Earlier quoted context omitted.
Where that falls down is that it fails to consider limits. Exponential growth cannot continue forever. At some point, something will limit it. It may be a physical limit, a supply-side resource limit, or an economic demand limit, but there will be a limit somewhere. Without limits, a single bacterium could fill the entire universe in a few years. Sometimes things do grow like that for a while, but Kurzweil's attempt…
True. However decades long periods of exponential improvement in technology is the norm, not the exception. The most spectacular example is Moore's law, but it is hardly alone. If you read The Innovator's Dilemma you will find plenty of other examples, ranging from the maximum range of a steam ship to the volume of dirt a backhoe can scoop per hour. The interesting questions are how much computing power you need to p…
Exponential growth of tools opens up an exponential number of different avenues of exploration - if computers didn't advance at all for ten years, we'd still come up with many more ways to use them. With them advancing exponentially, we can not only find different ways of using them but new fields where different forms of exponential growth can happen. And so-forth. There's no fixed frontier but a moving process.
This isn't saying it's all wonderful but it's all likely to be a bit beyond our ability to encompass it - to draw a circle around it.