In 1999 Anders Sandberg published a paper1 in which he pointed out the many advantages of reducing humans to computer programs ("infomorphs"), and identified a Jupiter Brain as a good compromise size, as it allowed for quite a lot of computation without too much of a communication delay as information traveled from one part to another.

Enter Robert Bradbury,2 who was not going to compromise size for nothin'. Taking the Dyson sphere as a starting point, he converted it to computronium, and had it use the entire energy output of the host star to run calculations... and then he fed all of the waste heat from this Dyson sphere into another, larger shell, surrounding the first sphere and processing just a bit slower. Repeat until entropy makes construction pointless. He named this construction a matrioshka brain, after the nested Russian Matryoshka dolls.

Because this megastructure consists of a series of heat engines which receive less and less input heat per square meter as they move out from the star, the layers would presumably run calculations at slower and slower speeds as one moves outwards. This makes communication between the layers asymmetrical, and subjective time -- from the viewpoint of the infomorphs -- seems to increase in speed as one moves closer to the star. Communication also becomes an issue given the distance from one side of each shell to the other side of the same shell, as the speed of light provides a probable limit on communication speed, and information must travel around the circumference of the sphere rather than directly across the host star. These factors mean that the internal, subjective universe(s) run on these computers have unique laws time and space that appear analogous to those in our universe.

It is perhaps worth noting that there is a conflict inherent in the construction of matrioshka brains. They are very big, expensive things to build, and those building them are not likely to want to move them later. The most stable stars, lasting as long (or longer) than the universe itself, are M dwarf stars (informally referred to as red dwarfs), and not coincidentally, these are some of the lowest energy stars. The most energy-rich stars, hypergiants, have a disturbing tendency to spit off pieces at the slightest provocation, and if you wait long enough, they will go supernova. This means that effective matrioshka design involves some hard choices in stability vs. processing power, a masterful proficiency in stellar husbandry, or the discovery of a white hole.

Matrioshka brains have become somewhat common in far-future science fiction, and are no longer considered particularly creative or interesting, although they are certainly sometimes useful. However, the novel Accelerando by Charles Stross is noteworthy as perhaps introducing the concept to more readers than any other work... as best as I can guess.

1. The Physics of Information Processing Superobjects: Daily Life Among the Jupiter Brains (.pdf)
2. In the anthology Year Million: Science at the Far Edge of Knowledge, edited by Damien Broderick, 2008.

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