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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": [
[
0.490392640202,
0.415734806151,
0.27778511651,
0.0975451610081,
-0.0975451610081,
-0.27778511651,
-0.415734806151,
-0.490392640202
],
[
0.461939766256,
0.191341716183,
-0.191341716183,
-0.461939766256,
-0.461939766256,
-0.191341716183,
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],
[
0.415734806151,
-0.0975451610081,
-0.490392640202,
-0.27778511651,
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-0.415734806151
]
],
"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
}Moon Festival example
Fictional practice · Moon Festival
What can the club build together, and what might each view leave out?
Follow a shared resource, compare three plans, and see which questions still belong to people.
This is a fixed example for learning. Exploring or changing a number here does not change a WeOpoly game, record anyone’s agreement, or make a decision.
Perspective focus
Whose responsibility brings this forward?
Focus highlights related records. It never changes the quantities, sources, or selection.
01 · Shared resource
Where do the batteries go?
Exceeds stated limit. 16 batteries of peak concurrent use compared with 12 recorded batteries; shortfall 4. Timing and reuse assumptions remain inspectable.
The overlapping time is a fixture assumption. Recharge or reuse between separate uses remains unknown. Inspect the sources before treating the calculation as a fact about any real event.
02 · Compare alternatives
What still fits next week?
Changing this number is a simulation. It does not add a helper or change a source record.
Swipe the table sideways to see results →
| Plan | Supply tokens of 12 | Preparation blocks of 8 | Next week of 3 | Result |
|---|---|---|---|---|
| 12 / 12 | 8 / 8 | 6 / 3 | Exceeds stated limitNeeds 3 more next-week blocks | |
| 5 / 12 | 4 / 8 | 6 / 3 | Exceeds stated limitNeeds 3 more next-week blocks | |
| 8 / 12 | 6 / 8 | 2 / 3 | Fits stated limits |
Shared resource records
These same objects appear in the map. Select one to inspect its source; the selected identity stays the same when you change views.
Relationship records
03 · Clarify the words
“More room” meant what?
The clarification updates the meaning of Leo’s concern. It does not say Maya agrees with a particular design.
04 · Keep the questions separate
What can this view actually answer?
- Can it work?
- The checks say what fits the stated quantities and timing. They are conditional on the fixture assumptions.
- Do we want it?
- No participant choice between these three plans is recorded. Maya’s possible response above is an example, not a vote.
- Who can decide?
- The applicable decision process and responsible human are not established in this fixture. This screen does not approve a plan.
- How well do we know?
- The quantities come from a fictional note; the overlapping time was added for the exercise. Reuse between separate times remains unknown. The status may change if those inputs change.