I think past acceleration is mostly about a large number of improvements that build on one another rather than a small number of big wins (as Katja points out), and future acceleration will probably be more of the same. It seems like almost all of the tasks that humans currently do could plausibly be automated without "AGI" (though it depends on how exactly you define AGI), and if you improve human productivity a bunch in enough industries then you are likely to have faster growth.

I expect "21st century acceleration is about computers taking over cognitive work from humans" will be the analog of "The industrial revolution is about engines taking over mechanical work from humans / beasts of burden."

From that perspective, asking "What technology short of AGI would take over cognitive work from humans, and how?" is analogous to asking "What technology short of a universal actuator would take over mechanical work from humans, and how?" The answer is just: a bunch of stuff that's specific to the details of each type of work.

Thoughts on some particular technologies, kind of at random:

• I think that most of that automation is likely to involve new software, and so the size of the software industry is likely to grow a bunch. Increasing productivity in the software industry (likely via ML) would then be an important driver of productivity growth despite software currently being a small share of GDP.
• I think that cheap solar power, automation of manufacturing and construction (including manufacturing industrial tools and construction of factories), and automation of service jobs are also very important stories.
• I think that west probably could be growing considerably faster even without qualitative technological change, so part of the story may be western countries either getting out of their current slump or being overtaken.

The other part of your post is about how much qualitative change would correspond to a doubling of growth rates. I think you are moderately underestimating the extent of historical acceleration and so overestimating how much qualitative change would be needed:

• I think the US over the last 200 years is a particularly bad comparison because at the beginning of the period it was benefiting a lot from colonization. Below I talk about the UK which I think is probably more representative. I chose the UK as the the most natural frontier economy after the industrial revolution, but I expect the exercise would be similar for other countries without complications.
• Looking at growth over the last 200 years hides the fact that there was a period of more rapid acceleration followed by a stagnation. If we instead compared 1800 to 1950 we'd see a larger change in growth rates accompanied by a smaller qualitative change. So that's probably more useful if you are looking for an existence proof (and I think low levels of current growth likely make acceleration easier).

In 1800 the US was growing rapidly in significant part because colonists were still taking new land and then increasing utilization of that land. So over the last 200 years you have a decrease in some kinds of growth and an increase in others. I don't know much about this and it may be completely wrong, but given that the US was growing so much faster than the rest of the world and that there's such a simple explanation that seems to check out, that's what I'd assume is going on. If that's right then it can still be OK to use the US as an example but you can't use raw growth numbers to infer something about technological change.

If you want to see what's happening in frontier economies since the industrial revolution then it seems more natural to use something like per capita GDP in the UK. If I look up the GDP per capita in the UK time series at Our World in Data and turn that into a graph of (GDP per capita growth rate) vs (time), I get:

So it seems to me like things really did change a lot as technology improved, growing from 0.4% in 1800-1850, to 1% in 1850-1900, to .8% in 1900-1950, to 2.4% in 1950-2000. What we're talking about is a further change similar in scope to the change from 1800 to 1850 or from 1900 to 1950.

(I don't know if there are other reasons the UK isn't representative. I think the most obvious candidate would be that 1900-1950 was a really rough period for the UK, and then 1950-2000 potentially involves some catch-up growth.)

I don't know what post to link to, but I recall at some point Robin Hanson articulated fully automated manufacturing as his guess about the next big bump in GDP doubling times.

The argument as I recall it:

• Full automation means automation of everything including building the factories themselves.
• Full automation plausibly requires advanced AI, but not full human-level AGI. So (especially if we believe in relatively slow AI progress) we might expect to see this significantly before an AGI-based boom.
• Fully automated manufacturing would make manufacturing much cheaper by cutting out the human cost, and automated manufacture of factories would allow rapid scaling, and rapid responses to economic demands, which would be dramatic and game-changing. Production cycles (from idea to prototype to hitting the market) would be dramatically shortened.

...there are somewhere between six and ten billion people. At any given time, most of them are making mud bricks or field-stripping their AK-47s. - Neal Stephenson, Snow Crash

When we think of new technologies, we typically think of expensive, high-tech innovations, like energy production, robotics, etc. I would suggest that broader adoption of existing technologies, including social technologies, would have a bigger global impact. 

For example, one technology that could dramatically impact GDP is improved managerial technology. This paper describes a study of this in India. Among the findings in the paper (or in references that it cites):

100% productivity spreads between the 10th and 90th percentile in US commodity-producing firms

A ratio of the 90th to the 10th percentiles of total factor productivity is 5.0 in Indian and 4.9 in Chinese firms

After improving management in the studied firms, "We estimate that within the first year productivity increased by 17%; based on these changes we impute that annual profitability increased by over $300,000. These better-managed firms also appeared to grow faster, with suggestive evidence that better management allowed them to delegate more and open more production plants in the three years following the start of the experiment"

FWIW, world GDP growth rates have if anything been decreasing over the last ~80 years 

Excluding AI, and things like human intelligence enhancement, mind uploading ect.

I think that the biggest increases in the economy would be from more automated manufacturing. The extreme case is fully programmable molecular nanotech. The sort that can easily self replicate and where making anything is as easy as saying where to put the atoms. This would potentially lead to a substantially faster economic growth rate than 9%. 

There are various ways that the partially developed tech might be less powerful.

Maybe the nanotech uses a lot of energy, or some rare elements, making it much more expensive.

Maybe it can only use really pure feedstock, not environmental raw materials.

Maybe it is just really hard to program, no one has built the equivalent of a compiler yet, we are writing instructions in assembly, and even making a hello world is challenging.

Maybe we have macroscopic clanking replicators.

Maybe we have a collection of autonomous factories that can make most, but not all, of their own parts.

Maybe the nanotech is slowed down by some non-technological constraint, like bureaucracy, proprietary standards and patent disputes.

Mix and match various social and technological limitations to tune the effect on GDP

I don't think any one of those would have an impact anywhere near that big. If nothing else, they'll each take long enough to mature that their impact will be spread out over many years. However, I would suggest the combination of distributed, autonomous manufacturing (of which 3D printing is one part), generative design, and materials informatics (and related informatics technologies) could get there.

Right now bringing new stuff to market and scaling it up is many times faster and cheaper for software than anything else. The more you can reduce the resource burden, and with it the number of people and organizations that have to buy in, to turning ideas into products, the smaller that gap can get. I would naively assume that this is analogous to any other catalyst - lower the energy barriers for the rate-limiting steps, and you get exponential speed-up. It also reduces the cost of entry and cost of failure, making it possible for many more people to participate in innovation.

One problem with this idea is that what I'm proposing is to essentially commoditize scale-up, manufacturing, and some parts of R&D, to make them nearly free. I'm making no attempt to work out the downstream effects of that on the service sector, which is a majority of GDP. I do think that's likely more a measurement problem with GDP (if a problem at all), though, and that the kind of improvement I'm suggesting could easily lead to a less-easily-measured acceleration of economic value growth.

Digital matter, in other words, molecular manufacturing. 

With a Star Trekian autogenous home synthesizer, one could expect Moore's Law-like growth.

A tricky thing here is that it really depends how quickly a technology is adopted, improved, integrated, and so on.

For example, it seems like computers and the internet caused a bit of a surge in American productivity growth in the 90s. The surge wasn't anything radical, though, for at least a few reasons:

1. Continued technological progress is necessary just to sustain steady productivity growth.

2. It's apparently very hard, in general, to increase aggregate productivity.

3. The adoption, improvement, integration, etc., of information technology was a relatively gradual process.

If we instead suddenly jumped from a world where no company has information technology to one where every company is using 2020-level information technology (and using it with 2020-level tacit knowledge, IT-enabling capital investments, IT-adapted business practices, complementary technologies, etc.), then the productivity growth rate for that year would probably have been very high. But the gradualness of everything flattened out the surge. Given how slowly diffusion happens globally, I actually wouldn't be surprised if the surge was totally invisible at the global level.

So if we want to predict that some technology (e.g. fusion power) will help surge the growth rate above some high threshold, we will also typically need to predict that its aggregrate impact will be unusually sudden.

How about a novel nootropic drug?  Or advancements in neurolink technology to enhance brain-computer interfaces?  Plus other biological and medical advancements that one could conceive of.  Weight bearing suits that ease repetitive stress and increase lifting capacity.  Personal climate controlled suits that make you comfortable anywhere.

Cloning. Increase world population by 9% per year and you'll add 9% in GDP fairly easily.

Which also points to GDP per capita being a more interesting measure?

China had a longer time that kind of growth through having good governance and effective economic policy. 

If a technology such as the seeing rooms that Cummings talked about suddenly allow decision making and governance to improve by a large margin, we might get that kind of economic growth. 

The fact that the cost of building subway tunnels increased rather then decreased isn't because energy prices or resource prices rose but because of a mix of lack of innovation and complex regulation. 

How about 3D bioprinting as a form of regenerative medicine?

It's been said that about half of all people have an IQ less than 100. Some psychologists have pointed out that those with IQs less than 90 have a difficult time finding good work in advanced knowledge-driven economies, and manual labor has been either exported to other countries or replaced with robots, leaving part of the labor pool underutilized.

So the shape of the idea that would generate 9%+ GDP growth is a set of technologies and/or political configurations that bring people of all IQs enthusiastically into the labor force. Not just employment opportunity, but situations that would be gleefully embraced, and productive, regardless of IQ. Work that is useful and fulfilling and worth doing for all involved.

This is not the actual idea, of course, only a statement of what might be its shape. If I actually had that idea, I would be talking to venture capitalists at this moment rather than typing this comment.

This would be good only for a temporary gain of three to six years of high growth. After that, we would be at full employment, and although the indirect gains would likely flow for a long time, national growth would likely fall below the 9% figure.

What's more important, though, is that such an outcome (bringing gleeful and productive employment to many) would make a lot of people happier, regardless of GDP growth.