The Singularity Is Near: When Humans Transcend Biology (90 page)

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 10
¹⁶
to 10
¹⁹
cps, imagine what our future civilization in 2099 with its 10
⁶⁰
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.”
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 accumulating at an accelerating pace. To help you keep pace, I invite you to visit Singularity. com, where you will find

• Recent news stories
  
• A compilation of thousands of relevant news stories going back to 2001 from KurzweilAI.net (see below)
  
• Hundreds of articles on related topics from KurzweilAI.net
  
• Research links
  
• Data and citation for all graphs
  
• Material about this book
  
• Excerpts from this book
  
• Online 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 Singularity
  
• Will Machines Become Conscious?
  
• Living Forever
  
• How to Build a Brain
  
• Virtual Realities
  
• Nanotechnology
  
• Dangerous Futures
  
• Visions of the Future
  
• Point/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 [email protected].

APPENDIX

The Law of Accelerating Returns
Revisited

The following analysis 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 analysis, we observe that computer power is a linear function of
W
. We also note that
W
is cumulative. This is based on the observation that relevant technology algorithms are accumulated in an incremental way. In the case of the human brain, for example, evolutionary psychologists argue that the brain is a massively 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 assumption. In general, innovations improve
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
V
by independent multiples.

As noted, our initial observations are:

The velocity of computation is proportional to world knowledge:

(1)
V
=
c
₁
W

The rate of change of world knowledge is proportional to the velocity of computation:

Substituting (1) into (2) gives:

The solution to this is:

and
W
grows exponentially with time (
e
is the base of the natural logarithms).

The data that I’ve gathered shows that there is exponential growth in the rate of (exponent for) exponential growth (we doubled computer power every three years early in the twentieth century and every two years in the middle of the century, and are doubling it every one year now). The exponentially growing power of technology results in exponential growth of the economy. This can be observed going back at least a century. Interestingly, recessions, including the Great Depression, can be modeled as a fairly weak cycle on top of the underlying exponential growth. In each case, the economy “snaps back” to where it would have been had the recession/depression never existed in the first place. We can see even more rapid exponential growth in specific industries tied to the exponentially growing technologies, such as the computer industry.

If we factor in the exponentially growing resources for computation, we can see the source for the second level of exponential growth.

Once again we have:

(5)
V
=
c
₁
W

But now we include the fact that the resources deployed for computation,
N
, are also growing exponentially:

The rate of change of world knowledge is now proportional to the product of the velocity of computation and the deployed resources:

Substituting (5) and (6) into (7) we get: