Loops That Amplify, Loops That Correct

Online, with a lab for each exercise: thinking-in-diagrams.aryehnielsen.com

Causal loopsPart II · Feedback · Chapter 4 of 12 · the first of two chapters on causal loops

• A change seems to feed itself.
• Something keeps drifting back to where it was, however hard anyone pushes on it.
• A fix worked for a while, then stopped, or began working against you.
• An explanation’s becauses run in a circle.
• People disagree about what causes what, and arguing hasn’t settled it.

A deadline costs you two nights’ sleep. Foggy on Wednesday afternoon, you have a coffee at three, finish the job, and lie awake until one. On Thursday, foggier, you have a double at two. By Friday the caffeine has you sleeping five hours a night.

At the weekend, noticing how tired you are, you go to bed at nine two nights running, and by midweek you’re yourself again.

One change fed itself: less sleep, more coffee, less sleep. The other corrected itself: the further behind you fell, the harder you caught up, until there was nothing left to catch up on.

Every name on the diagram is a variable: a quantity that can rise or fall, such as sleep debt or hours slept.

That rules out actions and events. Test a name by putting more in front of it: more afternoon caffeine makes sense; more drink coffee doesn’t. Naming a variable as an action is the bad diagram’s mistake.

An effect means that a change in one variable causes a change in another; its polarity shows which way. A + effect means they move in the same direction: more sleep debt, more afternoon caffeine. A − effect means they move in opposite directions: more afternoon caffeine, fewer hours slept.

+ doesn’t mean good and − doesn’t mean bad, and neither gives size: caffeine might cost ten minutes of sleep or two hours.

In a causal loop diagram every effect carries a polarity; an influence claim thinking-in-diagrams.aryehnielsen.com/framing/surfacing-influences/#influence-claims, drawn in an influence map, carries none until it is upgraded to a causal claim.

Sleep debt raises afternoon caffeine, caffeine cuts hours slept, and fewer hours slept raise sleep debt. A closed path of effects like this is a loop. A chain shows how one thing affects another; a loop shows how a thing ends up affecting itself.

A reinforcing loop makes a change snowball, in whichever direction it starts: debt brings coffee and more debt, but a good night likewise brings less coffee and another good night. A balancing loop makes a change settle, moving a variable toward a target and opposing any push away from it: the further behind on sleep you fall, the harder you try to catch up.

Each loop’s label, drawn inside it with a curved mark showing which way it circulates, is its kind and a number: R1, R2 for reinforcing loops, B1, B2 for balancing ones. Its name describes what it does, not what it’s about: spiral, not coffee.

The parity rule: a loop with an even number of − effects is reinforcing, and one with an odd number is balancing. Zero counts as even.

Each − effect reverses a change passing through it. Two reversals cancel, so the change comes back pointing the way it set out, and grows; one or three leave it pointing against itself, and it shrinks.

For the spiral, the lab’s check gives this working:

R1 (spiral) has 2 − effects (afternoon caffeine → hours slept, hours slept → sleep debt): an even number, so it is reinforcing, as declared.

At planetary scale, less Arctic sea ice reflects less sunlight, so the ocean warms, and warmer water melts more ice: again two − effects, so reinforcing.

A balancing loop closes a gap: the difference between the value someone wants and the value they have. Here it’s sleep debt, the sleep you need minus the sleep you get.

Draw it as its own variable, fed by the target from outside the loop. That shows the loop’s target, and raises two questions about any balancing loop: who set it, and could it move?

In a feedback control diagram, the words target, gap and measured value (the reading the target is compared with) are written above the names of the variables in those parts, and a person chooses the target: chapter 8’s target and gap thinking-in-diagrams.aryehnielsen.com/control/sense-compare-correct/#target-and-gap.

A delay, two short strokes across an effect, means that the change arrives later than the cause: late enough to change what the loop does. Sleep debt builds for days before anyone acts on it, so the effect from sleep debt to early nights carries a delay, and the spiral, whose changes arrive within a day, gets a head start.

In a balancing loop with a delay, the correction continues after the gap closes; the variable overshoots its target and oscillates instead of settling.

In a stock & flow diagram, a delay on a flow holds material in transit and a delay on a signal holds a reading of the material: chapter 7’s material and signal delays thinking-in-diagrams.aryehnielsen.com/accumulation/stocks-inside-feedback/#material-and-signal-delays.

A behavior note names, on the diagram, the behavior you expect the structure to produce: oscillation, overshoot, decline, then recovery. It makes the diagram a prediction: if what happens differs, the structure you drew is missing something.

Loops that share a variable are coupled: a change in one loop changes the other. In the full sleep diagram, the spiral and catching up share sleep debt, hours slept and the effect between them.

Which loop dominates depends on which is stronger at the time: early in the week, the spiral; once the debt is felt, catching up.

A leverage point is a variable proposed as the place to intervene, drawn as a box with a question mark on each side. In the sleep diagram it’s afternoon caffeine: cutting it weakens the spiral and leaves the slow balancing loop less to correct.

It’s a hypothesis, not a proven fix: someone else might propose early nights, arguing that noticing the debt sooner would help more. Either proposal can be tested against the diagram.

A causal loop diagram shows structure only, not size: when amounts decide the question you need numbers, which chapter 6’s stocks begin to supply.

Nor does it show sequence: for the order in which things happen, use a numbered list. A loop diagram of a sequence is the bad diagram’s mistake.

Nor everything: the sleep diagram leaves out stress, exercise and the deadline, keeping only the loops that explain the behavior in question.

When nothing feeds back, a sentence does the job.

What’s wrong with this diagram of keeping a household pantry stocked?

Its structure is sound: a closed loop, one − effect, labeled B1, a delay on the right effect. But its names, stock the shelves, order groceries and receive the delivery, are actions done in order and fail the more test, so the diagram is a to-do list bent into a circle, and its polarities mean nothing: what would more receive the delivery cause?

In the lab it passes every check, with a notice on each of its three names.

The correction keeps every effect, every polarity, the delay and the loop, and renames the three variables as quantities.

Now each effect is a checkable claim: more food in the pantry, fewer groceries ordered (−); more ordered, more delivered a few days later (+, delayed); more delivered, more food in the pantry (+). One − effect, so the loop is balancing: it holds the pantry near full. With the delay: reorder before the first delivery arrives and the pantry overfills.

Passing the checks means meeting the brief, not being right.

• Donella H. Meadows, Thinking in Systems: A Primer (Chelsea Green, 2008), chapter 1, on reinforcing and balancing loops, and chapter 2, on delays.
• Donella H. Meadows, Leverage Points: Places to Intervene in a System donellameadows.org/archives/leverage-points-places-to-intervene-in-a-system/ (Sustainability Institute, 1999), on leverage points.
• John D. Sterman, Business Dynamics: Systems Thinking and Modeling for a Complex World (Irwin/McGraw-Hill, 2000), chapter 5, on causal loop diagrams: polarity, a loop’s kind, delays, and naming variables as nouns rather than actions.
• John D. Sterman, “System Dynamics Modeling: Tools for Learning in a Complex World” doi.org/10.2307/41166098, California Management Review 43, no. 4 (2001), a short introduction to the same ideas.
• George P. Richardson, “Problems with Causal-Loop Diagrams” doi.org/10.1002/sdr.4260020207, System Dynamics Review 2, no. 2 (1986), on what polarity does and doesn’t mean.
• National Snow and Ice Data Center, Why sea ice matters nsidc.org/learn/parts-cryosphere/sea-ice/why-sea-ice-matters, on why melting ice speeds further melting.