Microsoft Word Kurzweil, Ray The Singularity Is Near doc

The Limits of Computation Revisited.
Let's consider some additional implications of the law of accelerating returns 
to intelligence in the cosmos. In chapter 3 I discussed the ultimate cold laptop and estimated the optimal computational 
capacity of a one-liter, one-kilogram computer at around 10
42
cps, which is sufficient to perform the equivalent of ten 
thousand years of the thinking of ten billion human brains in ten microseconds. If we allow more intelligent 
management of energy and heat, the potential in one kilogram of matter to compute may be as high as 10
50
cps. 
The technical requirements to achieve computational capacities in this range are daunting, but as I pointed out, the 
appropriate mental experiment is to consider the vast engineering ability of a civilization with 10
42
cps per kilogram, 
not the limited engineering ability of humans today. A civilization at 10
42
cps is likely to figure out how to get to 10
43
cps and then to 10
44
and so on. (Indeed, we can make the same argument at each step to get to the next.) 
Once civilization reaches these levels it is obviously not going to restrict its computation to one kilogram of 
matter, any more than we do so today. Let's consider what our civilization can accomplish with the mass and energy in 
our own vicinity. The Earth contains a mass of about 6 
°
10
24
kilograms. Jupiter has a mass of about 1.9 
°
10
27
kilograms. If we ignore the hydrogen and helium, we have about 1.7 
°
10
26
kilograms of matter in the solar system, 
not including the sun (which ultimately is also fair game). The overall solar system, which is dominated by the sun, 
has a mass of about 2 
°
10
30
kilograms. As a crude upper-bound analysis, if we apply the mass in the solar system to 
our 10
50
estimate of the limit of computational capacity per kilogram of matter (based on the limits for 
nanocomputing), we get a limit of 10
80
cps for computation in our "vicinity." 
Obviously, there are practical considerations that are likely to provide difficulty in reaching this kind of upper 
limit. But even if we devoted one twentieth of 1 percent (0.0005) of the matter of the solar system to computational 
and communication resources, we get capacities of 10
69
cps for "cold" computing and 10
77
cps for "hot" computing.
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Engineering estimates have been made for computing at these scales that take into consideration complex design 
requirements such as energy usage, heat dissipation, internal communication speeds, the composition of matter in the 
solar system, and many other factors. These designs use reversible computing, but as I pointed out in chapter 3, we 
still need to consider the energy requirements for correcting errors and communicating results. In an analysis by 
computational neuroscientist Anders Sandberg, the computational capacity of an Earth-size computational "object" 
called Zeus was reviewed.
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The conceptual design of this "cold" computer, consisting of about 10
25
kilograms of 
carbon (about 1.8 times the mass of the Earth) in the form of diamondoid consists of 5 
°
10
37
computational nodes, 
each of which uses extensive parallel processing. Zeus provides an estimated peak of 10
61
cps of computation or, if 
used for data storage, 10
47
bits. A primary limiting factor for the design is the number of bit erasures permitted (it 
allows up to 2.6 
°
10
32
bit erasures per second), which are primarily used to correct errors from cosmic rays and 
quantum effects. 
In 1959 astrophysicist Freeman Dyson proposed a concept of curved shells around a star as a way to provide both 
energy and habitats for an advanced civilization. One conception of the Dyson Sphere is quite literally a thin sphere 
around a star to gather energy.
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The civilization lives in the sphere, and gives off heat (infrared energy) outside the 
sphere (away from the star). Another (and more practical) version of the Dyson Sphere is a series of curved shells, 
each of which blocks only a portion of the star's radiation. In this way Dyson Shells can be designed to have no effect 
on existing planets, particularly those, like the Earth, that harbor an ecology that needs to be protected. 
Although Dyson proposed his concept as a means of providing vast amounts of space and energy for an advanced 
biological
civilization, it can also be used as the basis for star-scale computers. Such Dyson Shells could orbit our sun 
without affecting the sunlight reaching the Earth. Dyson imagined intelligent biological creatures living in the shells or 
spheres, but since civilization moves rapidly toward nonbiological intelligence once it discovers computation, there 
would be no reason to populate the shells with biological humans. 
Another refinement of the Dyson concept is that the heat radiated by one shell could be captured and used by a 
parallel shell that is placed at a position farther from the sun. Computer scientist Robert Bradbury points out that there 
could be any number of such layers and proposes a computer aptly called a "Matrioshka brain," organized as a series 
of nested shells around the sun or another star. One such conceptual design analyzed by Sandberg is called Uranos, 
which is designed to use 1 percent of the nonhydrogen, nonhelium mass in the solar system (not including the sun), or 

---

about 10
24
kilograms, a bit smaller than Zeus.
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Uranos provides about 10
39
computational nodes, an estimated 10
51
cps 
of computation, and about 10
52
bits of storage. 
Computation is already a widely distributed—rather than centralized—resource, and my expectation is that the 
trend will continue toward greater decentralization. However, as our civilization approaches the densities of 
computation envisioned above, the distribution of the vast number of processors is likely to have characteristics of 
these conceptual designs. For example, the idea of Matrioshka shells would take maximal advantage of solar power 
and heat dissipation. Note that the computational powers of these solar system-scale computers will be achieved, 
according to my projections in chapter 2, around the end of this century.