In a process, the time interval between salient events (that is, events that change the nature of the process, or significantly affect the future of the process) expands or contracts along with the amount of chaos. -
Ray Kurzweil,
The Age of Spiritual Machines:
When Computers Exceed Human Intelligence
Kurzweil frequently refers to two "sublaws", which are basically restatements of the above law:
Law of Increasing Chaos:
As chaos exponentially increases, time exponentially slows down (that is, the time interval between salient events grows longer as time passes).
Law of Accelerating Returns:
As order exponentially increases, time exponentially speeds up (that is, the time interval between salient events grows shorter as time passes).
Kurzweil gives the reader the following processes and illustrates how the frequency of significant events is related to the amount of chaos currently in each process.
The Universe (Increasing Chaos)
Our universe began as a single point in time and space, theoretically void of all
chaos. It was all downhill from there, baby.
After 10^-43 seconds of existence, the universe churned out something useful:
gravity. 10^-34 seconds later,
matter and
antimatter emerged in the form of
electrons/
positrons and
quarks/
antiquarks. Gravity was joined by the
strong nuclear force and the
electroweak force. In another 10^-10 seconds, the
electroweak force split into the
electromagnetic force and the
weak nuclear force. A measly 10^-5 seconds later,
quarks and
antiquark came together to form
protons and
antiprotons, respectively. At this point,
protons were slightly more abundant than
antiprotons, giving them the edge when the two annihilated each other and created
photons.
The amount of
chaos in the
universe was now exploding
exponentially, and time between
salient events saw a similar increase. It took an entire second for
electrons and
positrons to similarly annihilate each other, and another minute for
protons to begin forming heavier
nuclei, such as
helium and
lithium.
It wasn't until 300,000 years later that those
nuclei grabbed nearby
electrons and formed
atoms. After one billion years
matter condensed into clouds and formed
galaxies. Two billion years later, matter condensed further into stars and planets.
The
time between significant events went from ridiculously small (10^-43 seconds) to ridiculously large (two billion years) as the amount of
chaos went from ridiculously small (none) to ridiculously large. It goes the other way, too:
The Evolution of Life on Earth (Increasing Returns)
Two billion years after the creation of earth, life appeared (
Kurzweil defines "life" as
patterns of matter and energy that could perpetuate themselves and survive, like
DNA). For billions of years, these patterns organized themselves until, 3.4 billion years ago,
anaerobic prokaryotes emerged. DNA-based
genetics developed after some time, and 700 million years ago the first
multicellular plants and animals were formed. In the next 130 million years, the design of modern animals began to take shape, specifically a
spinal cord-based skeleton. Humanoids emerged 15 million years ago and evolved rapidly until the emergence of
Homo sapiens about 500,000 years ago.
This time, the increasing
order found in life forms as
evolution progressed led to a decrease in the time between significant events: it took billions of years for the first cell to evolve, but only several million years for that cell to evolve into complex life forms.
A Human Life (Increasing Chaos)
A human being begins as a single
cell. A cell is not exactly void of
chaos, but it is the most
orderly a human being will ever be. The cell begins to divide after several hours, the brain and other internal organs begin to form after several weeks, and the whole process is completed in several months. In the first few months after birth, the infant learns basic motor skills and looks around, rolls from side to side, and grasps objects. At 12 months, a human being will stand and begin to walk. Decades later, the human being will reach its physical peak and begin to deteriorate. The last significant event in the life of a human being is death, occurring in perhaps another 50 years.
Chaos increases, time between significant events increases.
The Evolution of Technology (Increasing Returns)
Finally,
Kurzweil shows the reader that as
technology is becoming increasingly orderly, its returns are increasing as well, specifically in the area of computation (
calculators,
processors, etc.).
Moore's Law on Integrated Circuits is a perfect example, but after mapping the computing power of 49 $1000 computers (from the
Analytical Engine in
1900, through the invention of
transistors and
integrated circuits and the emergence of
Moore's Law, to a
Pentium II PC in
1998),
Kurzweil found a similar
exponential trend.
The three laws and facts were taken from The Age of Spiritual Machines: When Computers Exceed Human Intelligence (ISBN 0-965-086131). I wrote the rest. If you think any of his facts are incorrect, I'd love to know.