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.

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