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The Dyson sphere is a hypothetical structure of immense size. It is a sphere that completely (or almost completely) encloses a star, making use of all the energy radiated away by the fusion reactions taking place in its core. The idea of a Dyson sphere was first formalized and popularized by renowned physicist Freeman Dyson in an 1959 article in Science entitled "Search for Artificial Stellar Sources of Infra-Red Radiation," though he originally got the idea from a 1945 science fiction novel by Olaf Stapledon entitled Star Maker.
Our sun has an energy output of around 4 x 10^26 watts, or approximately 100 million times humanity's total energy consumption throughout the past century every second. If this energy could be harnessed via a Dyson sphere, we would have enough power to sustain a population trillions of times our current population for many eons.
The original proposal for a Dyson sphere was not for a solid sphere, but a collection of ~10^5 objects which collectively absorb the bulk of the star's solar energy. Sometimes called a "Dyson swarm," this would allow the incremental construction of the system, with subcomponents orbiting the star independently. From the outside, such a swarm would appear black, emitting only infrared radiation. Some of our orbiting infrared telescopes have been searching for such bodies as Dyson spheres or swarms for decades, with no luck. If reflectors were used on the interior of the objects, the radiant energy might be directed only one way, making it hard to detect from a distance.
Preliminary calculations have shown that our solar system contains enough rigid matter to construct a Dyson swarm, but probably not a rigid Dyson sphere, which would have to be about a million km (600,000 miles) thick to be stable. A good candidate building material would be buckminsterfullerene, an allotrope of carbon with immense strength.
The Dyson sphere is often mentioned in conjunction with the Kardashev classification scheme, a method used to classify hypothetical civilizations by way of their energy sources. According to this classification scheme, a Type I civilization would be one which utilizes the power sources of an entire planet, a Type II civilization would be one that uses an entire star's output for power, and a Type III civilization would be that which uses an entire galaxy for power. A more speculative Type IV civilization would be one which harnesses the power of an entire universe. The construction of a Dyson sphere would place a civilization squarely in the Type II category.