Microsoft Word Kurzweil, Ray The Singularity Is Near doc

The Life Cycle of a Paradigm.
Each paradigm develops in three stages: 
1.
Slow growth (the early phase of exponential growth) 
2.
Rapid growth (the late, explosive phase of exponential growth), as seen in the S-curve figure below 
3.
A leveling off as the particular paradigm matures 
The progression of these three stages looks like the letter S, stretched to the right. The S-curve illustration shows 
how an ongoing exponential trend can be composed of a cascade of S-curves. Each successive S-curve is faster (takes 
less time on the time, or 
x
, axis) and higher (takes up more room on the performance, or 
y
, axis). 

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S-curves are typical of biological growth: replication of a system of relatively fixed complexity (such as an 
organism of a particular species), operating in a competitive niche and struggling for finite local resources. This often 
occurs, for example, when a species happens upon a new hospitable environment. Its numbers will grow exponentially 
for a while before leveling off. The overall exponential growth of an evolutionary process (whether molecular, 
biological, cultural, or technological) supersedes the limits to growth seen in any particular paradigm (a specific S-
curve) as a result of the increasing power and efficiency developed in each successive paradigm. The exponential 
growth of an evolutionary process, therefore, spans multiple S-curves. The most important contemporary example of 
this phenomenon is the five paradigms of computation discussed below. The entire progression of evolution seen in 
the charts on the acceleration of paradigm shift in the previous chapter represents successive S-curves. Each key event, 
such as writing or printing, represents a new paradigm and a new S-curve. 

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The evolutionary theory of punctuated equilibrium (PE) describes evolution as progressing through periods of 
rapid change followed by periods of relative stasis.
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Indeed, the key events on the epochal-event graphs do correspond 
to renewed periods of exponential increase in order (and, generally, of complexity), followed by slower growth as each 
paradigm approaches its asymptote (limit of capability). So PE does provide a better evolutionary model than a model 
that predicts only smooth progression through paradigm shifts. 
But the key events in punctuated equilibrium, while giving rise to more rapid change, don't represent 
instantaneous jumps. For example, the advent of DNA allowed a surge (but not an immediate jump) of evolutionary 
improvement in organism design and resulting increases in complexity. In recent technological history, the invention 
of the computer initiated another surge, still ongoing, in the complexity of information that the human-machine 
civilization is capable of handling. This latter surge will not reach an asymptote until we saturate the matter and energy 
in our region of the universe with computation, based on physical limits we'll discuss in the section "... on the 
Intelligent Destiny of the Cosmos" in chapter 6.
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During this third or maturing phase in the life cycle of a paradigm, pressure begins to build for the next paradigm 
shift. In the case of technology, research dollars are invested to create the next paradigm. We can see this in the 
extensive research being conducted today toward three-dimensional molecular computing, despite the fact that we still 
have at least a decade left for the paradigm of shrinking transistors on a flat integrated circuit using photolithography. 
Generally, by the time a paradigm approaches its asymptote in price-performance, the next technical paradigm is 
already working in niche applications. For example, in the 1950s engineers were shrinking vacuum tubes to provide 
greater price-performance for computers, until the process became no longer feasible. At this point, around 1960, 
transistors had already achieved a strong niche market in portable radios and were subsequently used to replace 
vacuum tubes in computers. 
The resources underlying the exponential growth of an evolutionary process are relatively unbounded. One such 
resource is the (ever-growing) order of the evolutionary process itself (since, as I pointed out, the products of an 
evolutionary process continue to grow in order). Each stage of evolution provides more powerful tools for the next. 
For example, in biological evolution, the advent of DNA enabled more powerful and faster evolutionary 
"experiments." Or to take a more recent example, the advent of computer-assisted design tools allows rapid 
development of the next generation of computers. 
The other required resource for continued exponential growth of order is the "chaos" of the environment in which 
the evolutionary process takes place and which provides the options for further diversity. The chaos provides the 
variability to permit an evolutionary process to discover more powerful and efficient solutions. In biological evolution, 
one source of diversity is the mixing and matching of gene combinations through sexual reproduction. Sexual 
reproduction itself was an evolutionary innovation that accelerated the entire process of biological adaptation and 
provided for greater diversity of genetic combinations than nonsexual reproduction. Other sources of diversity are 
mutations and ever-changing environmental conditions. In technological evolution, human ingenuity combined with 
variable market conditions keeps the process of innovation going.