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 cnn.com on Saturday morning, I was offered this top article:



The Earth is not flat!



Is the constant \(k\) positive or negative for some particular systems? In other words, is the world a safe and peaceful place?



\(X(t) = \text{linear size of the Universe}\)



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!



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 thatSo 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: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,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: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.