Wednesday, April 25, 2012

"Aja" Steely Dan 1977 LP

"Aja" was the first album for me that offered an optimistic feel about being alive. Not many albums have influenced us as much as "Aja." Fagen and Becker created a most unique flavor of Jazz, beautiful melodies, genius production and perfect performance blend to produce a masterpiece. 


‎"I cried when I wrote this song, sue me if I play too long" This infamous lyric, out of Deacon Blues, typifies the Aja project. Having already achieved everything they wanted to accomplish in the public eye, The Dan started writing the music that was in their hearts. This was the beginning of a new era for Donald Fagan.


Simply one of the best albums ever. I've had the album since I was a kid and I never get tired of the music. Fusion jazz at it's finest. Thanks Donald Fagan. You to Walter B!!

Saturday, April 21, 2012

Has Japan Passed tipping point? Part 1:


The Japanese Debt Crisis (Illustration from Shutterstock)
Some of the best-known research on financial crises asserts that countries get into trouble when debt-to-GDP ratios surpass 80%. With a national debt that now checks in at roughly 220% of gross domestic product, Japan, at least by rule of thumb, should have collapsed a long time ago. Yet Japan has — thus far — somehow avoided a debt crisis.
In fact, many investors have bet against Japan over the years . . . and lost. A common mistake over the past two decades has been shorting Japanese government bonds — trades which have mostly ended in a trail of tears. In a country where interest rates have moved slowly but consistently lower over the past two decades, investors who have gambled on the thesis that Japan’s financial structure is unsustainable have been forced to learn one of the harshest lessons of investing: There is little difference between being early and being wrong.
So, how exactly have interest rates in Japan remained so stubbornly low in the face of a persistently stagnant economy and high and growing debt? Why aren’t investors demanding higher rates of return? Can this economic anomaly continue? If so, for how long? If not, when does Japan cross the event horizon for a major shift in fortunes?
The answers to these questions have proven so elusive over the years that I figure it’s time to try to get to the heart of the matter. After all, it’s not just about Japan: A better understanding of Japan’s fragile economic imbalances sheds light on current events in Europe and the United States, which, in the aftermath of the 2008 financial crisis, have implemented policies similar to those that have been pursued by Japan.
The story begins with Japan’s post-war economic miracle. In order to rebuild its economy after the devastation of World War II, the Japanese government adopted an export model to boost export growth and import know-how. Japan invested heavily in education, research and manufacturing. A key element of the export model is, of course, accommodative monetary policy whereby a country uses credit creation, infrastructure development, and lower-than-market interest rates (known in monetary parlance as “financial repression”) to focus the country on exports. As the original “Asian Tiger,” Japan employed this strategy to great effect over the years, growing GDP sharply on the back of strong exports. As long as GDP and exports are growing, this model works. But when GDP stops growing and exports slow, the model fails. The point of failure for Japan was when its easy monetary policy stimulated a real estate and stock market bubble instead of fueling exports.
In 1985, the major economies of the world (United States, Japan, West Germany, France, and the United Kingdom) coordinated the Plaza Accord to reduce the value of the dollar relative to other major currencies (including the yen) with the specific intent of reducing trade imbalances. In the 24 months after signing the accord, the yen appreciated by 50%. By mid-1986, the rising yen had forced Japan into a recession (because the stronger yen harmed the country’s exports).
As illustrated by the dotted line in Figure 1, the Bank of Japan (BOJ) responded by reducing the official discount rate five times between January 1986 and February 1987, leaving it finally at 2.5% — which remained in effect until May 1989. The BOJ was ferociously trying to stimulate the economy with aggressive easing. In addition to low rates, the BOJ maintained high levels of money supply and credit growth, which drove the creation of the bubble as illustrated in Figure 2.

Figure 1: Yen Exchange Rate and BOJ Discount Rate
Yen Exchange Rate and BOJ Discount Rate
Sources: Bank of Japan, CFA Institute.

Figure 2: Percent Change in Money Supply (M2)
Japan: Percent Change in Money Supply (M2)
Sources: World Bank, CFA Institute.

The bubble manifested itself in both real estate and the stock market. It finally popped as the BOJ raised interest rates in 1989–1990, with historic collapses from which — even now, some 22 years later — the country has not recovered.
Nevertheless, Japan has been able to finance itself at extremely low rates during those 22 years. How? The financing of federal governments is much more complicated than the simple taxation of citizens. Governments finance themselves through some combination of direct taxation of citizens, taxation of businesses, tariffs on imports from other countries, build-up and usage of foreign currency reserves from international trade, issuance of debt, and money printing (if possible). Therefore, Japan’s ability to finance its federal government will be determined by the health of its GDP growth (which grows tax revenues, all else equal), its ability to grow federal tax revenues, its ability to control its budget, its ability and willingness to use its substantial foreign exchange reserves, and perhaps most importantly, its ability to continue selling bonds to the public. The secret of Japan’s ability to finance itself over the past 22 years is that it has used its current account surplus to create a closed loop — more money flows into Japan than flows out, and that net inflow is largely invested in JGBs (Japanese government bonds).
Here’s how it works: on the trade side, Japan exports more than it imports bringing more capital into Japan than leaving. Japan has maintained a trade surplus for about 30 years. And because of this persistent trade surplus, Japan has built up a large portfolio of foreign currencies.  These foreign currencies are then invested in foreign assets (e.g., U.S. Treasuries) earning Japan a steady stream of income. Because this portfolio is large, Japan — as a country — regularly earns more income on its foreign currency holdings than they pay out to foreign investors. In combination, the trade surplus and the income surplus brings new money into corporate Japan. Corporate Japan places that money into the banking system, which then gets levered up and dramatically expands its purchasing power. Then the banks, life insurance companies, and pension funds turn around and buy lots of JGBs (accompanied with much pressure/regulation by the Bank of Japan).
In fact, the major banks, such as Bank of Tokyo-Mitsubishi UFJ, Sumitomo Mitsui, and Mizuho, regularly buy JGBs — even viewing it as a “public mission” to support Japan. In addition, the Bank of Japan buys lots of JGBs on the open market, trying to drive up prices and drive down yields, thereby manufacturing low rates. While this monetization of debt creates inflationary pressures, it has thus far been offset by the deflationary pressures of a declining workforce and declining population. There are short-term fluctuations from year to year, but it is clear when looking at averages decade by decade that funding pressures in Japan have been growing over time.

Table 1: Breakdown of Funding Surpluses/Deficits as a % of GDP
Breakdown of Funding Surpluses/Deficits as a Percentage of GDP

As you can see in Table 1, this is the answer to the original question. This cash flow cycle is how Japan has funded itself over the past 22+ years. Only now, the profile is changing. The Japanese debt crisis is being spawned by a burgeoning fiscal deficit. As the fiscal deficit has expanded, it has placed greater pressure on the Japanese government to sell debt and on the Bank of Japan to purchase it. Of course, the BOJ has been stepping in and buying JGBs when corporate demand has not been strong enough to keep rates low, as illustrated in Figure 3.

Figure 3: JGBs Owned by the Bank of Japan (in ¥100 mm)
JGBs Owned by the Bank of Japan
Sources: Bank of Japan, CFA Institute.

Although Japan probably still is often thought of as a high-saving society, this is no longer true, at least for households. Japan’s household savings rate is now around 2% (down from a peak of 44% in 1990). So, in combination with chronic, large fiscal deficits, Japan’s low bond yields appear to present an oxymoron. However, Japan has also maintained a high corporate savings rate and low levels of fixed investment (both residential and nonresidential), making Japan a net exporter of capital. However, its fiscal profligacy is catching up with it: Its fiscal deficit has risen to more than 11% of GDP, where it remains today.
Up to now, Japan has been able to finance this funding deficit, as illustrated in Figure 4,  primarily by issuing bonds. Historically, these bonds have been purchased by the public through various channels, ranging from household purchases to corporations to domestic banks to the post office. However, the aging of Japan’s population is altering the fundamental demand structure for bonds.

Figure 4: Japan: Bonds Issued as a Percent of GDP
Japan: Bonds Issued as Percent of GDPSources: Ministry of Finance, CFA Institute.

Although the aging of Japan’s population has been much discussed over the years, it is just now beginning to manifest itself — and as people become old, they tend to spend their savings rather than accumulate more savings — a process known as dissaving. Ominously, Japan’s population declined for the first time in 2009 (and has been declining ever since). Already about 30% of Japan’s population is elderly; that figure is expected to grow to about 40% over the next 30 years or so. And given Japan’s welfare society system, their (shrinking) working-age population will save less and less as their burdens in supporting the dependent-age population (both young and old) grow more and more. According to a McKinsey study, savings rates in Japan decline markedly after people turn 50 years old. Given its demographic profile, Japan’s combination of aging and life cycle effects will continue unabated.
At present, Japan has just over 127 mm people. According to the National Institute of Population and Social Security Research, Japan’s population — 20 years from today — will shrink to about 118 mm by the year 2032 (with an even greater deceleration in the working age population). Today, Japan’s GDP per capita stands at about ¥3.7 mm per person. Assuming they can maintain this level over time and keeping inflation neutral, Japan’s GDP would shrink from ¥476 trillion today to about ¥442 trillion in 2032. Given the ongoing massive fiscal deficits which Japan finances through similar levels of debt issuance, their national debt levels will rise to ¥2.4 quadrillion (rising from ¥980 trillion today). Another big question mark is of course interest rate levels. Even assuming their average interest cost on debt remains unchanged from today’s levels, Japan’s debt service will consume over 50% of the federal budget by 2032 (up from 23% today). With a populace that does not favor immigration, it seems that the die is cast. Japan will inevitably age and shrink — but not its debt.

Tuesday, April 17, 2012

Turning Japanese is a Boon


Turning Japanese is a Boon

Rumplestatskin, a professional economist with a broad range of interests and a diverse background in property development, environmental economics research and economic regulation. Cross posted from MacroBusiness.
What few seem to appreciate, either inside or outside of Japan, is just how strong the resulting Japanese recovery from 2002-2008 was. It was the longest unbroken recovery of Japan’s postwar history, and, while not as strong as pre-bubble Japanese performance, was in fact stronger than the growth in comparable economies even when fuelled by their own bubbles.
How on Earth did Japan manage that with their ageing population and zero population growth? Indeed, Japan outperformed Australia in productivity growth since 2000 and very nearly kept pace with real GDP per capita growth.
Australia’s average annual real growth in GDP per capita since 2000 is 1.28%. While I can’t find a direct measure from the Japanese Statistical agency, using the World Bank data collection I can make a comparison of real GDP growth per capita of Australia and Japan using a common methodology. Using these statistics I find that Australia had a mean annual growth in real GDP per person since 2000 of 1.8% while Japan’s was 1.4%.
Notice in the graph, however, that Australia’s growth in real GDP per capita fell considerable from 2004, when population growth rates began to push up from 1.2% to a peak of 2.16% in 2008. Since 2002, when Japan’s real growth per person increased, the population growth rate declined from 0.2% the preceding 2 years to near zero (average 2003-2008 is -0.002%) till the financial crisis hit at the end of 2007.
Australia’s economic performance is terms of productivity growth looks pitiful in comparison to Japan. Average annual Total Factor Productivity growth since 2000 was a shy 0.47% (including a productivity recession in 2004-05) while Japan recorded a strong 1.77% over the same period (data from OECD here).
Of course there is always unemployment to consider.  The graph below shows that on this measure, Australia is also behind Japan (having been in front for just the period 2007-2008).  Some longitudinal data is here.
Recent research also suggests that Japan’s economic track record was unfairly blemished by asset price deflation followed by short recessions in the 1990s (1993, 1997 and 1998). The graph below (from here - including 20yr data set), shows Japan’s solid performance over the past decade, with their longest boom since WWII occurring from 2002-2008.
It appears that turning Japanese is not the tragedy it is made out to be by popular economic commentators. Here’s just one example of the popular perception-
As it turned out, Japanese investors lost nominal wealth equal to three entire years’ GDP. And the economy today hasn’t grown in 17 years or created a single new job.
Nor has the debt been reduced. Instead of permitting the private sector to destroy and pay off its debt, the public sector fought against it…borrowing heavily to try to bring about a recovery. Result: no recovery…and almost exactly the same amount of debt. But while the private sector paid off its debt, the public sector picked up the borrowing. Now it’s the government that owes money all over town.
Detractors cite the massive and growing public debt in Japan as a problem.  But if the debt is denominated in Yen, and interest rates are set near zero, the burden from the debt is minimal. In fact, Modern Monetary theorists might claim public debt in ones own currency is never a burden because government can enact future policys to pay down debt with freshly printed money. I’ll leave that particulars of this option to a future MMT debate.
The above graph confirms that Japanese government debt has replaced a substantial portion of private debt since the early 1990s. In my view this is a justified effort to keep the value of the yen stable by maintaining money in circulation – an approach that could be adopted in Australia in the coming decade, with government debt replacing household debt for the same reason.
One must keep in mind that it is probably not the intention of the Japanese government to ever pay off this debt. I am sure they are happy to continue to progress with a high savings rate, high productivity, high GDP, net exports and almost every other fundamental ingredient for economic success.  Turning Japanese appears to be about fundamental economic prosperity cradled in an unfamiliar monetary framework.


Documentary KYMATICA !


There are some things that come your way, and change your Life forever. KYMATICA, by Benjamin & Daniel Stewart, is one of them. And Honestly, I’m not exaggerating. Its not life-altering because it has a character that matches your personality or the protagonist has gone through the same life-shit that you have gone through, it changes your perspective, and that’s how it changes your life.


Kymatica is the most profound and insightful piece of art to explore the root cause of all corruption, deceit, evil, and war in our world since the dawn of man.  This film exposes the most esoteric and suppressed information about our history, anatomy, and spirituality.  Beginning with the creation of our planet, to how our earth gave life to all its inhabitants, Kymatica takes you step by step through the close relationship we have with our mother earth, and how a psychological disease has turned man against nature.


So, what is ‘KYMATICA’? To that, I must give you the same answer Morpheus gave to Neo, on being asked what the Matrix was,you can’t be told what KYMATICA is, you have to see it for yourself.Literally, “Kyma” means “Waves” in greek & Kymatica means “pertaining to waves”If you happen to be a pseudo-intellectual, I needn’t tell you that “Waves” is a metaphor for consistent evolution here. 
You probably know better. (pun intended)By the time you’re done watching this one & a half hour documentary, you’ll be baffled, yet strangely at peace, because that is the essence of this marvelous piece of work. The crappy editing wont bother you as the Plot is enough to steel your mind. 


KYMATICA talks about Human & Universal Consciousness & the correlation between all of it. It tells you how the Earth is an Organism in itself, and how the Universe is one too. Among other topics that’ll blow your mind, it talks about the Suppression of Human intent, and the gradual steps that have made us into a global society that lives in stress & fear. The Age of Fear, as our time has been called, is a fruit of our irresponsibility towards facing any insight, any reflection into our own selves. That’s the reason our society is in a constant state of competition instead of cooperation.


My words won’t certainly do any more justice to this documentary anymore, so go on & watch it for yourself.

Sunday, April 15, 2012

EXAMINED LIFE: Dr. Cornel West on TRUTH

Music is what we need when language fails us, but we cannot remain silent.

— Dr. Cornel West


Robert Glasper Trio - "Enoch's Meditation" "We Shall Overcome" MLK.

Jazz pianist Robert Glasper plays an original composition "Enoch's Meditation," with narrative from Martin Luther King's 1966 "We Shall Overcome" speech, Barack Obama's presidential election night victory speech from Grant Park in Chicago, audio from Dr. Cornel West, and a spontaneous piano reharmonization of the presidential anthem, "Hail to the Chief." This performance was recorded January 14th at WBGO Studios in Newark, New Jersey. Produced by Josh Jackson. Mix by Josh Webb, with assistance from David Tallacksen. Happy Inauguration 2009, from the jazz community!

Friday, April 13, 2012


Modeling Tipping Points


Intro
The term "tipping point" crops up frequently, especially in discussions of world events such as financial collapse and climate change. Like the word "sustainable" which gets used with increasing abandon, and often with little thought to the actual meaning of the word, so too the term tipping point can be elusive and used in contexts where it may or may not be suitable. I've probably been guilty of this myself, but recently my thinking on the subject has been greatly clarified and I hope to pass on what I've learned about what does, and does not, constitute a tipping point.
We will look at a couple of simple models that explore tipping points in an attempt to think more clearly about the problems of financial contagion and climate change, but first we must try and nail down a working definition of tipping points.
Straw, meet proverbial camel
So, what exactly is a tipping point? A tipping point can most easily be defined as a small change that can have a large effect on the end state of a system. For example, we have the well known proverb of the straw that breaks the camels back. In this scenario a linear increase in the weight of straw loaded onto the back of a camel leads beyond a certain point to an abrupt change in the health of said camel.

Fig 1. Straw weight plotted vs number of straws is a linear function. Health of camel vs straw weight crosses a direct tipping point in a step function.
That is a classic example of a small change, in this case the addition of one straw, crossing a direct tipping point and causing a disproportionately large effect by suddenly and completely disabling our unfortunate camel.
Next, we see another familiar example of what looks like an abrupt change, world population growth:

Fig 2. World population charted on a long time scale. Is this an example of a tipping point?
This curve, shaped like a hockey stick, is very familiar to those who study exponential growth and it would be easy to conclude that where we see a distinct kink in the curve there must have been some sort of a tipping point beyond which the population exploded. But is it really a tipping point? Not necessarily. One feature of exponential growth curves is the fact that the shape of the curve can change dramatically depending on your time frame. Zoom in far enough on the scale and what looked like a sharp kink becomes much more gentle, almost linear.

Fig 3. The same exponential functions charted at different scales. Only at the larger scales does the kink in the curve become pronounced enough to be mistaken for a tipping point.
Recall our definition of a tipping point: a small change that can have a large effect on the end state of a system. Kinks in curves on the other hand are not necessarily tipping points, they are just the result of exponential growth as seen from a sufficiently large perspective. Unlike the proverbial straw and our pitiful camel, there really is no point in the history of world population where we can say the addition of one more person suddenly caused the population to explode.
The domino effect
It's easy to see that our world has grown increasingly complex, especially since the industrial revolution and the introduction of massive energy subsides in the form of fossil fuels. Not just the explosion in population, but also the dramatic growth in almost all aspects of human society. The amount of resources we use, the number of artifacts available to help us consume those resources, the amount of waste produced by those artifacts, the size and complexity of our political and financial systems..., the list goes on.
People hold a variety of viewpoints on the future of these increasingly complex systems, from the extreme optimism of unbounded technological progress to the extreme pessimism of imminent catastrophic collapse followed by a future of post-apocalyptic hardship. However, as the inherent un-sustainability of our current system slowly becomes ever more apparent, seldom more starkly so than the near total collapse of the financial system in 2008, then so too the question of risk becomes vitally important.
Risk can be hard to quantify, especially catastrophic risk, which makes it all the more interesting that one way to approach that question is to model density. For example, picture a chessboard. Now randomly place some dominoes in an upright position on that chessboard, not too many, just a few scattered around. Knock over any one domino and there is little risk that it will knock over many of the other dominoes, maybe one or two, but certainly not all of them.


Fig 4. Low density of dominoes means less risk of contagion

Now place a large number of dominoes on the board. Knocking over any one domino will certainly knock almost all of them over. The risk has increased dramatically with the number of dominoes. Is this a simple linear relationship? Or is there a tipping point beyond which the addition of one more domino spells almost certain disaster?


Fig 5. Increase the density and the risk also increases, but is it a linear relationship?

Tipping points and firestorms
To help us explore this question we will turn to the percolation model familiar in physics. This model has good "fertility" which simply means that while it originated in the study of fluids percolating through a substrate, such as water through soil, it can also be applied with remarkably good results to other fields, such as forest fires.
For this example we turn once again to agent based modeling, for an introduction to this topic see the post Introduction to Agent Based Models. First, as in the other models, we start with a simple grid. We then randomly populate that grid with a forest at a given density expressed as the percentage of grid cells occupied by a tree, one tree per grid cell. Once again we apply one very simple rule based behavior:
1) Fire can only spread between immediately adjacent trees.
Now we can construct a simulation where a fire starts along the entire length of one edge of the grid and then we ask the question: How likely is it that fire will spread, or "percolate", from one side to the other?
Setting the density of trees to different values reveals a surprising result. The risk of catastrophic fire does not increase in a linear relationship with the density of the forest. Instead there is a tipping point at about 59% density.

Fig 6. A distinct tipping point in the percolation model at about 59% density. Beyond this threshold the risk of a firestom rises almost vertically to near 100 percent.
Below this value the chances are very low that the fire will spread very far as there simply is not enough paths between adjacent trees for the fire to follow. Set the density higher than that threshold, by even a small amount, and the risk of the fire spreading across the entire forest rises dramatically.

Fig 7. On the left, a random arrangement of trees at a density of 57% results in fires that consume only about 15% of the forest at most. On the right, increase the density by just a few percent to just above the threshold of 59% and it suddenly becomes much more likely the fire will spread to the other side and consume two thirds of the forest or more.
Tipping points and financial contagion
This model can also be applied with good results to other collections of entities connected by network paths, such as our increasingly complex financial system.

Fig 8. A typical network diagram. Like the forest, increase the density of connections and you risk crossing a threshold beyond which you greatly increase the chance that the entire system can collapse.
From this perspective, applying what we learned from the percolation model, it's easy to see that the higher the density of network connections then the more likely it is that a threshold will be crossed that greatly increases the risk of a collapse. The quants and other financial gurus behind the scenes at the mega-banks may have thought that creating the great, billowing, quadrillion dollar bubble of derivatives and other exotic couterparty casino bets would reduce risk by spreading it around the globe. Instead, it's much more likely that just exactly the opposite is true. Beyond a certain tipping point in the density of couterparty risk the odds of a catastrophic financial meltdown rises dramatically, just as we saw in 2008.
Ashvin: In one of its reports, Goldman recently analogized the Euro area to a dense forest, in which the risk of "financial fires" spreading extensively is very high and has only been made higher by policy responses. Perhaps one of the reasons EU leaders continue to create sovereign guarantees and contingent liabilities (debts) to address a sovereign debt crisis in a closed region is because they fail to understand the nature of tipping points that Jerry has clearly outlined above. Here is an excerpt from the report, courtesy of ZeroHedge:

4. Too Much Combustible Material Still Around

The Euro area is a financially closed region, with more than 85% of sovereign bonds held by residents of the area. If we add to this the fact that most claims against governments are held by financial institutions domiciled in the area, the risk of 'financial fires' spreading is high. The prevailing policy view that bigger 'firewalls' would make investors more comfortable about purchasing sovereign bonds of EMU countries. This is predicated on the idea that the existence of a funding backstop would prevent credit shocks in one of the EMU members from spreading to other issuers. That said, we doubt the current infrastructure can produce the same effects on markets as the ECB's long-term liquidity injections (LTROs). Our view is based on the following considerations.

Size: Even if we combine the full uncommitted capacity of the EFSF and the ESM (EUR700bn), the total would not be sufficient to backstop the bigger markets of Spain and Italy. The former's borrowing requirement (amortization plus deficit) over the next two years is EUR305bn, while the latter's amounts to EUR525bn.

Seniority: The ESM holds 'preferred creditor status' over existing bondholders (art.13 of the Treaty establishing the ESM). In practice, this means that if the facility is used to provide an EMU member country under conditionality, it would subordinate existing bondholders (twice, if the IMF also participates in a bailout). Given that investors are aware of this, they would require compensation to bear such risk. This could exacerbate, rather than mitigate, a crisis.

Governance: The existing vehicles cannot intervene pre-emptively in markets at signs of tension. Rather, they would be activated only after a full crisis has erupted. The procedure envisages that the ECB would ring an alarm bell should tensions threaten the stability of the Euro area. The sovereigns experiencing tensions would need to formally ask for help, and sign a memorandum of understanding, before any financial support can provided. Admittedly, a 'fast track' option is also available, based on 'light conditionality' and allowing the EFSF to intervene in secondary markets. Still, the fixed size of resources could raise questions on the effectiveness of the operations.
The truth is that the entire world, and especially the Euro area, is well past the point at which credit contagion can be isolated to a few minor locations and be extinguished with ease. Jerry has skillfully demonstrated the scientific foundation of this truth underlying not only our global financial system, but perhaps many of our environmental systems as well. And now I will send it back to Jerry for discussion of the latter.
Tipping points and climate change
Jerry: Few topics have been more liberally peppered with talk of tipping points than that of climate change. If you ask those people not in denial about global warming what the threshold for climate catastrophe is I suspect many will answer without hesitation "greenhouse gases" (GHG's), or perhaps "CO2". This is understandable, after all while climate science is certainly a complex topic it has been established that GHG's are the main drivers of global warming due to the well known and unambiguous physics of Earth's atmosphere. Thus, at least when it comes to public policy, it is relatively easy to get ones head around a key number like CO2 concentrations in parts per million.
Unfortunately, I believe this is a dangerous fallacy.
First, recall once again our definition of a tipping point: A small change that can have a large effect on the end state of a system. Due to our prodigious burning of hydrocarbons in the form of fossil fuels the amount of CO2 in the atmosphere is indeed growing exponentially, some would say super-exponentially, which is to say the rate of change is itself accelerating. But remember, a kink in a curve is not necessarily a tipping point. There really is no point at which we can say that adding one more part per million of CO2 will trigger climate catastrophe but below that level and, oh thank god, we are safe.
This is especially true when you consider the residence time of CO2 in the atmosphere which is measured in decades, if not centuries, due to the fact that the portion not absorbed by oceans or sequestered by buried vegetation is removed only by extremely slow geologic processes. The simple fact is, even if starting tomorrow all seven-billion-going-on-nine-billion people on Earth stopped emitting any CO2 whatsoever we would still suffer a de-stabilized climate and rising sea levels for decades to come due to the carbon we've already spewed into the atmosphere. This dynamic is greatly exacerbated by the extremely large thermal inertia of the world's oceans and icecaps. Put another way, we are probably only just now feeling the full effects of carbon that was emitted decades ago, with much worse to come. Such is the pernicious effects of very long feedback delays in a complex system.
The climate is a dynamic system that can be said to exist in an unstable equilibrium. This equilibrium is variable, the complex interactions of sun, sea, and atmosphere give rise to oscillations that are measured in decades and, in the case of ice ages and inter-glacials, millennia. Within that range however there has formed a kind of homeostasis that is conducive to life, a balance between the positive feedbacks that create reinforcing loops and the negative feedbacks which create regulating loops.
It is in this balance where the greatest danger of a tipping point can be found. Should any of the factors that contribute to positive feedbacks get too far out of bounds then this can tip the balance in favor of self-reinforcing behavior that, once started, can quickly take on a life of its own and overwhelm our capability to regulate it which will lead inexorably to accelerating or "runaway" climate change.
Melting permafrost. Dying forests. Acidic and anoxic oceans. Vanishing ice-cap albedo. These are just a few of the factors at the heart of global climate feedback loops, any one of which could be dangerous, but taken all together and greatly magnified by feedback delays measured in decades if not centuries then it becomes clear that the crisis we face completely dwarfs the problem of CO2 concentrations alone.
We are altering both the chemistry of the atmosphere and the composition of the biosphere at a rate orders of magnitude greater than that seen in the geologic past. At this point even cutting CO2 emissions to zero would be woefully inadequate, we would still need to take desperate measures in an attempt to restore the previous balance by putting in place global negative feedbacks. Reforestation, carbon sequestration, cloud seeding, all this and more while at the same time we power down and depopulate to levels last seen many decades ago. Unfortunately, given both the enormous challenge of such an undertaking compounded by the very long feedback delays in the climate system we would probably need to have started such a program many years ago. We may have already passed the tipping point of no return.
Conclusion
I hope this small excursion clears up some of the confusion surrounding the subject of tipping points. It's important first of all to understand what a tipping point actually is. Like others, I myself have often confused exponential growth as a tipping point when in truth it is really only a kink in a curve as seen from a sufficiently large perspective.
Next, it's important to understand the difference between direct and contextual tipping points. The example of the straw that broke the camels back is a direct tipping point, whereas the example of the forest fires is a contextual tipping point. Increasing the density of the forest by one more percent did not directly cause a firestorm, but it did cross a critical threshold where the chances of a firestorm greatly increased. Beyond that point all that was needed was a spark for catastrophe to follow, much like the subprime housing crisis was the spark that melted down the global financial system.
Finally, let us not become beguiled by talk of CO2 concentrations in the climate crisis. The real and present danger to countless future generations, if not all life on Earth, are positive feedbacks that are poised to cross a critical threshold (if they have not done so already), at which point they take on a life of their own and race away from our capability to damp them down and return the climate to the happy equilibrium we've enjoyed for these many millennia.
Further reading
A good presentation about climate change and positive feedbacks
Beyond the Tipping Point 


There is another kind of tipping point, which engineers call "phase change."In this situation, the load can be increased far beyond the point of equilibrium before it reaches a toggle point. An example of this might be the Greenland ice sheet, which can decay pretty far without substantial movement. 
Then, suddenly and without warning, the whole thing goes, something everyone thought should have happened much earlier. Or, using the straw-loading example, the calculated toggle point might be far exceeded before the camel's knees actually give out.


A sense of complacency might be a likely result when expected overloads do not result in collapse.


We are about to find out that economics and finance has a far bigger impact on your life than politics, and if you don't believe me let me finish with a very clear declaration, and hold me to this, come back at me years in the future.


The sovereign debt problems along with the costs of an aging population are going to revamp society in the most profound way, and the part that worries me, that includes violent social unrest, and those who don't understand it are just going to be road kill along the way.


"Michael Campbell (the brother of former B.C. Premier Gordon Campbell) made the above statement on his "Money Talks" radio show last Saturday on radio station CKNW in Vancouver, B.C.If anyone wishes to listen to these words for themselves click on the following link to CKNW's audio vault enter March 24 in the date drop down box, 8:00 AM in the time drop down box and then click on "listen". When the audio starts to play, move the slider ahead to 39 minutes and 30 seconds to hear the quote. (Put your mouse on the bar just above the "listen" tab, click the mouse, hold it down and then slide the pointer ahead on the bar. You have to release the mouse to see where you are, and then repeat the process again one or two times to get to the 39 minutes and 30 seconds mark.) You do not have to register on the website to use the audio vault. It is strictly click and play. CKNW's audio vault stores program audio for a period of 30 days.www.cknw.com/other/audiovault.html