Informing the Sustainable Pursuit of Happiness

: Although most people want to be happy, the pursuit of happiness involves an overwhelming number of choices and great uncertainty about the consequences. Many of these choices have signiﬁcant implications for sustainability, which are rarely considered. Here, we present an optimality model that maximizes subjective happiness, which can eventually account for sustainability outcomes. Our model identiﬁes the optimal use of time or energy to maximize happiness. Such models tell people how to invest in domains of happiness (e.g., work vs. leisure) and how to choose activities within domains (e.g., playing a computer game vs. playing a board game). We illustrate this optimization approach with data from an online survey, in which people (n = 87) either recalled or imagined their happiness during common activities. People reported decelerating happiness over time, but the rate of deceleration di ﬀ ered among activities. On average, people imagined spending more time on each activity than would be needed to maximize happiness, suggesting that an optimality model has value for guiding decisions. We then discuss how such models can address sustainability challenges associated with overinvesting (e.g., excessive CO 2 emissions). To optimize happiness and explore its implications for sustainability over long periods, models can incorporate psychological processes that alter the potential for happiness and demographic processes that make lifespan uncertain. In cases where less objective approaches have failed, a quantitative theory may improve opportunities for happiness, while meeting sustainability outcomes. to the third activity allocation (food shopping) can be found by subtracting the time allocated to the ﬁrst and second activities from the total duration (1 h). The maximal cumulative happiness is 48.92 units and corresponds to 13 min of video-chatting, 28 min of food shopping, 19 min of texting, and 0 min of talking on the phone. Additionally, we display a set of strategies that yield at least 95% of the maximal cumulative happiness. their own choices and their related sustainability implications; a di ﬀ erence between the curves for the same activity reﬂects the e ﬀ ect of the intervention. What is the uncertainty in parameters of happiness curves and sustainability implications? Analyze factors that inﬂuence the variance of parameters, such as initial of happiness and the rate of habituation and the associated sustainability implications.


Introduction
Life experience offers a common ground on which most people agree: happiness is worth striving for [1]. No other concept provides a more compelling index of how society promotes or inhibits the enjoyment of life [2]. Happiness eludes many people [3], however, and attempts to find happiness are often misguided [4] and have negative consequences for sustainability. For example, humans are manipulated to make choices that enhance pleasure (hedonic happiness) despite negative impacts on themselves, others, and the environment. These choices include overconsumption or addiction to drugs, services, or technology [5]. To complicate matters, our world changes rapidly through technological interventions, social media, and economic globalization-all of which influence people's values and behaviors. Yet, at the core, humans can be seen as organisms driven by factors that enhanced survival and reproduction in the past. The organs that regulate our emotions were shaped not to benefit individuals or the species, but only to enhance the transmission of genes [6,7]. In the modern world, however, our instincts can promote choices resulting in obesity, depression, distress, anxiety, fear, or morbidity [8,9]. For example, obesity has been linked to behaviors that enhanced fat storage during cycles of feast and famine in the post-agricultural era [10]. Similarly, distress, anxiety, and fear stem from perceived threats of competition or predation [11][12][13].
In contrast to the dangerous and unpredictable environments that shaped our nervous system, modern humans live in societies that cooperate to obtain the resources needed to survive (although not necessarily in an equitable or sustainable way). In developed nations, social services provided by police, schools, and hospitals promote survival and reproduction. In other words, some of the risks to human evolutionary success have been minimized by cooperation [14][15][16]. Thus, social systems leave us with biological machinery for risk and reward that are no longer adaptive in many circumstances [13]. Both brain and endocrine systems drive us in ways that they never could have driven us in the past. In such environments, the behaviors inherited from our ancestors might cause more harm than good, particularly when they reduce sustainability. Researchers must consider happiness in a modern context and develop models to enhance happiness in light of sustainability tradeoffs.
The pursuit of happiness also has major implications for the sustainability of human life. Many pleasurable activities cause people to consume resources and produce waste, thereby reducing sustainability. Some scholars have already recognized the important link between happiness and sustainability [17][18][19][20][21][22]. O'Brien [18] proposed that happiness research could inform sustainability research and practice, while others proposed that sustainability and happiness are complementary goals [23,24]. Tools have been developed to integrate happiness into sustainable forms of development [25][26][27][28] and transportation [29]. Vatovec and Ferrer [30] even created a game that blends the pursuit of happiness with the pursuit of sustainability. Our work seeks to build on these ideas by applying biological models of behavior to the study of happiness and sustainability.
To aid the pursuit of sustainable happiness, we draw insights from quantitative optimality models. Happiness, like any other currency, results from allocating time and energy to competing activities. Borrowing an optimality approach from economists, biologists developed models that predict how organisms should search for resources that enhance survival and reproduction [31][32][33]. Similar models can predict how humans should behave to maximize happiness, while also accounting for tradeoffs with social wellbeing or global sustainability. For example, Kroll and Pokutta [34] considered the combination of activities that would yield the most happiness in a day. Their model describes missed opportunities that occur when one cannot simultaneously engage in two or more activities that yield happiness. To apply their model, however, one must know how people accumulate happiness over time when engaging in potential activities. Static measures of happiness [35][36][37][38] tell us which activities make people happy, which is useful, but not how these activities confer happiness over time. Clearly, some activities confer happiness quickly whereas other activities require a longer investment. These dynamics are important for weighing options for happiness, as well as understanding the consequences of those options for sustainability (e.g., carbon emissions).
To account for temporal dynamics, Sprott [39] proposed mathematical functions to describe changes in happiness following major events. Similarly, Song et al. [40] modeled the temporal dynamics of happiness during periodic stimuli. These studies laid the groundwork for quantitative models that optimize conditions that lead to happiness. Such models complement existing frameworks for enhancing wellbeing (e.g., Keough [38]) and offer the same to sustainability. We build on these efforts to model happiness by parameterizing functions that describe changes in happiness over time. Our model distinguishes between a subjective feeling of happiness in a given moment (instantaneous happiness) and the sum of subjective feelings of happiness over longer periods (cumulative happiness). For instance, running a marathon may yield low (or even negative) instantaneous happiness for the first hour but high instantaneous happiness thereafter, leading to a positive cumulative happiness overall. We parameterize functions of instantaneous happiness with data collected from an online survey, in which people were asked to recall or imagine their subjective happiness during common activities. Then, we use these data to infer the combination of behaviors that either maximize cumulative happiness or guarantee a minimal cumulative happiness for a given period. Not surprisingly, people reported behaviors that fail to maximize happiness according to the model. Finally, we discuss ways to improve the model and develop a predictive theory of happiness for tackling personal, societal, and global issues related to sustainability.

Materials and Methods
To quantify how behaviors influence happiness, we constructed a mathematical model inspired by optimality models from behavioral ecology. The heart of this model is a set of happiness curves (Figure 1), which capture the known psychological phenomenon of habituation [9,[41][42][43][44][45]. We assume an asymptotic function, such that happiness accumulates rapidly at first but ultimately decelerates. Given curves for a set of activities, one can compute instantaneous happiness and cumulative happiness; the latter variable comes from integrating instantaneous happiness data over time. One can also determine how to divide time among activities to maximize happiness and, as discussed later, how to maximize happiness within constraints imposed by sustainability goals. model. Finally, we discuss ways to improve the model and develop a predictive theory of happiness for tackling personal, societal, and global issues related to sustainability.

Materials and Methods
To quantify how behaviors influence happiness, we constructed a mathematical model inspired by optimality models from behavioral ecology. The heart of this model is a set of happiness curves (Figure 1), which capture the known psychological phenomenon of habituation [9,[41][42][43][44][45]. We assume an asymptotic function, such that happiness accumulates rapidly at first but ultimately decelerates. Given curves for a set of activities, one can compute instantaneous happiness and cumulative happiness; the latter variable comes from integrating instantaneous happiness data over time. One can also determine how to divide time among activities to maximize happiness and, as discussed later, how to maximize happiness within constraints imposed by sustainability goals. Cumulative happiness decelerates over time for activities that lasted less than one hour. On average, participants indicated that the activities, particularly those in the lower chart, yielded less happiness and usually reduced happiness within an hour.
To parameterize our happiness model, we asked people to recall or imagine their level of happiness during common activities. These data were collected through Amazon's Mturk software. A survey link was distributed on the server with the intention of obtaining 100 participants, but only 87 people fully completed the survey. Consent from participants was not required because the survey was anonymous. Each participant was asked to imagine engaging in a set of activities with inspiration from Kahneman et al.'s [46] Method of Day Reconstruction (e.g., relaxing in nature or socializing with relatives). We also added other activities one could imagine doing in our modern world (e.g., texting). While imagining each activity, participants scored their instantaneous happiness at set time intervals. The maximum duration of each activity was 1, 2, or 3 h, with corresponding time intervals of 10, 20, or 30 min. Scores were on a scale of −5 to 5, where −5 was extremely unhappy and 5 was extremely happy. Participants also noted whether they would cease the activity before the maximum duration. Respondents took an average of 29 min to answer the 28 questions in our survey. To parameterize our happiness model, we asked people to recall or imagine their level of happiness during common activities. These data were collected through Amazon's Mturk software. A survey link was distributed on the server with the intention of obtaining 100 participants, but only 87 people fully completed the survey. Consent from participants was not required because the survey was anonymous. Each participant was asked to imagine engaging in a set of activities with inspiration from Kahneman et al.'s [46] Method of Day Reconstruction (e.g., relaxing in nature or socializing with relatives). We also added other activities one could imagine doing in our modern world (e.g., texting). While imagining each activity, participants scored their instantaneous happiness at set time intervals. The maximum duration of each activity was 1, 2, or 3 h, with corresponding time intervals of 10, 20, or 30 min. Scores were on a scale of −5 to 5, where −5 was extremely unhappy and 5 was extremely happy. Participants also noted whether they would cease the activity before the maximum duration. Respondents took an average of 29 min to answer the 28 questions in our survey.
We parameterized the happiness curve for each activity by interpolating the data through straight-line sections: each piece of the function is linear. Specifically, we extracted the following Sustainability 2020, 12, 9491 4 of 14 data for each activity: (1) the mean instantaneous happiness at each interval; (2) the mean time to reach maximum happiness; and (3) the mean duration of the activity. Consider one of the activities for which participants reported instantaneous levels of happiness over a 60-min period, which we denote as activity a. Surveys give instantaneous happiness every 10 min, yielding 7 values. Let us consider the mean instantaneous happiness for participants (h a ) at each time (t), where t i = i × ∆t; i ∈ {0, 1, 2, 3, 4, 5, 6}; ∆t = 10 min. We interpolated this mean instantaneous happiness at each time with a piecewise linear function denoted P a (t) defined on t ∈ [0, 60]. For instance, between t i and t i+1 , The cumulative happiness of activity a from time 0 to a period of time, τ ∈ [t k ; t k+1 ], ∀k ∈ {0, 1, 2, 3, 4, 5}, is denoted by H a (τ) and approximated by Given a set of activities, we can calculate the allocation of time to each activity that maximizes the cumulative happiness during a certain period. Here, we constrain the problem by limiting the maximum number of activities to four. We assume the first activity begins when t = 0 and ends when t = t 1 . To simplify the example, we assume that a person can switch between activities immediately, such that no time lag occurs before accumulating happiness from a new activity. Thus, the second activity begins at t 1 and ends at t 2 , the third activity begins at t 2 and ends at t 3 , and the fourth activity begins at t 3 and ends when t = 60 min.
Under these conditions, the cumulative happiness of four activities, denoted C(t 1 , t 2 , t 3 , a 1 , a 2 , a 3 , a 4 ), is The cumulative happiness C(t 1 , t 2 , t 3 , a 1 , a 2 , a 3 , a 4 ) depends on the choice of activities (a 1 , a 2 , a 3 , and a 4 ) and the switching times (t 1 , t 2 , and t 3 ). Importantly, the order of activities does not matter to this model but could matter to more dynamic models that account for favorite activities, habituation, mental state, or other factors. In the present case, however, we need only find the values of t 1 , t 2 , and t 3 and the activities a 1 , a 2 , a 3 , and a 4 that maximize happiness. Note that we do not consider the transit time between two activities (i.e., driving to the gym). For instance, if we considered a transit time between activities, we would remove time from the total time available for activities. For the sake of simplicity, we explore an example in which the transit time is set to 0 and the four activities are fixed: a 1 = video chatting , a 2 = talking on the phone , a 3 = texting , a 4 = f ood shopping . Therefore, the optimal switching times t * 1 , t * 2 , t * 3 are as follows:

Results
As demonstrated, cumulative happiness ultimately decelerated with time (Figures 1-3), such that investing twice the time in an activity yielded less than twice the happiness. This pattern results from a trajectory of instantaneous happiness that has two phases: an initial phase in which instantaneous happiness increases over time and a subsequent phase in which instantaneous happiness decreases over time (Figure 4). This decelerating return on an investment of time means that people should Sustainability 2020, 12, 9491 5 of 14 switch to a new activity before deriving as much happiness as possible from the current activity. For all activities, participants imagined engaging beyond the time required to maximize the instantaneous rate of happiness. We infer this suboptimal behavior by plotting the relationship between the reported duration of the activity and the time when cumulative happiness starts to decelerate ( Figure 5). Interestingly, people tended to overinvest in activities that confer the greatest happiness over a long period. For instance, participants imagined shopping for non-food items for more than 35 min, despite reporting a deceleration in happiness before 25 min. In these cases, happiness might have been maximized by switching to another activity shortly after the peak in instantaneous happiness.
To appreciate the value of switching activities at the best time, consider an example in which the subject must choose how to divide an hour among four activities: video chatting, talking on the phone, texting, and food shopping. When considering the happiness curves for these activities (Figure 6), experience may lead one to go food shopping the entire hour, because this activity steadily increases happiness over time. The optimal solution, however, differs from this simple strategy (Figure 7). To maximize cumulative happiness during an hour, one should video chat for 13 min, text for 19 min, food shop for 28 min, and talk on the phone for 0 min. In other words, given these data, talking on the phone for any time would decrease cumulative happiness. relationship between the reported duration of the activity and the time when cumulative happiness starts to decelerate ( Figure 5). Interestingly, people tended to overinvest in activities that confer the greatest happiness over a long period. For instance, participants imagined shopping for non-food items for more than 35 min, despite reporting a deceleration in happiness before 25 min. In these cases, happiness might have been maximized by switching to another activity shortly after the peak in instantaneous happiness. Cumulative happiness decelerates over time for activities that lasted less than two hours. Activities are divided into two categories: top panel shows activities that occur at home or work, whereas the bottom panel shows several forms of commuting between home and other places. In general, participants indicated that commuting detracted from happiness after less than an hour.  Cumulative happiness decelerates over time for activities that lasted less than two hours. Activities are divided into two categories: top panel shows activities that occur at home or work, whereas the bottom panel shows several forms of commuting between home and other places. In general, participants indicated that commuting detracted from happiness after less than an hour.    two phases during an activity. Here, we depict the curves describing (a) instantaneous and (b) cumulative happiness derived from intimate relations with a partner. During phase 1, (a) instantaneous happiness increases and (b) cumulative happiness accelerates over time. During phase 2, (a) instantaneous happiness decreases and (b) cumulative happiness decelerates with time. Figure 5. Overinvestment in activities. The mean duration of activity imagined by participants was often much longer than the time required to achieve the maximal rate of happiness. Figure 5. Overinvestment in activities. The mean duration of activity imagined by participants was often much longer than the time required to achieve the maximal rate of happiness. To appreciate the value of switching activities at the best time, consider an example in which the subject must choose how to divide an hour among four activities: video chatting, talking on the phone, texting, and food shopping. When considering the happiness curves for these activities (Figure 6), experience may lead one to go food shopping the entire hour, because this activity steadily increases happiness over time. The optimal solution, however, differs from this simple strategy (Figure 7). To maximize cumulative happiness during an hour, one should video chat for 13 min, text for 19 min, food shop for 28 min, and talk on the phone for 0 min. In other words, given these data, talking on the phone for any time would decrease cumulative happiness.

Viable set of happiness
Happiness maximum Figure 6. Activity happiness curves. Happiness curves for four activities included in our survey: food shopping (green), phone conversation (blue), video chatting (red), and texting (black). Figure 6. Activity happiness curves. Happiness curves for four activities included in our survey: food shopping (green), phone conversation (blue), video chatting (red), and texting (black).

Figure 7.
Optimal happiness solution for four activities. Total happiness accumulated during an hour according to time spent on four activities: shopping for food, video chatting, texting, and a phone conversation. Here, we consider the case of no talking on the phone (that corresponds to the optimal solution). Allocation of time to the third activity allocation (food shopping) can be found by subtracting the time allocated to the first and second activities from the total duration (1 h). The maximal cumulative happiness is 48.92 units and corresponds to 13 min of video-chatting, 28 min of food shopping, 19 min of texting, and 0 min of talking on the phone. Additionally, we display a set of strategies that yield at least 95% of the maximal cumulative happiness.

Discussion
Our discussion is organized into three sections, the first considering whether people make choices that maximize happiness. The second considers how scientists might refine quantitative theories of happiness via interdisciplinary and collaborative research approaches. Finally, we discuss Viable set of happiness Happiness maximum Figure 7. Optimal happiness solution for four activities. Total happiness accumulated during an hour according to time spent on four activities: shopping for food, video chatting, texting, and a phone conversation. Here, we consider the case of no talking on the phone (that corresponds to the optimal solution). Allocation of time to the third activity allocation (food shopping) can be found by subtracting the time allocated to the first and second activities from the total duration (1 h). The maximal cumulative happiness is 48.92 units and corresponds to 13 min of video-chatting, 28 min of food shopping, 19 min of texting, and 0 min of talking on the phone. Additionally, we display a set of strategies that yield at least 95% of the maximal cumulative happiness.

Discussion
Our discussion is organized into three sections, the first considering whether people make choices that maximize happiness. The second considers how scientists might refine quantitative theories of happiness via interdisciplinary and collaborative research approaches. Finally, we discuss how such models can enhance decisions that influence happiness in ways that also support a sustainable future.

Do People Make Choices That Maximize Happiness?
Even pleasurable activities can lose their appeal over time, as people habituate to conditions that make them happy [42,47]. The results of our study support this idea, as evidenced by the decelerating shape of happiness curves (see Figures 1-3). Given that respondents reported feeling less happy with a particular activity over time, one could maximize cumulative happiness by switching between activities when instantaneous happiness begins to decrease. To behave optimally, however, one must recognize a potentially small decrease in happiness-easier said than done (see Figure 3). They must also know which activity would lead to greater happiness at any moment. Although people might be unable to optimize happiness in practice, they might improve their happiness by reflecting on the assumptions and predictions of optimality models.
Our model not only predicts optimal behaviors, but it also predicts suboptimal behaviors that yield a certain threshold of happiness. Thus, we can search for suboptimal strategies that yield nearly the same return on investment as the optimal strategy. For example, we defined a set of strategies that confer at least 95% of the cumulative happiness derived from the optimal strategy described above ( Figure 5). Several combinations of activities confer near-maximal happiness, including combinations of two activities such as 20-25 min of texting followed by 35 min of food shopping. In this way, the model provides a means of minimizing the risk of unhappiness as much as a means of maximizing happiness.
The optimal behavior for maximizing happiness depends on the time required to switch between activities. In the example considered above, we assumed that people could switch instantaneously among talking on the phone, video chatting, and shopping for food. However, most activities require Sustainability 2020, 12, 9491 9 of 14 some period of preparation or travel, during which happiness might be sacrificed. Consider a situation in which one must choose between shopping and exercising on a treadmill during an hour (Figure 8). Assuming that the latter activity might require one to travel 30 min between a store and a gym, switching between activities would consume too much time to yield a sufficient benefit. Consequently, one should spend the entire hour performing one activity (in this case, exercising). Alternatively, if one could derive the same happiness by shopping online, one could maximize happiness by splitting the hour between exercising and shopping, assuming that one can eliminate the transit time by accessing the internet from the gym. This scenario illustrates the need to consider how quickly one could switch between activities under realistic conditions. above ( Figure 5). Several combinations of activities confer near-maximal happiness, including combinations of two activities such as 20-25 min of texting followed by 35 min of food shopping. In this way, the model provides a means of minimizing the risk of unhappiness as much as a means of maximizing happiness.
The optimal behavior for maximizing happiness depends on the time required to switch between activities. In the example considered above, we assumed that people could switch instantaneously among talking on the phone, video chatting, and shopping for food. However, most activities require some period of preparation or travel, during which happiness might be sacrificed. Consider a situation in which one must choose between shopping and exercising on a treadmill during an hour (Figure 8). Assuming that the latter activity might require one to travel 30 min between a store and a gym, switching between activities would consume too much time to yield a sufficient benefit. Consequently, one should spend the entire hour performing one activity (in this case, exercising). Alternatively, if one could derive the same happiness by shopping online, one could maximize happiness by splitting the hour between exercising and shopping, assuming that one can eliminate the transit time by accessing the internet from the gym. This scenario illustrates the need to consider how quickly one could switch between activities under realistic conditions.  . Optimal activity switching. The optimal strategy to maximize happiness depends on the time required to switch between activities. In the case where a person can switch instantaneously between shopping and exercise during an hour, one should exercise for half the time and shop for the other half. However, if we assume that one must drive 30 min switching between these activities, one should spend the entire hour exercising. The transit time is depicted along the negative dimension of the x-axis, reflecting the assumption that one accumulates no happiness while switching activities. The happiness curves were obtained from our survey of 87 participants (see text for details). The optimal strategies were solved according to the mathematical approach described in the methods. Importantly, we cannot know the generality of these results from a sample of 87 people, but these data enabled us to illustrate the use of happiness curves and infer two important messages. First, happiness decelerates over time, and does so at different rates for different activities. Second, people recalled or imagined investing more time in activities than would be needed to maximize cumulative happiness. We expect that future studies will confirm these patterns, while expanding our understanding of the factors that influence the shape of happiness curves. Further research will be needed to connect investment in common activities to a quantitative index of sustainability. This task will require collaboration among researchers focused on life-cycle assessments, social life-cycle assessments, and environmental footprints. We hope that our example will stimulate these researchers to refine and apply quantitative models of behavior that explore opportunities for happiness and sustainability.

Refining a Quantitative Theory of Happiness
A quantitative theory, based on happiness curves, enables one to consider psychological mechanisms that regulate happiness within and among people. First, novel activities can bring greater happiness than routine activities [48]. For instance, few people would agree that the 41st kiss from a partner brings the same pleasure as the first kiss; activities lose their appeal as they shift from novel to routine. However, their appeal could return after engaging in other activities for some time. This phenomenon results from neural mechanisms designed to acquire multiple resources for survival and reproduction [49]. Other activities become less pleasurable as they wear the mind or body. To introduce such effects in our model, one could add a happiness renewal function that replenishes the potential for happiness between bouts of activity. The longer the interval between bouts, the greater the potential for happiness in each bout. For instance, playing a video game brings pleasure but ultimately, one's eyes or hands will tire. Taking a two-minute break does little to restore one's ability to enjoy the game, but a two-hour break does more. The initial accumulation of happiness could even increase among bouts when experience makes an activity more enjoyable (e.g., playing a difficult video game). Similar modifications to happiness curves can account for psychological phenomena involving nostalgia, jealousy, or anticipation.
In this way, happiness curves can capture the properties of individuals as they respond to their environments. Since happiness evolved as a way for the brain to gauge performance against expectation, what made our ancestors happy does not necessarily make us happy [50,51]. All that mattered was that, on average, happiness guided our ancestors toward activities that promoted fitness in their environment. Likewise, what makes one person happy, does not necessarily make another one happy. Genetic predispositions and developmental environments shape happiness curves in ways that make each of us unique. For instance, someone whose literary tastes include horror novels might gain more happiness when starting a book by Stephen King than would someone whose literary tastes comprise romance novels and biographical nonfiction. The result of this match between interest and experience is a happiness curve with a steeper ascent and a higher plateau. By fitting the parameters of happiness curves to data for individuals, we begin to account for variation among individuals while describing the general patterns of human nature.
Future research could build on our simple model by accounting for factors that complicate the problem of maximizing happiness. First, the social context modulates the rates at which an activity makes someone happy. For instance, a person's happiness depends on her situation relative to the situations of others in her social group [52][53][54]. In our model then, the initial slope and asymptotic value of a happiness curve will depend on how an activity affects one's standing among peers. The same parameters depend on whether others engage in the same activity, particularly when one benefits from companionship or suffers from competition. Second, personal preference and experience creates a unique happiness curve for each person because of habituation; whether an activity feels novel or routine and pleasurable or difficult (e.g., work) depends on a person's history [42,43,55]. For instance, activities are classified as work if they require a substantial investment of time or energy before generating happiness. Thus, studying for an exam, working in an office, or renovating a house would all belong to the functional domain of work, although we might consider them unique in other ways. By abstracting the problem, decisions about how to pursue happiness become objective. In fact, the concept of domains (e.g., family, work, health) [56] might even become unnecessary; when pooled among domains, different activities only need to be ranked according to their ability to deliver happiness under the present circumstances. Moreover, as happiness curves are adjusted to an individual's experience, the interactions between domains are captured by tuning the parameters of each curve without explicitly recognizing domains. The curves could also be parameterized to capture differences among individuals resulting from genes, experience, or environment [52,57,58]. Third, we cannot know precisely how happy an activity will make us or how long we have to seek happiness. We will have to choose activities based on an expectation and some measure of uncertainty. Taken together, these complicating factors call for a theory, built upon the research herein, that deals with interactions, feedbacks, and probability.

Informing the Sustainable Pursuit of Happiness
The relationship between happiness and sustainability has been addressed by a few researchers [17,19,23,26,59,60] but work is needed to link these concepts. Further developing our quantitative theory of happiness while also accounting for sustainability implications requires collaboration between positive psychologists, sustainability scholars, and evolutionary biologists. As biologists continue to refine the mathematical tools of behavioral optimization, psychologists can use these tools to identify strategies that maximize happiness. Sustainability scientists and scholars can then contribute insights on related happiness-deriving activity emissions, environmental footprints, social costs, etc. However, psychologists will need to quantify happiness in ways that enable them to parameterize an optimality model. This task presents a series of challenges that we summarize as questions for future research and approaches for answering these questions, shown in Table 1. At the same time, biologists will benefit from considering how insights from positive psychology and sustainability enhance our understanding of animal behavior, especially given that human emotions evolved by natural selection [9,61]. Undoubtedly, further exchange of ideas between these disciplines will speed up the development of the theory and create opportunities to apply the models in academic, clinical, and commercial settings. Table 1. Psychologists, biologists, and sustainability scientists and scholars can address fundamental questions whose answers will enable us to develop and apply a quantitative theory of happiness and related sustainability implications.

Research Question Approach
What are the shapes of happiness curves for a reasonable set of activities ranked by sustainability implications?
Measure temporal patterns of subjective happiness during each activity in a controlled or natural setting, while also accounting for sustainability implications.
How does the capacity for subjective happiness renew between bouts of activity, and what are the sustainability implications of switching?
Control spacing between bouts of activities and measure subjective happiness and related sustainability implications.
How do genetic factors, developmental history, and social constraints influence happiness curves, and how do those factors impact our environment?
Seek associations between putative factors and parameters of happiness curves in a diverse pool of subjects, organized by related sustainability implications.
Do happiness curves depend on controlled interventions that guide sustainable behavior versus choices without intervention?
Compare happiness curves between groups of people either guided toward certain activities or left to make their own choices and their related sustainability implications; a difference between the curves for the same activity reflects the effect of the intervention.
What is the uncertainty in parameters of happiness curves and sustainability implications?
Analyze factors that influence the variance of parameters, such as initial rate of happiness and the rate of habituation and the associated sustainability implications.

Conclusions
Happiness is an emotional state driving human behavior and actions. Dynamical models have significant potential to help humans choose activities that maximize happiness. In this paper, we build the case for such models, drawing on dynamical optimization techniques using data from an online survey where people (n = 87) imagined or recalled their happiness levels during certain activities. We used this instantaneous data to develop cumulative happiness curves and optimal solutions to derive maximal happiness from a set of activities. We also consider the ways such models can be enhanced to consider the links between happiness-deriving activities and their sustainability implications (i.e., CO 2 emissions). Our results indicate that most people tend to overinvest in an activity before switching to a new activity. Such overinvestment could have negative effects on sustainability that could be avoided through careful analysis of the costs and benefits of an activity. In other words, people struggle to identify the diminishing happiness returns of an activity and fail to understand each activity's sustainability implications. Our efforts provide direction to use surveys and mathematical optimization techniques to maximize or ensure some minimum level of happiness where less objective methods have failed. The result could be future studies and techniques that aid humans in finding happiness, while balancing humanity's approach to a sustainable and regenerative future.