Why the singularity may never arrive
This all seems reasonable, and very well documented. He then goes on to extrapolate the graph and postulates, backed up by his extensive research, that eventually the graph will become so steep that it is effectively vertical. This is the singularity where technology moves at a pace so fast that it is more or less instantaneous. According to Kurzweil this spells a new paradigm, and we have no way of knowing shat will happen after the singularity has arrived. But it will be exciting times. Or scary if you are so inclined.
If the current trend continues, according to Kurzweil, a 1000$ computer will be able to match human intelligence within 15 years. Extrapolating further he argues that within 41 years a 1000$ computer will match the intelligence of the entire human race. While hard to grasp mentally it makes sense when you look at the data - the graph pointing to the future seems believable and filled with good data backing the theory.
But there's a problem.
Thomas Malthus Put forth his theory of limits to human growth in 1826 that bears some resemblance to Kurzweils theory. He found that historically human growth had grown exponentially, and that global food supply had grown linearly. When he extrapolated the two graphs into the future he saw disastrous consequences - since food supply would grow slower and slower compared to the human population he predicted widespread famine, wars over food and other miseries. What happened was that population growth declined and has halved since its peak in 1963.
If you look at a lot of natural growth phenomena, such as population growth, rabbits in Australia, or the growth of bacteria in a petri dish, they initially follow the same trend. It starts out with a few bacteria that multiply, these bacteria multiply again and so on. This gives the initial exponential growth that is very common in nature, and that human progress has also followed since the invention of the slide rule. But the bacteria don't grow out of the petri dish to consume the lab, the country and eventually the entire world. Why is that? Because they need resources to keep growing. When the resources start to run out the graph stops the exponential growth and flattens out like an S.
The same thing will happen with technology - eventually we will run into insurmountable barriers to growth and progress will stabilise at this level. It's just a question of what the barriers are - the food for progress so to say.
The real question is what these inurmountable barriers are, and when we will run into them.