Cognitive Scaffold

Preparing your thinking workspace

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MENTAL MODEL · M4591

Gibbs Phenomenon

Gibbs Phenomenon
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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

When using a continuous waveform to approximate a signal with a sudden change (discontinuity), there will be unavoidable overshoot and oscillation near the point of change, no matter how perfect the algorithm.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

Predict overreaction during transitions. When society or organizations undergo drastic transformation (discontinuity), do not expect a smooth transition. Initial overcorrection (overshoot) and repeated oscillation are mathematical necessities. When you see chaos, do not panic; it is the Gibbs glitch in the waveform fitting process.

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When using a finite Fourier series (or any smooth basis) to approximate a signal with a jump, there will be a fixed overshoot of about 9% near the jump point, which does not disappear as the number of terms increases (it only narrows). The essence is the structural cost of 'approximating discontinuity with continuous/smooth functions'. Metaphorical implication: drastic transformation (discontinuity) inevitably brings local overshoot and oscillation, which are inherent glitches of the approximation process, not execution errors.

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Source support: Explicit

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    zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E5%90%89%E5%B8%83%E6%96%AF%E7%8E%B0%E8%B1%A1ZH · Explicit
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