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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