By The Law of Accelerating Returns Kurzweil means that:
[T]echnological change is exponential, contrary to the common-sense “intuitive linear” view. So we won’t experience 100 years of progress in the 21st century — it will be more like 20,000 years of progress (at today’s rate). The “returns,” such as chip speed and cost-effectiveness, also increase exponentially. There’s even exponential growth in the rate of exponential growth. Within a few decades, machine intelligence will surpass human intelligence, leading to The Singularity — technological change so rapid and profound it represents a rupture in the fabric of human history. The implications include the merger of biological and nonbiological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light.It is true that there is no linear rate of progress, however, Kurzweil seems to hold the view that instead progress is always exponential in some sort of measured manner.
It is difficult to understand how he reaches this conclusion since most technological advancement can not be measured in terms of given units. The advance from black and white televisions to color to the advancement of remote controls are all advancements in televisions but how does one measure in any kind of unit the advance from black and white televisions to remote control televisions?
The best we can say is that there has been spectacular change without putting a specific rate of change in terms of any unit on it---something that is necessary for Kurzweil to do to make his claim that technological growth is exponential and thus always accelerating.
To be sure, some advances are measurable in units. The elevator in my office building is state of the art, it will take you from the ground floor to the 20th floor in seconds and you hardly notice you are moving. This is a much faster ride than the elevators in buildings down the street that were built decades earlier.The travel time difference between the sets of elevators could be measured, and for certain there is a remarkable increase in speed. But should we expect technology to always advance in every way at an exponential rate? Will elevator speed increase at an exponential rate over the next 10 years? I guess it is possible, but I don't see why it necessarily will.
Modern man has an edge in future growth because for the most part technological progress has not been lost (forgotten), so every generation doesn't have to reinvent the wheel or the internet or the microchip or the cell phone. This aids in growth. You can build upon what you know. So in many ways, there is a reason to be nearly as optimistic as Kurzweil, but there are potential stumbling blocks that Kurzweil doesn't appear to recognize.
First, and most plausible, there may be stumbling blocks to certain future advancements that require a long time to solve (if ever). Just because a person knows addition, subtraction, multiplication, division, differential calculus and multivariable calculus doesn't mean he is about to advance to proving the Pollock tetrahedral numbers conjecture.
A second problem is, of course, the possibility of a tragic technological step that reverses if not destroys advancement of the driver of technological advance: human beings. What if a scientist experimenting and attempting to make the next major advance, in say the biological field, instead accidentally creates a deadly virus that wipes out the human species? What if a bad actor because of advancing technology is able to create a nuclear bomb that can blow up the planet?
Finally, Kurzweil appears to keep his Law of Accelerating Returns in a sterile environment where changes in society are not considered an element that can impact technological advancement.
However, anyone who visited the Soviet Union before it collapsed would surely recognized how an oppressive society can suffocate and reverse technological advance. Hell, anyone driving through the burnt out South Bronx in the 1970s could recognize how regulations (in this case rent controls) could halt advance and reverse it,
In summary, Kurzweil's absolutist optimism for exponential growth in the future has many problems. The first being that most growth can not be measured in terms so that it can be properly declared that all growth is indeed exponential. And although technological advancement has been dramatic, it is not at all clear that it has been across the board exponential and that it must be exponential. It is clear that there are a number of other elements that could slow advancing technology or even reverse it, from experiments gone bad to oppressive states to difficult scientific problems that won't be readily solved. Indeed, a new Dark Age can not be ruled out.
As for Kurzweil's additional step of considering a world of singularity, that is, a world that includes the merger of biological and nonbiological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light. It's a fun thought experiment where one could point to how things could go wrong in hundreds of different ways or turn in a hundred other directions but I think we will have some time to think about this, exponential growth or not.
(Note: The thinking of Kurzweil was first brought to my attention durinmg a series of conversations with Dr.Michael Edelstein, a recent column by Dr. Gary North reinforced the idea that I should take a look at Kurzweil's writing.)