Why can a thermostat (or a body) hold steady, but a microphone near its speaker screams?
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After you watchWhy can a thermostat (or a body) hold steady, but a microphone near its speaker screams?
The short answer
Feedback direction and strength both matter. A correcting loop can settle an error, but a correction larger than twice the current error can make this simple discrete model oscillate farther away each turn.
Try this next
- What happens at 200% correction? Predict, set the right control to 200%, and watch whether the error shrinks, grows, or keeps its size.
- Does 100% correction overshoot? Set 100% and track the first correction turn.
- How can 250% make the error worse? Start one unit from the target and draw a 2.5-unit correcting move. Measure the new error on the other side.
Now you — bend it
- What if What if the right correction is 100%?Track how much error is left after the first turn.
- What if What if it is 200%?Compare size and sign separately.
- What if What if it is 175%?A correcting move of 1.75 error units leaves 0.75 on the other side.
Can you prove it?In this model, 200% correction keeps the error size unchanged. — Set the right control to 200%. Compare the error readouts over all eight turns and notice that the line keeps switching sides.
Design your own test:Before you flip the switch, predict out loud whether this loop will hold steady or rocket off the chart — then run it and check.
Explain it to a 6-year-old: Some loops push a wobble back so it calms down, and some loops make the wobble bigger and bigger until it screams.
The whole story
How it works
The introduction contrasts correcting and amplifying feedback. The hidden application uses two correcting controllers with exactly the same update: new error = old error minus correction fraction times old error. At 150%, each correction crosses the target and halves the error. At 250%, it crosses and leaves one and a half times the previous error. Normal and calm tellings use identical discrete turns.
What people get wrong
Correcting direction alone does not guarantee stability. Overcorrection can make a negative-feedback system oscillate farther away each turn. Correction size matters as well as direction.
The catch
Feedback can reject disturbances, but excessive correction, delays, and other system dynamics can cause oscillations or instability. This simple discrete model isolates correction strength; it is not a detailed thermostat or microphone model.
Questions kids ask
Why can correcting toward a target make the error grow?
A move can cross the target. If it crosses too far, the new error on the other side is larger than the old one.
What happens at 200% correction?
Each move crosses the target by exactly the previous error. The sign switches, but the size remains unchanged in this model.
What happens at 100% correction?
One move covers exactly the error and reaches the target. Later turns have zero error to correct.
Talk about it
- Guess first: name something at home that pushes back to stay steady, and something that piles on and grows. What makes them different?
- If a tiny nudge can explode in one loop but fades in the other, what do you think really decides which one happens?
- Where have you seen a snowball or a rumor or a fire start from almost nothing and grow huge — and what finally stopped it?
For grown-ups
The hidden model uses x_next = (1 − g)x. At g=1.5, the signed error reverses and its magnitude halves each turn; at g=2.5, its magnitude grows by 1.5. At g=2, it alternates without shrinking. Real feedback systems also include delays, inertia, and saturation, so negative feedback does not by itself guarantee stability.
Keep going
What else makes you wonder?
- Your body holds a steady temperature like a thermostat — what other things inside you might be quietly pushing back to stay steady?
- A snowball turning into an avalanche is a pile-on loop — what tiny thing have you seen grow huge from almost nothing?
- If a microphone screams until the speaker hits its loudest limit, what real-world pile-on loops finally run out of room to grow?