Putative extraterrestrial planets are being discovered at the rate of one a month. A subset of these exist in the liquid water zone and are thus capable of evolving life similar to that with which we are familiar. While perhaps not common, the development of technological civilizations seems possible for some of these worlds. If we are typical, the evolution of technological civilizations proceeds from a condition where physical laws are unknown to a state where the limits imposed by those laws are reached within a few hundred years. These limits (molecular nanotechnology on solar system scales) allow the construction of Dyson shell supercomputers ("Matrioshka Brains''1) with thought capacities a trillion trillion times greater than that of a human brain and longevities measured in billions to trillions of years. Natural selection at stellar and galactic scales would, over time, eliminate any civilizations lacking these prodigious capabilities. We must consider that astronomical observations such as the missing baryonic dark matter and the gravitational microlensing observations may indicate that many such entities exist and that our galaxy is currently a Kardashev Type III civilization.
Individual and species survival depends on transcending a hazard function composed of various subcomponents. On short time scales, hazards are primarily biological in nature (e.g. macroscale or microbial predators). On intermediate time scales they are of a geophysical nature (e.g. floods, earthquakes, volcanoes). At the longest time scales, natural astrophysical processes (e.g. orbital instabilities, stellar evolution, supernovas, gamma ray bursts) will eventually take their toll. Only individuals and civilizations that evolve to levels where their technological capabilities are capable of discovering (or predicting) and avoiding (or withstanding) the hazards they face will survive for billions of years.
A critical distinction can be made between species on the basis of their technological sophistication. Species that do not develop robust technologies (e.g. dinosaurs) have their fates sealed by the long term hazards. Species that do develop technological abilities (e.g. man) may discover the hazards they face (e.g. nuclear weapons, global warming, Near-Earth Asteroids, bioterrorism) and should over time develop strategies minimizing the risks that the hazards pose to the species and even individuals.
As species develop their technological abilities, they will expand the scale of their activities beyond their personal size scale (e.g. spears and fur coats) to much smaller scales (e.g. microelectronics, molecular biology, etc.) and much larger scales (e.g. oil tankers, space stations, etc.). These trends will be followed, perhaps at an ever accelerating pace [VV1993, DB2001, AJ2000], until they reach the point of significantly diminished investment returns or the limits imposed by the laws of physics. There appear to be two natural points where the nature of the universe contributes to significant changes in the rate of progress along these paths. At small scales, engineering may be limited to atomic-scale engineering (molecular nanotechnology [RPF1959, KED1981, KED1987, KED1992, RAF1999]). Following this path, a developmental barrier may be reached when all of the materials utilized by a technological civilization, including the civilization itself, are assembled atom-by-atom. The barrier is due to the difficulty of the controlled assembly of subatomic matter with similar charge repulsion and the limited lifetime of isolated neutrons. At large scales, mega-scale engineering may be limited to solar system sized structures such as Dyson shells [FJD1960]. This is due to material resource limitations of individual solar systems and the huge energy costs of transporting large amounts of matter over interstellar distances.
The decoding of the information carrier of a species (its genome), and a comprehension of the computational processes that enable it to think (understanding its "brain'' [WHC1996a, WHC1996b]), allow a species to begin the process of conscious self-evolution. The longevities of individuals and the civilization itself will increase as they understand and address the defects of their genetic programs and the hazards they face. The development of technologies to allow the transfer of "minds'' to more robust hardware seems feasible [HPM1987, MURG]. Species that choose not to follow this path retain a higher hazard function that increases the likelihood of their eventual extinction. Those that choose to self-evolve, will likely choose a path towards increased individual computational capacity and inter-individual communications bandwidth. This results in significantly higher individual and aggregate intelligence and radical shifts in how "individuals'' perceive themselves. Vulcan "mind melds'' become much more feasible when the minds are connected via high bandwidth fiber optics or radio links. The ultimate end point of these trends is the formation of a distributed replicated networked "mind'' supported by the most advanced computational architecture allowed by physical laws and engineering feasibility. Species avoiding the path of self-directed evolution, may still reach this point if they develop artificial intelligences whose operation they wish to preserve indefinitely [HPM1987, HPM1997, HPM1998, GSP1996].
Previous work has outlined the feasibility of designing self-replicating systems (SRS) [JVN1966, RAF1982]. Naturally evolved SRS such as bacteria exist and may have doubling times as short as 20 minutes [TDB1991, JCS1990]. This is not a limit, as these bacteria are an order of magnitude more complex than those that could be designed around a minimal genome [ARM1996]. Molecular nanotechnology greatly expands the design space and operating range for SRS. Initial estimates of the doubling times for 1 kg general purpose nanotechnology based manufacturing systems were 1 hour [KED1992]. More recent work on SRS architectures has shown that carefully designed SRS, organized as assembly lines, could have doubling times as low as 2 ms [JSH1999]. In these systems, the replicating time is likely to be limited by the heat removal requirements. Civilizations that use molecular nanotechnology SRS based manufacturing methods may transform planetary masses into manufactured materials over periods ranging from days to decades [RJB1998].
One architecture advanced civilizations may choose to adopt is that of a Matrioshka Brain [RJBMBHP, RJB1999]. Briefly, this is a layer of nested Dyson shells enveloping a star. Each shell layer consists of network of orbiting satellites containing power harvesting, computation, communications and heat radiation components constructed using molecular nanotechnology. Layers have architectures optimized for the operating temperature of the "computronium'' at specific distances from the star. The next section discusses some of the physical law and engineering constraints likely to be encountered by Matrioshka Brains being constructed by advanced civilizations.
The Available Energy Limit
Stars provide energy with little or no requirement for structural material.
Gravity provides the force to hold them together and drive the nuclear
fusion reactions. Relatively thin surfaces of a few microns are sufficient
to harvest the energy they produce [KED1992b].
Other energy production methods, such as fission or fusion reactors, require
significant amounts of structural material to produce and harvest useful
energy. If material is in short supply, stars seem to provide the best
"container'' for energy production. If stars can be reliably disassembled
[DRC1985], the energy production and matter consumption
rates may be managed over the long term by the civilization.
The Available Matter Limit
The nested layers of the computronium shells eventually utilize all
the matter in solar systems outside of the star. The natural composition
of solar systems is unlikely to provide optimal element ratios for the
"ideal'' computational architecture. Breeding the optimal element mix involves
a tradeoff between energy devoted to current computations and the time
until the elements required for constructing a better computational architecture
become available.
The Gravity Well Limit
The mass of objects (asteroids, planets, brown dwarfs) from which material
is extracted to construct computronium determines the rate at which a solar
system may be developed. Small planets may be restructured in days but
larger planets require centuries. Energy used to dismantle planets and
lift material out of gravity wells is energy that cannot be devoted to
computation or communication. If the present value of current computational
throughput is high relative to a somewhat greater amount in the future,
the rate of planetary dismantlement decreases after the less massive material
sources have been harvested.
Heat Production Limits
Studies of the physics of information processing have shown that when
computers erase bits, they increase entropy or produce heat [RL1961,
CHB1988].
This may be minimized by using reversible computing architectures that
minimize the number of bits that are erased in a calculation. Reversible
architectures require more matter for their computations and compute slower
than nonreversible architectures. Optimal architectures may be nonreversible,
and require greater matter and energy be dedicated to cooling them, or
may be reversible, and require greater matter be dedicated to the computational
elements.
Operating Temperature Limits
Computers that have the highest throughput are those that are the densest
(to minimize information transmission time delays). Computers, even those
that use reversible logic, generate heat and will melt unless the heat
is removed and radiated away. Computer operating temperatures are limited
by the maximum temperature at which the materials from which they are constructed
retain the properties required for computational accuracy. These properties
are related to the melting points of the computer materials and the boiling
points of the coolant materials, which in turn depend on inter-atomic and
inter-molecular bond strengths and material density.
The innermost computronium shell (closest to the star) may operate at thousands of degrees Kelvin, while the outermost layer may operate at temperatures slightly above the background radiation temperature. Operation below the background radiation temperature is useful only if the significant energy losses required to cool the computers below that temperature are offset by even greater increases in computational throughput. The operating temperature also contributes to the rate at which wear may occur and parts need to be disassembled and remanufactured.
Thermodynamics Constraints
Heat produced by computing flows through a thermodynamic waterfall
of decreasing potential energy as it radiates outward from the star. Computronium
layers power themselves from the differential between the temperatures
at which they harvest and radiate energy at declining Carnot efficiencies.
Radiator efficiency scales according to the Stefan-Boltzman Law with $T.
As the distance from the star becomes greater, the computronium temperatures
decrease and the mass required for the cooling fluid and radiators becomes
increasingly larger. This eventually results in an exhaustion of the available
construction material in solar systems similar to our own. Additional materials
may be harvested from the star, but only by making significant sacrifices
in the energy dedicated to computational activities.
Mass Transfer Constraints
The cooling of computational nodes requires the circulation of a cooling
fluid at very high pressures to maximize flow rates and minimize the volume
of the computers that the coolant occupies. There is a tradeoff between
the energy required to pump the coolant through the computer and the energy
available for actual computations. Higher pressures and coolant flow rates
are limited by the strength of the material from which the computer is
constructed and friction producing heat that limits the cooling efficiency.
Speed of Light Constraint
As the operating temperatures of computers declines, radiators become
larger, and the distance between the computational nodes increases. This
in turn increases the inter-node transmission time for photons and increases
the mass requirements for the photon detection systems due to increased
magnification or collecting area needs. The detection system mass requirements
may be minimized only by increasing power to the internode communications
beams (reducing power available for computation or coolant circulation)
or by accepting increased photon loss with an associated increase in communications
errors (presumably handled by error correction or retransmission).
Computer Architectural Constraints
Different computer architectures, such as Harvard architectures, cellular
automata, neural networks, quantum computers, etc. are optimal for solving
specific types of problems. The energy available to Matrioshka Brains allows
them to break and reform all of the atomic bonds in their computational
architectures in decades or less. This capability allows them to devote
significant "thought'' to precisely what they want to think about and then
reengineer themselves into optimal architectures for that purpose. The
time devoted to developing and constructing optimal architectures must
be balanced against the time required for equivalent "thought'' using a
more general purpose but suboptimal architecture. Architectures also tradeoff
operating temperature against computational error rate [AS1999].
This may be compensated for by redundant hardware (requiring more matter)
or software (reducing throughput).
Current technology trends allow engineers to begin imagining designs
for realistic computational architectures assembled at the atomic level
that consume all of the resources of solar systems. As shown above, the
tradeoffs that will need to be made by civilizations constructing Matrioshka
Brains are complex. It seems likely that humanity will develop the ability
to construct such entities within this century. In contrast, scientists
have speculated regarding computers that operate at subatomic scales and
temperatures of billions of degrees [SL2000, AS1999].
It seems that for the foreseeable future, these ideas belong best in the
realm of science fiction.
A critical aspect of self-awareness and intelligence is the ability to model the future [HPM1998, WHC1996b]. Therefore one of the processes to which a Matrioshka Brain may dedicate its resources is the modeling of the near term and far term space through which it travels. This is necessary to predict any potential hazards far enough in advance to minimize the energy and matter expended on altering course or otherwise protecting itself from the hazards of the galaxy or intergalactic space. The laws of physics and limits of engineering technologies would seem to drive civilizations toward a limited set of optimal architectures for living in various environments in space. The prodigious computational & memory capacities, construction capabilities, large size and extreme longevities suggest that Matrioshka Brains either currently are, or may in some future time become, a dominant "species'' in galaxies.
Matrioshka Brains are variants of Type II civilizations [NSK1964] that consume the entire power produced by stars. The original Dyson Shell proposal for such civilizations considered them an orbiting swarm of "biospheres'' [FJD1960] and failed to consider the possible rapid evolution of the physical form & interconnectivity requirements of members of such civilizations. This has resulted in misdirected searches for them since then. The ultimate optimization of such civilizations and their impact on the Fermi Paradox [EMJ1985] has been proposed [NSK1986, NSK1988] but largely ignored by astronomers and SETI proponents. The huge differences in "intelligence'' and interests of pre-Type I civilizations, such as our own, and Type II civilizations, make it unlikely that interaction between them occurs. The rapid construction capabilities enabled by molecular nanotechnology based self-replicating systems, allow very short transition times between the two stages, suggesting that the number of civilizations in a galaxy near our level should be small and that SETI strategies based on looking at visible stars at radio and optical wavelengths are unlikely to be successful.