Milan M. Ćirković

over all possible civilization's **histories** describes
the desired future in the most general form.[2]
However, it is illusory to hope to explicate the functional
Q in such general terms.
Instead, we shall use a greatly simplified “temporal” model, in which we assume
that the civilization is characterized by discrete individual
observers, countable (with their observer-moments) at any given
time. This may be mathematically expressed as:

_{}
(*)

where N(t) is the number of observers at epoch t of cosmic
time, and áσ(t)ñ the corresponding average
density of their observer-moments.[3]
The lifetime of the civilization considered spans the interval from
t_{min} to t_{max}, where the upper limit may—in
principle—be infinite. It is important to emphasize that we use
physical time here (i.e. we acknowledge validity of Weyl postulate
which enables one to define universal, “cosmic” timescale),
although it is possible to change coordinates to some subjective
timescale if more appropriate, in the manner of Dyson's biological
scaling hypothesis (Dyson 1979; Krauss and Starkman 2000), or
Tipler's Omega-point theory (Tipler 1994).[4]
There are **at least two** distinct ways in which cosmological
parameters enter into eq. (*):

1. Most obviously, values of cosmological
parameters determine absolute limits on t_{min} and
t_{max}. If the entire lifetime of the universe is equal to
t, than t_{max}
£ t. In addition, t_{min}
> 0, but also one may state that t_{min} ³ t_{*}, where t_{*} is the epoch of
formation of first stars of sufficiently high metallicity for
processes of chemical and biological evolution to take place.

2. The shape of the function N(t) is
dependent on the cosmological parameters when the nature of matter
distribution is taken into account. Namely, the power spectrum of
density perturbations determines which objects form as result of
gravitational attraction and decoupling from the universal Hubble
expansion (for a modern textbook treatment see Peebles 1993). On the
other hand, the size of the matter aggregates like stars, galaxies,
etc. is essential for answering the question how large parts of the
rest mass can be converted into energy for purposes of (intelligent)
information processing. It is plausible to assume that the **maximal **number of observers
is proportional to the energy consumed for such purposes, which can
be mathematically written as

_{}
(**)

where r_{i} denotes the relevant energy density,
and *q* < 1 is the
efficiency of whatever energy extraction process used by the
civilization. The reason why we consider the maximal number of
observers is that the exact number, of course, depends on the
sociological factors which are completely outside of the scope of
the present study. It may also strongly depend on the level of
technology (e.g. Sandberg 2000), and may radically decrease with the
further scientific and technological advancement (like in the
cyberpunk scenarios of “collective consciousness” development). Neglecting
this, we perceive that at least this upper limit is still
cosmologically determined, since both relevant densities
r_{i} and integration bounds are contained
in the cosmological discourse. Of course, the density áσ(t)ñ is even less
tractable from the point of view of the present knowledge, since it
may be expected to hinge crucially upon biological factors on which
we know little. However, for the purposes of present study, it is
enough to assume that it is non-zero function of time which either
increases or decreases slower than exponential.

**3. COSMOLOGICAL
REVOLUTION: A STORY**

How does the number of observer moments Q tally with various
cosmological models, including the realistic one? Let us first note
that it may be doubted whether such thing as the **exact** model can ever be
reached. Several simplifications come handy at this point.
Sufficiently high degree of symmetry leads to familiar Friedmann
models (or generalization of them including the cosmological
constant), and sufficiently small perturbations can be treated in a
familiar way. However, even the general outline on which the future
fate of a universe depends may not be obvious till some critical
epoch to any internal observers. In particular, as discussed in
detail in an illuminating essay by Krauss and Turner (1999),
realistic universes are notoriously difficult to analyze completely,
due to possible presence of very large (super-horizon) perturbations
which enter the visible universe only at some later epoch. From the
point of view of internal observers, there is no possibility to
avoid this ambiguity. In such position, it is natural that
priorities leading to maximization of the number of observer-moments
in (*) are contingent on the contemporary cosmological knowledge. As
Krauss and Starkman (2000) vividly put it, “funding
priorities for cosmological observations will become
exponentially
more important as time goes on.”

Let us investigate the following
imaginary situation. A civilization inhabiting a particular,
sufficiently symmetric universe, develops both theoretical and
observational astronomy to the point where it can make useful
working models of their universe as a whole. After an equivalent of
Einstein of that particular world develops formalism describing
curved spacetime at the largest scales, an equivalent of Hubble
discovers universal expansion, and equivalents of Penzias and Wilson
discover the remnants of primordial fireball, leading cosmologists
begin to support the flat baryonic universe with Ω_{B} = Ω
» 1. At first it seems that all
observations can be accomodated in the framework of such a model (we
suppose that light elements' abundances, for instant, are not
inconsistent with such high baryonic density, contrary to the
situation in **our
**observable universe!). Some circumstantial support for this
model comes from ingenious theoreticians of that civilization, who
discover that coupling of a universal scalar field to gravity leads
to the exponential expansion during the very early epochs. This
inflationary phase in the history of such a universe leads to
prediction that ïΩ - 1ï = e » 10^{-5},
while it is not clear whether the universe is marginally closed or
marginally open. In the latter case (favored by most of the
theoreticians in such a universe), the number of galaxies in their
universe is infinite, and therefore such a universe offers a very
optimistic prospects for survival of intelligence and life. There is
no event horizon in such universe, and the particle horizon is
(very) roughly given as the age of the universe in light years, i.e.
the maximal path traversed by light along the observer's past light
cone. What are prospects of intelligent beings to survive
indefinitely in such a universe?

Gradually, bolder
scientists begin to tackle physical eschatological issues. An
equivalent of Dyson in that world reckons that this civilization
can, in principle, indefinitely survive while exploiting sources of
energy in larger and larger volume (t_{max} =
¥). In addition, it was
suggested by some extremely speculative and ingenious cosmologists,
that non-zero cosmological shear can be manifested at later epochs,
providing in this manner additional energy which will be
proportional to the volume of the technologized space (although this
option has not been studied enough). Predominant attitude toward
maximization of (*) is, therefore, very optimistic and not
characterized by any sense of urgency. There are physical grounds to
expect Q_{max} = ¥.

Suddenly, a new and unexpected twist
occurs. New cosmological observations, and in particular two
superbly designed projects detecting standard candles at large
distances in order to make the best-fit estimate of the Hubble
constant, indicate a spectacular overthrow of the ruling paradigm.
After the dust settles (which lasts for years, and probably
decades), the new paradigm suggest that the universe is still
geometrically flat, but dominated by the cosmological constant term
Λ in such way that W = W_{B} + W_{L} = 1, W_{B} = 0.1, W_{L} = 0.9. Now, the situation
radically changes with respect to the envisaged number of possible
observer-moments given by (*). The universe is now found to possess
not only a particle, but an event horizon also, defined as the
surface through which any form of communication is impossible at all
epochs. This is a consequence of the fact that after a phase of
power-law expansion, the exponential expansion generated by
L sets in, thus
creating a second (future and final) inflationary phase in the
history of the universe (see Appendix I for some technical details).

There are further bad news for such a
civilization. The decrease in the metabolic temperature envisaged by
the Dyson-equivalent can not continue indefinitely, as was possible
before the “cosmological revolution”, since the de Sitter universe
possesses a minimal temperature, a circumstance following from the
quantum field theory, and described in some detail in the Appendix
I. This is an extremely
small temperature, but still finite, and below it nothing can be cooled without
expending precious free energy. Thus, the temperature scaling may be
continued only to the final value of t_{max} in (*). In
addition, one may not use any shear energy, since the equivalent of
the so-called “cosmological no-hair” theorem guarantees that
no significant shear remains during the exponential expansion
(Gibbons and Hawking 1977).

It seems obvious that the
“cosmological revolution” will
have important social and political consequences if the desire of
maximizing Q
in (*) remains the legitimate goal of considered civilization. There
could be no more leisurely activities in the framework of the second
paradigm. Although the survival cannot be indefinite, it still seems
that it can be prolonged for very, very long time—but only if one
starts early enough. Besides funding for cosmological observations,
one may expect that funding for interstellar and even intergalactic
expansion will suddenly rise. Colonization of other stellar and
(ultimately) galactic systems should better start early in the
Λ-dominated universe!

**4. DIFFICULTIES INVOLVED IN
ESTIMATES**

This story can teach us several
lessons. It seems that we are currently in the middle of the
“cosmological revolution” described above, although not as
dramatic, since there was never a consensus on the values of
cosmological parameters or the nature of matter constituents in the
actual human cosmology. Also, the currently inferred value for the
vacuum density W_{L}
is somewhat smaller, being about 0.7 (e.g. Perlmutter et al. 1999;
Zehavi and Dekel 1999). However, the qualitative nature of the
revolution and the implied potential change in the entire spectrum
of human social and technological activities are analogous.

Of
course, this counterfactual example may be regarded as rather
conservative. One may imagine much more drastic changes in the
dominant cosmological paradigm. Let us, for instance, suppose that
for some reason most cosmologists did accept classical steady state
theory of Bondi, Gold and Hoyle in late 1940’s, and that in the same
time the development of radio astronomy has been damped for several
more decades. The attitude of humanitarian thinkers seeking to
maximize Q
could be very well encouraged by the steady state concept of
creation of low-entropy matter in the manner conserving density of
matter fields. Not only did one have t_{max} = ¥,
one should also expect lim_{t®¥}
N(t) = ¥,
and there would have been no plausible reason to expect s(t)
to be anything but constant or even increasing function of time.
From the particular human point of view, therefore, the steady state
cosmology offered one of the most optimistic visions of the
future.[5]
(This is somewhat ironic, since the steady state model predicts
essentially the same exponentially expanding spacetime as the
Λ-dominated models.) As we know, after the fierce cosmological
battle in 1950’s and early 1960’s, the steady state theory has been
finally overthrown by discoveries of QSOs and the cosmic microwave
background, as described in a colorful recent history of Kragh
(1996). There has been no historical consensus about the exact
cosmological model accounting for observations ever since, but it
seems that we are on the verge of reaching one. However, it is
conceivable that cosmology of some other civilization passes
directly from the steady state into the Λ-dominated paradigm. This
seems, curiously enough, at least in one respect easier and more
natural than what has occurred in actual history (see Appendix II).
This paradigm shift **must
**be accompanied by a shift in technological and social priorities
if one expects Θ to be maximized.

However,
changes in cosmological paradigm currently underway in the real
world should not be regarded as the end of the story. As mentioned
above, perturbations of the scale larger than horizon scale are
expected to enter our visible universe only at some late epochs. In
the light of the argument above, one may expect that whatever the
cosmological paradigm is established on the timescale of next ~10^{1}
years, may be upset by observing the perturbations on superhorizon
scales (Krauss and Turner 1999). A recent intriguing study of Tipler
(1999) shows that cosmological conclusions reached by local
observations (i.e. those in the vicinity of the Milky Way) can be
highly misleading, and that one should be on guard with respect to
results of any local measurement of cosmological
parameters.

Let us try to estimate the effects of
belated technologization to the lowest order. It perhaps goes
without saying that any such estimate is notoriously difficult,
speculative and on the very fringe of the domain of founded
scientific speculation; some of the reasons, already mentioned,
include our almost perfect ignorance of the evolutionary
possibilities in the social domain, as well as the influence of
various technological advances on the average census of
observer-moments per observer, áσ(t)ñ. Even the simpler part of the
problem, the estimate on the possibilities and modes of evolution of
the number of observers N(t), poses almost intractable difficulties.
We may be virtually certain that the current exponential population
growth of humanity will be arrested at some future date, but whether
it will result in transition to some other (power-law?) growing
function, or tend to a stable asymptotic limit is impossible to
establish at this time. There are certainly several timescales
relevant for the history of an advanced technological community,
which are related to the “quantized” nature of physical
resources alluded to above (and which are, ultimately, consequences
of the cosmological power spectrum). This may roughly correspond to
Kardashev's famous classification of advanced intelligent
communities into three types, depending on the energy resources
available (e.g. tarter 2001 and references therein). However, there
has been no estimates of the timescales required for transition
between the types (and possible intermediate timescales
corresponding to radically new technologies of energy extraction).

Baryonic
mass of the Local Supercluster (henceforth LS) is of the order of
10^{15} solar masses (Oort 1983, and references therein),
and its luminosity several times 10^{12} solar luminosities.
Let us suppose that humanity will eventually technologize the entire
spatial volume of LS, and gather all its negentropy resources for
information processing. Let us also suppose that at whatever time
humans (or posthumans) embark on the process of galactic and
intergalactic colonization, the historical path of such colonization
will be essentially the same; this is a reasonable assumption, since
we expect that colonization timescale is significantly smaller from
the cosmological timescales characterizing large-scale changes in
the distribution of matter within LS. If we further assume (as many
of the prominent anthropic thinkers, following Carter’s well-known
argument, do) that we are the first technological civilization
within LS, we may ask the question how many observer-moments (or
conceivable human lives and experiences) we loose by postponing the
onset of colonization by D*t*?
The simplest (“zero-order”) estimate is just to assume that all
entropy produced by physical processes in LS during that interval is
proportional to the loss of information from the “pool” available to
the presumed “Type IV” future hypercivilization (i.e. the one
exploiting the energy resources of LS). Major entropy producing
process at present (and on the timescales relevant to the issue; see
Adams and Laughlin 1997) is stellar nucleosynthesis. Its products
are high-entropy photons escaping to intergalactic (and
intersupercluster) space and being there further redshifted due to
the universal expansion. Using the Brillouin (1962) inequality
(essentially the integral version of eq. (**)), we may
write

_{}bits,

where
_{}is
the Solar luminosity, and *q* is the (time-averaged) fraction of free
energy which the hypercivilization converts into work of its
computing devices. We expect that the temperature *T *at which
computations are performed to be close to the temperature of the
cosmic microwave background since the timescale even for
colonization of a huge object like LS is short by cosmological
standards, and thus such colonization is essentially isothermal. The
quantity of information lost per a century of delay in starting the
colonization is astonishing by any standard. For a conservative
estimate of *q* = 0.1, and using Dyson’s (1979) estimate of
“complexity” of an average present-day human being _{}bits
(quantity which is likely to grow in future, especially in the
posthuman stage, but which is still useful as a benchmark), the
**number of potentially viable human lifetimes lost** per a
century of postponing of the onset of galactic colonization is
simply (if we assume that the luminosity fraction in the equation
above is unity, which is probably an underestimate for a factor of a
few)

_{}.
(!!!)

Of
course, this is only the total integrated loss; if for some
currently unknown reason the colonization of LS is impossible or
unfeasible, while colonization of some of its substructures is
possible and feasible, this huge number should be multiplied by
fraction of accessible baryonic matter currently undergoing
significant entropy increase (essentially luminous stars). On the
other hand, our estimate is actually conservative for the following
reasons. There are other entropy-producing processes apart from
stellar radiation (notably the stellar black-hole formation becomes
more and more important as the time passes), and thus our estimate
is actually very conservative, since the lost quantity of
information is likely to be higher. Another reason why this estimate
should be taken as the absolute lower limit is the entire spectrum
of **existential risks** (see Bostrom 2001b), which have not been
taken into account here. Namely, the realistic history of posthuman
civilization would be the **convolution** of the integrand
functions in (*) with a risk function f_{risk}(t) describing
the cumulative probability of existential risks up to the epoch t
(and their presumed impact on the observer-moment tally). Obviously,
this function would be biased toward higher values at small values
of t (as measured, for instance, from the present epoch for humans),
since smaller—i.e. those not colonizing the universe—civilizations
are more prone to all sorts of existential risks. Thus, the risk
inherent in “colonization later” policy makes our estimate very
conservative (or “optimistic” from the point of view of lost
observer-moments). However, this estimate possesses the virtue of
being a natural extension of the Dyson’s concept of development of a
Type II (Kardashev) civilization: in order to truly technologize
domicile planetary system, an advanced society must strive to
capture and exploit the entire stellar energy output of its home
star, via Dyson spheres or similar contraptions (Dyson 1960).
*Mutatis mutandis*, the same arguments apply to larger scales
of density fluctuations, and in the L-dominated
cosmological model we are supplied by a natural cut-off at large
scales.

**5.
SUMMARY**

The above testifies to the simple
truth that awareness of the cosmological situation is a first step
toward true long planning for any community of intelligent observers
interested in self-preservation and achieving maximum of its
creative potential. However, in an evolving universe, the factor of
timing seems to set stringent limits on the efficiency with which
such intelligent communities are fulfilling their goals.
While those limits are certainly to be subject of much debate and
discussion in the future, the very fact of their existence makes
cosmology interesting from a transhumanist perspective.
Decision-making performed today, as far as humanity is concerned,
may have enormous consequences on very long timescales. In
particular, an overly conservative approach to space colonization
and technologization, may result (and in fact might have already
resulted) in the loss of substantial fraction of all possible
observer-moments humanity could have had achieved. It is our modest
hope that this cursory study will contribute to the wider and
livelier discussion of these issues and reaching other, more precise
predictions for intelligence’s cosmological future.

Finally, let us note that this
approach is not necessarily the only manner in which cosmology may
enter our everyday life. If some approaches in the fundaments of
quantum mechanics and its links to the human conscience are correct,
we may find ourselves in a situation where the cosmological boundary
conditions determine the nature of our perceptions and
self-awareness (Wheeler 1988; Dugić, Raković and Ćirković 2000).
This differs markedly from our approach in this essay, which is
based on classical cosmology (as well as classical logic and
probability theory). One may imagine that the future correct
physical theory of conscience will incorporate these elements, and
that they will *a fortiori* play some role in any policy-making
attempts based on such a theory.

**APPENDIX I**

Behavior of universe with large
positive vacuum energy density—commonly (and somewhat imprecisely)
known as the cosmological constant—L
has been investigated in several publications even before the
cosmological supernovae began to throw light on its reality
(Carroll, Press and Turner 1992; Krauss and Turner 1999; Ćirković
and Bostrom 2000). In the L-dominated
epoch, the scale factor behaves according to the de Sitter law,
i.e.

_{},

where the effective Hubble constant
is given as _{}.
In such a universe, after a transition period between
matter-domination and vacuum-domination, the event horizons of the size
given as:

_{}pc,

where *c* is the
speed of light, *H*_{0}
*º *100* h* km s^{-1} Mpc is
the present-day Hubble constant (parametrized in such way that *h* is dimensionless number of
order unity), and W_{L} is the
cosmological density of vacuum. Beyond this distance no
communication is possible at **any time**. This is very
different from the situation in the matter-dominated universes,
where the contribution of cosmological constant is very small or
completely vanishing, where there are only so-called particle
horizons, representing temporary obstacles to communication (i.e.
any two arbitrarily chosen points will get into region of causal
influence in finite time).

Minimal temperature of
the exponentially expanding (de Sitter) universe characterized by
cosmological constant L is given by the
equation (Gibbons and Hawking 1977):

_{} K,
(I. 2)

where *k* is the
Boltzmann constant. The expression under the square root on the
right-hand side of (I. 2) is close to unity, and h
» 0.6. Therefore, this temperature is
low beyond description, but as longer and longer timescales in the
future unfold, its finite value precludes the asymptotic process of
lowering metabolic rate of intelligent creatures of far future
suggested by
Dyson (1979) as a method for achieving immortality (Krauss and
Starkman 2000).

#### APPENDIX
II

Ironically enough, it would not be so extremely
difficult to confuse the classical steady-state cosmology with
L-dominated ones
if the level of sophistication of (neo) classical cosmological tests
(e.g. Sandage 1988) is not very high. Namely, the major
**observational** parameter used in empirical discrimination
between world models is the **decceleration parameter**
*q*_{0}, defined as

_{},

where *R* is the cosmological scaling factor. Of course,
this definition is not of much practical value. Instead, it can be
shown that in standard relativistic Friedmann-Robertson-Walker
cosmologies, *q*_{0} is related to densities in matter
and vacuum in the following way (with the usual assumption of
negligible pressure):

_{},

which delivers the “classical” value of 0.5 for Einstein-de
Sitter model (W
= W_{m}
= 1, W_{L}
= 0), but becomes strongly negative for the vacuum-dominated models.
In particular, for the extreme model considered above (W_{m}
= 0.1, W_{L}
= 0.9), we have

*q*_{0} = – 0.85.

It is well-known that, on the other hand, the
decceleration parameter in the steady-state model is

*q*_{0} = const. = –
1.

Obviously, the last two values are close enough for the clear
and unequivocal discrimination between them to be an extremely hard
observational task.

**Acknowledgements.** I use this opportunity
to express my gratitude to Olga Latinović, Vesna Milošević-Zdjelar,
Srdjan Samurović, Milan Bogosavljević and Branislav Nikolić for
their help in finding some of the references. The manuscript
enormously benefited from discussions with Nick Bostrom, Petar
Grujić and Fred C. Adams. Kind advice of Robert J. Bradbury, Mark A.
Walker and Mašan Bogdanovski is also appreciated. Technical help of
my mother, Danica Ćirković, has been invaluable in concluding this
project.

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**Footnotes**

[1] The
latter presents a separate problem, far from being solved in the
anthropic thinking. What constitutes a reference class is by no mean
clear, and some recent discussions (from different premises!) can be
found in Bostrom (2001) and Olum (2001).

[2] We
tacitly assume that Q
is well defined for each history. This conjecture may be impossible
to prove, but it does seem plausible in the light of our belief that
the reference class problem **will** eventually be solved.

[3] Important
assumption here is that histories of intelligent species are
**ergodic**, i.e. that the ensemble averaging is the same as
temporal averaging. Since ergodicity conjectures are notoriously
difficult to prove even for simple physical systems, we cannot hope
to improve upon this assumption in the present case. Note, however,
that most transhumanist issues are inherently
ergodic.

[4] From the
mathematical point of view, such transformation should be
non-singular except possibly at the boundary of the relevant region.
Such is the case with usually suggested transformations; for
instance, in the classical Milne universe, we have the connection
between the two timescales as t
= ln (t/t_{0}) + t_{0}, where t_{0} is a
constant (e.g. Milne 1940). The zero point of t-time occurs in the
infinite past of t-time.

[5] Although,
of course, such future could hardly be called eschatological, since
physical eschatology is trivial in an unchanging universe. In
addition, there is an entire host of very problematic features of
the steady state theory following from the application of the Strong
Anthropic Principle, since the very absence of obstacles to
unlimited growth of civilizations in such a universe would be the
clear sign that there must be a factor sharply limiting their
growth—since we have not perceived advanced civilizations of
arbitrary age in our past light cone (Tipler 1982; Barrow and
Tipler 1986). For the purposes of our present discussion, however,
we are justified in neglecting this complication, since it is always
possible to imagine a logically consistent cosmological model that
very slowly passes from a quasi-stationary to an evolutionary phase
(similar to the historically interesting Eddington-Lemaître model;
see Ćirković 2000).

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