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February 01, 2008

Singularity lite: one to two levels of faster technological change

The technological singularity is a hypothesized point in the future variously characterized by the technological creation of self-improving intelligence, unprecedentedly rapid technological progress, or some combination of the two.

I would want to focus on the aspect of "unprecendentedly rapid technological progress". I feel that a proxy for measuring "technological progress" can be the rate of human or world GDP growth (gross domestic product) or economic growth.

Money represents a near universal medium of exchange. You can change money for goods and services. Therefore, it is a proxy for increasing value and progress.

Economic growth would in general mean positive technological change. Faster growth would be faster technological change.

The Importance of Growth

From Tyler Cowan at the Marginal Revolution:
The importance of the growth rate increases, the further into the future we look. If a country grows at two percent, as opposed to growing at one percent, the difference in welfare in a single year is relatively small. But over time the difference becomes very large. For instance, had America grown one percentage point less per year, between 1870 and 1990, the America of 1990 would be no richer than the Mexico of 1990. At a growth rate of five percent per annum, it takes just over eighty years for a country to move from a per capita income of $500 to a per capita income of $25,000, defining both in terms of constant real dollars. At a growth rate of one percent, such an improvement takes 393 years. There are enormous long-run benefits of economic growth.


History of Economic growth

The shifts in rates of growth can be
clearly measured in the shift to a higher magnitude of growth rate. (Hanson)



Mode Doubling Date Began Doubles Doubles
Grows Time (DT) To Dominate of DT of WP
---------- --------- ----------- ------ -------
Brain size 34M yrs 550M B.C. ? "~16"
Hunters 230K yrs 2000K B.C. 7.2 8.7
Farmers 860 yrs 4700 B.C. 8.1 7.5
?? 58 yrs 1730 3.9 3.2
Industry 15 yrs 1903 1.9 >6.3


The 15 year doubling time is 4.7-4.8% GDP growth. An improvement of doubling time by 3-5 times would indicate another level of progress that is line with the long term historic trend.

Some things to examine are what were the sustainable technological and process innovations that enabled the historic shifts to sustainably higher levels of growth for human civilization overall. Also, what are current countries, regions, industries and companies that already have the next higher level of growth.

Note: There is no inevitability in higher levels of growth. Large segments of the world did not make the shift to Industry back in 1903. China was a later adopter. Much of Africa has not really adopted any of the innovations of Industry. Bad choices and lack of the various precursors and enabling factors can cause the inability to shift to higher levels of growth. It can be a haphazard process to remove the bottlenecks to higher growth or it can be a more directed and planned effort. There are many different ways to screwup growth corruption, lack of education, incorrect financial or economic system (one that does not reward or encourage higher productivity etc...)

Three times faster doubling would be 5 years to double or 15% annual growth. China has come close to this level of progress over several decades. China has at times achieved 12% annual GDP growth. 26% growth would be a doubling every 3 years. Warren buffet's investments made investments made in excess of 30% compounded annually between 1956 to 1969, in a market where 7% to 11% was the norm. There have been companies and industries which have sustained for a decade or three 26% compounded annual growth. Aspects of the Internet can be considered to have those levels of high long term growth rates.

China achieved its high levels of growth because it was catching up with past technological and business progress. So if some technology were to enable faster discovery of improved technological or process innovation, then the effect would be like more advanced nations also being in "catchup or higher growth mode". China also had higher rates of investment.

Technology that could provide vast improvements in the ability to find optimal solutions.

Giga-qubit and tera-qubit quantum computers. Dwave systems could be making a breakthough in quantum computers in 2008. It could change the rate of progress with vastly superior molecular models of the physical world.

In terms of capital inputs, if the drastically reduced energy costs combined with vastly increased supplies of energy and higher growth rates in energy supplies from say a breakthrough in nuclear fusion could also provide a sustainable increase in economic growth rate.

High performance printable electronics and faster and cheaper reel to reel production could increase growth rates and capital production.

Reconfigurable phase change chips could allow for in place hardware to be improved on the fly as easily as a software update.

DNA nanotechnology and synthetic biology seem to be reaching new levels of capability and could provide a steady stream of innovations (synthetic life, more efficient bio-fuels, etc...) and enable enhancements to human health and performance (physical and mental. I would focus less on whether intelligence is enhanced but whether productivity is enhanced and whether growth in productivity is sustainably improved (year after year there is some extra percentage improvement in additional productivity).

Continuing advances in robotics are a multiplier to human productivity. If robotic cars are able to convert commuting time into productive time for people that would be a one time 6-20% increase in productivity. There is a constant stream of successes in robotics and automation for handling some human tasks (vacuuming, dish washing, factory robots, etc...). Robotics needs to breakthrough more completely as able and seemless assistants to people. The artificial general intelligence (AGI) situation is when computers and AI can take over making faster innovations by themselves.

Wider and more successful adoption of the best business practices of the growth leading companies and industries combined with innovation and resource enhancing technologies should be able to sustain 10-20% growth rates even without AGI.

Urbanization and what a Higher Rate of Growth Means at the Industry, Corporate and Individual Leval

For the current growth cycle of Industrialization from 1903 to now, we are looking at almost seven doublings or 128 fold increase from 1903 to now. The shift was from 80-90% rural to cities for the developed world. Countries like China that are catching up are seeing the same shift at an accelerated pace. People in cities are two to three times more efficient and productive on per capita income basis.

So part of China's 8-12% growth is from 1-2% of people in the countyside shifting to small and large cities each year. Those people adapt and are absorbed into the higher productivity cities. So 2% people in a pipeline becoming 300% more productive and with 300% more income. This is a 6% boost to annual GDP growth. So the overall 5-12% growth masks far higher shifts to smaller population segments which propogate through the population.

This is similar to higher growth companies and Venture capital as well, where there are a portfolio of companies. Several fail but one is the ten or hundred bagger that raises the growth rate of the whole portfolio.

Looking over the long term of 105 years, it is a 100 times boost in productivity from $500 per person per year farm workers and low productivity industrial work (1903) to $50,000/year white collar work, information technologists etc...

The next wave would be 100 times over 21-35 years. If the people at the end are productive enough to justify $5,000,000/year then many new industries and waves of new products and services would be needed. Something approaching nanofactories would be needed for that level of commerce and scale of productivity.

Looking at what each 3-5 year and 6-10 year doubling and quadrupling, it means that every cycle a company either gets twice as big and then four times as big or they stay closer to the same size and trim down their workforce. That workforce would then become part of new companies to make up the increased economic size. IBM workers laid off while IBM stayed the same size to spawn new Intels, Ciscos and Microsofts but at a faster pace.

Economic Growth Models

Some background definition and theory:
The Exogenous growth model, also known as the Neo-classical growth model or Solow growth model is a term used to sum up the contributions of various authors to a model of long-run economic growth within the framework of neoclassical economics.

Total Factor Productivity (TFP) addresses any effects in total output not caused by inputs or productivity.

The equation below (in Cobb-Douglas form) represents total output (Y) as a function of total-factor productivity (A), capital input (K), labor input (L), and the two inputs' respective shares of output (α is the capital input share of contribution).

Y = A X K**α X L**(1-α)

Technology Growth and Efficiency are regarded as two of the biggest sub-sections of Total Factor Productivity, the former possessing "special" inherent features such as positive externalities and non-rivalness which enhance its position as a driver of economic growth.

Removing Human Population as a Limiting Factor in Growth

Robin Hanson describes how unlimited automation would remove the limitations of human population from the growth equations.

While machines have sometimes displaced human workers, they have much more often helped humans be more productive at tasks that machines cannot do. Machines have thus on net raised the value, and hence the cost, of human labor. And because people are essential, the limited rate of human population growth has limited the economic growth rate.

Once we have machines that can do almost all the tasks that people can do, however, this picture changes dramatically. Since the number of machines can grow as fast as the economy needs them, human population growth no longer limits economic growth. In fact, simple growth models which assume no other changes can easily allow a new doubling time of a month, a week, or even less.

Now admittedly, progress in robotics and artificial intelligence has been slow over the decades, primarily because it is so hard to write the software. And at these rates it could be centuries before we have software that can do almost all tasks that people do. The “upload” approach, however, of scanning human brains then simulating them in detail in computers, seems likely to succeed within the next half century or so.

The transition from farming to industry seems to have been more gradual than the transition from hunting to farming. Even such a “gradual” transition, however, would be very dramatic. Assume that a new transition was as gradual as the one to industry, and that the world economic growth rate was six percent in both 2039 and 2040, plus or minus a typical yearly fluctuation of half a percent.

If so, then in 2041, the increase in the growth rate might be the size of a typical fluctuation, and then in 2042 the growth rate would be a noticeably different eight percent. Growth would then be 14% in 2043, 50% in 2044, 150% in 2045, and 500% in 2046. Within five years the change would go from barely noticeable to overwhelming.


6 comments:

qraal said...

Hi Brian

Interesting and provocative essay there Brian. I wonder how long "super-growth" might last before it runs into Earth's thermal limits and has to majorly go off-planet?

Earth receives 174,000 terawatts from the Sun, bounces 52,200 back into space, absorbs and re-radiates the rest - some 121,800 terawatts. Human technologies and thermal processes use ~ 15 TW. Currently we waste ~ 60-80% of the heat we generate. If we improved efficiency while increasing growth the 4-5 fold improvement in efficiency would last but a few decades at most (2-2.22 doubling times.) We would then we thermalising energy gradiants and be squeezing every bit of useful work out of them. Just 13 doubling times after that we would match the Sun's input - a few doublings before that point things would be much too hot. Industry will need to off-world within 195 years at the very latest if industrial growth is to continue.

But for how long will one system be enough? In just 31 doublings after industry off-worlds we will match the Sun's energy output. That means Matrioshka Brain levels will appear within ~ 660 years.

And then?

bw said...

I was thinking about how this plays out longer term and will write some follow up articles to explore this and other issues.

In 1900, global energy consumption equaled 0.7 TW(=10**12 Watt.) Now DSP is up over 100 times and we use about 15TW. So there was an increase of 6 times the efficiency in energy usage to GDP. Plus I think there was some decoupling of GDP from resources. Things like information technology and other less resource intense industries. In the future to maintain hypergrowth we might need more virtual industries.

More GDP from less resources can go beyond just going to the limits of energy efficiency.

100,000 times more for Kardashev 1 all the energy on the planet. 3 of the big stages which if they are coming faster each time would happen very quickly. Definitely need to go offworld, but with fusion and nanotech not a problem.

Then the solar system, 10**26 power. 1 billion times. 4-5 major doubling cycles. (a major doubling cycle has seven doublings.) So if things are accelerating it happens even faster.

It seems we will either have to decouple economic growth from energy growth a lot more or use super tech to tap more power than solar.

Anonymous said...

Why go off world if you can live under the sea, on mountainous terrain, or in the desert?

Surely, if we possess the technology to live on another planet or moon/asteroid, we could just as easily live under currently inhospitable conditions on Earth, and do it much more cheaply too.

bw said...

Hypergrowth would mean filling up and using oceans, deserts etc...

Regular growth would mean that too, but hypergrowth means getting their sooner. The expectation is to fill out the current planet by growing 100,000 times from where we are now. I would expect starting to go offworld in a serious way at the same time as we totally fill out the oceans and deserts etc...

qraal said...

The growth limit is set by thermodynamics for industry based on Earth. I can believe efficiency improvements, but you can only go so far.

But trouble arises long before we get to the point of matching the Sun. Assuming a 1 degree rise in temperature is trouble for regular weather, and an effective temperature at the top of the atmosphere of 255 K currently, that means 3.8 W extra energy per sq.metre, some 2x10^15 W total. Even with a 5 fold efficiency improvement that's just 9.4 doublings.

Just how we would off-world industry in bulk is an interesting question too...

Rolle said...

I think it realy makes sense to think about how a post-singularity world behaves. Ths growth figures are very impressive. If we look at Hansons phase model, one could assume that we will even be getting new phases with more rapid growth. That of course means that even the whole universe will not last many centuries for ever increased growth. It might be interesting to calculate how long it actually would take before energy usage reaches "universal" magnitudes. It is of course possible that the next phase is the final one and that we will not see any more acceleration. That would of course be a very "todays human" centric model.