Push the vector idea to its limit and you get a Hilbert space: a vector space with an inner product, where you can measure the angle between any two points. Meaning stops being a list of attributes and becomes geometry — and similarity collapses to one number, the cosine of that angle.
It’s a strange comfort that “how alike are these two ideas?” reduces to a dot product. The embedding model places everything in the space; the inner product reads the closeness. Cybermeticism’s synthesis Σ(E) is the same move — a weighted blend of points resolved to a single position.
Links from this note
Evidence · meaning as geometry
The equation as geometry — K is constancy interpolated by age; the perceived envelope is C(Σ). Position is meaning, distance is similarity.
How it has been tended
Planted — meaning as geometry, similarity as cosine.
drift: The math may alienate; keep it intuitive.
Moved the map into the same 3D field — meaning as geometry, for real. The six families settle into their own regions and the bridges between them light up as gradient links, fading one family's color into the next. Hover a word to trace its web; click to focus and open it.
drift: Distinct lobes help, but the densest hub still crowds its labels.