Change in the real world is most often nonlinear unless we are speaking of the rare system near equilibrium. The 1970s brought a time of excitement for those of us engaged in modeling real world systems. Breakthrough after breakthrough came one after the other. They had to do with nonlinear mathematics. One example was Catastrophe theory.
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.
Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analysing how the qualitative nature of equation solutions depends on the parameters that appear in the equation. This may lead to sudden and dramatic changes, for example the unpredictable timing and magnitude of a landslide.
Catastrophe theory originated with the work of the French mathematician René Thom in the 1960s, and became very popular due to the efforts of Christopher Zeeman in the 1970s. It considers the special case where the long-run stable equilibrium can be identified with the minimum of a smooth, well-defined potential function (Lyapunov function).
Small changes in certain parameters of a nonlinear system can cause equilibria to appear or disappear, or to change from attracting to repelling and vice versa, leading to large and sudden changes of the behaviour of the system. However, examined in a larger parameter space, catastrophe theory reveals that such bifurcation points tend to occur as part of well-defined qualitative geometrical structures.
These breakthroughs were not just technical advances but were a tipping point themselves in that they changed our way of modeling the real world. No longer was the near equalibtrum linear model the weak crutch used for modeling. We began to see reality as it actually was using nonlinear math for our models.
A long time has passed and yet awareness of these breakthroughs seems to have not penetrated the minds of many people. One place where this is very dangerous is with respect to Global Warming and Climate Disruption (Climate Change).
There seems to be an illusion that warming and its effects will proceed a little at a time so that our delay in doing what needs to be done will make things a little worse as each time period passes. This is definitely not true. Here is but one of a growing number of alarms being sounded: Scientists Identify Possible 'Tipping Point' of Global Warming.
Scientists have long been concerned that global warming may push the Earth's climate system past a "tipping point," and a new study from Oregon State University (OSU) may have finally identified that threshold.
Read on below and we will explore this further.
First of all, thius has clearly happened before:
The study, published this week in the journal Science, suggests that this combined ocean warming may have forced the Earth's climate past the point of no return.
"Synchronization of two major ocean systems can amplify the transport of heat toward the polar regions and cause larger fluctuations in northern hemisphere climate," lead author Summer Praetorius, a doctoral student in marine geology at Oregon State, said in a press release. "This is consistent with theoretical predictions of what happens when Earth's climate reaches a tipping point."
For those nervous about our current predicament with global warming, Praetorius is quick to point out that this research doesn't necessarily mean that the same thing will happen in the future, "but we cannot rule out that possibility," she said.
No one has a crystal ball but warnings like this are not to be taken lightly. Certainly as we consider our present situation they need to shape the way we anticipate the way warming will occur in the future.
The OSU study is getting lots of attention because it has very important implications:Synchronization of North Atlantic, North Pacific preceded warming, end of ice age
The study found that synchronization of the two regional systems began as climate was gradually warming. After synchronization, the researchers detected wild variability that amplified the changes and accelerated into an abrupt warming event of several degrees within a few decades.
"As the systems become synchronized, they organized and reinforced each other, eventually running away like screeching feedback from a microphone," said Alan Mix, a professor in OSU's College of Earth, Ocean, and Atmospheric Sciences and co-author on the paper.
"Suddenly you had the combined effects of two major oceans forcing the climate instead of one at a time."
"The example that we uncovered is a cause for concern because many people assume that climate change will be gradual and predictable," Mix added.
"But the study shows that there can be vast climate swings over a period of decades to centuries. If such a thing happened in the future, it could challenges society's ability to cope."
What made this study unusual is that the researchers had such a detailed look at the geologic record. While modern climate observations can be made every day, the length of instrumental records is relatively short - typically less than a century.
In contrast, paleoclimatic records extend far into the past and give good context for modern changes, the researchers say. However, the resolution of most paleo records is low, limited to looking at changes that occur over thousands of years.
In this study, the researchers examined sediment cores taken from the Gulf of Alaska in 2004 during an expedition led by Mix. The mountains in the region are eroding so fast that sedimentation rates are "phenomenal," he said. "Essentially, this rapid sedimentation provides a 'climate tape recorder' at extremely high fidelity."
Let's try to put these ideas into perspective. less than a half century ago the kind of math and science that made it possible to see how such things could happen with mathematical models was born. I, for one, went wild with nonlinear models of physiological systems. My assumption was that whole fields of study would change direction. I developed a method for simulating very large nonlinear systems that should have been of interest to most of my colleagues and in places like the drug industry. I am now out of that field and the work and the techniques lie dormant. Linear thinking still dominates much of the fields we were working in.
It is very true that the new mathematical tools had impact in some places. Their use in technology of certain kinds changed many things. Chaos theory was born when nonlinear math allowed what seemed to be computer error to be interpreted another way.
Back in the 1960s I did my post doctoral training in Israel learning nonequilibrium thermodynamics. I brought what I learned to my first job at SUNY Buffalo where my first boss snapped it up and began large scale weather models. The breakthroughs made that obsolete. We now had more realistic methods to model the real world.
So here we are today with a bunch of real clowns in congress in charge of their actions on science. How much more divorced from reality can we get?
There is very little time if any before much of what is happening becomes irreversible. That means we will have destined future generations to struggle to survive because of our collective stupidity. Collective in this way. The deniers are one problem. The system of science that can not get its message across is another. The government that has too little understanding to see the urgency is another.
We have begun (Maybe too late?) to break our addiction to fossil fuels. Meanwhile the oceans warm and acidify, species undergo mass extinction, and we spend our time in politics as usual as if all this can wait until we win. If we can win.
You really do not need a weatherman to tell which way the wind is blowing. It is time to wake up!
5:58 PM PT: Thanks for putting it on the rec list....I hope it gets around