoyable than the other. Because provisioning generally falls under the category of work, whether or not it is done through the formal economy, it is assumed to incur a lower level of affect. The other activity, although sure to include many sub-activities that are unpleasant, is assumed to incur a higher overall average affect. Note that this analysis ignores any sense of eudaemonia that may result from either activity and is purely hedonic.

The model generates emergent outcomes through the integration of the state-dependent equations. These emergent features include the temporal evolution of food biomass, human population size, time allocation, neural structure, and experience. The details of these features are dependent on parameter choices, which were not exhaustively explored here.

The human population dynamically allocates the available time between the two available activities. This allocation is determined by the motivation to provision food, which is a function of the food supply rate relative to the population metabolic requirements, in competition with the motivation to do something other than provisioning food.

Human behaviour is exceedingly complex and cannot be predicted from first principles. Here, the motivational responses at the population scale are approximated by smooth response functions, reflecting competing tendencies to alter time allocation between activities in response to changes in relevant state variables. The simple model considers two motivational factors – mprovision and mother – each of which has a value between 0 and 1, indicating the relative drive to increase in the fraction of time devoted to the corresponding activity. To represent saturating responses to an input variable, the Holling type 2 formulation is used, since it provides stability and each usage introduces only one additional parameter (k). Each motivational factor is then weighted by a response coefficient r, which reflects the strength with which time is reallocated to the activity in response to the motivational factor.

The r and k parameters are intended to reflect the combined outcomes of individual psychology and societal processes (where societal processes include all cultural, social, political, and economic interactions). Neither of these parameters has a direct equivalence that can be measured precisely, a common occurrence in ecological modeling, and their values are chosen in order to produce reasonable model behaviour. Although they are held constant in the individual simulations shown here, they would not in reality be static properties of the population but could in theory be dynamically linked to neural structure state variables. However this would go beyond the simple scope of the current illustration.

Initial values for state variables were chosen to ensure stable integration. These initial values included a small human population and large food biomass, in order to allow the population to grow continually for a couple of centuries under typical parameter values. Parameter values are given in Table 2.

The model does not use input data to represent time-varying processes.

When initialized from a population density well below the steady-state value, the human population grows near-exponentially (Fig. 5a). The food biomass is drawn down (Fig. 5b), generating decreasing yields for the same effort (Fig. 5c). Hunger increases in response (Fig. 5d), which drives a greater Aprovision (Fig. 5e). The surplus (difference between the solid and dashed line in Fig. 5f) gradually shrinks, until after a couple of centuries the surplus reaches the point at which it constrains the growth rate. At this point the population growth rapidly declines to zero and Smass reaches a plateau (Fig. 5a). The transition from growth to plateau happens more sharply than under logistic growth because the modeled growth rate remains large even as the food surplus shrinks, and the constraint of food limitation on growth is imposed abruptly. This could be unrealistic for populations that have sufficient foresight to slow their growth rate in advance of food limitation but is perhaps realistic for populations in which reproductive rates do not decline in response to declining food surpluses. Note that mass is not strictly equivalent to the number of humans, since the mass per human could change.

Figure 6 shows the same experiment shown in Fig. 5, as well as a second experiment in which a single parameter value was changed: rother was increased by a factor of 4. This increase reflects a greater motivation within the population to engage in Aother rather than Aprovision. Such a motivation could reflect a desire for leisure, a societal focus on monumental architecture, or a culture of learning – these distinctions are not resolved here.

The higher rother (relative to rprovision) results in a smaller population size at steady state (Fig. 6a). This occurs even though the food shortage experienced by the population is the same at steady state: the population simply decides to allocate less time to provisioning because their priority is to engage in other activities. Because they provision less intensively, the food biomass remains more abundant (Fig. 6b), resulting in a greater provisioning efficiency (Fig. 6g). The greater allocation of time to other activities results in a large contrast in the neural structure, with Nother much greater than Nprovision in the population with high rother (Fig. 6i). Additionally, the steady-state affect is greater with high rother (Fig. 6j), given the assumption that other activities provide a higher affect than provisioning. Thus, the high rother experiment produces a smaller population of happier people with a more diverse neural structure.

Figure 6 illustrates an interesting nonlinear dynamic, particularly pronounced in the food-focused population (low rother). During the initial population growth phase, Aother remains relatively high, since food is abundant and hunger is low. This allows the development of Nother, indicating a more diverse neural structure within the population, and supports a high level of affect. However, as food limitation approaches, food shortages increase, and the low rother causes the population activity to shift rapidly to Aprovision. The Nother is no longer maintained at the high level, and the affect drops. One could conceive that such a century-timescale transient would be recalled by a society as having passed through a golden age, such as that mythologized in ancient Greece and frequently echoed throughout history.

This dynamic does not occur under all parameter combinations, and it should be borne in mind that the model is very simple. However, it serves to illustrate a straightforward interaction that would be expected to produce temporary golden ages with abundant food and time for other activities such as learning, producing art, and building public works.