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The Limits of Nanocomputing.
Even with the restrictions we have discussed, the ultimate limits of computers are 
profoundly high. Building on work by University of California at Berkeley professor Hans Bremermann and 
nanotechnology theorist Robert Freitas, MIT professor Seth Lloyd has estimated the maximum computational 
capacity, according to the known laws of physics, of a computer weighing one kilogram and occupying one liter of 
volume—about the size and weight of a small laptop computer—what he calls the "ultimate laptop."
58
The potential 
amount of computation rises with the available energy. We can understand the link between energy and computational 
capacity as follows. The energy in a quantity of matter is the energy associated with each atom (and subatomic 
particle). So the more atoms, the more energy. As discussed above, each atom can potentially be used for computation. 
So the more atoms, the more computation. The energy of each atom or particle grows with the frequency of its 
movement: the more movement, the more energy. The same relationship exists for potential computation: the higher 
the frequency of movement, the more computation each component (which can be an atom) can perform. (We see this 
in contemporary chips: the higher the frequency of the chip, the greater its computational speed.) 
So there is a direct proportional relationship between the energy of an object and its potential to perform 
computation. The potential energy in a kilogram of matter is very large, as we know from Einstein's equation 
E
= 
mc
2
, 
The speed of light squared is a very large number: approximately 10
17
meter
2
/second
2
. The potential of matter to 
compute is also governed by a very small number, Planck's constant: 6.6 
°
10
-34
joule-seconds (a joule is a measure of 
energy). This is the smallest scale at which we can apply energy for computation. We obtain the theoretical limit of an 

---

object to perform computation by dividing the total energy (the average energy of each atom or particle times the 
number of such particles) by Planck's constant. 
Lloyd shows how the potential computing capacity of a kilogram of matter equals pi times energy divided by 
Planck's constant. Since the energy is such a large number and Planck's constant is so small, this equation generates an 
extremely large number: about 5 
°
10
50
operations per second.
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If we relate that figure to the most conservative estimate of human brain capacity (10
19
cps and 10
10
humans), it 
represents the equivalent of about five billion trillion human civilizations.
60
If we use the figure of 10
16
cps that I 
believe will be sufficient for functional emulation of human intelligence, the ultimate laptop would function at the 
equivalent brain power of five trillion trillion human civilizations.
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Such a laptop could perform the equivalent of all 
human thought over the last ten thousand years (that is, ten billion human brains operating for ten thousand years) in 
one ten-thousandth of a nanosecond.
62 
Again, a few caveats are in order. Converting all of the mass of our 2.2-pound laptop into energy is essentially 
what happens in a thermonuclear explosion. Of course, we don't want the laptop to explode but to stay within its one-
liter dimension. So this will require some careful packaging, to say the least. By analyzing the maximum entropy 
(degrees of freedom represented by the state of all the particles) in such a device, Lloyd shows that such a computer 
would have a theoretical memory capacity of 10
31
bits. It's difficult to imagine technologies that would go all the way 
in achieving these limits. But we can readily envision technologies that come reasonably close to doing so. As the 
University of Oklahoma project shows, we already demonstrated the ability to store at least fifty bits of information 
per atom (although only on a small number of atoms, so far). Storing 10
27
bits of memory in the 10
25
atoms in a 
kilogram of matter should therefore be eventually achievable. 
But because many properties of each atom could be exploited to store information—such as the precise position, 
spin, and quantum state of all of its particles—we can probably do somewhat better than 10
27
bits. Neuroscientist 
Anders Sandberg estimates the potential storage capacity of a hydrogen atom at about four million bits. These 
densities have not yet been demonstrated, however, so we'll use the more conservative estimate.
63
As discussed above, 
10
42
calculations per second could be achieved without producing significant heat. By fully deploying reversible 
computing techniques, using designs that generate low levels of errors, and allowing for reasonable amounts of energy 
dissipation, we should end up somewhere between 10
42
and 10
50
calculations per second. 
The design terrain between these two limits is complex. Examining the technical issues that arise as we advance 
from 10
42
to 10
50
is beyond the scope of this chapter. We should keep in mind, however, that the way this will play out 
is not by starting with the ultimate limit of 10
50
and working backward based on various practical considerations. 
Rather, technology will continue to ramp up, always using its latest prowess to progress to the next level. So once we 
get to a civilization with 10
42
cps (for every 2.2 pounds), the scientists and engineers of that day will use their 
essentially vast nonbiological intelligence to figure out how to get 10
43
, then 10
44
, and so on. My expectation is that we 
will get very close to the ultimate limits. 
Even at 10
42
cps, a 2.2-pound "ultimate portable computer" would be able to perform the equivalent of all human 
thought over the last ten thousand years (assumed at ten billion human brains for ten thousand years) in ten 
microseconds.
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If we examine the "Exponential Growth of Computing" chart (p. 70), we see that this amount of 
computing is estimated to be available for one thousand dollars by 2080. 
A more conservative but compelling design for a massively parallel, reversible computer is Eric Drexler's patented 
nanocomputer design, which is entirely mechanical.
65
Computations are performed by manipulating nanoscale rods, 
which are effectively spring-loaded. After each calculation, the rods containing intermediate values return to their 
original positions, thereby implementing the reverse computation. The device has a trillion (10
12
) processors and 
provides an overall rate of 10
21
cps, enough to simulate one hundred thousand human brains in a cubic centimeter.