Solution The Planetarium Hypothesis

Real are the dreams of Gods.

John Keats, Lamia, I

Stephen Baxter has proposed an interesting variant on the zoo scenario. He calls it the planetarium hypothesis.64 (The speculation is far wilder than Ball's idea, but it merits the term "hypothesis" rather than "scenario" because it offers testable predictions.) Is it possible, Baxter asks, that the world we live in is a simulation — a virtual-reality "planetarium" engineered to present us with the illusion that the Universe is devoid of intelligent life?

The physics behind such an idea has a modern feel to it. Indeed, the planetarium hypothesis could only reasonably have been proposed in recent years — times that have seen an incredible increase in the power of computers. And yet the "things are not what they seem" concept that underlies the planetarium hypothesis is an established trope of science fiction. In Heinlein's novella Universe, the inhabitants of a generation ship (see page 63) find a Universe beyond the confines of their vessel. In a light-hearted short story by Asimov,

figure 20 In a well-designed planetarium we can lose ourselves in a realistic representation of the Universe.

written two years before Soviet satellites photographed the far side of the Moon, the first astronauts to orbit the Moon find not a cratered surface but a huge canvas propped up by two-by-fours. The "trip" was a simulation that enabled psychologists to study the effects of a lunar mission on the crew. The protagonist of The News from D-Street, a much more somber story by Andrew Weiner, discovers that the totality of his familiar yet strangely restricted world is the product of a computer program. More recently, mainstream media have explored the concept of people interacting with various engineered realities. Several episodes of the TV show Star Trek: The Next Generation, for example, were set on the "holodeck" — a technology that emulated material objects with which users could interact. The movie The Matrix had humans forcibly immersed in a virtual reality, this time through a technology in which brains were stimulated directly by implants. The protagonist of the movie The Truman Show was the unwitting star of a TV show that had him living inside an engineered reality; in this case it was a "low-tech" reality, a fake town below a painted dome designed by the show's producers.65

Many of these stories and movies have a haunting quality, perhaps because they touch upon matters of deep philosophical concern. After all, questions about the nature of reality, and about how each of us perceives the external Universe, have kept philosophers in business for millennia. The planetarium hypothesis suggests that our accepted understanding of the external Universe might be wrong. Exactly how wrong depends on the type of planetarium the ETC has provided for us ("low-tech" like Truman or "high-tech" like Matrix) and also its scope — the position of the boundary between human consciousness and external "reality."

The planetarium hypothesis taken to extreme is similar to solipsism. The true solipsist believes that everything he experiences — people, events, objects — is part of the content of his consciousness, rather than an external reality in which we share. It is not just that his is the only mind that exists. (The sole survivor of some planet-wide catastrophe might be correct if he believed his was the only mind, and yet he would not necessarily be a solipsist.) Rather, the true solipsist in principle can attach no meaning to the idea that other minds experience thoughts and emotions. It is an egocentric view of the Universe. The most extreme planetarium, therefore, would have an ETC generate an artificial Universe directly into my consciousness. The Universe appears to me to be empty because an ETC, for some reason, wants to fool me into so thinking.

Solipsism seems to lead nowhere and is rarely defended directly. (The true solipsist when defending his philosophy presumably has to inform his opponents they do not exist, which seems a ludicrous thing to do.) Less extreme planetaria still have a solipsistic flavor but are slightly less outra geous. For example, perhaps we humans are real but some or all of the objects we see around us are simulations — like the holodeck in Star Trek. Or perhaps reality consists of everything on Earth plus those places in the Solar System we have visited, but the stars and galaxies are simulated — like a large-scale version of The Truman Show dome.

Occam's razor gives us a good reason for rejecting all these planetaria. Suppose you throw a ball and watch its parabolic path: you will conclude the ball is an autonomous object obeying Newton's law of gravity. The alternative — that some system (whether an individual consciousness or a sophisticated virtual-reality generator) contains laws that simulate the properties of the ball and its motion under gravity — is a more complex explanation of the same phenomenon. Both explanations fit the observations. But Occam's razor tells us to use the simplest explanation, which in this case is that the ball is "real." It has an autonomous existence. We can make the same argument regarding our observations of the Universe.

On the other hand, if we are willing to put Occam's razor to one side for the moment and take the planetarium hypothesis seriously, Baxter shows how we can test whether we are living in certain types of engineered reality. This is an advance on the original zoo and interdict scenarios, neither of which make hard predictions.

Baxter points out that a fundamental requirement of a planetarium is that scientific experiments should always yield consistent results. (At this point, we do not ask why an ETC would bother simulating a Universe for our benefit. It is enough to note that a perfect simulation of a system — in other words, a simulation that cannot be distinguished from the original physical system by any conceivable test — can in theory be generated.) If an experiment highlights inconsistencies in the fabric of reality, then we might be led to postulate the existence of an "outside."

Physicists can calculate the information and energy demands required to create a perfect simulation of any given size. We can therefore ask whether an ETC has the capacity to meet the energy demands for the construction of any particular planetarium. (We have to assume that the planetarium designers are subject to the same laws of physics as us. If they are not — if, for example, they can alter the value of the Boltzmann constant — then we cannot take the argument further.)

It turns out that a K1 civilization could generate a perfect simulation of about 10,000 km2 of Earth's surface and to a height of about 1 km. In other words, a K1 civilization could not have generated a perfect simulation of the ancient Sumerian empire, much less our present world. Of course, a planetarium designer would not need to generate a perfect simulation in order to fool the people of Sumer; it would be unnecessary to emulate material 200 m below Earth's surface, for example, since humans of that time were unlikely to dig that deep. Various tricks and short-cuts would also be available to the planetarium programmer — but note the resulting simulation would not be perfect, and in principle an inconsistency might be revealed. The protagonist in Weiner's The News From D-Street finds himself in exactly this situation.

A K2 civilization could have generated a simulation to fool Columbus. But the voyages of Captain Cook might have uncovered inconsistencies in their planetarium design.

A K3 civilization could generate a perfect simulation of a volume with a radius of about 100 AU. This is a large distance. For comparison, Pluto, the outermost planet in the Solar System, lies at an average distance of 40 AU from the Sun; the Voyager 1 spacecraft, the most distant man-made object, is only slightly farther away than Pluto. So it is possible that humans are creatures in the simulation of some K3 civilization.

The Bekenstein Bound

Jacob Bekenstein66 showed how quantum physics places a limit to the amount of information a physical system can code. The uncertainty relations show that the amount of information inside a system of radius R (in meters) and mass M (in kilograms) can never be greater than the mass multiplied by the radius multiplied by a constant (which has a value of about 2.5 x 1043 bits per meter per kilogram). Nature permits a surprising amount of information to be encoded before the Bekenstein bound is reached. For example, a hydrogen atom can encode about 1 Mb of information — most of a floppy disk. A typical human can code about 1039 Mb of information — far more information than can be handled by any hard disk in existence.

Natural physical systems seem to encode much less information than Nature permits. But the Bekenstein bound gives planetarium designers plenty of opportunity to engineer perfect simulations of varying size and scope. Standard thermodynamic calculations give us the energy required to construct a perfect simulation of any particular size and mass.

With our present level of technology, therefore, we are incapable of testing whether our Universe is "real" or the result of a simulation developed by a K3 civilization. But as we probe more of the Universe, and have our probes travel well past Pluto and into the outer reaches of the Solar System, we will reach a point where we can be certain that any simulation is less than perfect. A simulation could exceed 100 AU, but it would not be a perfect simulation; our instruments could in principle detect the inconsistencies in such a lower-quality simulation. In a few years, Voyager 1 will pass the 100-AU boundary; if it bumps into a metal wall that has been painted black — well, the game will be up for the planetarium builders!

The planetarium hypothesis defies both Occam's razor and our basic intuition about how the Universe works. It verges on paranoia to suppose that a K3 civilization would go to such effort simply to persuade us that our Universe is empty. Baxter himself advances it only as a possibility to be eliminated (and I am sure he does not believe it to be true). But at least we can eventually eliminate it. In the decades to come, as we explore more of the Universe and test the fabric of reality at ever-larger distance scales, we will either find an inconsistency in the simulation or be forced to accept that the Universe is "real." And if it turns out the Universe is "real" — which I am sure most readers would be prepared to wager is the case — then we will have to look elsewhere for a resolution of the Fermi paradox.

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