A MOVABLE CHART OF SEMANTIC SPACE
Lensball.
One neighborhood at a time. A fixed universe underneath.
A discrete Lensball, with an explicit motion rule
The source is a frozen, corpus-fitted TF–IDF / 48-dimensional SVD model of wiki articles. It is a lexical embedding, not a pretrained neural model. No vectors are recomputed while exploring. Each marker retrieves its original page ID and captured revision.
The lens state is a unit center c and two orthonormal tangent axes u, v in the original vector space. A drag gives t = normalize(−Δx u + Δy v); the center and frame rotate together in the (c, t) plane by the drag angle. This parallel-transports the frame along each great-circle step, so orientation can depend on your path. Search and minimap jumps use the shortest great-circle route. Reset restores the initial frame. Drag alone explores the great 2-sphere spanned by the current frame; search and minimap jumps reach other source directions.
Selection uses angular distance acos(c·x), equivalent to cosine ranking. Source angle sets the radius on the front hemisphere; the tangent projection sets the bearing. Fade at the neighborhood edge keeps crossings continuous. Hidden dimensions lose geometry, and projected bearings can degenerate; points with vanishing tangent projection fade out. Local stress is normalized pairwise spherical-distance error after fitting one scale, measured on the displayed set. Lower is better; it is not a guarantee of fidelity.
The minimap is a fixed two-component PCA of the same vectors. White cross = lens center, gold ring = selected article, colored points = current neighborhood. Its projection can overlap or hide distances; it supplies orientation, not the navigation metric. Read the Lensball article ↗