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Graphs, projects and form fitting tables extend trends with the usual footnote of "all things being equal".

Life presents discontinuities, surprises that disrupt trends. The magnetic poles may move. Asteroids may strike the earth. Earthquacks may change the flow of rivers and oceans. Droughts, plagues, pestulance, world wars, world wide depressions ,etc. do happen and are promptly ignored by trend followers.

Oil may run out, politics may shift horribly,etc. I can not predit the future of economic growth. The best I can say is that there is a worldwide asset bubble of housing and credit that will collapse into desparate times. These desparate times in the last 200 years have lasted 10 to 25 years.

All things are not equal in economic history nor will they be in the economic future.


There are many disruptions that move us above and below the trendline, but we always move back to it.

Even the Great Depression moved us below the trendline for several years, only to see a recovery that got us right back to the trendline of where we would be if the Roaring 20s and GD never happened.

So unless a big asteroid hits the Earth and wipes humanity out entirely, any shock will cause merely a temporary deviation from the trendline.

The accelerating nature of this is undeniable, as the data can be plotted back 3000+ years.


The plot graphs a mere 45 years and this gives me a dilemma. First, disruptions may easily last 20 years. Second, using a very long period increases the odds of a world changing dark ages.

This is like predicting earthquakes and plagues. You know they will happen but not when.


But the first graph goes back thousands of years. There are many aberrations above and below the trendline, but it always reverted back to the mean.

In the future, there will also be aberrations, like the ones you mention, but things revert back to the mean after that.

Just look at the S&P500 over the last 20 years. The dot-com boom was an anomaly to the high side, and the bust took us below the trendline, but then we reverted back.

Only a superdisaster can fundamentally change the trendline. Something on the scale of the GD or WW2 did not.


The world spent tommorrows wealth by huge barrowing and promises that can not be kept. Social Security promise will ruin future generations standard of living along with medicare. The world wide credit bubble that created the upward trend is unsustainable.

The concept of reverting to the mean is linear thinking that I do not accept. It is a mathematical tool that statistically can prove whatever you want. I recall such graphs and thinking used by alarmists to claim the world would be entirely overtaken by aids in 15 years. Advocates of one sort or the other resort to such projections to persuade. I have seen too many projected trends fail to be realized.

Call me a sceptic of this technique or tool.


But it is not linear, it is exponential. Plus, even the GD and WW2 caused deviations from the trendline, that eventually had recoveries that got back to the trendline.

Can you give me an example of an event that permanently moved the trendline lower? That never had a recovery?


The phrase the Dark Ages (or Dark Age) is most commonly known in relation to the European Early Middle Ages (from about A.D. 476 to about 1000).

This concept of a "Dark Age" was first created by Italian humanists and was originally intended as a sweeping criticism of the character of Late Latin literature. Later historians expanded the term to include not only the lack of Latin literature, but a lack of contemporary written history and material cultural achievements in general. Popular culture has further expanded on the term as a vehicle to depict the Middle Ages as a time of backwardness, extending its pejorative use and expanding its scope.


During the 17th and 18th century, in the Age of Enlightenment, religion was seen as antithetical to reason. Because the Middle Ages was an "Age of Faith" when religion reigned, it was seen AS A PERIOD CONTRARY TO REASON, and thus contrary to the Enlightenment. Immanuel Kant and Voltaire were two Enlightenment writers who were vocal in attacking the religiously dominated Middle Ages as a period of social decline. Many modern negative conceptions of the age come from Enlightenment authors.


OK, so the Dark Ages lasted 500 years. But that was at a period when even the high-growth periods were at a fraction of 1% a year. So there is no evidence that this disrupted the trendline, and we certainly did recover to the trendline. The Dark Ages might have had growth of 0.1% a year, while the Roman era might have been 0.13% a year. Nearly unnoticable change within a single lifetime.

Plus, during the same period, China, India, and the Arab world were prosperous. Maybe Global GDP (which is what this is discussing) did now slow at all.

Plus, a depression (even if gthe Dark Ages was an economic depression, which it might not have been) that lasted 500 years then, and 11 years during the GD, would last only 3-4 years (like the dot-com bust) today. The steepening trendline and the accelerating shortening of boom-bust cycles necessitates this.


When the housing bubble bust takes the first world down, then Islam may take over Europe and the rest of subasia. Today's Islam is a very backwards, antitechnology culture.

Modern Islamic history begins in Arabia in the 7th century with the emergence of the prophet Muhammad. Within a century of his death, an Islamic state stretched from the Atlantic ocean in the west to central Asia in the east, which, however, was soon torn by civil wars (fitnas). After this, there would always be rival dynasties claiming the caliphate, or leadership of the Muslim world, and many Islamic states or empires offering only token obedience to an increasingly powerless caliph.

Nonetheless, the later empires of the Abbasid caliphs and the Seljuk Turk were among the largest and most powerful in the world. After the disastrous defeat of the Byzantines at the Battle of Manzikert in 1071, Christian Europe launched a series of Crusades and for a time captured Jerusalem. Saladin, however, restored unity and defeated the Shiite Fatimids.

From the 14th to the 17th centuries, one of the most important Muslim territories was the Mali Empire, whose capital was Timbuktu.

In the 18th century, there were three great Muslim empires: the Ottoman in Turkey, the Middle East, and the Mediterranean; the Safavid in Iran; and the Mogul in India. By the 19th century, these realms had fallen under the sway of European political and economic power.


One of every three babies in France is Islamic.


So France goes down. At the same time, 3 billion people are living in economies that are growing at more that 6% a year (China, India, Russia, Malaysia, Vietnam, Taiwan, Thailand, Pakistan, Afghanistan, Iraq).

I think the housing bubble will result in a medium-size recession (like the last one), but nothing more severe.

Plus, all the other historical examples you provided have all been followed by recoveries that got us back to the trendline.

Nothing has ever permanently ruined the trendline. Only drops and a rise back..


Disrupting the trend can be hundreds of years or merely decades. The expondential graph for a mere 45 years may easily get blown away.

There are more than 50 million muslims in Europe.


But the curve is steepening. The next 45 years will see a bigger magnitude gain than the whole 1800 years from 0 to 1800 AD.

50 million Muslims in Europe, but 350 million Muslims across India, Pakistan, Afghanistan, Malaysia, and Iraq are in economies growing at more than 6% a year..

Some Muslims can, in fact, partake in rapid economic growth. They still do terrorism, but we'll see which wins out..


What is the regression analysis or algorism used to create the trendline?

What are the mathematical assumptions, variables,levelof confidence for the formula?


I'll link to some of the academic papers I have researched on the issue.


Promising solar technology.



I technically agree that humans on earth are a singularity in themselves. (When compared to other genetic based life forms).

How is your thesis different from Ray Kurtzweil's thesis?

Please show your plots on a log-log scale, it will show the linear trend in GDP as a function of time. By showing them on a log x-linear y, it is very confusing because it looks like the curve is flattening out, and the older time points look like they are all compressed so small.

I believe the next step in singularity will be strong AI.

Will it arrive in time to save us westerners from our current economic predicament in the western world, and solve the problems of scarcity of resources, it's a damn good question.

Also, be very careful about global ecological trends that could cause serious disruption. I believe there are technical solutions to them(since the problems were created by technology), but they could take hundreds of years to resolve. Much like it is very hard to put an egg back together after it is broken, it could be hard to fix the earth climate after it is broken (even with all the coolest nanobots in the world)

Remember, that exponential GDP growth requires also exponential commodity growth. We are using more resources faster than at any time in history. We could be stuck for a while getting out of this mud hole. Billions of people may need to die to free up the resources. While in the long trend it may work itself it out, I sure ass hell wouldn't want to be around during that die off.

Ray Kurtzweil makes an argument that we can have get around this because of the huge untapped instrisic power of everyday materials, and so there are there is an almost boundless oportunity for increasing complexity.

Do you have anything to add to the above thesis?



I don't agree that exponential commodity growth is required. Note that more and more wealth creation is information-based (software, internet, etc.).

For example, the US economy produces the same number of megatons of material output today as in 1979, but the dollar output, in real terms, has doubled. This is due to so much new wealth creation in items that do not consume much physical matter.


Great blog, GK! I look forward to reading more. I second the request for log-log graphs.

I think these exponential trends are essential for understanding the world in which we live.


"I don't agree that exponential commodity growth is required. Note that more and more wealth creation is information-based (software, internet, etc.)."

Wealth in the US may be constant in terms of commidities. But you must also look at the exponential population growth trends around the world. The rest of the planet is going to attempt to attain the wealth of the average US consumer. This is going to require a massive amount of commidities. You can actually see this trend occurring right now. Commidity prices are skyrocketing from demand from India and China.

As a side note, it is why emerging markets and commidity investments are very good long term. Emerging economies are strongly outperforming the US economy in terms of growth, as a huge number of unproductive US workers are replaced by essentially slave labor working under communist or caste based systems.

Hopefully, those of us in the west, can use some of our great information technologies to exponentially reduce our commidity depedence, exactly at the same time the rest of the world starts sucking them all up.
(Solar, ethanol, nano-materials, are favorite current picks)



I feel that we already are. Also, refer to the January archives to see a brief article on why China will not surpass the US within the next 30 years.

Also, not all emerging economies grow faster than the US. Those in Asia do, but in Latin America and Africa, they do not.

Plus, US growth continues to outstrip Europe and Japan. If anything, they are getting left behind at a much faster rate than we are.


"As this growth is not just exponential, but exponential even in the second derivative i.e. the rate of increase also increases at ever-faster rates, [...]"

Forgive me, but isn't ALL exponential growth exponential in the second derivative? That's a mathematical property of exponential growth. If you are increasing at a rate proportional to your size, then your rate of increase is also increasing proportional to your size and so on...



Not at all. There can be exponential growth at a fixed rate (where it would be a straight line on a log scale chart), and exponential growth at an exponentially growing rate (where the line would be a curve on even a log scale chart).

Tracy Coyle

A factor that has changed in the last 150 years (and only partially accounted for statistically) is the growth of human population. It is not just the raw numbers, but the vast increase in human computing power. Innovation has been exploding as populations have sufficient food to feed them. THIS is going to continue to accelerate also.

Rick Gaber

A link to this has been added to "THE GAP BETWEEN RICH & POOR"


I don't really get the talk of "the singularity" as a specific event. If you'll remember your calculus class, exponential curves don't have singularities, and their nth derivative grows at the same rate all the others do times some factor^n. You could argue that we've been in a continuous "singularity" event since the 1500's, or the dawn of humanity, or the Cambrian explosion.


PS - your own graph shows a saturation trend. That is somewhat unsettling. I'm not one of those that believes we are running up against any intrinsic limits (our "intrinsic limits", even if no further innovation happens and we just stick with fission, are somewhat radically larger than what we have now). However, your thesis of the inevitability of exponential growth is somewhat challenged by your own data - it's never inevitable, merely probable. And it is always contingent on circumstances and how big the latest disaster happens to be. The roughness of the graph makes it impossible to make any predictions, except perhaps at infinity, because collapses exist on all degrees of scale.

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