Saturday, June 09, 2012

There ain't no nearby tipping points

The RIO+20 summit is less than two weeks away and the environmentalist apparatchiks are trying to invent methods to show the public that it has to hand out its freedoms and a significant part of its income to the new saviors of the world.

"Scientists" turned out to be a convenient vehicle for such political plans years ago and even though their trustworthiness dramatically decreased after some incidents that have shown why they're actually doing what they're doing, they're still a part of the game.

The environmentalist potentates control approximately two types of "scientists" whom they may pick to produce the desired results: the totally corrupt ones and the totally incompetent ones. In June 2012, much like at many previous moments, the United Nations chose the Goldilocks solution: scientists who can be bought and they're stupid as well.

When I opened on Saturday morning, I was offered this top article:
More record warmth as scientists warn of global tipping point
Well, our current temperature in Pilsen is 3-4 Celsius degrees below the normal temperature for this date so I think it would be ludicrous to talk about record warmth etc. If some readers live somewhere in Northern Siberia and their temperature is above the normal, well, let me mention that it's a coincidence. Some places are warmer than the normal, some places are cooler: see global temperature maps. It's been like that for billions of years.

The second meme that the CNN article tries to spread is that there are "tipping points"; you find similar articles in many other outlets, too. Physical scientists probably already found such comments too ludicrous so the environmentalist apparatchiks hired biologists to write about such tipping points. Now, biologists aren't educated enough to talk about such matters at all but that's the smallest detail in the environmentalist scheme of things. They tell us that we are approaching a rapture point in which the food supplies suddenly disappear and everything will die. Sure.

A tipping point looks or would look like this:

There is a value of a physical quantity – e.g. the position of a ship – that has the following property. On the right, safe side, the system is stable or quasi-stable, destined to oscillate around some "ordinary" positions for a long period of time. On the left side of the tipping point, the ship switches to a qualitatively different behavior in which the distance from the "stable valley" is increasing and the motion is accelerating.

Does the picture above correspond to the reality?

It doesn't. Why? I am sure that most of the environmentalist "scientists" will be surprised by this insight. But the reason is that
The Earth is not flat!
So the picture above, Flatearth1.JPG, doesn't describe a real property of the physical systems in Nature. Not only there aren't any infinite cliffs from which you may fall. There aren't any discontinuities like that in the fundamental laws of physics – and not even in most of the derived, effective laws of physics that govern various more complicated and emergent processes.

The vast majority of important enough feedbacks that we see around are negative feedbacks – those that tend to return systems closer to their equilibrium, stable or metastable positions, those that prevent systems from catastrophic runaway behaviors. Why is it is? Let me offer you some elementary maths. Consider function \(X(t)\) of time and imagine it is described by the following equation:\[

\frac{d^2}{dt^2} X(t) = k \cdot X(t)

\] This simple problem is representative of the discussion about positive and negative feedbacks. (Although the true equations for feedbacks are slightly different and they also admit "weak positive feedbacks" that strengthen the initial perturbations but aren't strong enough to lead to a runaway behavior.) What are the solutions to this differential equation? Well, for \(k\lt 0\), we get oscillating solutions\[

X(t) = A\cdot \cos(\omega t+\phi), \quad \omega^2=-k

\] Here, \(A\) is the amplitude, the maximum deviation from the equilibrium, and \(\phi\) is a phase shift. The frequency \(\omega\) is an increasing function of the constant \(|k|\). This is the safe behavior. On the other hand, the solution for \(k\gt 0\) is\[

X(t) = C\cdot \exp(\alpha t)+D\cdot \exp(-\alpha t), \quad \alpha^2=k.

\] It's composed of an exponentially increasing solution and an exponentially decreasing one. For generic initial conditions, the decreasing portion becomes negligible in the far future. So the far-future behavior is a dangerous, exponentially growing solution.

The differential equation above is very simple and clean and we won't find too many physical systems that obey it exactly. Instead, various physical systems are described by such an equation approximately. But even in this approximate situation, the following question appears very naturally:
Is the constant \(k\) positive or negative for some particular systems? In other words, is the world a safe and peaceful place?
If it is negative, like in negative feedbacks, Nature will be self-regulating and safe. If it is positive, like in strong positive feedbacks, Nature will destabilize itself. Can we answer this question? And shouldn't the positive and negative values of \(k\) be equally likely if you look at "all situations"?

The answer to the last question depends on how you count "all situations". At some fundamental level, if you count physics problems, it may indeed be equally natural to see both signs of \(k\). However, if you don't count abstract physics problems but their realizations in the world around you, the situation is completely different. You will observe almost no strong positive feedbacks, no tipping points!

Why is it so? It's simple. If something were predicted to exponentially grow, it would exponentially grow. If life depended on the condition that \(X(t)\) belongs to a narrow enough interval, the exponential growth would quickly and inevitably kick \(X(t)\) out of this interval and life would cease to exist very quickly – after a period of time that is proportional to the logarithm of the inverse initial perturbations. Logarithms are pretty much numbers of order one even for extreme values of the arguments so such a destabilization would occur very quickly.

After a short enough time, one of the following things would have to happen: either life etc. would die; or new, previously neglected terms in the equation would become important and they would add negative feedbacks and self-regulation. We know that life hasn't died for billions of years so the former possibility almost never happens; the latter possibility does happen but if it does, it means that the negative self-regulating effects prevail, after all.

So after a relatively short time, any physical system finds itself in a phase which is metastable, regardless of the timescale of the effective description we may want to choose. If the strong positive feedbacks remained dominant, it would either mean that life often dies away; or that some quantity \(X(t)\) may keep on exponentially growing, without affecting life. This latest possibility, a quantity \(X(t)\) that life doesn't depend on, is realized in the Universe, too. In particular,
\(X(t) = \text{linear size of the Universe}\)
started to exponentially grow a few billion years ago, due to the accelerating expansion of the Universe. It's driven by the dark energy, probably cosmological constant, experimentally discovered in 1998 (which became the dominant part of the energy density in the Universe a few billion years ago). In the future, \(X(t)\) will indeed be increasing almost exactly exponentially and the Universe will double each 10 billion years or so. Because the size of the Universe doesn't directly impact the phenomena that occur near the Sun or any other star we may declare our home sometime in the future, life may continue even if \(X(t)\) is extremely large.

There may exist stars even hundreds of billions of years from now and if we assume that people will be able to move from one dying star to another, the constant dilution of the stuff in the Universe may be compatible with life for quite some time, for many doublings of the size.

But if you think about it, the size of the Universe is really the only example of a "relatively inconsequential" quantity. Almost every quantity associated with the Earth etc. is potentially decisive when it comes to life. If it were exponentially growing, life could be killed within a few doublings; consider the doubling of absolute temperature from 300 to 600 kelvins. It hasn't happened so we know that these exponentially growing processes don't exist around us – or, to say the least, they aren't valid as approximations for too long. We may express the previous explanations by the following slogan:
If you look at the set of situations and objects as they exist in the world around us, the self-regulating ones and negative feedbacks dominate simply because the self-destructive ones with strong positive feedbacks have already gone extinct!
It's that simple. I've discussed similar things in 2007, in La Chatelier's principle and Nature's adaptation and in many other blog entries.

These simple considerations make it more surprising why some people such as Capitalist Pig Edward Measure are surprised by the existence of negative feedbacks. Measure links to an article about massive Arctic algae blooms that would start to absorb lots of carbon dioxide if the climate got warmer and/or if the concentration got much higher. (By the way, give me a break with the statements that such things had never occurred on Earth. Algae are among the oldest organisms and they have had much better conditions to thrive over there during the most ancient eons.)

Measure is surprised but should we be? In effect, he is surprised by... by the existence of life on Earth. When something becomes cheap and easily available, e.g. carbon dioxide, creatures and processes that need to consume it start to thrive. What a surprise. It's also true that if there is some shortage of something, the creatures and processes that need it will start to disappear, therefore reducing the consumption of this scarce resource. Nature always finds some tools to regulate itself. The only exception are physical situations with an exponential, runaway behavior but those situations don't last long.

It's obvious that our changes of the CO2 concentration etc. are totally unspectacular relatively to the geological history of our planet. The Earth has already seen 6,000 ppm and 10,000 ppm and even higher concentrations. They hadn't destroyed life. Our industrial changes of the CO2 concentration are tiny perturbations in comparison and because we know that the previous large changes hadn't caused a qualitative change of the behavior, our changes won't do it, either. For all purposes, our changes to the CO2 levels and many similar things are just tiny perturbations and their effect may be linearized. A tipping point with its qualitative change of the behavior requires the linear approximations to break down and we know for sure that they won't break down.

So the tipping points and runaway hysterias are completely indefensible. That's why physical scientists, including some of the more honest U.N.-sponsored climate scientists, realize that the only discussion is the linearized response of the temperatures to a CO2 doubling. This response may be approximated by a logarithmic dependence of the temperature on the concentration – which is even more stable or less dangerous a relationship than the proportional relationship – and the temperature change per CO2 doubling is comparable to a Celsius degree and this effect is negligible relatively to many other changes we observe.


  1. Quoting you:

    "After a short enough time, one of the following things would have to happen: either life etc. would die; or new, previously neglected terms in the equation would become important and they would add negative feedbacks and self-regulation."

    Like in the climate system. There are both positive and negative feedbacks.

    Some of them are "fast feedbacks" that happen in short timescales (months to years) like water vapor(positive), IR radiation increase(negative) and clouds(can be positive or negative depending on the cloud altitude).

    Other are “slow feedbacks” like ice sheet albedo (positive), biological carbon cycle feedbacks (like the thaw of the permafrost) and the carbonate-silicate-CO2 feedback (that removes CO2 from the atmosphere by reactions like CO2 + CaSiO3= CaCO3 + SiO2 that happen when acid rain falls on rocks.)

    “We know that life hasn't died for billions of years so the former possibility almost never happens; the latter possibility does happen but if it does, it means that the negative self-regulating effects prevail, after all."

    Yes, there is a strong negative feedback, IR radiation increase, and this is the one that prevents a runaway greenhouse effect on Earth that would increase temperature several hundreds of degrees. However, this only happens after a significant warming has taken place. In other words, the system has shifted towards a new equilibrium. How much Earth must warm before this happen is known as the climate sensitivity. Empirical evidence shows it is around 3ºC per doubling of CO2.

    The problem with variations of temperature of several degrees, as happened during glacial-interglacial periods (and will happen this century because of the mentioned climate sensitivity) is that those are strong climatic changes, much bigger than anything in human civilization history. And there are “tipping points” that of course are not enough to kill all life on earth, but certainly will harm human civilization.

    One example is the melting of ice sheets. Once the air and specially the ocean had warmed enough (like 2 or 3 ºC), the melting will cause more and more melting, triggering the collapse of the ice sheet in a few centuries. This means several meters of sea level rise per century. It happened countless times during deglaciations (in the glacial-interglacial transitions), and now it will likely happen with Greenland and West Antarctic Ice Sheets.

  2. To grossly simplify your post, you seem to be saying, "Here is a mathematical demonstration that prior fluctuations have been sufficiently large to tip any tipping points that humans might tip, and since we are still alive, those tippings were in our favor." I would suggest that the Kurzweilian technological singularity could well be an exception to your logic, since we may reasonably believe that modern civilization represents an excursion of the "intelligence/technological sophistication" parameter unprecedented in Nature. You implicitly agree with this notion in your June 15 post on how technological innovations make predictions about 2100 A.D. futile.

  3. Dear Benjamin, the Kurzeweil singularity refers to the emergence of extremely high artificial intelligence with the unbelievable and "divergent" progress in information technologies etc.

    While it may have a profound effect on the society, if there is anything meaningful about this concept at all, it has no impact on the climate - or Nature. I would almost say "it has no impact at all". The development of computers that may replace thinking humans is amazing and much more important for the society than a degree of warming. On the other hand, such new thinking machines don't cause any detectable climate change - even less so than fossil fuels.

    The Kurzweilian singularity is really about the concentration of the same "fun" and "intelligence" into an ever smaller amount of material. In this sense, it drives the total impact of the mankind towards zero, not infinity! So you got it upside down.

    I was not suggesting that there is no progress or positive feedbacks that have something to do with the humans. There are many. I was saying that Nature - the part of Nature that is doing pretty much the same thing as it did in the previous 4.7 billion years - has no such instabilities. The absence of runaway behavior surely holds for some systems only and I was careful not to contradict the fact that there's a lot of progress and exponentially growing quantities linked to mankind and technology. But they don't translate to unprecedented processes in Nature. What humans do in Nature is just "internally" different and "more concentrated" or "intensive", but when it comes to extensive parameters, it doesn't bring any real difference to the climate etc.

  4. More advanced technology reduces the amount we must affect nature, but increases the amount we can affect nature. Post-singularity technology would be essentially alive, and could live anywhere that conditions permit complex systems to exist, which might include much of the matter in the universe. Whatever this supertechnology assimilated it would radically alter. It is true that the technology could "decide" to restrain its proliferation so as to have a trivial effect on the structure of the universe, but this need not be the case. If intelligent agents attain the physical scale of planets or galaxies, distinguishing them from Nature ceases to make empirical sense, except to state that in principle, someone or something has a choice about the changes taking place.

  5. Dear Benjamin, totally plausible, don't get me wrong, I am willing to acknowledge and praise the ability of technology to access realms that are extremely large and extremely small, strong and weak.

    My point in this article was much more specific than this intruiging but unrestricted speculation about future technologies, however. What I really meant is that when the only variable is the CO2 concentration, there isn't any nearby critical threshold at which some important instabilities - runaway behavior - would get activated. These instabilities are what may be and has been excluded by the observation that similar and much larger concentrations in the past hasn't led to a threatening evolution - not even when other parameters were adjusted to random values that differed from the current ones.

    I don't claim to have proved that technologies is incapable of doing harm. It's surely able to do harm but this question would refer to too many diverse sub-questions...