The Shape of the Abstraction Space
Every prime and domain-specific abstraction, and the … canonical origin domains they call home, arranged so that similar structure sits close together. The four views below are one instrument — select a domain in any of them and the others follow.
Domain map
Domains whose abstractions have similar structural signatures sit near each other; bubble area is how many abstractions call the domain home. Click a bubble (or a row in the table) to select a domain: the others fade with measured distance — solid means structurally close, faint means far — and every view on the page follows. Scroll to zoom, drag to pan, double-click to reset. The fading, the lines, and the distance bands are explained under How the distances work, just below.
Nearest domains from
The selected domain's measured neighbors, nearest first. Distance is the raw number; Band puts it in context — both are explained under How the distances work, just below.
How the distances work
Distances from Distance matrix — all … pairs
Every domain's measured distance from the selected one — nearest first within each domain group, with the group header showing the group's average. Click any domain to re-anchor the profile; the full 65 × 65 grid is behind the toggle above.
Every domain against every domain in one grid, rows bundled into the eight canonical domain groups. The grid is symmetric — reading across a row or down a column gives the same numbers.
How to read it: pick a row and scan across — each cell is that domain's measured distance to one other domain; light means the two domains' abstractions have similar structural signatures, dark means they have little in common. The pale blocks along the diagonal are groups holding together internally; a mostly-dark row is a domain unlike nearly everything else; a pale patch away from the diagonal is two groups quietly sharing structure. Hover any cell for the exact pair; click a cell or a label to select that row's domain.
All … abstractions
Every abstraction as one dot — blue for primes, orange for domain-specific — laid out by the same structural similarity. This is the raw cloud the domain bubbles above summarize; hover a dot to identify it, click one to select its domain, and the selected domain's members light up.
Why two lobes? The honest answer is: mostly the corpus's own history, not a divide in human knowledge. The gap cuts across subject matter — mathematics alone has hundreds of entities on each side — but which lobe an entry lands in tracks when it joined the corpus almost perfectly: one lobe holds nearly every prime together with the longest-curated domain-specific entries, while the other is filled by the recent Wikipedia-mining campaign. The likeliest reading is that each authoring generation describes structure in its own style, and the embedding hears that accent alongside the structure itself — a caution worth carrying into any fine-grained reading of this cloud.
And the tight blue knot? The same caution, seen from the other side. In the full 384-dimensional space the primes are not unusually compact — they spread about as widely as the longest-curated domain-specific entries, and the recent additions are in fact the tightest population of all. The knot is the flattening at work: these two axes are the directions along which the domain-specific population varies most and the primes vary least, so the projection piles the primes into one spot. The most striking shapes in this picture are statements about the projection as much as about the space.