ScaleTrip methodology

A comparison you can reproduce

Start with a selected distance of 10 km. The reference dataset gives Mount Everest’s height as 8.85 km (height). The calculated length ratio is 10 ÷ 8.85 = 1.13×.

The input is the user’s chosen distance; the reference is a mountain height; the ratio is a derived calculation. Keeping these separate prevents a 10 km input from becoming a false measurement of Everest.

nearest = arg min |log₁₀(d / r)|
ratio = d / r

The nearest-reference rule compares logarithmic distance, so twice as large and half as large are equally far away. A match tells you which listed length is nearby; it does not make a walking route, altitude and diameter interchangeable.

From an input to a result: a reproducible method

Use the catalogue’s measurement definition and evidence role alongside the number. Unit conversion is exact when its definition is exact; a calculated ratio still inherits the limitations of its input values. This documentation describes the maintained production implementation, rather than a replacement animation algorithm.

Download the typed reference catalogue · Download current calculation-code excerpts · Catalogue version 8bb5fc4729cd.

Normalize length in SI units

d_m = d_km × 1,000
d_m = d_mi × 1,609.344
d_m = d_µm × 10⁻⁶ = d_nm × 10⁻⁹

Macro input accepts positive finite lengths inside its configured 1 m to 93 billion light-year display range; out-of-range input is rejected rather than silently clamped. Micro maps supported unit prefixes to metres, then uses a 1 m to 10⁻²⁰ m camera range. Those are interface limits, not newly established physical bounds.

Match ratios, not absolute gaps

Δ_i = |log₁₀(d) − log₁₀(r_i)|
nearest = arg min_i Δ_i
ratio = d / r_nearest

The numerical Macro result loops over the actual 71-entry catalogue. A strictly smaller logarithmic difference replaces the current match; an equal difference retains the earlier catalogue entry. Lower and upper references use strict numeric inequalities. Exact match absorbs only floating-point round trips: |r − d| ≤ max(r,d) × Number.EPSILON × 8. A visualization label has separate 0.045-log hysteresis to avoid flicker; this does not alter the numerical nearest-reference result. Micro uses the same strict logarithmic nearest rule on its 54-entry descending catalogue, after camera-range clamping.

Equal logarithmic distance means equal factors: 2r and r/2 are equally far from r. For adjacent positive reference lengths a and b, the theoretical changeover is their geometric mean √(ab); floating-point arithmetic decides a computed tie.

Separate screen compression from physical scale

p = (log₁₀d − log₁₀d_min) / (log₁₀d_max − log₁₀d_min)
δ = log₁₀r − cameraLog
I(δ) = exp[−0.5(δ / 0.34)²]

Macro uses camera-relative logarithmic distance and a continuous nominal 0.5–1.35 artwork scale, uniformly reduced when needed to fit the stage below the ruler. It reserves the width of each image and caption before placing the next reference, then interpolates the camera between them. This spacing keeps illustrations separate; it is a browsing layout. The two labelled bars use a common linear scale and the actual input/reference length ratio. Measurement definitions remain attached to each reference. Micro crossfades two scenes, with outgoing artwork scale 1→4.6 and opacity fading over local progress 0.34→0.78; this preserves a continuous journey without treating the artwork as a microscope image. The Moon teaching experiment is different: its diagram uses one common linear scale for diameters and separation.

Worked examples with stated inputs

Uncertainty and meaningful precision

The current comparison engine computes central values only; it does not propagate measurement uncertainty automatically. Missing uncertainty stays unknown. A default min=max in software is not evidence of zero error. Biological display bands are illustrative, and collider bounds are model-dependent constraints, not Gaussian errors.

For the chosen hair band alone, 50–100 µm divided by a fixed 2 nm gives 25,000–50,000. This is an illustrative sensitivity interval, not a confidence interval and not a population limit. More decimal digits from division do not add physical precision.

Reproduce the exact selection rule

The excerpt below is extracted from the maintained Macro source during build, rather than retyped. It expects the existing references array. The catalogue publishes reviewed values; unresolved values remain in the public visualizer’s app.js configuration but are withheld from the scientific distribution. Use the browser runtime when reproducing selection over all 71 software entries, and keep that distinction explicit.

function findContext(meters) {
  let nearest = references[0];
  let lower = null;
  let upper = null;
  let exact = null;
  let nearestDifference = Infinity;
  for (const reference of references) {
    const difference = Math.abs(Math.log10(meters) - Math.log10(reference.distanceMeters));
    if (difference < nearestDifference) { nearest = reference; nearestDifference = difference; }
    // Only absorb floating-point round trips, not visibly nearby values.
    if (Math.abs(reference.distanceMeters - meters) <= Math.max(reference.distanceMeters, meters) * Number.EPSILON * 8) exact ||= reference;
    if (reference.distanceMeters < meters) lower = reference;
    if (reference.distanceMeters > meters && !upper) upper = reference;
  }
  return { lower, nearest, upper, exact };
}

Use the worked Earth–Moon, hair/DNA and atomic comparisons to check these formulas with their primary sources. The Earth-interior experiment uses PREM density coefficients, spherical mass integration and hydrostatic pressure; its pressure/gravity outputs are model estimates and its P/S strip is a qualitative teaching model.

Earth–Moon model · Hair and DNA · Atomic length and charge radius · Seismic evidence and PREM