The answer is never. These are very foolish ideas put about by people with a crude understanding of economics and the production process.
For starters the focus is on those processes that lend themselves to exponential improvement. This is the wrong focus. Any chemist will tell you that the rate determining step is the SLOWEST part of the reaction. Not the fastest. Any project manager who uses critical path analysis knows he must speed up the LONGEST path of the overall project to reduce the completion time. Yet Kurzwell et al draw their analogy from Moores law where a tiny subset of productivity improvement has been very fast. Yet this improvement in information processing cost effectiveness has relied on a massively extended structure of production involving international trade.
What the focus should be on in overall productivity is inherent bottlenecks on the horizon. Not low-hanging fruit already with us.
Increases in productivity requires what the Austrian school calls “a lengthening of the structure of production” and not merely improvement in individual capital goods. There is an exception to this which I will get to later.
You could think of lengthening the structure of production as being akin to increasing the length of a conveyor. But manufacturing is an extension of logistics. And a factory either too large or small becomes a choke point. So the lengthening of the structure of production, in practice, requires more factories and more transport between them. Under our current model of cargo transport involving big cities, roads and big trucks, we would run into production bottlenecks very quickly. Particularly as truck use depreciates the roads directly.
Think of the notion that we are going to increase productivity AND shorten the production structure with 3-D printing. This is a much more foolish notion than thinking that photocopiers would make printing presses obsolete. Other technology maybe, but not the photocopier. If you could speed the 3-D printer up to compete with mass production, the room where these printers were held, would become choke points as people crowded around to provide resin and maintenance services.
How about nanotechnology? Amazing stuff but a big winner for productivity? No because the small stuff is always going to be high maintenance. Imagine trying to crank out faster production from a team of precision watch-makers and you will understand what I mean. Then even if those watch-makers are robots you will need more robots to do maintenance on them and all the way down the line. So we are never getting away from the reality that high productivity requires an extended production structure.
But there is one type of nanotechnology that has low maintenance costs and there is a name for that nanotechnology and that name is THE SEED. This brings me to the one area where we can get more productivity with a shorter production structure and we call this PERMACULTURE.
To increase productivity without the bottlenecks that stick out, we of course want durable producer goods accumulation and update. But the current model of big cities, trucks and roads is limiting us. A better model would be smaller settlements, canals, hydrogen dirigibles, and ubiquitous permaculture. But this more functional setup is not something achievable by 2025.
Looking closer at the singularity movement there is more going on than a sudden convergence of economic illiterates. These guys also have what looks to be some occult heresies on the fly. They have this idea of transhumanisnm. Here we have occult-inspired death-worship posing as a quest for everlasting life.
Its really these pseudo-religious considerations that explain the cluster of foolishness. Life extension is a good thing but it involves breaking the medical cartel, better nutrition, life extension techniques and bio hacking. But these guys idea of living forever involves a carbon atom free zone. They aspire to turn themselves into cyborgs and perhaps later download their immortal souls into some sort of version of the Internet. But machines require maintenance whereas the cell creates other cells. So who will maintain the grid in this fantasy? I would just wipe the software. Perhaps they expect machines to maintain other machines to maintain other machines to maintain this internet to house their immortal souls.
But not using the carbon atom, that is to say BIOLOGY, would unnecessarily hobble the production process. The better approach is to keep our telemeres longer and to keep our consciousness intact with our biological bodies.
There is more to this foolishness and I look to the blinkered attitudes that the Big Bang myth and ideological Darwinism propagate. This idea that evolution is so time limited leads people to underestimate the complexity of the the cell and of biological life more generally.
Its a bit like this Transformers fantasy of metallic machines taking over and reproducing themselves. But this sort of carbon-free reproduction is never going to be a competitive model.