The Singularity Is Near: When Humans Transcend Biology (23 page)

However, we also know that the number of MIPS in computing devices has been growing exponentially. The extent to which improvements in power usage have kept pace with processor speed depends on the extent to which we use parallel processing. A larger number of less-powerful computers can inherently run cooler because the computation is spread out over a larger area. Processor speed is related to voltage, and the power required is proportional to the square of the voltage. So running a processor at a slower speed significantly reduces power consumption. If we invest in more parallel processing rather than faster single processors, it is feasible for energy consumption and heat dissipation to keep pace with the growing MIPS per dollar, as the figure “Reduction in Watts per MIPS” shows.

This is essentially the same solution that biological evolution developed in the design of animal brains. Human brains use about one hundred trillion computers (the interneuronal connections, where most of the processing takes place). But these processors are very low in computational power and therefore run relatively cool.

Until just recently Intel emphasized the development of faster and faster single-chip processors, which have been running at increasingly high temperatures.
Intel is gradually changing its strategy toward parallelization by putting multiple processors on a single chip. We will see chip technology move in this direction as a way of keeping power requirements and heat dissipation in check.
⁴⁷

Reversible Computing.
Ultimately, organizing computation with massive parallel processing, as is done in the human brain, will not by itself be sufficient to keep energy levels and resulting thermal dissipation at reasonable levels. The current computer paradigm relies on what is known as irreversible computing, meaning that we are unable in principle to run software programs backward. At each step in the progression of a program, the input data is discarded—erased—and the results of the computation pass to the next step. Programs generally do not retain all intermediate results, as that would use up large amounts of memory unnecessarily. This selective erasure of input information is particularly true for pattern-recognition systems. Vision systems, for example, whether human or machine, receive very high rates of input (from the eyes or visual sensors) yet produce relatively compact outputs (such as identification of recognized patterns). This act of erasing data generates heat and therefore requires energy. When a bit of information is erased, that information has to go somewhere. According to the laws of thermodynamics, the erased bit is essentially released into the surrounding environment, thereby increasing its entropy, which can be viewed as a measure of information (including apparently disordered information) in an environment. This results in a higher temperature for the environment (because temperature is a measure of entropy).

If, on the other hand, we don’t erase each bit of information contained in the input to each step of an algorithm but instead just move it to another location, that bit stays in the computer, is not released into the environment, and therefore generates no heat and requires no energy from outside the computer.

Rolf Landauer showed in 1961 that reversible logical operations such as NOT (turning a bit into its opposite) could be performed without putting energy in or taking heat out, but that irreversible logical operations such as AND (generating bit C, which is a 1 if and only if both inputs A and B are 1) do require energy.
⁴⁸
In 1973 Charles Bennett showed that any computation could be performed using only reversible logical operations.
⁴⁹
A decade later, Ed Fredkin and Tommaso Toffoli presented a comprehensive review of the idea of reversible computing.
⁵⁰
The fundamental concept is that if you keep all the intermediate results and then run the algorithm backward when you’ve finished
your calculation, you end up where you started, have used no energy, and generated no heat. Along the way, however, you’ve calculated the result of the algorithm.

How Smart Is a Rock?
To appreciate the feasibility of computing with no energy and no heat, consider the computation that takes place in an ordinary rock. Although it may appear that nothing much is going on inside a rock, the approximately 10
²⁵
(ten trillion trillion) atoms in a kilogram of matter are actually extremely active. Despite the apparent solidity of the object, the atoms are all in motion, sharing electrons back and forth, changing particle spins, and generating rapidly moving electromagnetic fields. All of this activity represents computation, even if not very meaningfully organized.

We’ve already shown that atoms can store information at a density of greater than one bit per atom, such as in computing systems built from nuclear magnetic-resonance devices. University of Oklahoma researchers stored 1,024 bits in the magnetic interactions of the protons of a single molecule containing nineteen hydrogen atoms.
⁵¹
Thus, the state of the rock at any one moment represents at least 10
²⁷
bits of memory.

In terms of computation, and just considering the electromagnetic interactions, there are at least 10
¹⁵
changes in state per bit per second going on inside a 2.2-pound rock, which effectively represents about 10
⁴²
(a million trillion trillion trillion) calculations per second. Yet the rock requires no energy input and generates no appreciable heat.

Of course, despite all this activity at the atomic level, the rock is not performing any useful work aside from perhaps acting as a paperweight or a decoration. The reason for this is that the structure of the atoms in the rock is for the most part effectively random. If, on the other hand, we organize the particles in a more purposeful manner, we could have a cool, zero-energy-consuming computer with a memory of about a thousand trillion trillion bits and a processing capacity of 10
⁴²
operations per second, which is about ten trillion times more powerful than all human brains on Earth, even if we use the most conservative (highest) estimate of 10
¹⁹
cps.
⁵²

Ed Fredkin demonstrated that we don’t even have to bother running algorithms in reverse after obtaining a result.
⁵³
Fredkin presented several designs for reversible logic gates that perform the reversals as they compute and that are universal, meaning that general-purpose computation can be built from them.
⁵⁴
Fredkin goes on to show that the efficiency of a computer built from reversible logic gates can be designed to be very close (at least 99 percent) to the efficiency of ones built from irreversible gates. He writes:

it is possible to . . . implement . . . conventional computer models that have the distinction that the basic components are microscopically reversible. This means that the macroscopic operation of the computer is also reversible. This fact allows us to address the . . . question . . . “what is required for a computer to be maximally efficient?” The answer is that if the computer is built out of microscopically reversible components then it can be perfectly efficient. How much energy does a perfectly efficient computer have to dissipate in order to compute something? The answer is that the computer does not need to dissipate any energy.
⁵⁵

Reversible logic has already been demonstrated and shows the expected reductions in energy input and heat dissipation.
⁵⁶
Fredkin’s reversible logic gates answer a key challenge to the idea of reversible computing: that it would require a different style of programming. He argues that we can, in fact, construct normal logic and memory entirely from reversible logic gates, which will allow the use of existing conventional software-development methods.

It is hard to overstate the significance of this insight. A key observation regarding the Singularity is that information processes—computation—will ultimately drive everything that is important. This primary foundation for future technology thus appears to require no energy.

The practical reality is slightly more complicated. If we actually want to find out the results of a computation—that is, to receive output from a computer—the process of copying the answer and transmitting it outside of the computer is an irreversible process, one that generates heat for each bit transmitted. However, for most applications of interest, the amount of computation that goes into executing an algorithm vastly exceeds the computation required to communicate the final answers, so the latter does not appreciably change the energy equation.

However, because of essentially random thermal and quantum effects, logic operations have an inherent error rate. We can overcome errors using error-detection and -correction codes, but each time we correct a bit, the operation is not reversible, which means it requires energy and generates heat. Generally, error rates are low. But even if errors occur at the rate of, say, one per 10
¹⁰
operations, we have only succeeded in reducing energy requirements by a factor of 10
¹⁰
, not in eliminating energy dissipation altogether.

As we consider the limits of computation, the issue of error rate becomes a significant design issue. Certain methods of increasing computational rate, such as increasing the frequency of the oscillation of particles, also increase error rates, so this puts natural limits on the ability to perform computation using matter and energy.

Another important trend with relevance here will be the moving away from conventional batteries toward tiny fuel cells (devices storing energy in chemicals, such as forms of hydrogen, which is combined with available oxygen). Fuel cells are already being constructed using MEMS (microelectronic mechanical systems) technology.
⁵⁷
As we move toward three-dimensional, molecular computing with nanoscale features, energy resources in the form of nano–fuel cells will be as widely distributed throughout the computing medium among the massively parallel processors. We will discuss future nanotechnology-based energy technologies in
chapter 5
.

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.
⁵⁹

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.
⁶¹
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.