The Penalties of Precision: a Scale-Space Lens

· 2 min read · Send your thoughts via twitter or mail.

(Continuing Why Effort Scales Superlinearly with the Perceived Quality of Creative Work)

Thesis. Hierarchical levels emerge from the verifier’s speed, accuracy, and the strength of coupling between parts. ”Precision is expensive” because (a) global coupling turns every micro-adjustment into a system-wide test and (b) slow or noisy feedback forces repeated iterations. The sharpest cost jump occurs in the final refinement stage where curvature and noise dominate. The core metrics I see are:

Coupling: How far a local change propagates. Weak → cheap; strong → expensive.

Curvature: How fast quality falls off from the optimum. Flat basins forgive; sharp peaks punish.

Oracle: The verifier’s latency L and noise σ. High L or σ inflates iteration count.

Acceptance volume: Fraction of parameter space that keeps quality constant. Shrinks with tighter tolerance and steeper curvature, so the success rate of random micro-edits plummets.

A good example is the threading of a needle: coarse aiming is quick; the last millimetre is limited by vision delay and hand tremor.Below is a table where the levels are slices that can emerge out of that scale-space.

BBT: Big Beautiful Table

LevelResolutionEXAMPLESCouplingCurvatureOracleVerification Loop
MusicWritingSoftwareFine ArtsLatencyFidelity
⚙ general pattern · ♪ music · ✎ writing · ⌘ software · ⚘ fine arts
StructureMacro
(hours–weeks)
Global form
Tempo map
Tonal centers
Motif inventory
Argument arc
Outline goals
POV/tense
Scene beats
System architecture
Module boundaries
Data model
Release roadmap
Composition
Theme/narrative
Palette
Canvas/scale
coupledflatinstantclean⚙ Pattern: Coarse oracles; fast previews; freeze interfaces; rubric A/B; decouple with mocks.
♪ form/tempo diff; structure A/B. ✎ outline rubric + storyboard TTS. ⌘ ADR + architecture smoke tests. ⚘ storyboard slideshow + value-study grid.
SectionMeso‑1
(tens of minutes)
Section roles
Cadence plan
Harmonic rhythm
Texture arcs
Paragraph groups
Claim–evidence plan
Topic sentences
Lexical fields
Feature spec
Flow diagrams
Schema design
Component contracts
Thumbnail sketches
Value studies
Color roughs
Block-in shapes
mixedflatinteractiveclean⚙ Pattern: Contract checks before content; guided section preview loops; mock data to cut coupling; schema lint.
♪ section-loop playback; cadence plan checker. ✎ topic-sentence map + paragraph TTS. ⌘ API/contract lint + mock service. ⚘ thumbnail set + color roughs.
Meso‑2
(minutes)
Phrase structure
Voice-leading
Register layout
Counter-melody
Sentence flow
Coreference
Emphasis ladder
Rhetorical devices
Function breakdown
State machine
Component skeletons
Test outline
Underpainting
Layer plan
Focal-path
Edge hierarchy
mixedflatinteractiveclean⚙ Pattern: Live stepping; instant preview sandboxes; gray-box tests; highlight focus/flow; second-order tweak sizing.
♪ MIDI/REPL phrase coach + voice-leading overlay. ✎ coref & emphasis heatmap; rhetorical flow sim. ⌘ state-machine stepper + fixture runner. ⚘ grayscale check; focal-path + edge-hierarchy overlays.
TokenMicro‑1
(seconds)
Note choices
Articulation
Velocity lanes
Ornaments
Sentence syntax
Clause order
Theme→rheme
Punctuation
Line edits
Naming
Extract function
Formatting
Brush strokes
Color mixes
Glazing
Highlights
decoupledmediumofflinenoisy⚙ Pattern: Deterministic normals (auto-format/lint) to reduce noise; safe refactors with preview; isolate layers/components.
♪ meter overlay + velocity lanes; articulation assistant. ✎ syntax/parse tree; prosody & punctuation assistants. ⌘ rename/extract with test-impact preview. ⚘ brush-stroke isolation; local color mixer.
Micro‑2
(sub-second)
Micro-timing
Tuning cents
Envelopes
Transients
Prosody
Syllable weight
Alliteration
Micropauses
Typing symbols
Auto-complete
Semicolons
Completion
Dabs
Hairlines
Texture
Spatter
decoupledsharpofflinenoisy⚙ Pattern: High-SNR analyzers; snap-to-constraints to respect curvature; microbench/HUD for jitter; metronomic guidance.
♪ oscilloscope & transient analyzer + click-track; cents-tuning meter. ✎ syllable-stress analyzer; micropauses; kerning pair guard. ⌘ perf microbench + jitter HUD; completion with lint gates. ⚘ stabilizers/snap lines; hairline/texture guards.
RenderPico
(microseconds)
EQ attack
Limiter ceiling
Reverb tails
Dithering
Line breaks
Kerning
Widows/orphans
Encoding
Bundling
JIT/inlining
Bytecode layout
Minification
Pigment grain
Paper fiber
Varnish
Halftone/DPI
decoupledsharpofflineok⚙ Pattern: Bit-exact oracles; golden-master diffs; null/ABX tests; deterministic builds; CI "render lints."
♪ spectrum & loudness norms; limiter/dither checks; tail-reverb null tests. ✎ hyphenation/kerning proof; widow/orphan sweep; encoding checks. ⌘ bytecode/bundle diff; minification/JIT layout diff; reproducible build check. ⚘ ICC/soft-proof; DPI/halftone checks; pigment/varnish proof sheets.

Model Structure

Work is the invariant loop: propose → evaluate → refine. “Levels” are scale-space slices: as coupling rises or the oracle slows/noisifies, edits shift from micro to macro.

Effort Heuristic

Effort∝C⋅κ⋅(L+σ)⋅ε−γ,γ>1\text{Effort} \propto \htmlClass{var-coupling}{\mathbf{C}} \cdot \htmlClass{var-curvature}{\boldsymbol{\kappa}} \cdot (\htmlClass{var-latency}{\mathbf{L}} + \htmlClass{var-noise}{\boldsymbol{\sigma}}) \cdot \htmlClass{var-precision}{\boldsymbol{\varepsilon}}^{-\gamma}, \quad \gamma > 1

C coupling, κ curvature/local gradient, L oracle latency, σ oracle noise, ε tolerated error. ("Precision is expensive.")

Two Regimes

  • Macro / Structural: global coupling dominates; acceptance volume is broad → chunky rewrites, mockups.
  • Micro / Refinement: curvature + oracle (L, σ) dominate; acceptance volume is tiny → many corrective micro-loops.

References

  1. [1] Shannon, C. E. (1959). Coding theorems for a discrete source with a fidelity criterion IRE Convention Record, 7, 142–163.
  2. [2] Fitts, P. M. (1954). The information capacity of the human motor system in controlling the amplitude of movement Journal of Experimental Psychology, 47(6), 381–391.
  3. [3] Todorov, E., & Jordan, M. I. (2002). Optimal feedback control as a theory of motor coordination Nature Neuroscience, 5, 1226–1235.
  4. [4] Witkin, A. P. (1983). Scale-space filtering Proceedings of the Eighth International Joint Conference on Artificial Intelligence, Karlsruhe, pp. 1019–1022.
  5. [5] Simon, H. A. (1962). The architecture of complexity Proceedings of the American Philosophical Society, 106(6), 467–482.
  6. [6] Strasser, M. (2025). Effort scales & acceptance volume
BibTeX Citation 
@misc{strasser2025,
  author = {Strasser, Markus},
  title = {The Penalties of Precision: a Scale-Space Lens},
  year = {2025},
  url = {https://markusstrasser.org/},
  note = {Accessed: 2025-11-13}
}