Exponential Growth Curves

In his 1999 book, The Age of Spiritual Machines, Kurzweil proposed The Law of Accelerating Returns, according to which the rate of change in a wide variety of evolutionary systems - including but not limited to the growth of technologies - tends to increase exponentially. He gave further focus to this issue in a 2001 essay titled The Law of Accelerating Returns. Whenever a technology approaches some kind of barrier, according to Kurzweil, a new technology will be invented to allow us to cross that barrier. He predicts this will become increasingly common, leading to technological change so rapid and profound it represents a rupture in the fabric of human history.

 

Many technologies are subject to the law of accelerating returns. The exponential trend that has gained the greatest public recognition has become known as Moore’s Law.

 

Kurzweil predicts that after 60 years of devoted service, Moore’s Law will die a dignified death no later than 2019. By that time, transistor features will be just a few atoms in width and the strategy of ever-finer photolithography will have run its course.

 

 

The Law of Accelerating Returns

 

Evolution applies positive feedback in that the more capable methods resulting from one stage of evolutionary progress are used to create the next stage.

 

As a result, the rate of progress of an evolutionary process increases exponentially over time. Over time, the “order” of the information embedded in the evolutionary process (i.e. the measure of how well the information fits a purpose, which in evolution is survival) increases.

 

A correlate of the above observation is that the “returns” of an evolutionary process (e.g. the speed, cost-effectiveness, or overall “power” of a process) increase exponentially over time.

 

In another positive feedback loop, as a particular evolutionary process (e.g. computation) becomes more effective (i.e. cost effective), greater resources are deployed toward the further progress of that process. This results in a second level of exponential growth (i.e. the rate of exponential growth itself grows exponentially).

 

Biological evolution is one such evolutionary process.

 

Technological evolution is another such evolutionary process. Indeed, the emergence of the first technology-creating species resulted in the new evolutionary process of technology. Therefore, technological evolution is an outgrowth of – and a continuation of – biological evolution.

 

A specific paradigm (a method or approach to solving a problem, e.g. shrinking transistors on an integrated circuit as an approach to making more powerful computers) provides exponential growth until the method exhausts its potential. When this happens, a paradigm shift (i.e. a fundamental change in the approach) occurs, which enables exponential growth to continue.

 

Moore’s Law

 

Moore’s Law is a computing term that originated around 1970; the simplified version of this law is the observation that processor speeds, or overall processing power for computers, will double every two years.  A quick check among technicians in different computer companies shows that the term is not very popular but the rule is still accepted.

 

To break down the law even further, it specifically stated that the number of transistors on an affordable CPU would double every two years (which is essentially the same thing that was stated before) but ‘more transistors’ is more accurate.

 

The observation is named after Gordon E Moore, co-founder of the Intel Corporation, who described the trend in a 1965 paper. His prediction has proven to be accurate, in part because the law is now used in the semiconductor industry to guide long-term planning and to set targets for research and development. The capabilities of many digital electronic devices are strongly linked to Moore's law: quality-adjusted microprocessor prices, memory capacity, sensors and even the number and size of pixels in digital cameras. All of these are improving at roughly exponential rates as well.

 

This exponential improvement has dramatically enhanced the effect of digital electronics in nearly every segment of the world economy. Moore's Law describes a driving force of technological and social change, productivity, and economic growth in the late 20th and early 21st centuries.

 

Sources and further reading:

 

http://www.kurzweilai.net/the-law-of-accelerating-returns

 

http://en.wikipedia.org/wiki/Accelerating_change#Kurzweil.27s_The_Law_of_Accelerating_Returns

 

http://www.mooreslaw.org/

 

http://en.wikipedia.org/wiki/Moore's_law

 

 

 

 

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