Kurzweil's projections of the future (as I understand them) are based on the assumption of exponential growth ... compounding information ... which is happening in many fields. This results in sharp cost declines and expanding innovation. This growth is often ignored in the early stages of compounding from a very low basis.
The rate of exponential growth is actually accelerating in some instances as the progress in various fields such as AI, Nano technology, and biology increasingly feed into each other. The consequence can be a "singularity" in 2045 when computer based intelligences significantly exceed the sum of human brain power.
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