Survey Article: When and What is the “Hinge of History”?
Joe Roussos
Philosophy, Institute for Futures Studies, Sweden
Julia Adler
Politics, Institute for Futures Studies, Sweden
Tim Campbell
Philosophy, Institute for Futures Studies, Sweden
Emma Engström
Technology in Society, Institute for Futures Studies, Sweden
Karim Jebari
Philosophy, Institute for Futures Studies, Sweden
and
Anders Sandberg
Futures Studies, Institute for Futures Studies, Sweden
I. INTRODUCTION
Imagine you are in your mid-twenties and receive an offer for a job overseas. The position is intellectually stimulating, meaningful, well-paid, secure and offers excellent opportunities for advancement. However, accepting it requires that you relocate to a faraway country for years, leaving behind your current job, your family and your friends. The choice will significantly affect the trajectory of your life: if you accept the offer, your career will take a new direction, you will meet new people, and you will become part of a different culture. Although you have made important decisions before, none has felt as significant. And while you may make important decisions in the future, you suspect that none will be as consequential. In this sense, you are at a “hinge moment” in your life.
Many argue that humanity as a whole finds itself at a similar moment in its collective history. They speak of the hinge of history as a period in which decisions have far-reaching and even irreversible consequences for civilization. Attention has focused especially on existential risks: human extinction, permanent civilizational collapse and other events which leave some humans living but in a radically reduced form. In much of its current usage in philosophy and futures studies, the term “hinge of history” traces back to Parfit:
We live during the hinge of history. Given the scientific and technological discoveries of the last two centuries, the world has never changed as fast. We shall soon have even greater powers to transform, not only our surroundings, but ourselves and our successors. If we act wisely in the next few centuries, humanity will survive its most dangerous and decisive period. Our descendants could, if necessary, go elsewhere, spreading through this galaxy.1
Such a dangerous and decisive period was denoted the “time of perils” by Sagan.2 Sagan and Parfit both imagine a bounded period of troubles, after which great things await. This is a core part of the idea: both risk and capability are high during that period, and at least risk is significantly lower thereafter.3 It is our capability that turns a “time of perils” into a hinge: good choices will make the difference between disaster and the bold future beyond.
In this survey we explore the idea of the hinge of history, attempt to define it precisely, and assess if it is possible to determine whether we currently live at the hinge of history. Our aims are motivated by the idea’s popularity in public media4 and recent popular books such as Yudkowsky and Soares’ If Anyone Builds It, Everyone Dies.5 The latter argues that the AI apocalypse could be imminent unless we choose wisely, triggering a review in The New York Times that began: “In the future, if there is a future,…”6. The concept is influential in the Effective Altruism community. In What We Owe the Future, MacAskill argues that we are living in an extraordinary time, characterized by fast technological development, scientific advancement, economic growth, moral progress and expanding interconnectedness.7 Others in the movement describe ours as “the most important century.”8
Part of what motivates us is the variation in popular manifestations of this idea. In some cases the hinge is a very short period of a few years, while for Parfit it was several centuries. It is typically taken as given that whether we live at a hinge is important, but to some this is because the hinge is a last chance to act while for others it is a window of time with special capabilities. In much of the work above it is “the” hinge, a singular point in history, but more moderate thinkers allow that importance comes in degrees.
To those who see technology as bringing about a unique hinge, with a short duration and nearby risk horizon, the following simplified scenario illustrates the concept:
Ali the AI engineer. Ali lives in a world on the brink of creating an artificial superintelligence. Once created, it could easily destroy the world. Whether it does so depends on whether its values are aligned with humanity’s, or misaligned in such a way that it decides to kill us. Ali is in charge of installing the AI’s values module. Suppose that they are choosing between two modules, only one of which will succeed at alignment. If Ali chooses correctly, humanity will flourish in a benign AI future. If Ali gets it wrong, humanity will be destroyed. What they do will determine the future trajectory of the world. It could have very good outcomes, or very bad ones. This action is much more important than any action which comes after it because humanity’s decision-making powers will be limited ever after. Ali stands at the hinge of history in this world.
In reality, many decisions with such high stakes are likely to be distributed and political, so we might wish to read Ali as representing a group, potentially one requiring complex coordination.9
Given rising perceptions of threat and empowerment we think it is no surprise that the hinge idea is popular now. “A time of threat and empowerment” is not intended as a precise definition of the hinge (we will discuss that later) nor are these perceptions an argument for or against the hypothesis that we currently live at a hinge. It may be that the sense of empowerment is mistaken, in which case the present would fail to be a true hinge. It could also be that this will be our reality from now on, in which case there is nothing distinguished about the present. We explore this below.
Talk of the hinge of history is compelling because it is grand and metaphorical. But this also makes it nebulous and open to interpretation. It is therefore challenging to navigate the different nuances and focuses of authors discussing the hinge. Some emphasize human agency, outlining a decision theory for the hinge, while others focus on the nature of the perils involved; some suggest that human influence increases over time, driven by advances in technology and knowledge, while others argue that it declines, since the past can shape the future, but not the reverse. Thus, if the concept of the hinge of history is to be useful for decision making, it needs a clearer definition. This would enable better assessments of the claim that we now live at the hinge. It would also help us see more clearly what we need to do if we now live at the hinge, and what we should prioritize if we do not.
In this article, we consider six possible definitions of the “hinge of history”; five are either found in, or based on, existing literature, and one is a novel proposal that aims to improve upon the limitations of the others. Despite making this proposal, we ultimately find all definitions unsatisfactory. There may be other definitions which do better, but those who believe that the concept of the hinge of history has practical significance bear the burden of demonstrating this. In our view, what remains is a rhetorical device with expressive content but without much factual content: calling the present “the hinge of history” might mobilize action but it is not worth seriously investigating whether it is true.
The article is structured as follows. We begin, in Section II, by reviewing how the hinge of history concept has been discussed in historical and contemporary literature. We then establish some criteria for a useful definition of a “hinge of history” in Section III, and use them to evaluate five definitions in, or based on, the contemporary discussion, as well as one new definition, in Section IV. We find that all six definitions fail to meet our criteria and that some encounter additional problems. In section V, we consider the question of whether we live at a hinge or even “the” hinge, and how we would know this. We conclude with reflections on the term’s rhetorical uses and whether these survive our critical analysis.
II. HISTORICAL PRECEDENTS
Before attempting to define the hinge precisely it will be helpful to further develop our intuitive grasp of the idea by situating it historically. One might think that claiming that we live at the hinge of history is just the hubris of the present: surely everyone thinks that their moment is the most important? In this historical overview, we demonstrate that this is not so. Instead, the particular elements of the hinge idea are quite rare. We trace some plausible contributing elements to its popularity, highlighting rapid technological development and felt control over the future.
We begin with macrohistory. There are many macrohistorical views precluding hinges, or placing them firmly in the past. Cyclical history (e.g., Ancient Greece) denies fundamental change. End of History views (e.g., Hegel, Fukuyama) typically place that end in the near past. According to these views, we have no agency over the future course of history, either because nothing will happen or because history will repeat itself. Macrohistorical models tend to be globally deterministic, even if they can contain hinge-points. They describe society as “driven by impersonal forces rather than forceful persons”, perhaps with opportunities for vanguards to make their mark but with a structure largely set by non-human forces.10 Conversely, Popper’s broadside against macrohistorical models in The Poverty of Historicism argues for historical indeterminism that also precludes any predictable hinges of history.11 There may indeed be supremely important times and decisions, but they cannot be predicted in advance. The claim that we live at a hinge needs to navigate a path between the Scylla and Charybdis of determinism and indeterminism to be valid.
Jaspers introduced the idea of the Axial Age, the period from 800 BCE to 200 BCE when many of Eurasia’s major philosophical, religious, and intellectual traditions emerged independently.12 While contested,13 it might represent a major transition in history with lasting effects brought about (somehow) by individual human action. It might thus represent an example of a past hinge—a very extended one, spanning six centuries. These models can be combined, as in the civilizational trajectory model of Baum et al.14 This model may be likened to a civilizational game of snakes and ladders, where disasters can set back humanity repeatedly or cause extinction, but there may be opportunities to stabilize the world or reach some transformative posthuman or astronomical positive state. In this view, there may be hinge points where trajectories may be launched, but the number of such points may be indeterminate.
Though we claim that most people would not have identified their time as the most important, we acknowledge that there are examples of claims with some similarities. Perhaps most salient are millenarist claims about an imminent fundamental transformation of society. The corrupt past and present will be replaced by a new order. However, these claims are fundamentally eschatological and not dependent on human action. God, destiny, or historical forces are causing the transformation and the main issue for the believer is to be on the right side of history, not to influence how it goes. A modern example is radio pastor Ralph Sockman’s line: “the hinge of history is on the door of a Bethlehem stable.”15 These “hinges” tend to be short, perhaps a single instant like the rapture or a lifetime like that of Jesus.
Apocalyptic visions also represent hinge-like but somewhat distinct claims. The end of the world might hold ultimate importance, but there is no history afterwards. Traditionally, apocalypses are part of the eschatological framework of their culture, holding meaning but being outside human influence. (This is not universal: the Aztec and Nahua seemed to think that the apocalypse could be averted through sacrifice.16 That might be a rare case where the end of the world in a religion was potentially human dependent.) This shifted in the modern era, where it could be brought about by human action but lacked profound meaning (instead of a meaningful end, an end to meaning).17
There is no shortfall of rulers and court historians proclaiming their present situation as epochal, but many of these have been parochial. Most pre-modern cultures had a static or cyclic view of history where, as noted, fundamental change simply does not happen. Early modern thinkers considered their era epochal, with long-lasting global consequences, but did not frame this as being the most important event in history. For instance, Kant believed that his time was an age of enlightenment, when freedom of expression would give individual free-thinkers the chance to spread their rational ideas. This, in turn, would lead to the gradual enlightenment of the public, meaning “the exit from [mankind’s] self-incurred immaturity.”18
Technology played an important role in the emergence of the modern hinge concept. One aspect of this was the sheer rate of technological advancement in the industrial revolution. Consider Harrison, writing in the late 19th century:
Take it all in all, the merely material, physical, mechanical change in human life in the hundred years, from the days of Watt and Arkwright to our own, is greater than occurred in the thousand years that preceded, perhaps even in the two thousand years or twenty thousand years.19
This acceleration, and the power to control the natural world and improve human conditions, led to the sense that something was special about this period of history. Jeans extended this thought to the present also dominating the future:
[…fate] has selected for us what is, perhaps, in some ways the most sensational moment of all in the life of our race.20
Moving into the twentieth century, von Neumann noted that nuclear energy, greater automation, improved communications, and partial or total climate control would put humanity in an unprecedented, unstable situation.21 Freud echoed this view, suggesting that “the present time deserves a special interest.”22
Other elements of the hinge idea appear throughout the twentieth century. Wells proposed a plan for remaking the world using science and rationality, emphasizing how humanity’s new powers could liberate it from danger and misery.23 However, he did not claim this would be a pivotal moment. Similarly Fyodorovich Fyodorov’s idea of the Common Task of Humanity involved remaking and unifying the world, but was formulated more as a divine command.24 In both cases, however, these changes would be initiated by human action rather than historical force or God.
Lewis came quite close to the hinge as we now conceive of it.25 He argued that earlier generations exert power over later generations due to their choices, and that this power increases due to advances in science. Eventually, there will be a generation of people (or rather a subset of it) that can determine the dispositions of all subsequent generations, locking in whatever values they so choose. In Lewis’s view, this is the true crossroads, and there is no guarantee that it produces a good future.
Von Neumann famously used the term “singularity” in regard to the change described above, but it is unclear what agency he thought humans had over it, and whether it could contingently set the direction of history.26 Later authors discussed ways this situation may be put under control,27 but also how it could accelerate into a technological singularity, where superhuman technological forces would become dominant.28 While the singularity concept has been used in multiple ways a red thread is that, were it to happen, it would represent a transition to a different mode of history—and in many versions, actions leading up and during this event would cause important path-dependency.29 Perhaps the most salient example is the discourse about superintelligent AI, where setting pre-singularity goals of AI (or AI governance) could strongly affect the long-term future.30 We observe that accelerating technology tends to shorten both the time-horizon of the hinge and its duration, with authors focusing on AI risk offering some of the shortest estimates of each.31
In 1966, Platt argued that many growth curves are showing signs of changing from exponential to S-shaped, but that the current era is the fastest change ever. “If this is true, the present generation is the hinge of history.”32 Nevertheless, while much is driven by the nature of science and technology, he notes that there is a real risk of nuclear annihilation, and that it is up to this generation to restructure the world to be good and survivable: “The world has now become too dangerous for anything less than Utopia.”33 This might well have been the essay that made the term popular in its modern, non-religious sense.
Thus, there seem to be two ingredients in the spread of the “hinge” concept: increased awareness and prevalence of existential risks, and recent advances in knowledge and technology, such that we feel empowered to address these risks. These authors wrote in the wake of the first atom bomb attacks in WW2, and in a Cold War context where great power conflict meant that the threat of nuclear destruction was clear and present. This was perhaps the first example of an existential threat that was anthropogenic, globally-recognized, and which humanity had the power to avert. This combination of high-risk/high-agency emerged again with climate change. Driven by advances in industrialization, and made understandable by advances in science, it is a risk whose mitigation clearly depends on human actions. Most recently, the development of AI algorithms has spurred a growing concern that their applications could pose existential risks. This threat is similar to nuclear war: it originates from technology that we can sculpt and regulate in better or worse ways.
A similar, but distinct concept is that of a “turning point” or “critical juncture” in history. A moment in the past, such as the French Revolution,34 is identified as a point of massive significance and change. Defenders of these concepts stress the path dependence of history and note that there are critical events which lock in self-reinforcing patterns35 or where the gradual accumulation of change leads to a qualitative transformation once a threshold is reached.36 Although often deprecated as problematically involving historical counterfactuals, or because of an association with Whig History,37 these concepts have been given recent methodological defenses which stress the importance of a long time perspective, specification of the mechanisms by which structures are transformed, and testing the claim with disciplined counterfactuals.38 There are crucial differences between “turning points” and “hinges”, however. “Turning point” is a historiographic concept and its application is typically to a moment in the past, while the “hinge of history” has been used both historically and predictively. The claim that something is a turning point is not typically action guiding. In their more modern form turning points are tied to deep structural changes, while we will argue that the hinge concept is tied to human agency. Our critique of the concept of the hinge of history is not a critique of the historical concept of a turning point, since both the content and contexts of use differ. From here on, the “hinge of history” will be taken to refer to the forward-looking concept as deployed by futurists, rather than its cousin in historical and especially religious writing.
This brings us back to our starting points: Sagan and Parfit. Sagan is perhaps the thinker whose formulation of the hinge idea most clearly illustrates our hypothesis that its germination is linked to the risk and control brought about by technology. He posed the challenge as a race between (technological) power and civilizational wisdom, unfolding over a timeline of centuries. “If we continue to accumulate only power and not wisdom, we will surely destroy ourselves.”39 It is this general idea that we now turn to defining precisely.
III. CRITERIA FOR A DEFINITION OF A HINGE
We wish to define the “hinge of history” (HH) in a way that makes it clear what it means and how we would know if we lived at it. First, we will establish some criteria for a good definition of the HH, and derivative notions such as “influentialness.”40 We draw this list from our understanding of the term’s historical development (as sketched above), its use in academic literature,41 public media,42 and discussion fora.43 We use the following three criteria.
A. Centered on Human Action
Human action is central to the idea of the HH. This is explicit in Parfit, writers on existential risks like Ord, and futurists like Sagan. The hinge concept is not about causally important moments beyond our reach, such as the Big Bang, nor natural variations in processes that humans cannot possibly control, such as vacuum decay. Consider the film genre of asteroid impact disasters. Armageddon (1998) might be said to contain a hinge moment, as evidenced by the heroes saving the day by diverting the asteroid. Von Trier’s Melancholia (2011), by contrast, does not: the film traces an inevitable progression towards annihilation. This means that if one believes that human history is impervious to deliberate human action, and follows deterministically from structural forces, then there are no hinges. This could be the case if a seeming hinge moment leads down one path rather than another, only for the paths to merge in the future.44 Thus, the definition should relate to variations in outcomes of human actions rather than variation in outcomes in general.
B. Decision-relevant
The HH matters. It should not be an irrelevance or triviality that we live at the HH. This is explicit in MacAskill, who argued that it is “crucially important” that the hinge hypothesis is evaluated.45 Additionally, a core part of the concept is that we can do something about the hinge: it isn’t merely an inflection point in history, but a leverage-point we can use to influence history’s direction.
This narrows the scope set by criterion 1. Not all processes related to human action are decision-relevant. Some complex human processes are very difficult, or perhaps impossible, for decision-makers to change, such as urbanization, the demographic transition or secularization. The fact that an important human-initiated process takes place at a given moment does not necessarily make that moment a hinge. Those processes need to be amenable to being influenced by decisions at the particular moment.
Two things follow from this criterion. First, the hinge must be either in the present or the future. This distinguishes the concept we investigate here from hinges and turning points as studied in history. Second, the hinge needs to be identifiable, at least in principle. In order to be a useful concept for informing decisions, decision makers need to know about it. If the hinge is defined in terms of something we cannot observe, this will count against that definition.
C. Resource-focused
Additionally, we suggest that the definition of the HH concretely relate to the allocation of resources such as attention, power, effort, knowledge, engagement, money, and time. Labelling the present as the hinge is often a call to action, encouraging decision-makers to commit significant resources in light of this moment’s special position in time. To take an example favored by Effective Altruists: a rich philanthropist who knows they live at a hinge prefers spending their resources now to exert influence, while one who knows that a hinge lies in the future prefers to save their resources until then. Linking to claims about resources helps to resolve the role that the timing and duration of the hinge plays in motivating action: nearby, short hinges motivate immediate deployment of resources, whereas further off or extended hinges may be better addressed by first gathering or growing resources.
IV. CANDIDATE DEFINITIONS
In relation to the three criteria above, this section considers six definitions of the HH, working from more vague and less formal towards more precise and formal.
A. The Time of Perils
The “time of perils” offers one way of making precise the hinge of history. Neither Sagan nor Parfit offers a definition, so we infer one from the links they drew between the importance of the present, its heightened risks, and the potentially glorious future that awaits if we make the right choices. We can formulate this into a claim, following Thorstad.46
The Time of Perils Hypothesis: Per unit time extinction risk is much higher now than it has been historically, and will remain so for a few centuries. Extinction risk will thereafter permanently decline to very low levels.
There are two important components of this hypothesis:
Elevated risk: Extinction risk is now higher than it has been in the history of humanity.
Future reduction of risk: Extinction risk will be drastically and permanently reduced if human civilization persists for a certain period of time.
The first part is often accepted, though it is worth noting that it is hard to see how one could prove it. However, the second component is controversial. In a recent article, Thorstad notes that proponents of the time of perils hypothesis merely assert that existential risk will decline due to some underspecified mechanism such as “increased wisdom.”47
As Parfit is central to our discussion, it is no surprise this idea matches the broad strokes of our criteria. The risks causing the time of perils are due to human action (and other human properties): in Sagan it is a risk of catastrophic choices due to an imbalance of human power (due to technology) and wisdom—which is echoed in Ord.48 What makes the time of perils a hinge is that we can make certain choices which avert catastrophe. Humanity’s future could be short and brutal or long and potentially very good,49 depending on how we manage those risks. One area of divergence between later uses and Parfit’s is that he appears to be comparing the present to the past and asserting obliquely that the present moment is unique: humanity’s “most dangerous and decisive period.”50 However, his characterization does not help us compare present and future times.
Parfit’s comments are brief and metaphorical, likely not intended as a precise definition. He offers no way to determine when precisely to act. The metaphors of Parfit, like those of Sagan, imply that the required action is great and collective, but offer little help to decide how large a share of our collective resources we should commit. This (inferred) definition is thus too abstract to meet our second and third criteria.
Moreover, this definition relies on the time of perils hypothesis and thus on the future reduction of risk claim, which requires motivation. As Thorstad has noted, for the time of perils hypothesis to be correct, extinction risk needs to be reduced by many orders of magnitude thereafter for humanity to be able to cash in on the long expected future. Absent arguments for a spike in extinction risk, now or at another point in time, it is undesirable to link the definition of a hinge to such a spike.
B. The Most Important Period
In a series of blog posts, Karnofsky argues that “the 21st century could be the most important century ever for humanity.”51 He does not specifically define the HH, although he relates his blog posts to MacAskill’s work (discussed below). The rough formulation he uses repeatedly could function as a definition of the hinge: the most important century ever for humanity.
Picking out this century implies a comparison with the future. However, “importance”, like “influential” and “hingey” (which co-occur in online and popular discussions of the hinge) is not clearly defined. This makes it difficult to operationalize the definition, which is part of our second criterion of decision-relevance. That is, it is unclear what beliefs a person ought to hold to justifiably believe that the hinge is in this century, nor is it clear what observations they should make to form those beliefs.
Here are two illustrations of the vagueness of “importance.” First, this definition might pick out a century in terms of consequences while neglecting agency. Human choice could matter, but it is not explicit: importance in terms of events is not distinguished from importance in terms of outcomes of decisions (a feature that is more explicit in Häggström’s definition below). To illustrate: the most important year in an individual’s life could be the year that that person’s hometown is destroyed (e.g., by a volcano), even if this event could not have been prevented. Sheer importance, in this sense, is not enough to be a hinge. Such a definition would fail to meet our first criterion.
Second, although there is no explicit link to resource usage, a natural move might be to say that the most important century is when resources should be expended (to address the important issues at hand). However, spending-urgency does not have to coincide with importance, if resources grow faster than importance recedes. For example, assume that this century (21st) is the most important one, and that the importance of the 31st century is 99% of that of the current century, but invested resources will increase in value 10 times in the coming 1000 years; then it might make sense to invest the money, other things being equal. So, focusing on importance doesn’t lead to clear action guidance, even in the narrow domain of spending-vs-investing. Such a definition would fail to meet our third criterion due to this ambiguity about how to manage resources.
C. A Period with Disproportionate Influence Over the Long-term Future
The hinge is an important concept in Effective Altruism, and thus features significantly in discussions on the Effective Altruism Forum, a platform dedicated to discussions around how to do the most good. The forum maintains a glossary and its definition of the hinge of history is: “a hypothetical time in human history in which humanity has disproportionate influence over the long-term future”, with the clarification that “The long-term future focuses on possible ways in which the future of humanity may unfold over long timescales” (our emphasis).52
This definition is centered on human influence over humanity in the far future. Hence it revolves around outcomes due to human agency, not natural catastrophes that humans could not prevent, meeting the first criterion. This definition is about influence, but not about how to spend resources, however, failing to meet our third criterion. In particular, it focuses on humanity’s influence on the long-term future.
One terminological issue with the definition is that because “the long-term future” is characterized as the future of humanity, the definition seems to assume that there will be a long-term future for humans, i.e., that humanity will not go extinct before then. However, this issue can be resolved either by dropping the stipulation “of humanity” from the characterization of the long-term future or by stipulating that the future of humanity can include future times at which humanity does not exist (perhaps such a future is still “of humanity” in the sense that it results from decisions made by humanity).
Another potential issue with the definition is that it does not imply that more is at stake in certain decision contexts, e.g., those within the hinge of history, than in those outside the hinge. There are two reasons for this.
First, due to its inclusion of terms that are not well clarified, such as “disproportionate” and “influence”, it is unclear what the definition might mean for decision-making. For instance, it does not imply that during the hinge of history, a person, or group of people, will face a choice in which certain of their options have greater expected total value than in other choice contexts. The human “influence” might be due to collective patterns of behavior that cannot be significantly changed through interventions at the level of states or non-government organizations, for example. A period can be influential without this influence being something we can steer.
Second, the definition leaves open the possibility that humanity can exercise its influence over the short term in a way that creates more value, or expected value, than any exercise of its “disproportionate” influence over the long term. That humanity has influence over the long term future at a certain time T, where this influence is disproportionate to the influence humanity has over the long term at any time other than T, is consistent with humanity having not much influence at all over the long-term future at T. Perhaps humanity has almost no influence over the long term at any time. The definition therefore doesn’t connect the concept of the hinge of history with the stakes involved in decision-making at the hinge.
D. The Period with the Most Influential People
Next, we turn to another definition in terms of influence, due to MacAskill. MacAskill does not define the hinge concept directly, but specifies the hinge of history hypothesis (HHH) as follows:
HHH: We are among the very most influential people ever, out of a truly astronomical number of people who will ever live.53
“Influential” here is defined in terms of the expected value that can be created with a unit of resources when considering only “direct expenditure” of those resources.54 The more expected value you get by directly expending a unit of resources, the more influential you are. (The emphasis on expected value, both here and in our discussion of the remaining definitions below, does not involve commitment to a specific moral theory, such as utilitarianism, or even welfarism. What is of value can include not only individual welfare, but knowledge and understanding, achievement, aesthetic value, virtue or moral worth, equality, freedom, desert, love, friendship, a special concern for those who are least privileged, and many others.55)
Direct expenditure is something like spending money on a specific measure or project, such as supporting an organization that distributes insecticide-laced bed nets in malaria-infested areas. It is contrasted with “investing” resources, which primarily means saving resources in an asset that yields a financial return, such that greater resources are available for expenditure in the future.
There is one important caveat, which is that MacAskill also includes under “investment” a certain kind of expenditure: spending resources to increase one’s potential influentialness in the future. The example given for this investment-expenditure is building up the community of effective altruists,56 who would presumably then have more power to act in future in line with the investor’s values. The basic difference seems to be that “direct expenditure” aims at bringing about a specific outcome in the present, while investment aims at increasing one’s ability, or the ability of one’s successors, to bring about outcomes in the future.
Here, the hinge concept has morphed into a narrower claim concerning the optimal timing of philanthropic donations. It may seem to be a paltry replacement for the grandeur of Sagan and Parfit’s ideas (definition A). In their wider conceptions, the hinge could occur at a time when there is no money and no philanthropists, and, if the hinge lies in the far future, this may well be true. On the other hand, definition A is focused on whether present people are in an empowered position relative to the past, while MacAskill is concerned with whether present people are in an empowered position relative to the future, which is more relevant for decision making.
Before discussing how to derive a definition of the hinge from MacAskill’s HHH, let us note some issues. One concerns “influentialness.” This is defined in terms of the potential to create expected value per unit of resources. Suppose I have 100 USD, which I can either spend now on making the world better, or save and spend in 20 years. Suppose that if I save the 100 dollars then in 20 years it will have grown to 1000 dollars, and that if I spend 1000 dollars in 20 years, I can do twice as much good as I would if I were to spend the 100 dollars now. Spending 1000 dollars in 20 years creates more expected value than spending 100 dollars today. But it doesn’t create more expected value per dollar spent. It will be less efficient: ten times as much money buys twice as much utility. By MacAskill’s definition, the future me who spends 1000 dollars 20 years from now is less influential than the present me who spends the 100 dollars today. This seems wrong, or at least debatable, as the future me does more good in expectation. The issue is linking the definition of “influence” to financial efficiency. This links influentialness to things like the rate of return on investments, which may turn out to be important but should not, we think, be built into the definition.
Another issue is the distinction between direct expenditure and investment.57 It appears to be an attempt to distinguish between action and deferral. But when investing resources, e.g., by buying a portfolio of stocks, a decision maker also impacts the world. The price of the purchased stocks may change, and the money invested becomes available for someone else to spend.58 Setting this aside, the distinction is inconsistently specified. MacAskill says that direct expenditure includes spending resources to change values in a way that persists over time,59 and that investment includes using resources to increase the number of impartial altruists.60 Changing people’s values seems very similar to growing a community of people with a certain set of values. Why isn’t building up a community then a form of direct expenditure? Or if it is investment, why is it the only exception to what otherwise seems to be a financial conception of investment? The carve out specifically for building up the EA movement is suspect in the context of defining a concept which might motivate philanthropists to donate in line with EA advice.
We can now turn to the question of defining the hinge. As noted above, MacAskill instead defines the HHH—the claim that we live at the hinge—by saying that it means we are amongst the most influential people to ever live. There are several ways we might use this to define the hinge itself.
I. The hinge is the period (say 100 years) during which the very most influential people (out of a truly astronomical number of people) live.
II. The hinge is the period during which average influentialness (or expected influentialness) is highest, for the people living at that time.
III. The hinge is the period during which total influentialness is highest, compared with all other periods of the same length.61
There are issues with each of these. Our prior discussion of problems with the concept of influentialness apply to all three definitions. Definition I seems most affected by a peculiarity of MacAskill’s HHH: it is tied to the existence of a truly astronomical number of people. But then, as both Mogensen and Häggström point out, if we go extinct tomorrow, then there is no HH because there is not a truly astronomical number of people who ever live.62 (Mogensen also argues that switching from assuming a large total population to a large expected total population does not escape this difficulty for MacAskill’s definition.) Moreover, demographic projections suggest that the human population will likely diminish after the 21st century, drastically in some scenarios, due to falling fertility rates.63 The number of births per woman has declined from around five to around two in the last half-century and an indefinite continuation of this trend implies human extinction. So if a large population is baked into the definition, then demographic trends make it harder to establish that there is any time that is a hinge, so defined.
Definition II, in terms of average influentialness, seems to neglect situations in which the most crucial choices are concentrated in a few hands. Recall Ali the AI engineer. Their choice may be the most impactful choice ever made, but this need not imply that average influentialness is highest at Ali’s time. Perhaps Ali lives at peak population, and so later, smaller generations will have higher average influentialness. Moreover, this interpretation is a poor fit for MacAskill, given his focus on investment. Most people have very little money to spend or invest. MacAskill’s target audience seems to be the top 1% of wealth holders globally—people living in developed countries, high-income earners, and so on—and especially the top 0.1%. But the claim that this percentile is especially influential (in his sense) is not the same as the claim that the average person living today is so.
Definition III also seems to fail to capture what is happening in the Ali story. Ali’s choice is impactful but it seems odd to shoehorn this into an account involving saving vs spending resources. Further, let us note a problem with the implications of all these definitions. If we think that the hinge is in the future, we are encouraged to invest rather than expend our resources, where investment involves literal financial investment and movement building. We now question the viability of investment as a means of stockpiling resources and influence against a future HH. The implication in MacAskill seems to be that it is possible to save indefinitely, accruing resources against a crucial hinge moment centuries or millennia away (e.g., on p.347). But there is little evidence of multi-century financial investment succeeding, and most examples of wealth accumulation on the order of centuries are deeply entangled with political domination, oppression, and expropriation.64 We can think of no examples of an entity with a continuous values-based identity surviving across millennia, except perhaps the Catholic Church. But since the average philanthropist does not have the ability or wherewithal to found a new catholic church, this is hardly compelling evidence that long-term investment is a viable route to future influence.
We offer the reader an interpretative dilemma: either MacAskill assumes that the current economic and financial system will persist indefinitely or he thinks the relevant timelines are quite short. The former assumption we find highly implausible. The latter is more plausible, in light of increased concerns about AI risk in the coming years and decades. However, even if one believes that the relevant options for when the hinge is “now” or “soon”, building this short timeline into the definition of the hinge risks making the concept unusable for those who disagree and who wish to argue that the hinge lies far in the future.
In summary, this definition has conceptual issues relating to key terms such as influentialness, and the link between MacAskill’s HHH and our target definition of the hinge is unclear. Nonetheless, this work meets some of our criteria. It is clearly focused on human action, and indeed is admirably decision-relevant: it relates explicitly to the specific decision of spend-or-save. It is also resource-focused, but in a narrow fashion that generates several problems for the usefulness of the concept by anyone other than EAs. The vagueness around the distinction between direct expenditure and investment is a fundamental challenge for its relevance for decision-support.
E. The Period with Largest Variance in Outcome Value
Next, Häggström provides a mathematical definition of the hinge. He defines the “hingeyness” of a time t as a function, H(t), which measures how pivotal t is for the rest of history.65 Hence, the hinge is the period when H(t) achieves its maximum. He then defines a random variable U, which he describes as “a utilitarian measure” of the value of the world throughout its history. (Note, however, that U is in fact just a cardinal utility function; it can represent a wide range of non-utilitarian values, such as those mentioned in Section III.D.) U∞ represents the total value of the world from the beginning to the end of time. He defines Dt as a complete description of the world until time t, and uses that to define the expected value of the world, given how things have gone until t: Et = E[U∞ | Dt]. To express the idea that “now” is the hinge, Häggström introduces τ as a label for a suitable duration for “now”, such as 100 years (or the present century). We now have the ingredients of Häggström’s definition of what is at stake at time t: H(t) = Var[Et+τ|Dt]. That is, the conditional variance now (the present century) of the total value of the world, given how things have been up to the start of now (the start of the present century). This reflects how much the expected value of the total value of the world at t+τ varies in the time period between t and t+τ. It follows that the hinge of history is the time, t, such that for any other time t′, the variance at t is higher: Var[Et+τ|Dt] > Var[Et′+τ|Dt′].
The core idea is that the variance of the set of possible expected values of the world captures how much is at stake at time t: the greater the variance, the more is at stake. The hinge is the time with the largest variance.
This definition is centered on the set of possible expected outcomes from the perspective of the whole history of the world. However, there is no connection to human action, which is our first criterion. As Häggström himself points out, this definition does not track which part of the variance derives from human choices in the time interval between t and t +τ. Instead, it provides a “God’s eye view” of the most important time in history. Additionally, the probabilities of the different possible outcomes (as specified in terms of the values of the world at the end of time) are not probabilities that anyone could know. Hence this definition doesn’t meet our third criterion relating to resources. For our purposes, then, it is unsuitable.
Perhaps a natural thought is that we can modify Häggström’s definition so that hingeyness is understood as how much human actions can impact the expected value of the whole world. This brings it much closer to our own suggestion, below. Following Häggström’s setup, hingeyness would be the conditional variance now (the present century), given how things have been up to now (the start of the present century), of the expected value of the world as a function of which actions humans could perform now (during the present century). The core idea is that this variance captures how much is at stake at time t: the greater this variance, the more is at stake. The hinge can then be defined as the time with the largest variance. (We can label this definition E′.)
This definition gets around our objection to Häggström. It satisfies our first criterion. It would, of course, be very hard to establish that now satisfies the definition, since it requires evaluating the potential impact of all possible human actions in different eras, including future eras. It is also unclear whether it can meet our second and third criteria. Knowing that we lived in the period with the highest variance would leave us ignorant of which decisions are the crucial ones. Knowing that we lived at this kind of hinge could motivate a general increase in care, but not a specific marshalling of resources to some end. For instance, if the crucial decisions are not identified, we are in the dark with respect to whether we should save, spend, or adopt some combination of both save and spend, at the hinge. In this way, the definition is worse than the MacAskill-inspired one (D) considered above. Definition E′ is also particularly sensitive to the duration of the “now”—switching from a century to a decade could alter whether a particular moment is part of a hinge.
F. The Period with Greatest Choice Importance
Given our dissatisfaction with the literature, we offer here a new proposal. Rather than focusing on outcomes, we focus on choices. A natural way of understanding the hinge is roughly as the period of time containing the most important choices. There are several ways we might understand the importance of choices, and to define them we need some basic decision theoretic ingredients.
A choice involves at least two options, or possible actions, labeled O1, O2, etc. As we are typically uncertain when we make decisions, we will need to consider different possible states that the world might be in, labeled S1, S2, etc. An outcome is a particular way that things could go, if we take one of our options. We can label it with a pair of option and state: (O1, S1), (O1, S2), etc., but it is important to remember that describing an outcome involves describing all the things that happen as a result of the action. In the spirit of the longtermist slant of this literature, we take the outcomes to include all effects throughout the future of the world after the choice is made. Outcomes can be evaluated, and we will assume that the values assigned to outcomes are objective and that they can be represented numerically: V(O1,S1), V(O1,S2), etc. Traditionally, in decision theory, the value of an option is defined as the expected value of doing it, taking into account all its possible outcomes. Defining an expected value requires specifying some probabilities, and these are typically the credences of the decision maker.66
With this in place we can specify several ways of ranking choices by importance.
Maximum outcome value difference: rank choices based on the difference in value between the best and worst outcome
Maximum variance difference: rank choices based on the highest risk of the options, defined as the variance of the value of the outcomes of that option
Maximum expected value difference: rank choices based on the difference between the highest and lowest EV option
These rankings will not agree in general. Each can be used to define the hinge, as the period of time which contains the most important choice as defined above. For example, consider the maximum outcome value difference definition. Let Δt be a period of 100 years around time t. The hinge of history is the time period Δt containing the choice with the greatest difference between its best possible outcome and its worst possible outcome.
As this definition ranks choices, which are made by different people at different times, it assumes that the relevant values are comparable and that it is meaningful to compare expected values. Recall that we assumed that the values of outcomes were objective—this was to represent the fact that we are interested in ethical evaluation rather than subjective prudential valuation. But the probabilities in our decisions may still be subjective, which poses problems for interpersonal comparisons. If Tim and Joe face the same decision, with the same values for the outcomes, but have radically different credences, then definitions 2 and 3 above will represent those choices as having very different importances. So we may need to place some constraints on the degree of subjectivity involved in assessing choice-importance.
Although this is more of a schema of potential definitions than a specific one, we can compare it to our criteria. By centering on choices, this definition meets the criterion of focusing on human action. It can easily be restricted in such a way that the hinge is in the present or future. Arguing that a particular period is the hinge presumably would involve identifying the important choices it contains, and arguing that they are the most important choices in history. (That is by no means easy, since it will require a comparison with unknown future choices.)
It is less clear whether this would be decision-relevant. Does knowing that the choices you make are the most important ones ever change how you would make them? In this kind of decision-theoretic setting it is difficult to see how it would; after all, the description of the decision already includes all the outcomes of the decision stretching into the future. The ranking of this choice compared to other future choices seems like useless additional information. But, stepping away from the formalism, the same MacAskill-type considerations about accruing resources to put yourself into a better position for future decisions seem to apply. So, while these definitions are less tied to specific decisions of the spend-or-save variety, they can presumably be made to connect with decisions of that sort.
Similarly, the connection to resources is less direct. This is in part due to an improvement: this definition avoids an excessively specific attachment to systems of finance. In so doing, it may also sacrifice some of the clarity that MacAskill’s definition provided in terms of what is to be done.
G. Comparing the Definitions
A summary of our evaluation is found in Table 1, which shows that none of the definitions fully meet the three criteria, even though three partially meet them (C, D and F). Given the vagueness around EA’s (C) and MacAskill’s (D) definitions, we reason that choice importance (F) provides good-enough decision support for assessing whether now is HH, as detailed in below.
Definitions evaluated by three criteria
| HH definition | Human action | Decision- relevance | Resources | Comment |
| A. The time of perils | ✓ | Vague, centered on the presence vs. the past | ||
| B. Most important period | ~ | ~ | Vague overall | |
| C. Period with disproportionate influence over the long-term future | ~ | ~ | ~ | Vague, focused on long-term effects |
| D. Period with most influential people | ✓ | ~ | ~ | Overly narrow, conceptual issues |
| E. Period with the largest variance in outcomes | Measures objective importance | |||
| E′. Period with the largest variance due to human action | ✓ | Sensitive to duration | ||
| F. Period with greatest choice importance | ✓ | ~ | ~ | Operationalization remains an issue |
✓ indicates that a definition meets a criterion fully, ~ indicates partial fulfillment, and a blank space indicates lack of fulfillment.
We do not claim that this survey exhausts all possible definitions. Its purpose is to highlight some issues in translating the rhetorically powerful idea into an operationalizable, usable concept for decision making. There may be a definition out there that meets our three criteria—whose relevance we are pretty confident about. A particular challenge is in preserving the ambition and grandeur of the metaphor while making a concept that is usable in practice. A narrow technical definition, like MacAskill’s, might be conceptually clearer but nonetheless commit a user to making claims about the far future that are hard to establish. Thus, operationalization remains an issue for even the most relevant definition we can conceive of (definition F in Table 1).
V. DO WE LIVE AT A HINGE OF HISTORY?
Clearly, the reason that many of the authors discussed above introduce their definitions is to make clear their claim that this is a hinge moment. How can we know whether that is so?
Although some definitions discussed above focused on singular moments of importance, they can all admit of degrees: defining a hinge as one of potentially many crucial points rather than the singular most important or influential moment. So, there are two hypotheses to consider.
Weak Hinge of History Hypothesis (HHH): The present moment (or a period around now) is a hinge of history, however defined.
Strong HHH: The present moment (or a period around now) is the hinge of history—the single moment which most embodies whatever properties are used to define hinges.
How would one determine the truth of either hypothesis? One can start the assessment by identifying important choices that we face now or will in the near future. As we have seen, this is how many argue: they point out the threats we face (such as great power conflict, AI, engineered pathogens, and climate change), note their links to recent technological developments and observe that much of it is within our control. But this move gets us only partway: it argues that there are important choices in our general neighborhood, but it is insufficient for establishing either hypothesis. To get to the Weak HHH we need to argue that these are among the most consequential choices that will ever be made.
The literature on existential risk does contain some arguments to this effect. There are a few common ingredients. First, human extinction is very likely irreversible. This is uncontroversial. Second, human extinction is an astronomically bad outcome. This is somewhat more controversial, as it often involves evaluating the badness of human extinction in terms of the number of possible future lives that would not be lived. How many possible future lives there are, and how they should be valued, are all points of significant contention, as is framing the badness of extinction in these terms at all. Third, these arguments tend to assume that the background level of existential risk is low, and that once we navigate these difficult choices, it will be low for a long time.67 For example, they might note that we live on a single planet and that spreading to two or more will diversify our exposure to risks, reducing the likelihood of extinction. However, if this is wrong and humanity can expect to face constant, high levels of risk throughout its future then the choices we make now are consequential but not in a way that is distinguished enough to make this a hinge point. (Or, in a way which trivializes the concept.) To fit the definitions above, these considerations then need to be translated into their terms: importance, influentialness, variance of outcome-value, or importance of choices. The various issues we discussed above will complicate this.
Nonetheless, this gives us a picture of how one could argue for the Weak HHH. Once we allow a graded account of hinges, this seems more plausible. At the moment, two potentially dangerous technologies—AI and biotechnology—are in their infancy and choices we make now will influence their development. We are similarly at an important time for addressing climate change. Identifying these challenges and identifying their long-range impacts is laudable. If the “hinge of history” rhetoric ended there, it would be benign—a rhetorical flourish to focus attention on the fact that we can act to change these outcomes.
Our criticism focuses on two further moves. First, the attempt to turn this piece of political rhetoric into a precise analytical concept. Second, the shift from a graded notion of importance towards the implausible Strong HHH—the claim that this is history’s unique pivot point. We do not see any plausible way of establishing that claim. Discussions of the hinge tend, like many topics in long-term futures studies, to involve considerations on the order of millions of years. We cannot establish beyond doubt that no more consequential choices will arise in the future. The long future is almost totally opaque to us: if humanity survives that long, it may undergo changes that we cannot today conceive of.
If we shift away from seeing this as a literal claim, we can ask: what rhetorical purposes are served by claiming that this is history’s unique hinge moment? It sharpens the call to action. If this is merely one important moment among many, then many may dither. Some because they suspect that their evaluation of importance diverges from those of the alarm-raisers. Others because they prefer to defer action, either until the last possible moment for their own action or in the hope that some future generation can avert the catastrophe. Perhaps our interlocutors do not truly believe that this is “the” hinge of history. They merely say so for pragmatic purposes. If that is so, however, then they undermine those purposes by attempting to transform “the hinge of history” from a grand metaphor into a precise analytical concept.
VI. CONCLUSION
The hinge of history is a metaphor, a rhetorical device for encouraging people to raise their sights and act with the long-term consequences in mind. We are not criticizing rhetoric of this sort, and indeed feel the force of examples like Ban Ki-Moon’s statement: “We are the first generation that can end poverty, the last that can end climate change. We have the power to decide the fate of our planet.”68 This article has not been a study of this sort of political rhetoric, nor do we discourage awareness-raising and mobilization by means of highlighting enormous threats and our capacity to avert them. Instead, this has been a study of an attempt to transform one species of this rhetoric into a precise analytical concept.
Attempts to formulate any rhetorical flourish precisely are likely to lose some of the original force and grandeur, but it might be hoped that these losses will be made up for with gains in precision, unambiguous conditions for its use, and thus clear implications for what we should do. What we have shown is that this is not so in the case of the hinge of history.
The idea that it is important to establish, in some precise way, that this is the most important time and these are the most important choices seems, to us, misguided. However, several of the related concepts and concerns discussed above can be useful, determinable, and motivating for action. We may be able to look back and say “that was a turning point.” If there are severe existential risks, that is a strong reason to act promptly and to apply significant resources to ameliorate those risks. This does not require us to make claims that we live at the most important moment in history, nor to work out precisely what that would even mean.
Notes
- Parfit 2011, vol. 2, p. 616. [^]
- Sagan 1994, p. 173. [^]
- Ord 2020; Thorstad 2022. [^]
- Fisher 2020. [^]
- Yudkowsky and Soares 2025. [^]
- Marche 2025. [^]
- MacAskill 2022a. [^]
- Karnofsky 2021. [^]
- We doubt that this scenario is realistic. Nor is it intended to pump any intuitions about the choice described. Its purpose is simply to draw together elements of the hinge of history concept, as we read it, in sources like those described above. [^]
- Galtung and Inayatullah 1997, p. 6. [^]
- Popper 1957. [^]
- Jaspers 1953. [^]
- Bellah and Joas 2012. [^]
- Baum et al. 2019. [^]
- Sockman 1944, p. 71. [^]
- Read 1998. [^]
- Moynihan 2020. [^]
- Kant 1784/1996, p. 58. [^]
- Harrison 1886, p. 424. [^]
- Jeans 1929, p. 17. [^]
- von Neumann 1955. [^]
- Freud 1930/1961, p. 145. [^]
- Wells 1928. [^]
- Young 2012. [^]
- Lewis 1943. [^]
- Ulam 1958. [^]
- Platt 1966; Koestler 1967/1990. [^]
- Vinge 1993. [^]
- Cf. Sandberg 2013. [^]
- Bostrom 2014. [^]
- E.g., Yudkowski and Soares 2025. [^]
- Platt 1966, p. 195. [^]
- Ibid., p. 200. [^]
- Hobsbawm 1962. [^]
- Sewell 1996. [^]
- Needham 1969. [^]
- Butterfield 1931/1981. [^]
- Hawthorn 1991; Bunzl 2004. [^]
- Sagan 1994, p. 185. [^]
- MacAskill 2022b, p. 335. [^]
- E.g. ibid.; Mogensen 2024; Häggström 2025. [^]
- Fisher 2020. [^]
- EA Forum 2025. [^]
- The notion that history may be “robust” has been developed by Jebari (2021). [^]
- MacAskill 2022b, p. 354. [^]
- Thorstad 2022; 2023. [^]
- Thorstad 2023. [^]
- Ord 2020. [^]
- In what sense could this future be “very good”? Typically, these definitions seem to assume an aggregating view of value, in which having a very large future population (possibly spread across many planets) contributes to making the future very good, assuming that the people living have good lives (defined in some sense suitable to aggregation), live in a just society, etc. [^]
- Parfit 2011, p. 616. [^]
- Karnofsky 2021. [^]
- EA Forum 2025. [^]
- MacAskill 2022b, p. 339. [^]
- Ibid., p. 335. [^]
- The relevant value function can even accommodate lexical priority of some values over others. [^]
- MacAskill 2022a, p. 335, fn. 13. [^]
- Mogensen 2024. [^]
- This is even true if the money were to be saved in cash, since holding cash is the equivalent of lending money to the government that issued the currency that you hold. [^]
- MacAskill 2022b, p. 347, fn. 32. [^]
- Ibid., p. 335, fn. 13. [^]
- Note again that we can easily consider multiple hinges by relaxing these definitions, replacing “the” with “a” and considering moments of roughly equal importance. [^]
- Mogensen 2024; Häggström 2025. [^]
- Spears et al. 2024. [^]
- Moreover, even if we assume that wealth in a foundation will continue to accumulate after the death of a decision-maker, it is almost always often the case that decision makers lose power after they die, in the sense that they lose the ability to influence events according to their will. Unless a decision maker can, like Hari Seldon in Asimov’s “Foundation,” predict the future with a high degree of certainty, their influence will likely decline over time. Consequently, it is important to distinguish between “impact” (the change that a decision maker makes in the world) and “power the degree to which a decision maker can make an impact according to their intended aims. While the prophet Mohamed has had a huge impact on the world since his death, we cannot be certain as to whether this impact is consistent with the aims that he had. Creating an institution that projects one’s impact over many centuries may make a person powerful, but this is not necessarily the case. [^]
- Häggström 2025, p. 2. [^]
- If we want a more objective definition we could substitute the credences of a particular agent with either the epistemic probabilities based on our best available knowledge, or even the objective probabilities of various outcomes, so that we get an objective expectation defined in a way similar to Häggström’s Ut—i.e., where the probabilities come from the natural variability of the world. [^]
- Thorstad 2023. [^]
- Ban 2015. [^]
ACKNOWLEDGEMENTS
Work on this article was conducted at the Mimir Center for Long-term Futures Research of the Institute for Futures Studies in Stockholm. Special thanks to Thomas Moynihan for help with and discussion about Section II. Thanks also to the IFFS Politics, Philosophy and Economics reading group for their input, and to the Mimir Center reading group for discussions which led to this article. Author contributions were as follows. Roussos conceived of and managed the project, organized the material, wrote material for Sections I, II, V and VI, and edited the paper for consistency. Adler performed the literature review and wrote material for Section II. Campbell wrote material for Sections III and IV, including crafting the proposed definition at the end of Section IV. Engström wrote material for Sections I, III, IV and VI, edited the paper for consistency, and contributed to project management. Jebari wrote material for Sections I and III. Sandberg wrote most of Section II. All authors participated in editing and revising the paper.
COMPETING INTERESTS
The authors declare that they have no competing interests.
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