Climate Catastrophe

This is an interesting, simple model of global ice age dynamics, from:

“A Catastrophe Model of the Paleoclimate”, Douglas R MacAyeal, Journal of Glaciology, Vol 24 No 90, 1979

It illustrates a pitchfork bifurcation as a slice through a cusp catastrophe. It’s conceptually related to earlier models by Budyko and Weertmans that demonstrated hysteresis in temperature and ice sheet dynamics.

The model is used qualitatively in the paper. I’ve assigned units of measure and parameter values that reveal the behavior of the catastrophe, but there’s no guarantee that they are physically realistic.

The .vpm package includes several .cin (changes) files that reproduce interesting tests on the model. The model runs in PLE, but you may want to use the Model Reader to access the .cin files in SyntheSim.

Catastrophe.vpm

 

Gumowski-Mira Attractor

I became aware of this neat model via the Vensim forum. I have no idea what the physical basis is, but the diverse and beautiful output it generates is quite amazing.

Interestingly, if you only looked at time series of this sequence, you’d probably never notice it.

This runs in any version of Vensim. gumowski mira.mdl

Big data and the power of personal feedback

In a recent conversation about data requirements for future Vensim, a colleague observed that the availability of ready access to ‘big data’ in corporations has had curious side effects. One might have hoped for a flowering of model-driven conversations about the firm. Instead, ubiquitous access to data has led managers to spend less time contemplating what data might actually be important. Crucial data for model calibration are often harder to get than they were in the bad old days, because:

  • The perceived time scale of relevance is shorter than ever; there are no enduring generic structures, only transient details, so old data gets tossed or ignored.
  • Prevalent databases are still lousy at constructing aggregate time series.
  • Zombie managerial instincts for hoarding data still walk the earth.
  • Users are riveted by slick graphics which conceal quality issues in the underlying data.

Perhaps this is a consequence of the fact that data collection has become incredibly cheap. In the short run, business is about execution of essentially fixed strategies, and raw data is pretty darn useful for that. The problem is that the long run challenge of formulating strategies requires an investment of time to turn data into models (mental or formal), but modeling hasn’t experienced the same productivity revolution. This could leave companies more strategically blind than ever, and therefore accelerate the process of inadvertently walking off a cliff.

Around the same time, I ran into this Wired article about the power of feedback to change behavior. It details a variety of interesting innovations, from radar speed signs to brainwave headbands. I’ve experimented with similar stuff, like Daytum (found here, clever, but soon abandoned) and the Kill-a-watt (still used occasionally).

In the past two or three years, the plunging price of sensors has begun to foster a feedback-loop revolution. …

And today, their promise couldn’t be greater. The intransigence of human behavior has emerged as the root of most of the world’s biggest challenges. Witness the rise in obesity, the persistence of smoking, the soaring number of people who have one or more chronic diseases. Consider our problems with carbon emissions, where managing personal energy consumption could be the difference between a climate under control and one beyond help. And feedback loops aren’t just about solving problems. They could create opportunities. Feedback loops can improve how companies motivate and empower their employees, allowing workers to monitor their own productivity and set their own schedules. They could lead to lower consumption of precious resources and more productive use of what we do consume. They could allow people to set and achieve better-defined, more ambitious goals and curb destructive behaviors, replacing them with positive actions. Used in organizations or communities, they can help groups work together to take on more daunting challenges. In short, the feedback loop is an age-old strategy revitalized by state-of-the-art technology. As such, it is perhaps the most promising tool for behavioral change to have come along in decades.

But the applications don’t quite live up to these big ambitions:

… The GreenGoose concept starts with a sheet of stickers, each containing an accelerometer labeled with a cartoon icon of a familiar household object—a refrigerator handle, a water bottle, a toothbrush, a yard rake. But the secret to GreenGoose isn’t the accelerometer; that’s a less-than-a-dollar commodity. The key is the algorithm that Krejcarek’s team has coded into the chip next to the accelerometer that recognizes a particular pattern of movement. For a toothbrush, it’s a rapid back-and-forth that indicates somebody is brushing their teeth. … In essence, GreenGoose uses sensors to spray feedback loops like atomized perfume throughout our daily life—in our homes, our vehicles, our backyards. “Sensors are these little eyes and ears on whatever we do and how we do it,” Krejcarek says. “If a behavior has a pattern, if we can calculate a desired duration and intensity, we can create a system that rewards that behavior and encourages more of it.” Thus the first component of a feedback loop: data gathering.

Then comes the second step: relevance. GreenGoose converts the data into points, with a certain amount of action translating into a certain number of points, say 30 seconds of teeth brushing for two points. And here Krejcarek gets noticeably excited. “The points can be used in games on our website,” he says. “Think FarmVille but with live data.” Krejcarek plans to open the platform to game developers, who he hopes will create games that are simple, easy, and sticky. A few hours of raking leaves might build up points that can be used in a gardening game. And the games induce people to earn more points, which means repeating good behaviors. The idea, Krejcarek says, is to “create a bridge between the real world and the virtual world. This has all got to be fun.”

This strikes me as a rehash of the corporate experience: use cheap data to solve execution problems, but leave the big strategic questions unaddressed. The torrent of the measurable might even push the crucial intangibles – love, justice, happiness, wisdom – further toward the unmanaged margins of our existence.

My guess is that these technologies can help us solve our universal personal problems, particularly in areas like health and fitness where rewards are proximate in time and space. There might even be beneficial spillovers from healthier, happier personal lifestyles to reduced resource demand and

But I don’t see them doing much to solve global environmental problems, or even large-scale universal problems like urban decay and poverty. Those problems exist, not for lack of data, but for lack of feedback that is compelling to the same degree as the pressures of markets and other financial and social systems, which aren’t all about fun. In the US, we’re not even willing to entertain the idea of creating climate feedback loops. I suspect that the solutions to our biggest problems awaits some other technology that makes us much more productive at devising good strategies based on shared mental models.

The rise of systems sciences

The Google books ngram viewer nicely documents the rise of various systems science disciplines, from about the time of Maxwell’s landmark 1868 paper, On Governors:

Click to enlarge.

We still have a long way to go though:

Further reading:

A Dynamic Synthesis of Basic Macroeconomic Theory

Model Name: A Dynamic Synthesis of Basic Macroeconomic Theory

Citation: Forrester, N.B. (1982) A Dynamic Synthesis of Basic Macroeconomic Theory: Implications for Stabilization Policy Analysis. PhD Dissertation, MIT Sloan School of Management.

Source: Provided by Nathan Forrester

Units balance: Yes, with 3 exceptions, evidently from the original publication

Format: Vensim

Notes: I mention this model in this article

A Dynamic Synthesis of Basic Macroeconomic Theory (Vensim .vpm)

Update: a newer version with improved diagrams and a control panel, plus changes files for a series of experiments with responses to negative demand shocks:

Download NFDis+TF-3.vpm or NFDis+TF-3.zip

The model runs in Vensim PLE, but you’ll need an advanced version to use the .cin and .cmd files included.

A note on the bathtub analogy

Adapted from “A note on the bathtub analogy,” Pål Davidsen, Erling Moxnes, Mauricio Munera Sánchez, David Wheat, 2011 System Dynamics Conference.

Abstract

The bathtub analogy has been used extensively to illustrate stock and flow relationships. Because this analogy is frequently used, System Dynamicists should be aware that the natural outflow of water from a bathtub is a nonlinear function of water volume. A questionnaire suggests that students with one year or more of System Dynamics training tend to assume a linear relationship when asked to model a water outflow driven by gravity. We present Torricelli’s law for the outflow and investigate the error caused by assuming linearity. We also construct an “inverted funnel” which does behave like a linear system. We conclude by pointing out that the nonlinearity is of no importance for the usefulness of bathtubs or funnels as analogies. On the other hand, simplified analogies could make modellers overconfident in linear formulations and not able to address critical remarks from physicists or other specialists.

See my related blog post for details.

Units balance.

Runs in Vensim (any version): ToricelliBathtub.mdl ToricelliBathtub.vpm

The Economic Long Wave

This is John Sterman’s model of long waves (long-duration economic cycles), driven by capital accumulation dynamics. This version is replicated from a JEBO article,

STERMAN, J. D. (1985) A Behavioral Model of the Economic Long Wave. Journal of Economic Behavior and Organization, 6, 17-53.

There’s some interesting related literature (including other economic models in this library). From Sterman’s publications list:

STERMAN, J. D. & MOSEKILDE, E. (1994) Business Cycles and Long Waves: A Behavioral, Disequilibrium Perspective. IN SEMMLER, W. (Ed.) Business Cycles: Theory and Empirical Methods. Boston, Kluwer Academic Publishers.

STERMAN, J. D. (1994) The Economic Long Wave: Theory and Evidence. IN SHIMADA, T. (Ed.) An Introduction to System Dynamics. Tokyo.

STERMAN, J. D. (2002) A Behavioral Model of the Economic Long Wave. IN EARL, P. E. (Ed.) The Legacy of Herbert Simon in Economic Analysis. Cheltenham, UK, Edward Elgar.

STERMAN, J. D. (1985) An Integrated Theory of the Economic Long Wave. Futures, 17, 104-131.

RASMUSSEN, S., MOSEKILDE, E. & STERMAN, J. D. (1985) Bifurcations and Chaotic Behavior in a Simple Model of the Economic Long Wave. System Dynamics Review, 1, 92-110.

STERMAN, J. D. (1983) The Long Wave. Science, 219, 1276.

KAMPMANN, C., HAXHOLDT, C., MOSEKILDE, E. & STERMAN, J. D. (1994) Entrainment in a Disaggregated Economic Long Wave Model. IN LEYDESDORFF, L. & VAN DEN BESSELAAR, P. (Eds.) Evolutionary Economics and Chaos Theory. London, Pinter.

MOSEKILDE, E., LARSEN, E. R., STERMAN, J. D. & THOMSEN, J. S. (1993) Mode Locking and Nonlinear Entrainment of Macroeconomic Cycles. IN DAY, R. & CHEN, P. (Eds.) Nonlinear Economics and Evolutionary Economics. New York, Oxford University Press.

MOSEKILDE, E., THOMSEN, J. S. & STERMAN, J. D. (1992) Nonlinear Interactions in the Economy. IN HAAG, G., MÜLLER, U. & TROITZSCH, K. (Eds.) Economic Evolution and Demographic Change. Berlin, Springer Verlag.

THOMSEN, J. S., MOSEKILDE, E. & STERMAN, J. D. (1991) Hyperchaotic Phenomena in Dynamic Decision Making. IN SINGH, M. G. & TRAVÉ-MASSUYÈS, L. (Eds.) Decision Support Systems and Qualitative Reasoning. Amsterdam, Elsevier Science Publishers.

THOMSEN, J. S., MOSEKILDE, E., LARSEN, E. R. & STERMAN, J. D. (1991) Mode-Locking and Chaos in a Periodically Driven Model of the Economic Long Wave. IN EBELING, W. (Ed.) Models of Self Organization in Complex Systems. Berlin, Akademie Verlag.

STERMAN, J. D. (1988) Nonlinear Dynamics in the World Economy: The Economic Long Wave. IN CHRISTIANSEN, P. & PARMENTIER, R. (Eds.) Structure, Coherence, and Chaos in Dynamical Systems. Manchester, Manchester University Press.

STERMAN, J. D. (1987) Debt, Default, and Long Waves: Is History Relevant? IN BOECKH, A. (Ed.) The Escalation in Debt and Disinflation: Prelude to Financial Mania and Crash? Montreal, BCA Publications.

STERMAN, J. D. (1987) An Integrated Theory of the Economic Long Wave. IN WANG, Q., SENGE, P., RICHARDSON, G. P. & MEADOWS, D. H. (Eds.) Theory and Application of System Dynamics. Beijing, New Times Press.

STERMAN, J. D. (1987) The Economic Long Wave: Theory and Evidence. IN VASKO, T. (Ed.) The Long Wave Debate. Berlin, Springer Verlag.

RASMUSSEN, S., MOSEKILDE, E. & STERMAN, J. D. (1987) Bifurcations and Chaotic Behavior in a Simple Model of the Economic Long Wave. IN WANG, Q., SENGE, P., RICHARDSON, G. P. & MEADOWS, D. H. (Eds.) Theory and Application of System Dynamics. Beijing, New Times Press.

And from Christian Kampmann,

“The Role of Prices in Long Wave Entrainment” (with C. Haxholdt, E. Mosekilde, and J.D. Sterman), International System Dynamics Conference, Stirling, U.K. and at the Spring 1994 ORSA/TIMS conference, Boston, MA. 1994.
“Disaggregating a simple model of the economic long wave” International Conference of the System Dynamics Society, Keystone, CO, 1985.
The long wave model was the guine pig for Kampmann’s interesting ’96 conference paper that combined a graph-theoretic identification of a set of feedback loops having independent gains with eigenvalue analysis,
Kampmann, Christian E.   Feedback Loop Gains and System Behavior
There also used to be a nifty long wave game, programmed on NEC minicomputers (32k memory?), but I’ve lost track of it. I’d be interested to here of a working version.

Economic Cycles: Underlying Causes

Nathaniel Mass’ model of economic cycles, replicated from his 1975 book, Economic Cycles: An Analysis of Underlying Causes, which unfortunately seems to have disappeared from the Productivity Press site (though you can still find used copies).

I haven’t checked, but I’m guessing that the model is quite similar to that in his PhD thesis, which you can get from MIT libraries here. Here’s the abstract:


The models: mass2.mdl mass2.vpm

These don’t have units defined, unfortunately – I’d love to have a copy with units if you’re so inclined.

The Dynamics of Commodity Production Cycles

These classic models are from Dennis Meadows’ dissertation, the Dynamics of Commodity Production Cycles:

While times have changed, the dynamics described by these models are still widespread.

These versions should work in all recent Vensim versions:

DLMhogs2.vpm DLMhogs2.mdl

DLMgeneric2.vpm DLMgeneric2.mdl

 

Setting up Vensim compiled simulation on Windows

If you don’t use Vensim DSS, you’ll find this post rather boring and useless. If you do, prepare for heart-pounding acceleration of your big model runs:

  • Get Vensim DSS.
  • Get a C compiler. Most flavors of Microsoft compilers are compatible; MS Visual C++ 2010 Express is a good choice (and free). You could probably use gcc, but I’ve never set it up. I’ve heard reports of issues with 2005 and 2008 versions, so it may be worth your while to upgrade.
  • Install Vensim, if you haven’t already, being sure to check the Install external function and compiled simulation support box.
  • Launch the program and go to Tools>Options…>Startup and set the Compiled simulation path to C:Documents and SettingsAll UsersVensimcomp32 (WinXP) or C:UsersPublicVensimcomp32 (Vista/7).
    • Check your mdl.bat in the location above to be sure that it points to the right compiler. This is a simple matter of checking to be sure that all options are commented out with “REM ” statements, except the one you’re using, for example:
  • Move to the Advanced tab and set the compilation options to Query or Compile (you may want to skip this for normal Simulation, and just do it for Optimization and Sensitivity, where speed really counts).

This is well worth the hassle if you’re working with a large model in SyntheSim or doing a lot of simulations for sensitivity analysis and optimization. The speedup is typically 4-5x.