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|Subject: Catastrophe theory, instability, risk||Date: 10/9/2012 2:13 PM|
|Author: WendyBG||Number: 405636 of 440079|
By STEVEN STROGATZ
A field known as catastrophe theory explores how slow continuous changes in the force applied to a system (like the gradually increasing load on a camel’s back) can trigger rapid discontinuous jumps in its response....
...intersections [between a line and a curve] often represent answers. Solutions. States of equilibrium. In mathematical models of economies, or ecosystems, or other kinds of dynamical systems, intersections are where variables come to rest and settle down. In economic models, for example, the equilibrium price of an item is set by the intersection of supply and demand curves. If that intersection suddenly vanishes, the price has to jump.
What’s especially worrisome is that the jump occurs without warning. An intersection, by its very nature, doesn’t fade away. It exists until it doesn’t...
....the “fold catastrophe” is the most basic scenario in catastrophe theory. It’s important because in its aftermath there are no other intersections in sight. Whatever the system is going to do next, it’s going to be something radically different. It has to leap to a different state.... [end quote]
This article reminds me of the striking, memorable 2006 article by John Mauldin:
Fingers of Instability
By John Mauldin
August 25, 2006
This week we revisit some ideas on how change occurs. We are in a transition in the world economy, and it sometimes helps to think about how these transitions take place. What is the mechanism for change? Can we see it coming soon enough to avoid the problems and take advantage of them? ...
How Change Happens
By John Mauldin
August 17, 2012
Imagine, Buchanan says, dropping one grain of sand after another onto a table. A pile soon develops. Eventually, just one grain starts an avalanche. Most of the time it is a small one, but sometimes it builds on itself and it seems like one whole side of the pile slides down to the bottom.
They learned some interesting things [about nonequilibrium systems]. What is the typical size of an avalanche? After a huge number of tests with millions of grains of sand, they found that there is no typical number. "Some involved a single grain; others, ten, a hundred or a thousand. Still others were pile-wide cataclysms involving millions that brought nearly the whole mountain down. At any time, literally anything, it seemed, might be just about to occur."
The piles were indeed completely chaotic in their unpredictability.
Imagine peering down on the pile from above, and coloring it in according to its steepness. Where it is relatively flat and stable, color it green; where steep and, in avalanche terms, ‘ready to go,’ color it red.
What do you see? They found that at the outset the pile looked mostly green, but that, as the pile grew, the green became infiltrated with ever more red. With more grains, the scattering of red danger spots grew until a dense skeleton of instability ran through the pile. Here then was a clue to its peculiar behavior: a grain falling on a red spot can, by domino-like action, cause sliding at other nearby red spots.
If the red network was sparse, and all trouble spots were well isolated one from the other, then a single grain could have only limited repercussions. But when the red spots come to riddle the pile, the consequences of the next grain become fiendishly unpredictable. It might trigger only a few tumblings, or it might instead set off a cataclysmic chain reaction involving millions. The sandpile seemed to have configured itself into a hypersensitive and peculiarly unstable condition in which the next falling grain could trigger a response of any size whatsoever."
Scientists refer to this as a critical state....
…after the pile evolves into a critical state, many grains rest just on the verge of tumbling, and these grains link up into ‘fingers of instability’ of all possible lengths. While many are short, others slice through the pile from one end to the other. So the chain reaction triggered by a single grain might lead to an avalanche of any size whatsoever, depending on whether that grain fell on a short, intermediate or long finger of instability....
The problem with long term macroeconomic stability is that it tends to produce unstable financial arrangements.... [end quote]
I remembered John Mauldin's 2006 insight when the financial crisis hit in 2008. Seldom has a financial analyst's insight been so right-on as Mauldin. Mike Shedlock (Mish) also traced the roots of the 2008 financial crisis daily, starting in 2004.
Today's Control Panel shows a pattern of complacency that implies stability and low risk. Borrowers are accepting low risk premiums (though not as low as 2005 -- assuming that sovereign debt is actually risk-free, a dangerous assumption). Stock investors are greedily following the trend to ever-higher valuations, reminiscent of the familiar bubbles of the past 15 years, as if the real economy was actually growing fast enough to justify the share price growth.
In fact, the "Fingers of Instability" permeate the world Macro economy even more today than they did in 2008, when Europe appeared to be stable. Despite the summer vacation, Europe is slipping into recession, the numbers don't add up and the crisis is bound to continue.
Greeks are rioting as Andrea Merkel visits Greece ahead of a potential default in late November. The IMF reported that Greece was likely to miss its goals.
The U.S. "fiscal cliff" is looming in only 2 months. I would be astonished if Congress smoothly resolved the issues.
Macro fundamentals from money supply to demographics are so out of balance that it's scary. The "Minsky moment" of sudden debt unwinding and financial collapse may transfer from the private sector to the central banks, which have taken on immense debts backed by fiat currencies since the last crisis. Could the market suddenly reject these fiat debts, refusing to buy long-term bonds so yields suddenly rise -- devastating the balance sheets of the central banks?
Catastrophe theory reminds us that instability can lead to sudden crises, as we saw just 4 years ago.
Be careful out there. The U.S. economy is at stall speed, barely holding its own (and possibly already in recession).
Fingers of instability permeate the international financial system. The risk is high of a sudden crisis.
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