How many lives does the
future hold?
Toby Newberry

Global Priorities Institute | May 2021
GPI Technical Report No . T2-2021

How many lives does the future hold?1*
1. Introduction
The total number of people who have ever lived, across the entire human past, has been estimated ataround 100 billion.2 The total number of people who will ever live, across the entire human future, is
unknown - but not immune to the tools of rational inquiry. This report estimates the expected size of the
future, as measured in units of ‘human-life-equivalents’ (henceforth: ‘lives’). The task is a daunting one,and the aim here is not to be the final word on this subject. Instead, this report aspires to two moremodest aims. First, to provide a robust defense of the claim that ‘the future is vast in expectation’: evenon the conservative assumption that humanity’s future remains Earth-bound over the long-term, thisreport estimates that it can be expected to hold at least 100 trillion lives. The report’s second aim is topresent an earnest, if somewhat more speculative, estimate of the true size of the future. This requiresthat we venture further from established research, meaning the associated estimate depends on several
simplifying assumptions, and should be interpreted as less robust. Nevertheless, this report finds that the
future is truly immense in expectation: on the order of 1030 lives, or more than a billion billion times thetotal number of people who have ever lived.
The remainder of Section 1 sets out the report’s structure, background, and scope. Sections 2-4 form themain body of the report, and divide the central estimate into four distinct scenarios. Section 2 considers
the scenario in which humanity remains Earth-bound over the long term. Section 3 considers three
scenarios involving space settlement, distinguished by whether the human future is bounded by the size of
the Solar System (3.1), the Milky Way (3.2), or only by known physical limits (3.3). For each of the
scenarios in Sections 2-3, the relevant estimate is further subdivided into an estimate of duration, and an
estimate of the average number of lives per century.Section 4 then introduces the prospect of digital
persons, which can be glossed as ‘the possibility that some fraction of humanity’s morally-relevant
successors will be instantiated digitally, rather than biologically’. Together, Sections 1-4 lay thegroundwork for a simple Monte Carlo model, which outputs an estimate of the expected number of
future lives, and in which readers are invited to submit their own degrees of credence in each scenario.
Section 5 addresses Brandon Carter’s Doomsday Argument, which sits outside of the central estimate, butwhich potentially impacts its outcome. Section 6 concludes.
Perhaps surprisingly, there are no serious pre-existing attempts to estimate the expected number of future
lives. While there is a wealth of existing research that is directly relevant to the estimate, and which
provides many individual pieces of the overall puzzle, no such piece constitutes a proper precedent.3 To
take one example, the United Nations (2019) has made projections of expected global population, butthese extend only until the end of this century. Perhaps the closest thing to a precedent occurs in Nick
Bostrom’s Superintelligence, where Bostrom estimates that at least 1035 human lives could be created overthe entire future, given known physical limits. He further estimates that at least 1058 human lives could becreated if we allow for the possibility of digitalpersons (Bostrom, 2014, 101-2).4 However, these figures
1*

I am grateful to Will Macaskill, Toby Ord, Carl Shulman, Matthew van der Merwe, and Anders Sandberg forcomments on an earlier version of this report. Nevertheless, this is still a working draft, and likely contains errors(for which I take full responsibility). Please send helpful comments to tobias.newberry@philosophy.ox.ac.uk.
2This estimate comes from Kaneda & Haub (2020).
3This includes work in ecology on the carrying capacity of the Earth and the life-span of the biosphere,work inphilosophy on existential risk, and work in physics and engineering on the viability and limits of space settlement.
Much of this features in the discussion to follow.
4This estimate is an update to earlier work (Bostrom, 2003).

fall short of representing a proper precedent in two ways. First, they concern how many people could exist,
rather than how many people will exist in expectation. Second, they are intended to be extremely
conservative. Among other things, Bostrom assumes that each star system can support an average of one
billion lives per century - a figure that is smaller than almost all estimates of Earth’s carrying capacity, andmany orders of magnitude less than what our Solar System could plausibly support. As a result, Bostrom’s
figures are primarily useful in Section 4, as an estimate of the relative resource-efficiency of digital, rather
than biological, lives.
The scope of this report is limited in two important ways. First, it is limited in terms of the number ofscenarios considered. In principle, one could divide up possible futures in an arbitrarily fine-grainedmanner, theoretically yielding continued improvements to the quality of the estimate.5 However, the aim
here is just to capture those scenarios with the greatest impact on expected value. As a rule, then, any
scenario not discussed below is considered out of scope, unless there is a compelling reason to think it
would significantly alter the overall estimate.6 Second, the report is limited in which questions about
post-humanity it aims to address. In particular, the report explicitly assumes that ‘human-life-equivalents’
will remain a meaningful unit, morally speaking, over cosmological timescales.7 As a result, most questions
about which specific kinds of post-humanity appear plausible, and the grounds for thinking this unit will
apply in each case, are considered out of scope.

2. Earth
Suppose humanity remains Earth-bound over the long-term: how many lives can the future be expected
to hold? To answer this question, we first estimate the duration of our species’ expected lifespan on Earth(in centuries), before estimating the average expected number of lives per century. The duration estimate
is further divided into two sets of considerations: those concerning our ‘natural’ lifespan, and thoseconcerning our ‘artificial’, or ‘all-things-considered’ lifespan. This section first summarises the evidence
around humanity’s natural lifespan, then assesses how artificial considerations affect this, before turning
to the estimate of lives per century, and combining these to estimate the overall size of the future in this
scenario.
Using geological evidence to determine the current age of our species, Snyder-Beattie et al (2019) estimate
an extreme upper bound of 1 in 14,0008 as the background rate of human extinction risk per year, andsuggest that the true rate is probably less than 1 in 87,000. They demonstrate that if the rate of riskwere
any higher than this, it would be extremely surprising to discover that humans have been around for as
long as we have.9 These figures predict that humanity can expect a further 87,000 years on Earth withouta natural extinction event occurring, and imply that recorded history represents at most 6% of humanity’s
total expected natural lifespan. The authors then corroborate their estimates with four further sources of5

For example, one could consider the scenario in which space settlement is bounded by the size of the local
supercluster. This would theoretically improve the overall estimate quality, on the reasonable assumption that morenarrowly specified scenarios can be estimated with greater accuracy.
6
For example, ‘what about scenarios involving digital persons?’ would have been a reasonable objection had thereport omitted Section 4. On the other hand, ‘what about scenarios where space settlement is bounded by the sizeof Mars (say, because Earth is destroyed and further settlement proves unfeasible)?’ appears out of scope.
7
By contrast, ‘human lives’ will plausibly lose relevance over long enough timescales, perhaps as a result of evolution
by natural selection, or else through other transformative processes.
8
More precisely, they estimate only a 1 in a million chance that the annual risk is greater than 1 in 14,000, relative toa rate of 1 in 10-8.
9
One might worry that this reasoning is vulnerable to observer selection bias. However, Snyder-Beattie et alconsider these sorts of effects, and further demonstrate that their estimates are unlikely to be severely biased in thisway.

empirical evidence: the average lifespans of mammalian species (1-10 million years) and hominins (~970
thousand years)10, as well as the frequencies of mass extinction events (1 in every 30-100 million years),and natural catastrophes that might plausibly trigger human extinction11 (from 1 in 17,000 years to lessthan 1 in a billion years years12). This supplementary evidence is consistent with 87,000 years as a lower
bound on humanity’s expected lifespan on Earth, and, considered as a whole, suggests that the true
expected value may exceed this by several orders of magnitude. A reasonable estimate of this true natural
lifespan, accounting for all of the factors given above, is 1 million years (Ord, 2020, 379).
Of course, this estimate is limited in at least two important ways. On the one hand, it ignores the risk ofhumanity authoring its own destruction - something that could dramatically shorten our species’ lifespan.
On the other hand, it ignores the prospect that we might develop tools to safeguard our future, and findsolutions to most or all of the risks we face on Earth. In light of these limitations, we might think thathumanity’s all-things-considered lifespan is either longer or shorter than the estimate above.
For the first limitation, experts have put the total risk of existential catastrophe (including those of ourown making) at 30% over the next 500 years (Leslie, 1996, 146-7), at least 25% over the long-term(Bostrom, 2002), around 17% over the next century (Ord, 2020, 167), and around 50% over the longterm (Ord, 2020, 169). These individual predictions are broadly in keeping with existing aggregations. For
example, a survey of participants at the Global Catastrophic Risk Conference in Oxford, 2008, found a
median estimate of 19% as the overall risk of humanextinction prior to 2100 (Sandberg & Bostrom,2008). Somewhat more conservatively, the prediction platform Metaculus lists the median probability of‘human extinction by 2100’ at 1%, based on more than 700 individual estimates (Metaculus, 2021).
Overall, then, there is broad agreement that the risk of human extinction in the next 100 years most likely
falls somewhere between 1 and 20%, with experts favouring estimates in the upper end of that range.
This is high enough to make extinction risk a central problem of our time, but, as we shall see, not so highas to have an outsized impact on humanity’s expected lifespan.
For the second limitation, there are clear precedents for humanity having reduced risk in this way, such as
via existing asteroid detection measures.13 It is also true that the higher level aim of ‘achieving existential
security’, or getting to a place where existential risk is very low, and stays very low, appears viable (Ord,
2020, 198-91). However, the crucial point to note is that these two limitations have a strikingly asymmetriceffect on expected lifespan. At most, a high estimate of anthropogenic risk could reduce humanity’s
expected lifespan from 1 million years (based on the background rate of risk) to 0 years. By contrast,
considerations pushing in the other direction could extend our lifespan on Earth by hundreds of millionsof years, perhaps until the end of the biosphere (inapproximately one billion years), or even beyond.
Because of this asymmetry, one would need implausibly high confidence in the chance of near-term
existential catastrophe, relative to long-term existential security, for these ‘artificial considerations’ to
imply an abbreviation of humanity’s expected lifespan. On balance, then, we can treat the natural lifespan10Note that this narrower reference class is not necessarily more reliable than the mammalian species, since it isconfounded by the central role our own species played in the extinctions of many other hominins.
11
Mass extinctions are defined by the fossil record. ‘Natural catastrophes’ include supervolcanoes and large meteor
impacts, among other events. The frequency of such catastrophes can be estimated independently of their impacts
on living things.
12
The figure of 1 in 17,000 years refers to the risk of (smaller) supervolcanic eruptions. There may seem to be atension between this number and the overall estimate of extinction risk: how can an extinction-level event happen
once in every 87,000 years, when there is a supervolcanic eruption once in every 14,000 years (on average)?
However, the authors note that only larger supervolcanic eruptions plausibly threaten human extinction, in whichcase none of these risk frequencies comes close to the upper bound.
13
See, for example, Newberry (2021).

as a conservative estimate of the all-things-considered lifespan, while noting that the human future on
Earth could well be much shorter, but also has a significant chance of being substantially longer.
Alongside an estimate of duration, the scale of humanity’sfuture depends on how many lives per century
Earth can sustain over the long term. The UN Department of Economic and Social Affairs projects that
global population will reach approximately 11 billion people by the year 2100. This provides aconservative estimate of the number of lives per centuryover the long run, on the assumption that world
population remains steady at this level indefinitely. At first blush, this assumption might appear
implausible: historically, the world population has not been well-characterised as remaining steady at any
level.14 On balance, however, the 11 billion figure appears conservative. While published estimates ofEarth’s environmental carrying capacity range as low as two billion, almost all are over 4 billion, and somerange into the hundreds or thousands of billions (reflecting the possibility that technology could facilitate
significantly higher population levels on Earth). It is therefore safe to treat 11 billion as a conservativelower bound on the average number of lives per century over the remainder of humanity’s expected
lifespan, while noting the possibility for significantly higher figures.
Putting together the estimates of at least 11 billion lives per century with the expected natural lifespan of
1 million years gives us a prediction that, in expectation, the future holds at least 100 trillion lives. This isalready a thousand times more lives than everyone who has ever lived, and, as we shall see, hardly
approaches the upper limits of what the human future is likely to hold.

3. Space settlement
We now consider three scenarios where humanity eventually expands beyond Earth. In these scenarios,
the number of future lives is limited not by what this planet can support on its own, but by the resourcesof the Solar System, Milky Way galaxy, or Affectable Universe. For each scenario, the analysis consists ofthree parts. First, a brief argument that one should have at least non-negligible credence in the relevant
scenario.15 Second, an estimate of the scenario’s implications for humanity’s expected lifespan. Third, anestimate of its implications for the average number of lives per century.

3.1 The Solar System
The balance of scientific evidence suggests that settling the Solar System is already technologically viable,
at least in some minimal form. To date, we have successfully sent unmanned craft to a wide range oflocations throughout the Solar System, and proposals to begin Martian settlement over the next several
decades have been seriously considered by both government agencies and private companies.16 However,the scenario under consideration here requires that we go further than this minimal form. Specifically, it
requires that humanity settles the Solar System up to the limit of its carrying capacity (this is the same
assumption made in the Earth-bound case). While it is reasonable to be somewhat less confident in thiseventuality, our existing achievements nonetheless provide evidence in its favour, and to the best of ourcurrent knowledge there are no hard barriers imposed by physics that preclude Solar System settlement of
this sort. Further, the claim that it will eventually be viable is a modest one: denying it would require strong
evidence that this will remain out of reach over the coming centuries and millennia. It would therefore beoverconfident to hold negligible credence in this scenario.

14

With the possible exception of some times in prehistory.
In one sense, these arguments are not necessary, since readers are free to input their own credences in the model.
16
SpaceX is actively pursuing a proposal of this sort (see, e.g. Drake, 2016).
15

Unfortunately, many of the methods used to estimate humanity’s expected life-span on Earth break downwhen we consider space settlement. In particular, reference class forecasts based on the lifespans of othermammalian or hominin species are significantly less relevant, because none of these other species
expanded beyond Earth. Estimates based on the incidence of mass extinction events, and the frequencyof natural catastrophes, are also less relevant: all known categories of mass extinction, and almost all
natural catastrophes, have effects that are confined to Earth. While none of this is to say that reasonableestimates of humanity’s expected life-span cannot be made for these scenarios, it is true that the evidential
base gets somewhat thinner as we consider grander scenarios. To reflect this, the estimates below typicallyconsist of an upper and lower bound, together with a simplifying assumption about the distribution of
possibilities, as opposed to an overall ‘best guess’.
In the case of the Solar System, there are at least three considerations that might inform the estimate.
First, since Solar System settlement does not preclude humanity continuing on Earth, we can take theearlier figure of one million years as a reasonable lower bound on expected lifespan in this scenario.
Second, the main lifetime sequence of the Sun will last for another five billion years, and can serve as aconservative upper bound on expected lifespan.17 Third, there are several known natural risks that could
have Solar System-wide effects: gamma-ray bursts, nearby supernovae, and the risk that the vacuum of
space itself might collapse. However, each of theserisks is relatively well-understood, and all are
sufficiently small as to have virtually no impact on the overall estimate. For example, the risk of vacuum
collapse has been well-characterised at no higher than 1 in 10 million per century (Tegmark and Bostrom,2005), with best-guess estimates suggesting it is as low as 1 in 10600 per year (Buttazzo et al., 2013). It
therefore represents a life expectancy of at least one billion years, and has a negligible overall effect on theestimate here. Together, these considerations imply that humanity’s expected lifespan in this scenario will
fall between one million and five billion years. If we assume the relevant probability density is uniformly
distributed across this interval, we arrive at an average life expectancy of around 2.5 billion years.
The carrying capacity of the Solar System is most plausibly limited by available energy, which provides anestimate of the expected number of lives per centuryin this scenario.18 The total power output of the Sun
is approximately two billion times that which sustains all life on Earth, and represents a highly
conservative estimate of the total power available to a technologically mature civilisation.19 Combining thiswith the earlier estimate for Earth’s carrying capacity, which was itself highly conservative, we produce anestimate of around 20 quintillion biological humans for the carrying capacity of the Solar System.
When multiplied by the earlier estimate of humanity’s expected lifespan, conditional on settling the Solar
System (2.5 billion years, or 25 million centuries), this figure (20 quintillion lives per century) produces anestimate of around 1027 lives for the expected size of the future. Even for someone who considers
substantial Solar System settlement to be a one in a million shot, this amounts to a thousand billion billion
expected future lives.20
17

In the same way that the natural end of the biosphere does not necessarily spell the end of life on Earth, it ispossible that a civilisation capable of surviving until the end of the Sun’s main lifetime sequence would be capable ofsurviving into the red giant phase. In this sense, the five billion year figure is conservative.
18
It is tempting to think that the carrying capacity would also be limited by the current availability of terrestrial
habitats; for instance, the surface areas of Mars, Venus, and the rocky moons. In fact, there are strong reasons tofavour the construction of off-planet habitats: construction is more energy-efficient outside of gravity-wells, and in
the absence of atmospheric weather.
19
It is conservative in that it uses a figure for the total Solar energy incident on Earth, only a small fraction of whichgoes towards sustaining human life. Moreover, only a small fraction of the Sun’s total mass-energy is released aslight.
20
This calculation assumes that the rate of settlement is ‘fast’ relative to humanity’s expected lifespan, such that the
average number of lives per century, in the long run, approximately equals the carrying capacity. However, given that3.2 The Milky Way
Conditional on Solar System settlement being achieved, it appears highly plausible that humanity could
expand to other star systems across the Milky Way. To motivate this claim, consider the fact that by the1970s we had already reached an important milestone in interstellar transit: sending the Voyager I and IIprobes beyond our Solar System, and into interstellar space. The Voyager probes also used considerably
weaker propulsion mechanisms than current technology permits21, and do not reflect the cutting edge ofwhat humanity could achieve as regards interstellar transit. It would therefore seem overconfident tobelieve that humanity will never expand beyond our Solar System, even given the fullness of time.
Furthermore, because this scenario assumes Solar System settlement, the viability of interstellar transit isessentially all it needs to get off the ground: a civilisation that is capable of settling one Solar System
would plausibly be able to settle other systems, provided it can get to them.
Once more, the increase in the scale of the scenario comes with a corresponding increase in both
expected duration and expected carrying capacity. With respect to duration, we can make a similar seriesof moves to those in the preceding sub-section. First, we can take the expected duration in the case of
Solar System settlement as a lower bound on the expected duration here. The question of a reasonable
upper bound is more difficult, since the Milky Way does not have as well-defined a lifetime sequence as
the Sun. Here, we use the end of the stelliferous era - the time after which very few new stars form - toplay this role. This will happen in approximately ten trillion years (Adams & Laughlin, 1999). However, it
is worth noting that the end of the stelliferous era is not really a good proxy for the maximum possible
lifespan of a galaxy-wide civilisation.22 Nevertheless, its inclusion here permits us to make illustrative
estimates, while reflecting the facts that (1) simple and effective proxies for this upper bound are few andfar between, and (2) the upper bound can be expected to fall somewhere between the upper bounds for
scenarios 3.1 and 3.3. Similar to Solar System settlement, there are very few known natural risks that could
cause extinction at an interstellar scale. However, because of the greater timescales involved, the risk of
vacuum collapse is potentially relevant to the estimate here. Based on the evidence cited in the previous
section, a reasonable assumption is that there is at least a 50% chance that vacuum collapse either does
not exist, or else operates on timescales even longer than those considered here. This consideration cantherefore be treated as approximately halving the duration estimate. If we again assume a uniform
distribution, these numbers result in an average expected duration of around 2.5 trillion years.
For carrying capacity, the calculation is quite a bit simpler: we can simply take the estimate for this Solar
System and multiply it by the number of stars in the Milky Way.23 This gives an estimate of around 1025
lives per century as the carrying capacity of our galaxy. Together, these figures produce an estimate ofaround 1035 lives for the expected size of the future, conditional on humanity settling the Milky Way.

we are talking about billions of years, ‘fast’ could in this context mean ‘over the course of hundred of thousands ofyears’.
21
For example, it has long been known that nuclear power could produce enough thrust to reach speeds measured
in percentage points of the speed of light - severalorders of magnitude faster than the voyager probes (see, e.g.
Dyson, 1968).
22
One obvious weakness here is that a galaxy-wide civilisation could plausibly survive beyond the end of thestelliferous era: there would still be stars even when star formation ceases, and it may be possible to derive additionalenergy in other ways (see, for example, footnote 30, below).
23
Between 100 billion and 400 billion. Two other points may also be worth noting. First, the Milky Way will collidewith the Andromeda galaxy in some 4.5 billion years, adding a further ~trillion stars to those within reach of aninterstellar civilisation. Second, this method is limited by the fact that not all stars are identical to the Sun.

3.3 The Affectable Universe
Moving from interstellar to intergalactic settlement involves another step-change in scale. While we haveno precedent for sending material over intergalactic distances, recent work demonstrates that this isachievable using standard physics (Sandberg and Armstrong, 2013).24 Theoretical evidence of this sort,even from experts, should weigh less than the more practical evidence for interstellar transit, but it would
still seem unduly sceptical to believe that intergalactic travel is close to impossible.
However, it does not seem likely that settlement beyond the Milky Way would meaningfully impact the
duration of humanity’s expected lifespan. As in the previous scenario, the end of the stelliferous era marksa plausible upper bound to this lifespan - and the end of the stelliferous era is not confined to the MilkyWay.
Of course, the prospect of settling other galaxiesdoes have significant implications in terms of carrying
capacity. Our Local Group, to which the Milky Way belongs, contains around 80 galaxies or dwarf
galaxies, most of which hold many millions of stars.At the most extreme limits, the ‘affectable universe’ the portion of the universe within our power to impact causally25 - contains around 20 billion galaxies(Ord, 2020, p233). As a result, we might expect an intergalactic civilisation to support hundreds, millions,or even billions times more lives per century than one confined to a single galaxy. To arrive at an estimateof carrying capacity, we use the size of our LocalGroup as a lower bound on the number of galaxies
humanity might reach, with the total affectable universe as an upper bound, and again assume a uniform
distribution.26 This gives an estimate of around 4 billion galaxies, conditional on humanity achieving
intergalactic settlement. If we then assume that each of these galaxies could support, on average, as many
lives as the Milky Way (1025 per century), we arrive at an estimated carrying capacity of around 1035 lives
per century for the affectable universe.27
Multiplying this figure (1035) by the estimated same expected duration as in the Milky Way scenario (50trillion years) gives an expected 1046 lives for the total size of the future.

4. Digital persons
So far, we have estimated the expected number of future lives in four different scenarios. Importantly,
these are estimates of the expected number of biological lives: among other things, they are based onevidence about the number of present-day humans the Earth can support. In this section, we turn toconsider the prospect of digital persons. Following the same pattern as above, we begin by motivating the
scenario’s plausibility, before addressing its implications for the expected size of the future. However,digital persons merit a slightly different treatment in terms of how the prospect fits into the overall model.
For the scenarios addressed in Sections 2 and 3, each successive scenario (approximately) entailed all
previous scenarios, such that one’s credence over the full set should sum to 1. By contrast, we treat digital
24

That is, without exploiting speculative assumptions, e.g Einstein-Rosen wormholes.
This region is sometimes referred to as the universe’s ‘Event Horizon’.
26This is a simplification. One way it could be improved upon is by assuming a uniform distribution over‘civilisational expansion speed’, rather than over the number of galaxies reached (this would reduce the expected
number of galaxies by about a half). One could also make further refinements to the speed distribution, drawing on
available information about which physical barriers might place hard limits on this. However, improvements in thisdirection seem unlikely to alter the estimate by more than an order of magnitude, and so have been omitted here(see, for a partial explanation, the first limitation mentioned in the introduction).
27
As with stars, there is considerable variation in the size and composition of galaxies. This means that the simple
multiplicative method used here is only informative as a broad illustration of scale, and should not be read as
authoritative.
25

persons as an independent prospect, which would act as a constant multiplier to the estimates in eachother scenario. In other words, the assumption is that the development of digital persons is more or lessindependent of different levels of space settlement.28
There is a consensus among experts about the viability of humanity eventually creating artificial general
intelligence, and even broad agreement that the relevant timescale is years or decades, rather thancenturies or millennia. A survey of more than 300 machine learning experts, carried out in 2016, asked
about the timeframe until an AI system would be ‘able to accomplish every task better and more cheaply
than human workers’. On average, the experts predicted a 10 percent chance of this happening as soon as
2025, and a 50 percent chance of it happening by 2061. These timeframes are corroborated by a separate
survey from 2014, where machine learning experts estimated 2075 as the median year by which this levelof AI development would most likely be achieved.29 The second survey also recorded the proportion ofexperts who think humanity will never achieve this level of AI development, and found this to be a small
minority, at only 16.5%.30 In light of this, it would be unreasonable to hold very low levels of credence inthis prospect, especially over the long term.
Of course, the creation of artificial general intelligencedoes not necessarily amount to digital persons, inthat the relevant digital entities need not be ‘people’ (morally speaking). We should therefore treat theprospect of digital persons as somewhat less likely than artificial general intelligence. However, in theabsence of compelling reasons for thinking digital persons are impossible, the fact that experts agree on
the viability of artificial general intelligence, with relatively high confidence, seems sufficient to motivate
non-negligible credence in this scenario.
If a significant fraction of humanity’s morally-relevantsuccessors were instantiated digitally, rather thanbiologically, this would have truly staggering implications for the expected size of the future. As noted
earlier, Bostrom (2014) estimates that 1035 human lives could be created over the entire future, given
known physical limits, and that 1058 human lives could be created if we allow for the possibility of digital
persons. While these figures were not intended to indicate a simple scaling law31, they do imply that digital
persons can in principle be far, far more resource efficient than biological life. Bostrom’s estimate of thenumber of digital lives is also conservative, in that it assumes all such lives will be emulations of humanminds; it is by no means clear that whole-brain emulation represents the upper limit of what could beachieved. For a simple example, one can readily imagine digital persons that are similar to whole-brain
emulations, but engineered so as to minimise waste energy, thereby increasing resource efficiency.
Here, we include estimates of the ‘digital carrying capacity’ for each of the scenarios considered so far - inother words, the number of digital persons we might expect the Earth, Solar System, Milky Way, orAffectable Universe to support. These should not be understood as authoritative, but rather are intended
to further illustrate the extraordinary impact that digital persons could have on the expected number of
future lives. In the model linked below, we invite readers to input their own estimates of the relative
resource efficiency of digital versus biological life, as well as the fraction of humanity’s future resources
they expect to support digital entities. For each of the scenarios in Sections 2-3, we then multiply the
resource fraction by the expected number of future lives, and scale the outcome of this by the efficiency
28

If anything, the development of digital persons would simplify space settlement (in the same way that unmanned
space missions are simpler than those with crews). In this sense, the assumption of independence can be regarded ashighly conservative.
29
Technically, they were estimating the year in which there is a 90% chance of the existence of machineintelligence“that can carry out most human professions at least as well as a typical human.”
30
Again, this is technically the fraction of respondents who thought ‘there is no year by which I am 90% surehumanity will have achieved this level of AI development.’
31
I.e. that 1058/1035 = 1023 digital lives can be supported for each biological life, at any scale.

estimate. Finally, the resulting product is added back to the expected number of biological lives (minus
those that have been ‘converted’ to digital entities). This gives an estimate of the total number of lives,
both digital and biological, for each scenario.
How many digital lives might the Earth support? One way of estimating this is to assume that solar
energy could be converted to digital consciousness at approximately the same rate that energy from foodis converted to biological consciousness in the human brain (i.e. about 20 watts). On Earth, the total
average solar irradiance at surface level is on the order of 1,730 terawatts. Making the conservative
assumption that 1% of this might be available to support digital persons, we arrive at an estimatedcarrying capacity of around 140 trillion lives.32
Applying this same method to the other scenarios, we get similar increases in scale. For the Solar System,
we can take 1% of the Sun’s total power output (~1024 watts) as our starting figure. Dividing this by 20
gives a digital carrying capacity of around 1023 lives. For the Milky Way, we can simply scale this by the
number of stars in our galaxy, which gives a digital carrying capacity of around 1034 lives. Finally, we canscale this by the number of galaxies in the Affectable Universe (8 billion), which gives a digital carrying
capacity of close to 1044 lives. Especially for the latter two scenarios, these figures are conservative in thatthey ignore the prospect of energy from sources other than starlight. As Ord (MS) notes, only a tiny
fraction (less than 0.1%) of stellar mass will eventually be radiated as starlight, and there may be otherways that technologically advanced civilizations could generate energy.33

5. The Doomsday Argument
One might worry that all of the above reasoning can be undone on purely probabilistic grounds, byappeal to something like the Doomsday Argument. There are at least three points worth making aboutsuch a move, which, taken together, suggest that it does not succeed in undercutting the case presented
above. In essence, the Doomsday Argument makes the point that it would be highly unusual to findoneself in a highly unlikely position: if all peoplewho will ever be born were ordered by their date ofbirth, 90% of them would find themselves in the first 90% of people. By the same token, we should think
there is only a small chance we are in the first small percentage of people who will ever be born - implyingthat the chance of there being many, many more people born in future is equivalently small.
The first point to note about this is that it remains highly contentious: anthropic reasoning is an unsettled
field in general, and there is no consensus that the Doomsday Argument, in particular, succeeds. In fact,
the argument remains beset by proposed rebuttals, and it is not at all clear it will escape this continued
onslaught unscathed. To take one example, the ‘Self Indication Assumption’34 states that, ceteris paribus, anobserver should reason as if they are randomly selected from the set of all possible observers. As an attackon the Doomsday Argument, we can gloss this as the claim that ‘if more people are born overall, there isa greater chance I will be among them’. Assuming Bayesianism, the size of this effect precisely cancels out
the effect of the Doomsday Argument, suggesting the argument provides no information whatsoever
about the total number of people who will ever exist.
Second, notwithstanding the argument’s name, the actual prediction it makes is that the expected numberof people who will ever live is infinite, given infinite time. Mathematically, the argument’s central claim
32

I.e. This is 1% of 170,000 terrawats, divided by 12.
For example, feeding matter into black holes may be a far more efficient way of accessing energy.
34This principle was first proposed by Dennis Dieks (1992), and given its current name by Nick Bostrom (2002). It
has been defended by Bartha & Hitchcock (1999), and, more recently, Ken Olum (2001).
33

implies that the eventual population, measured in multiples of the number of people who have lived sofar, will fit a Pareto distribution: such a distribution has an infinite mean (Ord, MS).
Third, the Doomsday Argument remains, at most, a way of setting a prior: it claims that, in the absence ofother evidence, one can estimate the total number of people who will ever live based on one’s likely birth
position. But, as the reasoning above should make clear, it is far from the only evidence available. Overall,these considerations imply that most aspects of the Doomsday Argument, including its basic
philosophical soundness, and the direction it points in this particular case, remain in question. It should
not be treated as a strong objection to the foregoing arguments.

6. Conclusion
The preceding considerations provide the foundations for a simple Monte Carlo model. Table 1
summarises the various estimates of duration and carrying capacity that are used in the model, anddefended above, using my best guess estimates of expected duration and expected carrying capacity ineach case. Table 2 presents three further model parameters that do not fit cleanly into the same
framework, including the relative efficiency of digital versus biological life. Finally, Table 3 summarises theoutputs of the model for a person who is sceptical of the arguments above. In particular, this person
thinks that humanity stands no chance whatsoever of settling the affectable universe or the Milky Way,and only a 1 in 10,000 chance of settling the Solar System. Further, they estimate that only a trillionth ofhumanity’s future resources will go towards supporting digital persons. Even with these scepticalestimates in place, the expected future is almost unimaginably vast: extending over millions or billions ofyears, and containing some 1028- that is, 10 billion billion billion - lives.
Scenario

Duration (centuries)

Carrying capacity(lives per century)

How many lives does
the future hold?

Earth (Homo sapiens 103
reference class)

1010

1013

Earth (homininreference class)

104

1010

1014

Earth (mammalianreference class)

104

1010

1014

Earth (massextinctions referenceclass)

106

1010

1016

Earth (digital
persons)

104

1014

1018

The Solar System

108

1019

1027

The Solar System(digital persons)

107

1023

1030

The Milky Way

1011

1025

1036

The Milky Way

1011

1034

1045

(digital persons)
The Affectable
Universe

1010

1035

1045

The Affectable
Universe (digital
persons)

1010

1044

1054

Table 1: core estimates35

Parameter

Estimate

Number of stars in the Milky Way

1011

Number of galaxies humanity could potentiallyreach

103 - 1010

Table 2: misc. parameters

Inputs for different scenarios‘An extremely conservative reader’

Credence in scenario 2: Earth~1

Credence in scenario 3.1: The Solar System

10-4

Credence in scenario 3.2: The Milky Way

0

Credence in scenario 3.3: The Affectable Universe0

Fraction of humanity’s future resources devoted
to scenario 4: digital persons

10-12

Resource efficiency of digital lives relative tobiological lives

109

How many lives does the future hold?

1028

Table 3: Example estimate
Ultimately, it is the fact that humanity’s potential is so remarkably vast that drives the estimate of expectedvalue. In terms of duration, it is at least prima facie possible that humanity could last until the end of
Earth’s biosphere, the death of the Sun (~5 billion years), or the death of the last stars (~10 trillion years).
In terms of population, it is possible that the number of people alive at any one time could far exceed
present levels, especially when taking into account the prospects of digital persons, and of humanity
continuing beyond Earth. Crucially, the argument that our future is vast in expectation requires only asmall degree of credence in such expansive possibilities. By contrast, the claim that our future will be
35

Estimates in excess of 1 quadrillion are rounded to the nearest order of magnitude.

anything shorter than a million years, or contain any fewer than 100 trillion lives, in expectation, would
require both extraordinary scepticism about these grander futures, and extraordinarily high confidence
that humanity will cause its own destruction in relatively short order.

7. References
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Kaneda, T., Haub, C. (2020). ‘How many people have ever lived on Earth?’, Population Reference Bureau.
Leslie, J. (1996). The End of the World: The Scienceand Ethics of Human Extinction.Routledge.
Metaculus (2017). ‘Will humans go extinct by 2100?’, accessed 4/5/2021
https://www.metaculus.com/questions/578/human-extinction-by-2100/.
Müller, V. & Bostrom, N. (2016). ‘Future Progress in Artificial Intelligence: A Survey of Expert Opinion’in Fundamental Issues of Artificial Intelligence, Müller, V. ed., Synthese Library, Berlin: Springer.
Ord, T. (2020). The Precipice. London: Bloomsbury.
Ord, T. (MS). ‘The edges of our universe’. arXiv:2104.01191
Sandberg, A. & Bostrom, N. (2008): “Global Catastrophic Risks Survey”, Technical Report #2008-1,
Future of Humanity Institute, Oxford University.
Snyder-Beattie, A., Ord, T., and Bonsall, M. (2019). ‘An upper bound for the background rate of humanextinction,’ Sci Rep 9, 11054.
Tegmark, M. & Bostrom, N. (2005). ‘Is a Doomsday Catastrophe Likely?’ Nature, 438(7069).
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