Entropy tends to Zero, at the Boundaries

Testing Indistinguishability – If you make a math test too easy, you can’t distinguish between your students because everyone scores full; likewise, if you make it too hard, you still can’t distinguish as every scores a zero.
Evaluation – If you tend to evaluate all employees too leniently, you tend to lose differentiation and end up subverting the purpose of the evaluation. Likewise, for being too strict.
Relationships – If you give your wife too little money, or give her too much, either way the marriage doesn’t work.

The Sorites‐style triviality – If you grant every borderline case of “heap” to be a heap (or deny them all), the paradox disappears—but so does any ability to mark a meaningful boundary.
Explosion in classical logic – Once a system contains one contradiction, anything whatsoever follows. Proof then distinguishes nothing: every statement is provable.
Radical egalitarian distributions – A rule that every person must have exactly the same goods under all circumstances blocks any comparison of outcomes; utility differences are driven to zero, so welfare criteria cannot rank states of the world.

Ceiling / floor effects on Likert or IQ tests – Items that everyone endorses (“2 + 2 = 4”) or no one can solve supply no variance; factor analysis literally drops them.
Weber–Fechner saturation – At very low intensities a light is invisible; at very high intensities it is blinding white. In either case the retina delivers no graded signal about brightness differences.
Go/No-Go tasks with extreme deadlines – If the deadline is extreme, participants either always respond (liberal setting) or never respond (conservative setting); d′ collapses to zero.

The Laffer curve endpoints – At a 0 % tax rate and a 100 % tax rate, revenue is 0; fiscal authorities gain no information about elasticity of the base.
Price ceilings/floors set far from equilibrium – A binding ceiling below marginal cost causes chronic shortages; a sky-high floor causes chronic surpluses. In both states the observable quantity traded is pinned, concealing buyers’ real valuations.
Perfect insurance / infinite risk aversion – With complete actuarial insurance or absolute dread of risk, marginal willingness to pay for additional risk reduction flattens to zero.

Photographic exposure – Zero exposure yields a black negative; massive over-exposure yields a clear sheet. Neither reveals anything about the subject.
Sensor saturation – An accelerometer pegged at 0 g or its maximum rating can no longer differentiate small jolts or additional shocks.
Thermistor extremes – Resistance at cryogenic or red-hot limits flattens, so temperature differences are undetectable.

pH indicator bands – Litmus is uninformative below ≈4 (always red) or above ≈8.3 (always blue).
Titrations past equivalence – Once the end-point is overshot, extra titrant produces the same colour, masking concentration differences.

Michaelis-Menten plateaus – With [S] ≪ Km, reaction rate ≈0; with [S] ≫ Km, rate maxes at Vmax. Small changes in enzyme amount are invisible at either edge.
Drug‐response sigmoids – Sub-therapeutic doses and fully saturating doses both show little incremental change; dosage differences matter only in the middle.
Epidemiology: herd immunity extremes – In a fully susceptible or fully immune population, R₀ estimation from new-case counts is impossible.

Classifier thresholds at 0 or 1 – Predicting the positive class for every case or for none gives 100 % recall or 100 % specificity but zero discriminatory power (AUC = 0.5).
Biometric Systems – A face recognition or other biometric system with a very low threshold will match everyone erroneously, and one with a very high threshold will never match at all.
Hash functions with tiny output spaces – If the range is only one bucket, every key collides; if it equals the number of keys, collisions never occur but distribution information is lost for compression and similarity search.

Zero-variance variables – Any variable with the same value for all observations drops out of regression; its coefficient is undefined.
Uniform priors on unbounded supports – A truly flat improper prior cannot update likelihood ratios; posterior equals likelihood up to scale, giving no Bayes factor differentiation.

Phoneme distinctions at extremes of VOT – Below a few ms and above ~100 ms, listeners hear categorical /b/ or /p/ with perfect certainty; fine gradations vanish.
Writing systems stripped to all-caps or no capitals – Losing case distinction removes a common cue for proper nouns, titles, and sentence starts.

Amplitude extremes in mixing – Tracks mixed at −∞ dB are inaudible; at 0 dB full-scale they clip to a square wave. Either way nuances of timbre disappear.
Tempo detection – At very slow or very fast tempi, beat-tracking algorithms assign the same default (half-time or double-time) pulse to all songs, erasing stylistic differences.

Contrast extremes in drawing – Pure white on white or black on black canvases (e.g., Malevich’s White on White) intentionally erase form; the viewer cannot discern compositional variation.
Pixel art at maximal or minimal resolutions – One-pixel images or gigapixel mosaics both prevent the human eye from observing mid-scale structure.

Zero-tolerance versus total discretion – Mandatory minimums (everything punished) and no-enforcement regimes (nothing punished) both fail to express proportional condemnation or locate marginal deterrence.
Infinite vs zero damages in tort – Nominal $1 or punitive “rule-out-of-business” awards each prevent courts from signalling nuanced culpability levels.

Binary agree/disagree on complex attitudes – Opinions collapse to two piles, obscuring intensity gradients.
Social network density extremes – Fully connected (clique) or fully disconnected (isolate) graphs carry no information about relative centrality or brokerage.

Maximalist vs minimalist ritual calendars – If every day is a major feast or none are, distinctions of sacred time vanish; ranking of festivals is impossible.

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