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   John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 07-May-2026 03:06:34 JST John Carlos Baez

   LEVERAGE POINTS

   When trying to confront the Anthropocene, we are everywhere faced with the difficulty of wisely intervening in complex systems. Here another idea from system dynamics becomes important: “leverage points”, which are places in a system where a small change can make a big difference.

   Leverage points were brought to the fore by one of the most prominent practitioners of system dynamics, Donella Meadows [Me3]. Meadows learned a lot from Forrester at MIT in the early 1970s, and she was deeply concerned with environmentalism and sustainability. In 1972 she helped write the famous study The Limits to Growth [Me1]. The huge controversy surrounding this should make clear that any model is no more accurate than its assumptions. It also shows that system dynamics is less helpful as a method of long-term prediction than as a focal point for community discussion and strategizing.

   In the early 1990s, while attending a meeting on international trade, Meadows compiled a typology of leverage points [Me2]. One of her key observations was that less effective interventions tend to be quantitative—essentially, turning knobs—while more effective ones involve restructuring the system, or changing its entire goal. Many, but by no means all, of her leverage points are neatly framed in the language of system dynamics:

   https://donellameadows.org/archives/leverage-points-places-to-intervene-in-a-system/

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   [Me3] Meadows, D. H. 2008. Thinking in Systems: A Primer. Edited by Diana Wright. White River Junction, VT: Chelsea Green Publishing.

   [Me2] Meadows, D. H. (1999). Leverage points: Places to intervene in a system. Hartland, Vt., The Sustainability Institute, 1999. Available at https://donellameadows.org/wp-content/userfiles/Leverage_Points.pdf

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     Hobson Lane (hobs@mstdn.social)'s status on Thursday, 07-May-2026 03:09:54 JST Hobson Lane

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     @johncarlosbaez
     sounds like "Dynamics and Controls" in Mechanical Engineering. Or "Social Evolutionary Dynamics" in Biology programs. Or Game Theory in computer science. Or all 3. Definitely not Economics, though, i cant find any science or math in Economics

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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 07-May-2026 03:09:55 JST John Carlos Baez

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     CONCLUSIONS

     System dynamics seeks to be a general framework for thinking about both social and biological systems. We need to develop it more, and fast, for it to be useful in time. But it is already a useful tool for taking lessons from nature and applying them to the world we now inhabit. It is not so much a formalism for making long-range predictions about what *will* happen, as a way to find what *can* happen, and seek leverage points. Rather than a tool for top-down management, it is a tool we can all use.

     .....

     Okay, that's the end of this long series! This was just a draft of what I'm writing, and I feel it needs another pass. It doesn't quite come together the way I want, tightly tying together the themes of *learning from nature* and *system dynamics*.

     Thank you for your attention to this matter.

     (10/n, n = 10)

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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 07-May-2026 03:09:56 JST John Carlos Baez

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     Leverage exploits "tipping points": critical points beyond which a significant and often unstoppable change takes place. There is already extensive work on how our interventions in the biosphere may trigger unwanted tipping points, and how to spot these before they happen, for example through the slowing of the return to equilibrium after perturbations [Sc]. We have learned much about tipping points through observations of the natural world. But now researchers are starting to apply these lessons to “positive tipping points”: ways in which social and biological systems can fall into better states [Ot,Ta]. Farmer and others have called for more research on these [Fa], and it will be important to integrate them into the theory of system dynamics.

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     [Sc] Scheffer, M. (2009). Critical Transitions in Nature and Society. Princeton, NJ: Princeton University Press.

     [Ot] Otto, I. M., et al. (2020). Social tipping dynamics for stabilizing Earth’s climate by 2050. PNAS 117(5), 2354-2365. https://doi.org/10.1073/pnas.1900577117

     [Ta] Tàbara, J. D., et al. (2018). Positive tipping points in a rapidly warming world. Current Opinion in Environmental Sustainability 31, 120-129. https://doi.org/10.1016/j.cosust.2018.01.012

     [Fa] Farmer, J.D., et al. (2019). Sensitive intervention points in the post-carbon transition. Science 364(6436), 132-134. https://doi.org/10.1126/science.aaw7287

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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 07-May-2026 03:09:57 JST John Carlos Baez

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     The most impactful leverage points of all, items 1-4—namely mindset, goals, distribution of power and rules—are also the hardest to formalize and study systematically.

     Nonetheless, these were an explicit focus of the 2019 Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services Global Assessment and its follow-on synthesis [Ch], which list eight leverage points for saving biodiversity. The focus was on high-impact forms of social transformation, such as change in mindset. For example, one was “visions of a good life”: visions that downplay GDP growth and focus on trust in neighbors, access to care, opportunities for creative expression, and the like. These are difficult to quantify, but they may be very important for significant change!

     (6/n)

     [Ch] Chan, K.M.A., et al. (2020). Levers and leverage points for pathways to sustainability. People and Nature 2(3), 693–717. https://doi.org/10.1002/pan3.10124

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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 07-May-2026 03:09:58 JST John Carlos Baez

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     But a general theory of structural changes in a network that can dramatically transform its behavior in a chosen way seems to be in its infancy. New research on the mathematics of building networks from smaller parts [Bae,LPMO] and the emergent feedback loops that result [BC] may be helpful here.

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     [B] Baez, J.C. (2025). Double categories of open systems: the cospan approach. To appear in Applied Categorical Structures. Available at https://arxiv.org/abs/2509.22584

     [LPMO] Li, X., Patterson, E., Mabry, P. L., & Osgood, N. D. (2025). Compositional system dynamics: the higher mathematics underlying system dynamics diagrams and practice. Available as https://arxiv.org/abs/2509.18475

     [BC] Baez, J.C. & Chaudhuri, A. (2026). Motifs and emergent feedback in labeled graphs. To appear in Compositionality. Available at https://arxiv.org/abs/2506.23375

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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 07-May-2026 03:09:59 JST John Carlos Baez

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     There is by now a useful quantitative theory of items 7-9 on Meadows’ list: that is, the effects of parameters and feedback loops. There are methods to find feedback loops and predict the response of a system to changes in the strength of its feedback loops [G,Ka], determine which nodes in a network have most control over its overall behavior [LSB], and infer parameters from observed data [ROO].

     Less is known about the more impactful items 5 and 6: that is, the response of a system to changes in its structure, such as adding or removing a feedback loop. Important work has been done, from Mason’s gain formula [Mas], to results putting fundamental limits on what additional feedback loops can achieve [SBG], to work on “food web rewiring” of ecosystems in a changing world [Bar,Ma].

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     [G] Goncalves, P. (2006). Eigenvalue and eigenvector analysis of dynamic systems. Proceedings of the 2006 International System Dynamics Conference. Albany, NY: System Dynamics Society. https://proceedings.systemdynamics.org/2006/proceed/papers/GONCA394.pdf

     [Ka] Kampmann, C.E. (2012). Feedback loop gains and system behavior. System Dynamics Review 28(4), 370–95. https://doi.org/10.1002/sdr.1483

     [Mas] Mason, S.J. (1953). Feedback theory: some properties of signal flow graphs. Proceedings of the IRE 41(9), 1144–56.

     [Bar] Bartley, T.J., et al. (2019). Food web rewiring in a changing world. Nature Ecology & Evolution 3(3), 345-354. https://doi.org/10.1038/s41559-018-0772-3

     [Ma] Ma, A., et al. (2025). Network rewiring conserves the topology of drought-impaired food webs. Communications Biology 8(1), 1641. https://doi.org/10.1038/s42003-025-09035-2

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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 07-May-2026 03:10:00 JST John Carlos Baez

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     Some, but by no means all, of these leverage points can be neatly framed in the language of system dynamics. This is easiest for items 5-9. Parameters and the strengths of positive and negative feedback loops can be read off a stock and flow diagram. Similarly, positive and negative feedback can be read off from a causal loop diagram. What Meadows calls “material flows” are simply what we call “flows” in a system structure diagram, while her “information flows” are called “links”. On the other hand, items 1-4—paradigms, goals, distributions of power and rules—are not visible in any of the diagrammatic models used in system dynamics. They are more difficult to precisely define.

     Meadows described her list as hastily drawn up, based on personal experience, and subject to revision [Me2]. Given this, we might hope for it to be merely the seed for an extensive theory of leverage points, rigorously formulated and experimentally tested.

     Unfortunately this is not yet quite the case! While her ideas have been further developed [Mu,MuJ], there is still much to be done to understand leverage points.

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     [Me2] Meadows, D. H. (1999). Leverage points: Places to intervene in a system. Hartland, Vt., The Sustainability Institute, 1999. https://donellameadows.org/wp-content/userfiles/Leverage_Points.pdf

     [Mu] Murphy, R. J. A. (2022). Finding (a theory of) leverage for systemic change: A systemic design research agenda. Contexts: The Journal of Systemic Design 1. https://systemic-design.org/contexts/vol1/v1004/

     [MuJ] Murphy, R. J. A., & Jones, P. H. (2020). Leverage analysis: A method for locating points of influence in systemic design decisions. FormAkademisk 13(2), 1–25.

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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 07-May-2026 03:10:01 JST John Carlos Baez

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     4) The rules of the system (incentives, punishments, constraints). These are the agreements that fix the system’s scope, degrees of freedom, and what counts as a legitimate move. They sit above parameters and information because they determine which parameters exist and which channels of information matter.

     3) The distribution of power over the rules of the system. This refers to who gets to write, change, interpret, and enforce the rules. Control over rule-making is more consequential than any particular rule, because it governs how the entire rule set can evolve.

     2) The goals of the system. These are what the whole system is actually optimizing for. A shift in goal cascades downward: stocks, flows, feedbacks, rules, and even the distribution of power reorganize to serve it.

     1) The mindset or paradigm. This is the deep, usually unstated view of how reality works from which goals, power structures, rules, and culture all descend. Changing this is the most radical intervention available, and also the one most fiercely resisted at the collective level.

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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 07-May-2026 03:10:02 JST John Carlos Baez

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     In order of increasing effectiveness, this is her original list of nine kinds of leverage points (which she later expanded to twelve):

     9) Constants, parameters, numbers. These are numerical settings—rates, standards, thresholds, quotas, etc. They absorb enormous attention but rarely change a system’s fundamental behavior.

     8) Negative feedback loops. These are self-correcting mechanisms that pull a stock back toward a goal whenever it strays.

     7) Positive feedback loops. These are self-reinforcing mechanisms where more produces more. Reducing the gain on a runaway positive loop is typically a more powerful intervention than strengthening whatever negative loop is trying to contain it.

     6) Material flows. These are the physical plumbing of the system. Once built this is expensive and slow to change, so the leverage is concentrated in the original design; afterward one mainly works around its bottlenecks.

     5) Information flows. Who sees what, and when. Delivering the right signal to the right actor at the right moment is often cheap relative to rebuilding physical structure, and missing information is one of the commonest causes of malfunction.

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