Earth System Economics: a bio-physical approach to the human component of the Earth System

The study of humans has largely been carried out in isolation from the study of the non-human Earth system. This isolation has encouraged the development of incompatible philosphical, aspirational, and methodological approaches that have proven very difficult to integrate with those used for the non-human remainder of the Earth system. Here, an approach is laid out for the scientific study of the global human system that is intended to facilitate seamless integration with non-human processes by striving for a consistent physical basis, for which the name Earth System Economics is proposed. The approach 5 is typified by a foundation on state variables, central among which is the allocation of time amongst available activities by human populations, and an orientation towards considering human experience. A framework is elaborated which parses the Earth system into six classes of state variables, including a neural structure class that underpins many societal features. A working example of the framework is then illustrated with a simple numerical model, considering a global population that is engaged in one of two waking activities: provisioning food, or doing something else. The two activities are differentiated 10 by their motivational factors, outcomes on state variables, and associated subjective experience. While the illustrative model is a gross simplification of reality, the results suggest how neural characteristics and subjective experience can emerge from model dynamics, including transient golden ages. The approach is intended to provide a flexible and widely-applicable strategy for understanding the human-Earth system, appropriate for physically-based assessments of the past and present, as well as long-term model projections that are naturally oriented towards improving human well-being. 15 Copyright statement. TEXT


Introduction
Over the past four decades, Earth system science has developed a rich understanding of interactions between the myriad physical, chemical and biological components of our planet (Steffen et al., 2020). By considering the Earth as a single system, which is itself comprised of a hierarchy of mechanistically-interacting subsystems, Earth system science has facilitated the 20 challenge of thinking across vast scales of space and time, and contextualized global change within the long-term evolution of life (Lenton et al., 2011). In its quest to understand planetary functioning, this new science has succeeded in crossing many describes a simple numerical model of the global human system, inspired by simple models of the global carbon cycle (e.g. (Sarmiento and Toggweiler, 1984)), as an illustration of how the framework can be operationalized. Section 6 provides analysis and discussion of the model. Section 7 offers concluding comments. 95 Figure 1. ESE provides a bridge between the Earth system science approach, typified by Earth system models, and the diverse fields of human study.
4. The spatial and temporal dynamics of human interactions with ecosystems and consequences for biodiversity. Tight coupling with physically-based biodiversity models can provide new tools with which to test hypotheses regarding early mass extinctionsdue to hunter-gatherers, or the controls on future threats to ecosystem stability in a spatially-explicit context.

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5. Mechanistic linkages between subjective well-being and the biophysical consequences of societal actions. How could human lived experience vary given different societal pathways and within physical constraints, including coupled Earth System impacts such as climate change and biodiversity loss?
Most of these complex problems have been addressed by other means, especially at local scales, but all remain incompletely resolved. The ESE approach can provide a novel global, integrated view, while prompting new avenues for mechanistic insight.

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The approach is expected to be more widely applicable than indicated by this short list.

Guiding principles of Earth System Economics
In a nutshell, ESE aims to quantify physical aspects of the human-Earth system (state variables), including how the physical state is dynamically altered by human actions (time allocation) and consequences for the nature of human experience. In this section, a few general principles are discussed, as motivation for the framework which follows.

Striving for physical foundations
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 130 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 demograph-135 ics, 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 140 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.

Quantification of activities
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 hours per day. The activities in which a population is engaged determine its impact on the biophysical 150 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, using a screen/computer. The activity may be subjectively enjoyable or unpleasant, depending on the quality of the text and disposition of the reader. The 155 optimal strategy to classifying activities would involve as little subjective interpretation as possible, and be grounded as firmly as possible on 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 160 together include all possible activities available to the population. Thus, the fractional distribution of time between the activities must sum to exactly one. 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.

Subjective experience
Humans live rich inner lives, and individuals can be either filled with joy or tormented by suffering, depending on what 165 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: eleven of the seventeen goals are oriented towards improving the life experience of humans, while only six are oriented toward maintaining physical health, material welfare and non-human aspects of the planet. Given that subjective experience appears to be the : a : top priority for most of humanity, it is explicitly included as an essential component of the ESE approach.

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Despite its importance, the biophysical understanding of subjective experience remains rudimentary (e.g. Alexander et al. (2020)). 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 wellbeing has made great strides in providing large datasets on how people themselves evaluate their life experiences (Diener et al., 2018). These can be considered along two axes: 175 1. affect: 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 (Csikszentmihalyi and Larson, 2014), or by asking a candidate to rank the pleasantness (Gershuny and Sullivan, 2019) or unpleasantness (Kahneman and Krueger, 2006) of different activities.
2. cognitive life evaluation and eudaemonia: for the former of these two :::: these ::::: reflect : time-integratedmeasures, : , ::::: rather :::: than 180 ::::::::: momentary ::::::: aspects :: of ::::::::: well-being. :::: For :::::::: cognitive ::: life :::::::::: evaluations, : the subject is asked to consider their life as a whole, and evaluate their level of satisfaction with it, usually on a 10-point scale. The results are often correlated reasonably well with affect, and can be predicted to some degree from material and non-material variables (Helliwell et al., 2012;Barrington-Leigh and Galbraith, 2019). The term eudaemonia refers :: to a fulfillment of purpose, and is often oriented towards philosophical goals of what life ought to be, rather than one that is desirable on purely hedonic terms (Ryan and 185 Deci, 2001). Although a major concern of society on historical timescales, often addressed through religion, eudaemonia has been less studied in recent years, with less effort dedicated to developing quantitative indices.
These axes of subjective wellbeing 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.

Drawing on all fields of human-related science
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.

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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 (Leshem, 2016). 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 200 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 very distantly related to mainstream economics.

Focus on population-level interactions
ESE focuses on humans at the population level as the primary interactive unit. Of course, human behaviours and experiences 205 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 (Anderson, 1972). What's 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 (Simini et al., 2012;Alessandretti et al., 210 2020).
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 (Wold and Whittle, 1957 could itself be motivated for 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.

Applicability to any point in time
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, 230 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.

Focus on emergent consequences of predictable aspects
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 twelve hours, but are almost completely unpredictable on a timescale of one month. Yet, on a coarser scale, seasonal and even decadal climate forecasts are now reasonably good (Smith et al., 2019).
Similarly, societal dynamics include a vast variety of interacting, nonlinear processes that are extremely challenging to predict, 240 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 direct forcing ::::::: inclusion : of tipping points if they are identified through other means.

Earth System Economics conceptual framework
Humans have an intellectual ability to foresee the future that is unparalleled amongst other forms of life, and an apparently infinite scope to modify their biophysical surroundings. How could these features possibly be captured in a numerical assessment? To paraphrase George Box, the answer is that it can be done through countless ways, none of which is perfect, but some of which can be useful. And, as written in a discussion of Box's aphorism by Truran (2013), 'it may be necessary to create a 250 model that takes a totally different perspective in order to improve upon currently accepted models.' Here, a new perspective on the human system is proposed that is consistent with the ESE principles outlined in Section 3, and forms an intuitive and inclusive structure that aligns well with observational data. To be tractable at the global scale, the framework ::::::: definition : is hierarchical, so that it can be used at a high level of aggregation. The framework is inclusive, encapsulating the entirety of the global human system, while aiming to facilitate the representation of its mechanistic properties.

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At the same time, the categories are conceptually straightforward to expand into disaggregated detail, with as little ambiguity as possible, and spatial disaggregation should be easy to apply. This proposed framework is intended as a superstructure within which analyses or models could be developed, through further work.

State variables
The ESE framework is defined by state variables. Each state variable represents some physical aspect of the human-Earth 260 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 to do so with current technology) and is subject to physical constraints.
physically embodied, but is nonetheless subject to the limitation of 24 hours per day, and is unambiguously defined for a population within a given spatial-temporal domain.
Soma. The living ensemble of human bodies and their bio-physical 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 270 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 (Ascoli, 2015) 275 as well as our responses to stimuli (Lindquist et al., 2012). The biophysical characteristics of our brains lie at the foundation of core societal traits such as knowledge and behaviours, as well as subjective experience (Lindquist et al., 2012;Boyer, 2018).
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 (Sporns et al., 2005)), such as the number of associations encoded by synapses.

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Other possibilities would be topological descriptions of the neural structure, e.g. 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 290 generally co-occur (Barrett, 2017). 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 295 planet (Henrich, 2017). 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, 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 300 organisms, nor does it include waste. Instead, these are considered 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 and rock, the ocean and 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, 305 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 (Gershuny and Sullivan, 2019) for a useful overview). In a simple form, the allocation of time can be considered as the emergent outcome of competing motivations, expressed at the population level. Here :: 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 310 caused directly by the activity (the 'what'). For example, although a cook in a restaurant may be personally working in order to get money, the physical outcome of the action is to produce enjoyable food, and food is therefore the relevant motivating factor.
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, etc.). The variables in this class are simply the fraction of time (e.g. hours per day) devoted to each activity by the population.

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Next, a simple model is presented that illustrates how the ESE framework could be operationalized in a global model.

Model overview
The model considers three activities: sleeping, supplying food to the population (provision), and doing something else (other) . The production of the edible food resource E f ood by living organisms (including agriculture) is given as a fraction φ edible of the total Net Primary Production (NPP, in gCd −1 ); agriculture is not considered dynamically here for simplicity, so φ edible 330 is fixed, and the rate at which the existing E f ood is harvested depends on the fraction of available time spent collecting and providing it to the population, A provision . Neural structures evolve over time, but for simplicity this model does not simulate any feedbacks of the neural structures on motivations or technology. Rather, these cultural / social features are held fixed. Also for ease of interpretation, the mass of provisioning Things T provision is held constant in the simulations.
Model architecture, shown within the conceptual framework of Figure 2. Dependencies are shown as arrows: i) hunger influences time allocation, ii) Time allocation to provision, A provision and the availability of provisioning Things T provision 355 influence the per capita extraction rate of edible food E edible , iii) the extraction of E edible supports the metabolism and growth of human biomass S mass , iv) time allocation between activities A provision and A other influences population affect, X af f ect , v) time allocation influences the population neural structure between N provision and N other .

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m provision = shortage f rac k f ood + shortage f rac ::::::::::::::::::::::::::::: (2) The value of the half-saturation constant k shortage :::: k f ood : determines the relative strength with which the population is motivated to respond to a given shortage, with a smaller value responding more strongly to smaller starving ::::::::::::: under-nourished fractions and saturating more quickly :::::: (Figure :: 4). Shortage is the fraction of the population that obtains insufficient food to meet metabolic requirements, and is estimated by assuming a normal distribution of individual shortages around the average 475 surplus, where the surplus is defined as the difference between the total food supply and the total food required to support the metabolic needs (ω plus maximum potential growth µ max )of the population.

Hankering
Obtaining food is a primary concern for all animals, but they also tend to spend some fraction of time doing other things.
Depending on the species, they might invest time developing burrows or nests, engaging in courtship and mating, or resting in 480 a safe place. Humans, more than any other animal, are characterized by the wide range of activities they engage in : in :::::: which ::: they ::: are ::::::::: motivated :: to ::::::: engage, : other than obtaining food. As the purpose here is to provide a simple illustration, all possible non-provision activities are combined under a single activity, A other . The associated motivation ::: The ::::::::: associated ::::::::::: motivational ::::: factor is termed here the hankering for non-provision activities.
Human activity can then ::::: human ::::::: activity ::: can modify φ edible , increasing it through deliberate modifications including agriculture and aquaculture, or decreasing it by destructively harvesting and over-hunting/fishing. Human activity could also modify NPP, In the second term, λ(d −1 ) represents the consumption of potentially-edible material by all non-human organisms such as other mammals, birds, insects, fungi or bacteria. This non-human consumption is assumed to be first order with respect to E f ood , for simplicity. The decay constant would be expected to vary with food type and environment, but would generally be on the order of weeks.

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The use of linear dependences is sure to be inappropriate, given that there will be an optimum mass of tools per person, optimal resources will be harvested first, and diminishing returns would be expected to lead to a sublinear dependence on A provision S mass (note this is equivalent to labour in the similar Cobb-Douglas production function, which typically has an exponent <1, (Cobb and Douglas, 1928)). This approach could potentially be improved :::: upon : in future.
Next, the human capacity for food ingestion is given by the product of the human population S mass and the sum of the 550 population average biomass-specific metabolic rates ω human : ω : and the potential net growth rate µ. Any excess of food pro-visioned beyond this limit is assumed discarded. An average value of ω human : ω : is calculated assuming a per capita energetic requirement of 10 MJ d −1 and food energy content of 30 kJgC −1 (Alexander et al., 2017). The value of the maximum growth rate µ max , the population growth rate when the rate of food provisioning is non-limiting, influences the transient behavior of the model but not the steady-state outcome, as discussed below. Because µ max is the maximum net growth rate, equal to the 555 birth rate minus the death rate (for constant individual body size), its value reflects both the fertility rates of the population and the mortality due to disease, violent deaths and old age. The fertility rate is dependent on cultural and societal characteristics, while the rate of death depends on cultural and societal characteristics as well as exposure to pathogens. Because the cultural and societal aspects of both fertility and mortality are complex, the model simply considers how the net result decreases below the potential maximum when assuming zero growth among the fraction of the population experiencing a food shortage, so 560 that µ = (1 − shortage)µ max :::::::::::::::::::::::: µ = (1 − shortage f rac )µ max . Food waste is not treated explicitly, but could be considered as an implicit component of the uncertainty in ω human : ω, ::::: along :::: with ::::::: ejested :::: food.

Neural activation 565
For illustration, one metric of subjective wellbeing is used here: the affect balance associated with different activities. It is assumed that a population-average level of affect α occurs under each activity, 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 570 overall average affect. Note that this analysis ignores any sense of eudaemonia that may result from either activity, and is purely hedonic.
Thus, the instantaneous average affect of the population at time t is given by the time-weighted mean of the activity-specific affects, which can be rewritten for this two-activity model as giving a linear decrease with A provision below a maximum affect α other .

Neural structure
A simple model is used for changes in the neural structure of the population, based on two assumptions. First, that the rate of 580 new synapse formation is constant and randomly distributed within the cortex, and second, that only synapses that are being fired will be strengthened and persist (Ascoli, 2015). (Thus, one does not learn how to play piano by riding a bicycle.) 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 modification of ::: The :::: basic ::::::: dynamic ::: by ::::: which :::: time ::::::::: allocation ::::::: modifies : the neural structure .
There could also be overlap between the neural structures of different activities due to commonalities, not resolved here.
It is essential that this quantification says nothing about the functional utility of the structural changes. Many of the ac-595 cumulated synapses may contribute little, or even be deleterious. The processes by which the brain selects and amplifies the functional utility of certain synaptic modifications, while dampening others, remains an important topic of research in neuroscience (Richards and Frankland, 2017). Nonetheless, the fact that synapses are strengthened in response to activation is well-established (Ascoli, 2015) and it is expected that future work can improve on this crude representation.

Approach to steady state population
When initialized from a population density well below the steady state value, the human population grows near-exponentially ( Fig. 5 a). The food biomass is drawn down (Fig. 5 b), generating decreasing yields for the same effort (Fig. 5 c). Hunger increases in response (Fig. 5 d), which drives a greater A provision (Fig. 5 e). The surplus (difference between the solid and dashed line in Fig. 5 f) 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 S mass reaches a plateau (Fig. 5 a). 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 620 :::::::: equivalent :: to ::: the ::::::: number :: of ::::::: humans, ::::: since ::: the :::: mass ::: per :::::: human ::::: could ::::::: change.   6.2 Dependence on :: of population size on r hunger /r hankering :::::::::::::::: r provision /r other Figure 6 shows the same experiment shown in Fig. 5, as well as a second experiment in which a single parameter value was changed: r hankering ::::: r other was increased by a factor of 4. This increase reflects a greater motivation within the population to engage in A other , rather than A provision . Such a motivation could reflect a desire for leisure, a societal focus on monumental 625 architecture, or a culture of learning -these distinctions are not resolved here.
The higher r hankering ::::: r other : (relative to r hunger :::::::: r provision ) results in a smaller population size at steady state (Figure 6 a).
This occurs even though the hunger ::: 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 (Figure 6 b), resulting in a greater provisioning efficiency ( Figure 6 630 g). The greater allocation of time to other activities results in a large contrast in the neural structure, with N other much greater than N provision in the population with high r hankering ::::: r other (Figure 6 i). Additionally, the steady state affect is greater with high r hankering ::::: r other (Figure 6 j), given the assumption that other activities provide higher affect than provisioning. Thus, the high r hankering ::::: r other : 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 r hankering :::: r other ).
During the initial population growth phase, A other remains relatively high, since food is abundant and hunger is low. This allows the development of N other , indicating a more diverse neural structure within the population, and supports a high level of affect. However, as food limitation approaches, hunger increases :::: food :::::::: shortages ::::::: increase and the low r hankering ::::: r other : causes the population activity to shift rapidly to A provision . The N other is no longer maintained at the high level, and the affect drops.

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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 (Baldry, 1952) 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 the ability to devote abundant time to :::: time ::: for other activities such as learning, producing art and building 645 public works.

Conclusions
The global human system can appear overwhelmingly complex, which has contributed to the general hesitance to include it within Earth System ::::: system : science on a common footing with the atmosphere, ocean, terrestrial ecosystem, marine ecosystem and cryosphere. The first part of this paper (sections 2-4) has laid out a simple but inclusive approach, focused on observable, 650 biophysical quantities, intended to provide a scalable global perspective and help build a common footing by bridging the natural-social science gap. The ESE approach simplifies the human system by boiling it down to what humans are doing with their time, and what are the biophysical outcomes of those activities, :::::::: including ::: the :::::::: outcomes ::: on :::::: humans ::::::::: themselves. It is hoped that, by focusing on these key elements, a useful body of work can be developed that will provide a novel vision ::::: novel :::::: insight on humanity's place within the Earth system.

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The second part of the paper (sections 5-6) illustrated the ESE approach with a numerical model, of a type that has proven highly useful in carbon cycle science: inclusive, based on a small number of simple principles, and focused on emergent properties. The model dynamically simulates , for the global human population, the ::: the partitioning of available time between provisioning food and doing something else, according to motivations that reflect the net outcomes of socially-and culturallydependent responses to state variables. Although the model ignores many important features (e.g. seasonality, agricultural 660 dynamics, food storage, tools and machinery) and was not comprehensively calibrated with data, it illustrates a :: one : hypothetical mechanism for producing golden ages through the coupled interaction of time allocation with ecological feedbacks.

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Code availability. All MATLAB code used to run the model and generate figures is available for download from the Zenodo archive at http://doi.org/10.5281/zenodo.4660554.
Author contributions. EDG is the sole contributor.
Competing interests. The author declares no competing interests.