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Connections join points. Fibers show curved paths. Subsets show smaller shapes within the same map.
Connections join neighboring roots. Fibers show paths inside the S7 → S4 Hopf fibers. Both use the same fixed root IDs. These mathematical relationships do not establish shared meaning.
How Looking Glass uses these words
Find meanings sends your words to the dictionary service. Choose the definitions that fit, or leave a word open. Nothing is saved to your account. Review in my space keeps a temporary draft for you to review and save there. This view looks up dictionary definitions; it has no voice input or AI-written reply.
Fibers sends the 240 E8 representatives through the retained S⁷→S⁴ calculator. Beads follow a declared path inside each fiber. Connections shows their fixed E8 Coxeter-plane positions and mathematical neighbors. Subsets selects a named root system. Numbers preserve each root’s identity; different points can overlap in a projection.
After every word has a chosen, mapped definition, the result marked in Fibers follows the same calculator using the exact octonion product. The drawing and the clarification questions are separate outputs; neither establishes sentence meaning.
Color highlights possible dictionary meanings. Thin root-neighbor lines describe geometry. Stronger word links join consecutive chosen records in your sentence and appear only after you choose both definitions. Neither kind establishes equivalent meaning or agreement.
Dictionary wording was compressed into eight coordinates by the existing experimental atlas. Several senses can occupy one root. A root choice and its octonion product are not measurements of a person, consent, or truth.
Your response stays on this page. Changing words, language, or dictionary choices clears it. Review in my space separately keeps a temporary draft in this tab; it is not an agreement or a saved explanation.
Geometry, dictionary version & source hashes
{
"geometry": {
"schema": "looking-glass.e8-coxeter-geometry/v1",
"sourceFile": "E8 Coxeter Plane.html",
"sourceSha256": "2e0668f6764369e241acb36b9df7fed2770475264c59e117fd5bc357d2ab1eeb",
"sourceBytes": 45942,
"modelGeometryDigest": "sha256:fd8ac2058aee11bfb68ed69dec7aa424db56db465e8e61724cfdbda89e58472a",
"geometryDigestEncoding": "sha256 of e8-plane-data.json UTF-8 bytes including final newline",
"donorCommit": "1394c395fdfb6e55a30a4578900fcc939866883c",
"donorPath": "lib/math/e8-octavian.ts",
"donorSourceSha256": "2f1cea4852320ba674a4e493e267cb695345db8e859f6b4d9146c384e14c7a7e",
"coordinateConvention": "standard E8 roots; roots2 = 2r; r has squared norm 2",
"planeConvention": "Q rows 2p and 2p+1; p=0,1,2,3; exponents 1,7,11,13",
"assignmentConvention": "exact max dot(integer vector, roots2); ties ordered lexicographically; zero unassigned",
"assignmentScope": "240 root sectors, not nearest point in the full E8 lattice"
},
"hopfDisplay": {
"version": "looking-glass/mirror-s7-s4-trajectory/v1",
"geometryDigest": "sha256:fd8ac2058aee11bfb68ed69dec7aa424db56db465e8e61724cfdbda89e58472a",
"hopfVersion": "looking-glass/hopf-s4/S-sub/height-first/v1",
"split": "S-sub",
"outputOrder": "height-first",
"splitMap": "q1=(x0,x1,x2,x4); q2=(x3,x7,x5,-x6)",
"formula": "H(q1,q2)=(|q1|²-|q2|²,2q1 conjugate(q2)) for |q1|²+|q2|²=1",
"charts": "h>=0: a=sqrt((1+h)/2) real, b=conjugate(c)/(2a); h<0: b=sqrt((1-h)/2) real, a=c/(2b)",
"gauge": "north: lambda=q1/a; south: lambda=q2/b; (a lambda,b lambda) recovers the original S7 point",
"trajectory": "lambda(t)=lambda(0) exp(i t) exp(j 2t) exp(k 3t); one closed trajectory within the full right-unit-quaternion S3 fiber",
"period": 3.14159265359,
"samples": 192,
"projection": "R8 -> R3: scale .62 times orthonormal DCT-II rows k=1,2,3; then the shared rotating orthographic camera",
"projectionRows": [
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],
"scale": 0.62,
"view": {
"centerX": 360,
"centerY": 346,
"radius": 310,
"screenScale": 440,
"pitch": 0.62,
"yaw": -0.55,
"roll": 0.22
},
"boundary": "Float64 drawing derived from the declared exact S7/S4 calculation. The path is not the whole S3 fiber. Distinct points and fibers can overlap after projection; no collision offsets or semantic relationships are inferred."
},
"displaySignificantDigits": 12,
"atlas": null
}