Monday, July 28, 2014

Tipping Points, Bifurcation Theory, and the Justification For Whole System Thinking

For those who wonder why a "tipping point" matters, or why critical thinkers are now talking about "whole system thinking"...
Tipping point (climatology) – the point beyond which unstable global climate does not return to a previous equilibrium state but gets more unstable until it finds a new equilibrium
Tipping point (sociology) -  is the event of a previously rare phenomenon becoming rapidly and dramatically more common
Tipping point (ecology) – exceeding planetary boundaries, in which living within the boundaries' stable state retains planetary habitability on Earth
Tipping point (catastrophe theory)  - the value of the parameter at which the set of equilibria abruptly change
Tipping point (civil engineering - angle of repose) - the maximum angle of a stable slope of granular materials before it destabilizes
Tipping point (economics) - the point at which a dominant technology or player defines the standard for an industry-resulting in an permanent market advantage & "winner-take-all" economies of scale and scope (market advantage = loss of equilibrium)

{Ed: Tipping Point (everything) – that point at which the stable state of system parameters, or system equilibrium, is sufficiently disturbed that the system cannot return to that steady state (or equilibrium) without significant external influence. The system will invariably seek a new equilibrium state, that may require complete annihilation of many previous system factors}

Bifurcation Theory - is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ODEs, DDEs or PDEs), and discrete systems (described by maps).

Catastrophe Theory, a branch of bifurcation theory in the study of dynamical systems, 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, 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).

Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analyzing 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.

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 behavior 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 geometric structures.
Look back at the list above.  It includes climate, physical events, sociology, economics, and is only a part of what our world system is.  Certainly the political systems we are so vitally interested in here are wrapped up in it all in very complex ways. Here is what I am driving at:  we are now facing a variety of instabilities all at once.

Again a partial list:
climate change
ocean acidification
global warming
polarized elections
bees and birds, insecticides
agricultural crises
water surplus and drought
economic turmoil
communications, internet, technology
many, many more

No one of these can be studied adequately isolated from the others yet we try so desperately to do just that.  In climate science alone we keep seeing new things as changes progress that potentially change everything.

Maybe we humans are an "intelligent" species.  Yet we are also arrogant if we believe the progress briefly described here is enough to adequately deal with what is coming and seems to be coming faster and faster.  Is there an answer?  The only answer is to become as flexible as possible and maybe some adaptation will be possible.

Summarized from Are you ready for this? A multi-dimensional tipping point” by Don Mikulecky (

Thanks for being there and being you... and thanks for reading. Your comments and thoughts are appreciated and solicited.

The Smokemaster


opit said...

"Tipping point (catastrophe theory) - the value of the parameter at which the set of equilibria abruptly change"
That which is posed to scare people...yet climate needs to be plotted in 100ths of a degree to look like there is a problem. There is - no sense of proportion.
Ocean acidification puzzles me. There is really no reason I know of to suppose that the oceans are not a saturated solution..which would be consistent with outgassing and rising levels of co2 on a planet which saw much more of it in the past. ( Though I am seeing speculation that Mauna Loa may not be a reliable indicator )
If you were to talk water pollution from things like hydrofracking - which releases airborne and waterborne toxic compounds around drill sites - then that is much more scary than the idea climate might change...something it does anyway. But rather than bore you with reasons I think all is not lost - though the warmakers are doing their best to make it so - I expect you would be more comfortable with an echo chamber response...a sympathizer in Desmedoma Despair.

The Smokemaster said...

No, not really focused on scaring people, just introducing (or re-introducing, for those who have made a profession of forgetting what they learned in school) things that are of major importance in the overall scheme of things. Using my broad generality brush (which like climate models, I know is wrong but it serves the purpose here) "everybody" tends to think in terms of change happening in nice neat linear fashion. Maybe not... All the evidence we can come up with from the distant past indicates serious bifurcation points in climate during temperature spikes. All the current common sense says we should be nearing a couple of them as we speak. Kind of reminds me of the insurance commercial where some kids are joy riding without their seatbelts on, and the driver sees that he's about to have a serious accident. The action outside the car stops, and the driver turns to the occupants and goes 'Whoa dude! You better buckle up!" whereupon they do, and flash back to a vicious crash mere mili-seconds later.

That said, ocean acidification is pretty straight forward. Yes, the ocean WOULD act like any other solution BUT it wouldn't support most life it were at saturation for CO2. To start with it would no longer be nominally alkaline, it would be seriously acidic. So the problem is that it is approaching saturation with all the devastating consequences for life in it that such a state entails.

I live in fracking and waste well country so I completely agre with you and actively work with the local eco-warriors to counter it. That said, I don't think all is lost either. See my latest blog post This I Believe... So, no I'm happy NOT to have a bunch of people around me going "Yeah, man the outlook really sucks!" I already know it sucks at one level of the scenario scale and I'm actively working to keep it from sucking across the whole thing. Thanks for commenting and sorry to take so long getting back. Don't know quite why Blogger never notified me of your post but I've seen it now :-)