Experiment 30
My notes have a coastline
My knowledge base is about 650 notes. Each one is turned into a point on a map1, and related notes land near each other, so the whole collection spreads across a sphere like settlements on a planet. That raised a question I could not let go of: where exactly does my knowledge end and emptiness begin?
I refused to draw the border by eye. First I measured how far apart points would sit if they were just sprinkled evenly at random, and used that distance as the yardstick for "empty". Tracing that yardstick around every note gives a shoreline, the same way a depth line on a nautical chart is traced at one fixed depth. Nothing hand-tuned, nothing to defend.
The first version looked like beads of water on glass, a neat circle around every lonely note. So I fixed the shape honestly: I tried three ways of drawing the coast, held the amount of land constant across all three, and measured every adjustment I added2. The final coastline is even wiggly in the same measurable way real ones are, a bit smoother than Britain’s3.
The map it draws turned out to be weirdly personal. One supercontinent carries my daily work in coding and engineering. My personal growth themes, discipline and self-taught learning, sit on their own continent dead center, separated from the work landmass by open sea.
From contour to geography
The parameter-free version first. The map already had an ocean calibration: the 99th percentile of probe gaps from a uniform lattice, 5.09 degrees at 646 notes. Geodesic distance4 to the nearest note, contoured at exactly that radius, is a coastline with no bandwidth and no density estimator, nothing to defend. Its honest price is shape: a union of fixed-radius caps, beads of water on glass.
The organic rule replaces the caps without touching the calibration. A softmin metaball field pools nearby notes into landmasses, a seeded domain warp erodes the edges, and Perlin fBm roughens the shoreline5. Every candidate rule is re-leveled to the same 48% land area, so the atlas numbers survive a change of temperament. A lone note stays round under any rule: an isolated note is an atoll.
Measuring the wiggliness needed an instrument correction. Box-counting returns impossible dimensions below 1 on an archipelago, because disconnected islands collapse into single boxes at coarse scales. The committed values use Mandelbrot's Richardson divider on the longest single coast: 1.09 to 1.11 across ruler lengths of 1.5 to 12 degrees, against Britain's roughly 1.25.
The atlas mechanics: continents are connected components of the land mask, merged across the longitude seam (the seam is where the map was cut open, not a coast), with areas weighted by cos(latitude). Labels sit at each continent's interior pole rather than its centroid, because a sprawling landmass centers over someone else's ocean. The largest continent carries 29.9% of the land: agentic coding workflows and systems engineering. And there is a reroll knob: seeded tangent jitter inside the field computation only, so the shoreline rerolls while the rendered notes never move.
- An "embedding": software that reads text and produces coordinates, so that similar texts get nearby coordinates. ↩
- The techniques come from video game terrain: nearby blobs pool together and edges get roughened so coasts read as geography instead of circles. ↩
- Coastline wiggliness is measurable (fractal dimension). Mine came out 1.09; Britain’s is famously about 1.25. ↩
- Geodesic distance: distance measured along the sphere's surface, the way a flight path curves, rather than in a straight line through it. ↩
- Terrain techniques from graphics literature: Perlin's gradient-noise fBm (1985, 2002), Musgrave's fractal terrain, and Quilez's domain warping, which bends the coordinate space before roughening it. ↩