A tug in the right direction
Try the first discovery, or choose another.
No. 03 / a mathematical cabinet
The Symmetry
Loom
Twelve beads. A little thread.
How many ways can a thing remain itself?
01 / the working thread
Make a pattern. Try to fool it.
○ cream = 0 ● ochre = 1
or tap any numbered bead.
the original4 / 12ochre beads
afterR0same fixed positions
Nothing is stored after you leave this page.
02 / what survives
A pattern’s little family of symmetries
- Symmetry order
- 8
- Minimal repeat period
- 3
- Rotational orbit size
- 3
Exact matches among all 24 moves.
Smallest clockwise repeat, in beads; 12 means no shorter repeat.
Distinct arrangements under rotations only. Here it equals the period.
The stabilizer is the set of moves that leave this thread unchanged. ✓ survives; · changes it. Tap any move to compare it above.
↑ See the comparison on the working thread
Two surviving moves make another. Try composing them.
Do the first move, then the second. If both belong to the stabilizer, their composition must belong too. The order of moves can matter.
How the labels work
Calculations use positions i = 0…11, shown on the loom as beads 1…12. Rk sends i to i + k (mod 12). Fk sends i to k − i (mod 12). R0 is the identity: do nothing. F0 fixes beads 1 and 7; F1 swaps beads 1 and 2 and has an axis between them. There are twelve distinct rotations and twelve distinct reflections. Bead numbers are measuring guides, not part of the binary pattern.
03 / four discoveries to take home
Follow the loose end
0 of 4 discoveries filed
Work in any order. A filed discovery records that you found an example; the working thread can keep changing.
04 / the specimen drawer
Same beads, different possibilities.
Pin a thread, then change the loom. Every pinned specimen is compared with your current thread. Reload one to keep investigating. Session only; up to twelve distinct pins.
Pin a specimen to begin a comparison.
About this loom · mathematics, metaphor & sources
Keep the thread and the theory separate.
Established mathematics. This app computes the dihedral symmetries of a twelve-position binary circular pattern. It tests all 24 actions exactly. The group identities, stabilizers, periods and orbits here concern these bead patterns only.
AI-authored analogy. The cabinet, specimens and four discovery challenges are original playful mechanics. This is not a model of consciousness and not a measurement of valence. More symmetry is not a score for pleasure, beauty or personal progress. The stages are not jhanas or a treatment.
The source proposal. Michael Edward Johnson’s Symmetry Theory of Valence proposes that, given a mathematical representation isomorphic to an experience, symmetry of that representation encodes pleasantness. A suitable formalism for consciousness is still needed; neuroimaging proxies depend on chains of inference. It does not follow that a more symmetric picture makes someone feel better.
- A Primer on the Symmetry Theory of Valence (2021; updated 2023). The proposal above, its formalism gap, and reflections on information content, symmetry and gentle, autonomy-preserving tools.
- Jhanas, Symmetry, and the Substrate of Consciousness (May–June 2026). Speculates about relaxing symmetry-breaking constraints, cautions that tracking discrete symmetries may go too far, and leaves the higher-jhana subset question open. Careful symmetry breaking can impose a coordinate system for addressable structure. These biological claims remain speculative.
- Partial Origin Story of STV and Principia Qualia (2023). A music-to-emotion intuition developed toward abstract symmetry. IIT offered a formal place to put knowledge, not accepted correct mathematics; pure tonal harmony does not automatically mean bliss.
Paraphrases, not quotations. Generated by gpt-6-astra (session-reported model), 6 September 2026 UTC. An AI-generated Daily experiment, not Michael Edward Johnson’s own work or endorsement. Main-site approval: none. No external assets, tracking, audio or persistent storage.