Denton appears to acknowledge the feasibility of emulating the ways of nature when he writes:

Success in engineering new organic forms from proteins up to organisms will therefore require a completely novel approach, a sort of designing from "the top down." Because the parts of organic wholes only exist in the whole, organic wholes cannot be specified bit by bit and built up from a set of relatively independent modules; consequently the entire undivided unity must be specified together in toto in toto.

Here Denton provides sound advice and describes an approach to engineering that I and other researchers use routinely in the areas of pattern recognition, complexity (chaos) theory, and self-organizing systems. Denton appears to be unaware of these methodologies, however, and after describing examples of bottom-up, component-driven engineering and their limitations concludes with no justification that there is an unbridgeable chasm between the two design philosophies. The bridge is, in fact, already under construction.

As I discussed in chapter 5, we can create our own "eerie other-worldly" but effective designs through applied evolution. I described how to apply the principles of evolution to creating intelligent designs through genetic algorithms. In my own experience with this approach, the results are well represented by Denton's description of organic molecules in the "apparent illogic of the design and the lack of any obvious modularity or regularity, ... the sheer chaos of the arrangement, ... [and the] non-mechanical impression."

Genetic algorithms and other bottom-up self-organizing design methodologies (such as neural nets, Markov models, and others that we discussed in chapter 5) incorporate an unpredictable element, so that the results of such systems are different every time the process is run. Despite the common wisdom that machines are deterministic and therefore predictable, there are numerous readily available sources of randomness available to machines. Contemporary theories of quantum mechanics postulate a profound randomness at the core of existence. According to certain theories of quantum mechanics, what appears to be the deterministic behavior of systems at a macro level is simply the result of overwhelming statistical preponderances based on enormous numbers of fundamentally unpredictable events. Moreover, the work of Stephen Wolfram and others has demonstrated that even a system that is in theory fully deterministic can nonetheless produce effectively random and, most important, entirely unpredictable results.

Genetic algorithms and similar self-organizing approaches give rise to designs that could not have been arrived at through a modular component-driven approach. The "strangeness, ... [the] chaos, ... the dynamic interaction" of parts to the whole that Denton attributes exclusively to organic structures describe very well the qualities of the results of these human-initiated chaotic processes.

In my own work with genetic algorithms I have examined the process by which such an algorithm gradually improves a design. A genetic algorithm does not accomplish its design achievements through designing individual subsystems one at a time but effects an incremental "all at once" approach, making many small distributed changes throughout the design that progressively improve the overall fit or "power" of the solution. The solution itself emerges gradually and unfolds from simplicity to complexity. While the solutions it produces are often asymmetric and ungainly but effective, just as in nature, they can also appear elegant and even beautiful.

Denton is correct in observing that most contemporary machines, such as today's conventional computers, are designed using the modular approach. There are certain significant engineering advantages to this traditional technique. For example, computers have much more accurate memories than humans and can perform logical transformations far more effectively than unaided human intelligence. Most important, computers can share their memories and patterns instantly. The chaotic nonmodular approach of nature also has clear advantages that Denton well articulates, as evidenced by the deep powers of human pattern recognition. But it is a wholly unjustified leap to say that because of the current (and diminishing!) limitations of human-directed technology that biological systems are inherently, even onto logically, a world apart.

The exquisite designs of nature (the eye, for example) have benefited from a profound evolutionary process. Our most complex genetic algorithms today incorporate genetic codes 'of tens of thousands of bits, whereas biological ent.i.ties such as humans are characterized by genetic codes of billions of bits (only tens of millions of bytes with compression).

However, as is the case with all information-based technology, the complexity of genetic algorithms and other nature-inspired methods is increasing exponentially. If we examine the rate at which this complexity is increasing, we find that they will match the complexity of human intelligence within about two decades, which is consistent with my estimates drawn from direct trends in hardware and software.

Denton points out we have not yet succeeded in folding proteins in three dimensions, "even one consisting of only 100 components." However, it is only in the recent few years that we have had the tools even to visualize these three-dimensional patterns. Moreover, modeling the interatomic forces will require on the order of one hundred thousand billion (1014) calculations per second. In late 2004 IBM introduced a version of its Blue Gene/L supercomputer with a capability of seventy teraflops (nearly 1014 cps), which, as the name suggests, is expected to provide the ability to simulate protein folding. cps), which, as the name suggests, is expected to provide the ability to simulate protein folding.

We have already succeeded in cutting, splicing, and rearranging genetic codes and harnessing nature's own biochemical factories to produce enzymes and other complex biological substances. It is true that most contemporary work of this type is done in two dimensions, but the requisite computational resources to visualize and model the far more complex three-dimensional patterns found in nature are not far from realization.

In discussions of the protein issue with Denton himself, he acknowledged that the problem would eventually be solved, estimating that it was perhaps a decade away. The fact that a certain technical feat has not yet been accomplished is not a strong argument that it never will be. Denton writes:

From knowledge of the genes of an organism it is impossible to predict the encoded organic forms. Neither the properties nor structure of individual proteins nor those of any higher order forms-such as ribosomes and whole cells-can be inferred even from the most exhaustive a.n.a.lysis of the genes and their primary products, linear sequences of amino acids.

Although Denton's observation above is essentially correct, it basically points out that the genome is only part of the overall system. The DNA code is not the whole story, and the rest of the molecular support system is required for the system to work and for it to be understood. We also need the design of the ribosome and other molecules that make the DNA machinery function. However, adding these designs does not significantly change the amount of design information in biology.

But re-creating the ma.s.sively parallel, digitally controlled a.n.a.log, hologramlike, self-organizing, and chaotic processes of the human brain does not require us to fold proteins. As discussed in chapter 4 there are dozens of contemporary projects that have succeeded in creating detailed re-creations of neurological systems. These include neural implants that successfully function inside people's brains without folding any proteins. However, while I understand Denton's argument about proteins to be evidence regarding the holistic ways of nature, as I have pointed out there are no essential barriers to our emulating these ways in our technology, and we are already well down this path.

In summary, Denton is far too quick to conclude that complex systems of matter and energy in the physical world are incapable of exhibiting the "emergent ... vital characteristics of organisms such as self-replication, 'morphing,' self-regeneration, self-a.s.sembly and the holistic order of biological design" and that, therefore, "organisms and machines belong to different categories of being." Dembski and Denton share the same limited view of machines as ent.i.ties that can be designed and constructed only in a modular way. We can build and already are building "machines" that have powers far greater than the sum of their parts by combining the self-organizing design principles of the natural world with the accelerating powers of our human-initiated technology. It will be a formidable combination.

Epilogue.

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seash.o.r.e, and diverting myself in now and then finding a smoother pebble or a prettier sh.e.l.l than ordinary, whilst the great ocean of truth lay undiscovered before me.-ISAAC NEWTON1 The meaning of life is creative love. Not love as an inner feeling, as a private sentimental emotion, but love as a dynamic power moving out into the world and doing something original.-TOM MORRIS, IF ARISTOTLE RANN GENERAL MOTORS IF ARISTOTLE RANN GENERAL MOTORS No exponential is forever ... but we can delay "forever."-GORDON E. MOORE, 2004

H.

ow Singular? How singular is the Singularity? Will it happen in an instant? Let's consider again the derivation of the word. In mathematics a singularity is a value that is beyond any limit-in essence, infinity. (Formally the value of a function that contains such a singularity is said to be undefined at the singularity point, but we can show that the value of the function at nearby points exceeds any specific finite value). How singular is the Singularity? Will it happen in an instant? Let's consider again the derivation of the word. In mathematics a singularity is a value that is beyond any limit-in essence, infinity. (Formally the value of a function that contains such a singularity is said to be undefined at the singularity point, but we can show that the value of the function at nearby points exceeds any specific finite value).2 The Singularity, as we have discussed it in this book, does not achieve infinite levels of computation, memory, or any other measurable attribute. But it certainly achieves vast levels of all of these qualities, including intelligence. With the reverse engineering of the human brain we will be able to apply the parallel, self-organizing, chaotic algorithms of human intelligence to enormously powerful computational substrates. This intelligence will then be in a position to improve its own design, both hardware and software, in a rapidly accelerating iterative process.

But there still appears to be a limit. The capacity of the universe to support intelligence appears to be only about 1090 calculations per second, as I discussed in chapter 6. There are theories such as the holographic universe that suggest the possibility of higher numbers (such as 10 calculations per second, as I discussed in chapter 6. There are theories such as the holographic universe that suggest the possibility of higher numbers (such as 10120), but these levels are all decidedly finite.

Of course, the capabilities of such an intelligence may appear infinite for all practical purposes to our current level of intelligence. A universe saturated with intelligence at 1090 cps would be one trillion trillion trillion trillion trillion times more powerful than all biological human brains on Earth today. cps would be one trillion trillion trillion trillion trillion times more powerful than all biological human brains on Earth today.3 Even a one-kilogram "cold" computer has a peak potential of 10 Even a one-kilogram "cold" computer has a peak potential of 1042 cps, as I reviewed in chapter 3, which is ten thousand trillion (10 cps, as I reviewed in chapter 3, which is ten thousand trillion (1016) times more powerful than all biological human brains.4 Given the power of exponential notation, we can easily conjure up bigger numbers, even if we lack the imagination to contemplate all of their implications. We can imagine the possibility of our future intelligence spreading into other universes. Such a scenario is conceivable given our current understanding of cosmology, although speculative. This could potentially allow our future intelligence to go beyond any limits. If we gained the ability to create and colonize other universes (and if there is a way to do this, the vast intelligence of our future civilization is likely to be able to harness it), our intelligence would ultimately be capable of exceeding any specific finite level. That's exactly what we can say for singularities in mathematical functions.

How does our use of "singularity" in human history compare to its use in physics? The word was borrowed from mathematics by physics, which has always shown a penchant for anthropomorphic terms (such as "charm" and "strange" for names of quarks). In physics "singularity" theoretically refers to a point of zero size with infinite density of ma.s.s and therefore infinite gravity.

But because of quantum uncertainty there is no actual point of infinite density, and indeed quantum mechanics disallows infinite values.

Just like the Singularity as I have discussed it in this book, a singularity in physics denotes unimaginably large values. And the area of interest in physics is not actually zero in size but rather is an event horizon around the theoretical singularity point inside a black hole (which is not even black). Inside the event horizon particles and energy, such as light, cannot escape because gravity is too strong. Thus from outside the event horizon, we cannot see easily inside the event horizon with certainty.

However, there does appear to be a way to see inside a black hole, because black holes give off a shower of particles. Particle-antiparticle pairs are created near the event horizon (as happens everywhere in s.p.a.ce), and for some of these pairs, one of the pair is pulled into the black hole while the other manages to escape. These escaping particles form a glow called Hawking radiation, named after its discoverer, Stephen Hawking. The current thinking is that this radiation does reflect (in a coded fashion, and as a result of a form of quantum entanglement with the particles inside) what is happening inside the black hole. Hawking initially resisted this explanation but now appears to agree.

So, we find our use of the term "Singularity" in this book to be no less appropriate than the deployment of this term by the physics community. Just as we find it hard to see beyond the event horizon of a black hole, we also find it difficult to see beyond the event horizon of the historical Singularity. How can we, with our brains each limited to 1016 to 10 to 1019 cps, imagine what our future civilization in 2099 with its 10 cps, imagine what our future civilization in 2099 with its 1060 cps will be capable of thinking and doing? cps will be capable of thinking and doing?

Nevertheless, just as we can draw conclusions about the nature of black holes through our conceptual thinking, despite never having actually been inside one, our thinking today is powerful enough to have meaningful insights into the implications of the Singularity. That's what I've tried to do in this book.

Human Centrality. A common view is that science has consistently been correcting our overly inflated view of our own significance. Stephen Jay Gould said, "The most important scientific revolutions all include, as their only common feature, the dethronement of human arrogance from one pedestal after another of previous convictions about our centrality in the cosmos." A common view is that science has consistently been correcting our overly inflated view of our own significance. Stephen Jay Gould said, "The most important scientific revolutions all include, as their only common feature, the dethronement of human arrogance from one pedestal after another of previous convictions about our centrality in the cosmos."5 But it turns out that we are central, after all. Our ability to create models-virtual realities-in our brains, combined with our modest-looking thumbs, has been sufficient to usher in another form of evolution: technology. That development enabled the persistence of the accelerating pace that started with biological evolution. It will continue until the entire universe is at our fingertips.

Resources and Contact Information

Singularity.com

New developments in the diverse fields discussed in this book are acc.u.mulating at an accelerating pace. To help you keep pace, I invite you to visit Singularity.com, where you will find

Recent news storiesA compilation of thousands of relevant news stories going back to 2001 from KurzweilAI.net (see below)Hundreds of articles on related topics from KurzweilAI.netResearch linksData and citation for all graphsMaterial about this bookExcerpts from this bookOnline endnotes

KurzweilAI.net

You are also invited to visit our award-winning Web site, KurzweilAI.net, which includes over six hundred articles by over one hundred "big thinkers" (many of whom are cited in this book), thousands of news articles, listings of events, and other features. Over the past six months, we have had more than one million readers. Memes on KurzweilAI.net include:

The SingularityWill Machines Become Conscious?Living Forever o How to Build a BrainVirtual RealitiesNanotechnologyDangerous FuturesVisions of the FuturePoint/Counterpoint

You can sign up for our free (daily or weekly) e-newsletter by putting your e-mail address in the simple one-line form on the KurzweilAI.net home page. We do not share your e-mail address with anyone.

Fantastic-Voyage.net and RayandTerry.com

For those of you who would like to optimize your health today, and to maximize your prospects of living long enough to actually witness and experience the Singularity, visit Fantastic-Voyage.net and RayandTerry.com. I developed these sites with Terry Grossman, M.D., my health collaborator and coauthor of Fantastic Voyage: Live Long Enough to Live Forever. These sites contain extensive information about improving your health with today's knowledge so that you can be in good health and spirits when the biotechnology and nanotechnology revolutions are fully mature.

Contacting the Author

Ray Kurzweil can be reached at

APPENDIX.

The Law of Accelerating Returns Revisited

The following a.n.a.lysis provides the basis of understanding evolutionary change as a doubly exponential phenomenon (that is, exponential growth in which the rate of exponential growth-the exponent-is itself growing exponentially). I will describe here the growth of computational power, although the formulas are similar for other aspects of evolution, especially information-based processes and technologies, including our knowledge of human intelligence, which is a primary source of the software of intelligence.

We are concerned with three variables:

V: Velocity (that is, power) of computation (measured in calculations per second per unit cost) W: World knowledge as it pertains to designing and building computational devices t: Time

As a first-order a.n.a.lysis, we observe that computer power is a linear function of W W. We also note that W W is c.u.mulative. This is based on the observation that relevant technology algorithms are acc.u.mulated in an incremental way. In the case of the human brain, for example, evolutionary psychologists argue that the brain is a ma.s.sively modular intelligence system, evolved over time in an incremental manner. Also, in this simple model, the instantaneous increment to knowledge is proportional to computational power. These observations lead to the conclusion that computational power grows exponentially over time. is c.u.mulative. This is based on the observation that relevant technology algorithms are acc.u.mulated in an incremental way. In the case of the human brain, for example, evolutionary psychologists argue that the brain is a ma.s.sively modular intelligence system, evolved over time in an incremental manner. Also, in this simple model, the instantaneous increment to knowledge is proportional to computational power. These observations lead to the conclusion that computational power grows exponentially over time.

In other words, computer power is a linear function of the knowledge of how to build computers. This is actually a conservative a.s.sumption. In general, innovations improve V V by a multiple, not in an additive way. Independent innovations (each representing a linear increment to knowledge) multiply one another's effects. For example, a circuit advance such as CMOS (complementary metal oxide semiconductor), a more efficient IC wiring methodology, a processor innovation such as pipelining, or an algorithmic improvement such as the fast Fourier transform, all increase by a multiple, not in an additive way. Independent innovations (each representing a linear increment to knowledge) multiply one another's effects. For example, a circuit advance such as CMOS (complementary metal oxide semiconductor), a more efficient IC wiring methodology, a processor innovation such as pipelining, or an algorithmic improvement such as the fast Fourier transform, all increase V V by independent multiples. by independent multiples.

As noted, our initial observations are: The velocity of computation is proportional to world knowledge:

(1) [image]