Will the US economy collapse again?
Why the US economy (maybe) is collapsing
Let's forget about Trump for a moment. Can the economy of what is still the richest and most powerful state on earth suddenly collapse? I don't mean a normal economic crisis, but a collapse that is qualitatively different and probably more dramatic than all previous recessions. That sounds far-fetched, but there are mathematical signs that are summarized under the term critical slowing down.
I have no idea whether this is happening through derivatives or through a particularly unfortunate tweet, I'm not an economist either. But you don't have to know anything about the inner workings to find out whether a system becomes unstable. That sounds strange at first, but it is in the nature of complex systems. Wherever many components are related in many ways and doing things all the time with themselves and other actors, you will find fundamental similarities. It does not matter whether it is a question of spin systems, coral reefs or the global economy. One of these similarities is their propensity for critical transitions - such systems can drastically change their properties quite suddenly.
This possibility is the downside of stability. Dynamic systems usually return to normal after a stroke of fate; such a normal state is called an attractor. For example, the labor market collapses in a recession, but after a recovery phase it approaches the pre-crisis trend. A forest devastated by a storm will be the same again in a few decades. If, on the other hand, the damage is too great, the system quickly changes into a completely different state after the crisis. It is then also stable, but we usually don't like it quite as much as the original attractor.  In arid areas, deforested forests turn into deserts.
Critical transitions come suddenly ...
Such critical transitions are likely to be quite common. Studies have identified various candidates: the earth's climate, ocean currents, financial markets, the human brain ... With some of them, a sudden collapse would be quite uncomfortable for us. Unfortunately, we only know afterwards where the critical point is and what happens then. And of course who is to blame.
At the moment we are mainly concerned with ecosystems. For example coral reefs. In years with high water temperatures, the corals of a reef bleach, in the years after they recover. But if too many corals die, algae overgrow the reef, the old community disappears and what remains is an ecosystem in which corals and the wildlife that depend on them can no longer gain a foothold. And with that, the fishing industry of an entire country may already be finished.
Which brings us back to the subject of economics. Animals and plants have one major disadvantage vis-à-vis governments and companies: they do not continuously generate measurement data about their own condition. Genetic engineering would be in demand. In contrast, there are tons of numbers about economic developments. And large data sets are needed to find the telltale signs of a system close to the critical transition - the mathematical description of critical slowing down  makes this clear:
the maximum real part of the eigenvalues of the Jacobian matrix tends to zero as a bifurcation point is approached. As a result the dynamical system becomes increasingly slow in recovering from small perturbations.
One can imagine that a dynamic system recovers from external disturbances because it is located in an abstract “basin of stability” - like a marble in a cup. A dynamic system is never statically in equilibrium, but rolls around in its basin of stability. As it moves away from the stable state, its tendency to roll back increases.
Such a system approaches the critical point in that the basin of stability becomes more and more shallow - until the system rolls over the "edge" at some point, driven by its own random movements or an external disturbance. Then it ends up in the stability basin of a new attractor, the next cup.
... but not without warning.
Four essential predictions about the behavior of the system near the critical point can be derived from this picture: First, as the flatness increases, it takes longer and longer for the system to roll back from the edge of its basin to the center - it takes longer and longer for recovery. Second, the edges are less steep, so the system can reach more places in the cup - so the system becomes more and more variable. Third, movement within the pelvis is slower, so successive states of the system become more and more similar - a statistically measurable property known as autocorrelation. Fourth, the shallow stability basin is sometimes asymmetrical, so that in such cases the system tends to adopt states more often at the transition to the neighboring basin.
The exciting question is, of course, whether this model actually works in systems that are of interest to us. In ecosystems the effect can basically be regarded as proven, on the one hand the effect can not only be reproduced well in computer simulations, one also encounters effects that are not obvious from the theory itself. For example, for the above-mentioned collapse from forest to desert, which also reflects the fact that approaching critical transitions also change the spatial structure. Testing the predictions in practice, however, has proven to be more difficult, largely because the data is difficult to come by.
There are now various studies on real systems. A while ago I ran into Nature again such a publication on the way. In the experiment, an ecosystem of large macroalgae was disturbed to different degrees on different patches. The resistance to penetration by another species community is then measured based on the distribution of both species communities after a disturbance. This is a case in which a critical transition is reflected in the spatial structure of systems. Another example is the observation that insect pests are increasingly unevenly distributed in the time before a large population explosion.
An experiment in which the ever slower recovery was actually observed directly began in 2007 at Peter Lake in the USA. The researchers gradually put predatory fish into the lake, which then turned from algae-dominated to a clear body of water, and in the time before the algae regenerated more and more slowly. In 2012, another group demonstrated the effect on photosynthesis-inducing cyanobacteria in the laboratory. A similar study on yeast appeared in the same year.
From theory to practice
These experiments confirm the effect in principle, but also show that none of this is as easy as it sounds. First of all, it is quite time-consuming to observe ecosystems in such detail that one can get such time series. Even more problematic is that the four signs often do not appear together, so that one cannot rely on the more easily measured autocorrelation and stronger fluctuations. Conversely, it has been shown that there are false-positive collapse warnings.
The warning signs can also appear at transitions that change the system only in a very subtle way, for example its sensitivity to certain influences. Of course you look stupid if you have just prophesied the apocalypse in the latest nature paper. There are even systems in which a transition shows the classic critical slowing down, but the same transition in the opposite direction does not. This has been the case with plankton blooms.
Behind all these difficulties there is a fundamental, as yet unanswered question: Which systems does this apply to and how do you find out? If you do not see any signs of critical slowing down in a system, this can mean two things, among other things: Either the system is sufficiently far from collapse - or the model simply does not apply here. Conversely, there can be other reasons for what are actually clear signs of critical slowing down.  However, the experimental and theoretical evidence clearly shows that if you find them, that's a reason to get nervous.
In 2014 an article on the US economy made a notable statement:
This time  the recovery took longer than in 2001. And in 2001 it took longer than in the 1990s, which in turn took longer than in the 1980s.
Other analyzes show that volatility has tended to increase for some parameters over the past 30 years, and headlines like “volatile calm” sound suspiciously like some kind of autocorrelation. That is a bit unsettling, but still no reason to panic: If a collapse is on the horizon, it does not mean that it will come anytime soon. Symptoms often show up long before the critical transition, so it could possibly be another 50 years, and by then we have other problems.
Above all, however, the experts argue whether there is critical slowing down in economic systems at all. A contradiction comes from an Indian team who deduces from the analysis of stock indices that there are no such signs for crises - but this leaves the possibility open that systemic risks express themselves through critical slowing down. On the other hand, three economists from the Netherlands measured a systematic increase in response times when analyzing interest rate swaps in euros and dollars in the run-up to the bankruptcy of Lehman Bros. But they come to the conclusion that another indicator warns more effectively.
But I would not dismiss critical slowing down in economic systems out of hand. It is possible that the financial crises themselves are not critical transitions - after all, they are not collapses into a new stable state, but only dents. That would mean that they are the faults themselves, the correction of which is slower and slower until the actual collapse occurs. The data quoted above can be interpreted accordingly.
Or financial systems could simply have a completely different kind of dynamic, for example a stochastic process. Above all, however, the markets are a controlled system that hardly anyone is interested in collapsing - on the contrary. There is hardly a possible global development that humanity would act against as globally united as against the transition of the financial markets into another state, whatever that may be.
 Rottnest Island is an exception. The island was forested until a few decades ago, and the quokkas lived in the more open areas near the beaches, so that in the forest itself the trees could always grow back. Then large parts of the forest were cut down, the quokkas have spread out in the areas that had become free - and all the young trees that were growing again were immediately fed so that the forest could not grow back and the island is now a kind of heather full of quokkas. In some regions, attempts are now being made to artificially bring the forest back - by surrounding all the tree saplings with small anti-Quokka fences. Undoing a transition to a new stable state is very tedious.
 Strictly speaking, critical slowing down only means that the system recovers from malfunctions more and more slowly. It can be shown that the phenomenon must appear in all continuous differential equations when one approaches a critical point. However, it has been shown that two of the other three signs of the collapse - autocorrelation and greater fluctuation range - follow mathematically to a considerable extent from this falling recovery rate.
 A cautionary example is provided by the time series of the sea ice anomaly in the Arctic, which at first glance shows a significantly higher range of fluctuation since 2007 - a classic sign of collapse in a system that we expect to collapse almost every hour. But it's not all it seems As Tamino explains here in his blog, the variance here has a different origin: the annual cycle, which has to be factored out for the anomaly, has become stronger, so that a remainder of the seasonal fluctuations appear in the actually adjusted time series. If this trend is taken into account, the fluctuation disappears in the anomaly. Possibly the amplified cycle itself is due to collapse-induced variance, but to answer that question, the anomaly is the wrong time series. Critical slowing down is particularly interesting in climate research because there is consensus that the tipping points of the climate cannot be modeled for the time being. In addition, there are already indications of previous climate changes that signs of a critical transition are emerging in advance.
- Published in: biology, climate and environment, mathematics, politics, technology
- Keywords: attractor, critical slowing down, dynamics, collapse, critical transition, USA, economy
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