by Ray Kurzweil
Setting a Date for the Singularity. A more modest but still profound threshold will be achieved much earlier. In the early 2030s one thousand dollars’ worth of computation will buy about 1017 cps (probably around 1020 cps using ASICs and harvesting distributed computation via the Internet). Today we spend more than $1011 ($100 billion) on computation in a year, which will conservatively rise to $1012 ($1 trillion) by 2030. So we will be producing about 1026 to 1029 cps of nonbiological computation per year in the early 2030s. This is roughly equal to our estimate for the capacity of all living biological human intelligence.
Even if just equal in capacity to our own brains, this nonbiological portion of our intelligence will be more powerful because it will combine the pattern-recognition powers of human intelligence with the memory- and skill-sharing ability and memory accuracy of machines. The nonbiological portion will always operate at peak capacity, which is far from the case for biological humanity today; the 1026 cps represented by biological human civilization today is poorly utilized.
This state of computation in the early 2030s will not represent the Singularity, however, because it does not yet correspond to a profound expansion of our intelligence. By the mid-2040s, however, that one thousand dollars’ worth of computation will be equal to 1026 cps, so the intelligence created per year (at a total cost of about $1012) will be about one billion times more powerful than all human intelligence today.66
That will indeed represent a profound change, and it is for that reason that I set the date for the Singularity—representing a profound and disruptive transformation in human capability—as 2045.
Despite the clear predominance of nonbiological intelligence by the mid-2040s, ours will still be a human civilization. We will transcend biology, but not our humanity. I’ll return to this issue in chapter 7.
Returning to the limits of computation according to physics, the estimates above were expressed in terms of laptop-size computers because that is a familiar form factor today. By the second decade of this century, however, most computing will not be organized in such rectangular devices but will be highly distributed throughout the environment. Computing will be everywhere: in the walls, in our furniture, in our clothing, and in our bodies and brains.
And, of course, human civilization will not be limited to computing with just a few pounds of matter. In chapter 6, we’ll examine the computational potential of an Earth-size planet and computers on the scale of solar systems, of galaxies, and of the entire known universe. As we will see, the amount of time required for our human civilization to achieve scales of computation—and intelligence—that go beyond our planet and into the universe may be a lot shorter than you might think.
I set the date for the Singularity—representing a profound and disruptive transformation in human capability—as 2045.
The nonbiological intelligence created in that year will be one billion times more powerful than all human intelligence today.
Memory and Computational Efficiency: A Rock Versus a Human Brain. With the limits of matter and energy to perform computation in mind, two useful metrics are the memory efficiency and computational efficiency of an object. These are defined as the fractions of memory and computation taking place in an object that are actually useful. Also, we need to consider the equivalence principle: even if computation is useful, if a simpler method produces equivalent results, then we should evaluate the computation against the simpler algorithm. In other words, if two methods achieve the same result but one uses more computation than the other, the more computationally intensive method will be considered to use only the amount of computation of the less intensive method.67
The purpose of these comparisons is to assess just how far biological evolution has been able to go from systems with essentially no intelligence (that is, an ordinary rock, which performs no useful computation) to the ultimate ability of matter to perform purposeful computation. Biological evolution took us part of the way, and technological evolution (which, as I pointed out earlier, represents a continuation of biological evolution) will take us very close to those limits.
Recall that a 2.2-pound rock has on the order of 1027 bits of information encoded in the state of its atoms and about 1042 cps represented by the activity of its particles. Since we are talking about an ordinary stone, assuming that its surface could store about one thousand bits is a perhaps arbitrary but generous estimate.68 This represents 10–24 of its theoretical capacity, or a memory efficiency of 10–24.69
We can also use a stone to do computation. For example, by dropping the stone from a particular height, we can compute the amount of time it takes to drop an object from that height. Of course, this represents very little computation: perhaps 1 cps, meaning its computational efficiency is 10–42.70
In comparison, what can we say about the efficiency of the human brain? Earlier in this chapter we discussed how each of the approximately 1014 interneuronal connections can store an estimated 104 bits in the connection’s neurotransmitter concentrations and synaptic and dendritic nonlinearities (specific shapes), for a total of 1018 bits. The human brain weighs about the same as our stone (actually closer to 3 pounds than 2.2, but since we’re dealing with orders of magnitude, the measurements are close enough). It runs warmer than a cold stone, but we can still use the same estimate of about 1027 bits of theoretical memory capacity (estimating that we can store one bit in each atom). This results in a memory efficiency of 10–9.
However, by the equivalence principle, we should not use the brain’s inefficient coding methods to rate its memory efficiency. Using our functional memory estimate above of 1013 bits, we get a memory efficiency of 10–14. That’s about halfway between the stone and the ultimate cold laptop on a logarithmic scale. However, even though technology progresses exponentially, our experiences are in a linear world, and on a linear scale the human brain is far closer to the stone than to the ultimate cold computer.
So what is the brain’s computational efficiency? Again, we need to consider the equivalence principle and use the estimate of 1016 cps required to emulate the brain’s functionality, rather than the higher estimate (1019 cps) required to emulate all of the nonlinearities in every neuron. With the theoretical capacity of the brain’s atoms estimated at 1042 cps, this gives us a computational efficiency of 10–26. Again, that’s closer to a rock than to the laptop, even on a logarithmic scale.
Our brains have evolved significantly in their memory and computational efficiency from pre-biology objects such as stones. But we clearly have many orders of magnitude of improvement to take advantage of during the first half of this century.
Going Beyond the Ultimate: Pico- and Femtotechnology and Bending the Speed of Light. The limits of around 1042 cps for a one-kilogram, one-liter cold computer and around 1050 for a (very) hot one are based on computing with atoms. But limits are not always what they seem. New scientific understanding has a way of pushing apparent limits aside. As one of many such examples, early in the history of aviation, a consensus analysis of the limits of jet propulsion apparently demonstrated that jet aircraft were infeasible.71
The limits I discussed above represent the limits of nanotechnology based on our current understanding. But what about picotechnology, measured in trillionths (10–12) of a meter, and femtotechnology, scales of 10–15 of a meter? At these scales, we would require computing with subatomic particles. With such smaller size comes the potential for even greater speed and density.
We do have at least several very early-adopter picoscale technologies. German scientists have created an atomic-force microscope (AFM) that can resolve features of an atom that are only seventy-seven picometers across.72 An even higher-resolution technology has been created by scientists at the University of California at Santa Barbara, who have developed an extremely sensitive measurement detector with a physical beam made of gallium-arsenide crystal and a sensing system that can measure a flexing of the beam of as little as one picometer. The device is intended to provide a test of Heisenberg’s u
ncertainty principle.73
In the time dimension Cornell University scientists have demonstrated an imaging technology based on X-ray scattering that can record movies of the movement of a single electron. Each frame represents only four attoseconds (10–18 seconds, each one a billionth of a billionth of a second).74 The device can achieve spatial resolution of one angstrom (10–10 meter, which is 100 picometers).
However, our understanding of matter at these scales, particularly in the femtometer range, is not sufficiently well developed to propose computing paradigms. An Engines of Creation (Eric Drexler’s seminal 1986 book that provided the foundations for nanotechnology) for pico- or femtotechnology has not yet been written. However, each of the competing theories for the behavior of matter and energy at these scales is based on mathematical models that are based on computable transformations. Many of the transformations in physics do provide the basis for universal computation (that is, transformations from which we can build general-purpose computers), and it may be that behavior in the pico- and femtometer range will do so as well.
Of course, even if the basic mechanisms of matter in these ranges provide for universal computation in theory, we would still have to devise the requisite engineering to create massive numbers of computing elements and learn how to control them. These are similar to the challenges on which we are now rapidly making progress in the field of nanotechnology. At this time, we have to regard the feasibility of pico- and femtocomputing as speculative. But nano-computing will provide massive levels of intelligence, so if it’s at all possible to do, our future intelligence will be likely to figure out the necessary processes. The mental experiment we should be making is not whether humans as we know them today will be capable of engineering pico- and femtocomputing technologies, but whether the vast intelligence of future nanotechnology-based intelligence (which will be trillions of trillions of times more capable than contemporary biological human intelligence) will be capable of rendering these designs. Although I believe it is likely that our future nanotechnology-based intelligence will be able to engineer computation at scales finer than nanotechnology, the projections in this book concerning the Singularity do not rely on this speculation.
In addition to making computing smaller, we can make it bigger—that is, we can replicate these very small devices on a massive scale. With full-scale nanotechnology, computing resources can be made self-replicating and thus can rapidly convert mass and energy into an intelligent form. However, we run up against the speed of light, because the matter in the universe is spread out over vast distances.
As we will discuss later, there are at least suggestions that the speed of light may not be immutable. Physicists Steve Lamoreaux and Justin Torgerson of the Los Alamos National Laboratory have analyzed data from an old natural nuclear reactor that two billion years ago produced a fission reaction lasting several hundred thousand years in what is now West Africa.75 Examining radioactive isotopes left over from the reactor and comparing them to isotopes from similar nuclear reactions today, they determined that the physics constant alpha (also called the fine-structure constant), which determines the strength of the electromagnetic force, apparently has changed over two billion years. This is of great significance to the world of physics, because the speed of light is inversely proportional to alpha, and both have been considered unchangeable constants. Alpha appears to have decreased by 4.5 parts out of 108. If confirmed, this would imply that the speed of light has increased.
Of course, these exploratory results will need to be carefully verified. If true, they may hold great importance for the future of our civilization. If the speed of light has increased, it has presumably done so not just as a result of the passage of time but because certain conditions have changed. If the speed of light has changed due to changing circumstances, that cracks open the door just enough for the vast powers of our future intelligence and technology to swing the door widely open. This is the type of scientific insight that technologists can exploit. Human engineering often takes a natural, frequently subtle, effect, and controls it with a view toward greatly leveraging and magnifying it.
Even if we find it difficult to significantly increase the speed of light over the long distances of space, doing so within the small confines of a computing device would also have important consequences for extending the potential for computation. The speed of light is one of the limits that constrain computing devices even today, so the ability to boost it would extend further the limits of computation. We will explore several other intriguing approaches to possibly increasing, or circumventing, the speed of light in chapter 6. Expanding the speed of light is, of course, speculative today, and none of the analyses underlying our expectation of the Singularity rely on this possibility.
Going Back in Time. Another intriguing—and highly speculative—possibility is to send a computational process back in time through a “wormhole” in space-time. Theoretical physicist Todd Brun of the Institute for Advanced Studies at Princeton has analyzed the possibility of computing using what he calls a “closed timelike curve” (CTC). According to Brun, CTCs could “send information (such as the result of calculations) into their own past light cones.”76
Brun does not provide a design for such a device but establishes that such a system is consistent with the laws of physics. His time-traveling computer also does not create the “grandfather paradox,” often cited in discussions of time travel. This well-known paradox points out that if person A goes back in time, he could kill his grandfather, causing A not to exist, resulting in his grandfather not being killed by him, so A would exist and thus could go back and kill his grandfather, and so on, ad infinitum.
Brun’s time-stretching computational process does not appear to introduce this problem because it does not affect the past. It produces a determinate and unambiguous answer in the present to a posed question. The question must have a clear answer, and the answer is not presented until after the question is asked, although the process to determine the answer can take place before the question is asked using the CTC. Conversely, the process could take place after the question is asked and then use a CTC to bring the answer back into the present (but not before the question was asked, because that would introduce the grandfather paradox). There may very well be fundamental barriers (or limitations) to such a process that we don’t yet understand, but those barriers have yet to be identified. If feasible, it would greatly expand the potential of local computation. Again, all of my estimates of computational capacities and of the capabilities of the Singularity do not rely on Brun’s tentative conjecture.
ERIC DREXLER: I don’t know, Ray. I’m pessimistic on the prospects for picotechnology. With the stable particles we know of, I don’t see how there can be picoscale structure without the enormous pressures found in a collapsed star—a white dwarf or a neutron star—and then you would get a solid chunk of stuff like a metal, but a million times denser. This doesn’t seem very useful, even if it were possible to make it in our solar system. If physics included a stable particle like an electron but a hundred times more massive, it would be a different story, but we don’t know of one.
RAY: We manipulate subatomic particles today with accelerators that fall significantly short of the conditions in a neutron star. Moreover, we manipulate subatomic particles such as electrons today with tabletop devices. Scientists recently captured and stopped a photon dead in its tracks.
ERIC: Yes, but what kind of manipulation? If we count manipulating small particles, then all technology is already picotechnology, because all matter is made of subatomic particles. Smashing particles together in accelerators produces debris, not machines or circuits.
RAY: I didn’t say we’ve solved the conceptual problems of picotechnology. I’ve got you penciled in to do that in 2072.
ERIC: Oh, good, then I see you have me living a long time.
RAY: Yes, well, if you stay on the sharp leading edge of health and medical insights and technology, as I’m trying to do,
I see you being in rather good shape around then.
MOLLY 2104: Yes, quite a few of you baby boomers did make it through. But most were unmindful of the opportunities in 2004 to extend human mortality long enough to take advantage of the biotechnology revolution, which hit its stride a decade later, followed by nanotechnology a decade after that.
MOLLY 2004: So, Molly 2104, you must be quite something, considering that one thousand dollars of computation in 2080 can perform the equivalent of ten billion human brains thinking for ten thousand years in a matter of ten microseconds. That presumably will have progressed even further by 2104, and I assume you have access to more than one thousand dollars’ worth of computation.
MOLLY 2104: Actually, millions of dollars on average—billions when I need it.
MOLLY 2004: That’s pretty hard to imagine.
MOLLY 2104: Yeah, well, I guess I’m kind of smart when I need to be.
MOLLY 2004: You don’t sound that bright, actually.
MOLLY 2104: I’m trying to relate on your level.
MOLLY 2004: Now, wait a second, Miss Molly of the future. . ..
GEORGE 2048: Ladies, please, you’re both very engaging.
MOLLY 2004: Yes, well, tell that to my counterpart here—she feels she’s a jillion times more capable than I am.
GEORGE 2048: She is your future, you know. Anyway, I’ve always felt there was something special about a biological woman.
MOLLY 2104: Yeah, what would you know about biological women anyway?
GEORGE 2048: I’ve read a great deal about it and engaged in some very precise simulations.
MOLLY 2004: It occurs to me that maybe you’re both missing something that you’re not aware of.
GEORGE 2048: I don’t see how that’s possible.
MOLLY 2104: Definitely not.
MOLLY 2004: I didn’t think you would. But there is one thing I understand you can do that I do find cool.
MOLLY 2104: Just one?