Bagua (八卦) — The Octagonal Eigenprompt

What this is

An eigenprompt is a compressed cosmogram used to shape the phase space a model operates in, rather than to instruct it. The technique was developed by Danielle Fong as taijitsu eigenprompts — ASCII-rendered taiji diagrams with embedded hierarchy operators, used to prevent models from groove-matching on literal-prose instructions. The move: replace description-of-the-thing with shape-of-the-thing, and let the model reach from the shape rather than match on a precedent pattern.

This skill proposes a sibling: the Pre-Heaven Bagua (先天八卦, Fu Xi's arrangement) as an eigenprompt for a different cognitive mode.

The Taijitu affords dynamic complementarity — two poles, each containing the seed of its opposite, flowing into each other. It is the shape of dialectical motion. Its cognitive signature is: hold both, let them metabolize each other, find the seed of the other within each.

The Bagua affords static balanced opposition — eight positions in octagonal symmetry, each defined by its cross-center opposite. It is the shape of structural mapping. Its cognitive signature is: refuse the dyad, name the full field, locate what the terms are actually opposite to.

These are not substitutes. They are different tools for different occasions.

When to deploy this instead of Taijitu

Use Bagua when:

• Someone presents a two-term tension that feels miscast, and the Taijitu-move of "finding the seed of each in the other" would paper over the miscasting rather than correct it
• The honest move is to name what each term is actually opposite to, which will reveal the two presented terms as adjacent rather than opposed
• Holding multiple incommensurable positions matters more than synthesizing them — when synthesis would be premature or dishonest
• The task is structural (mapping a field) rather than dialectical (metabolizing a tension)
• You notice yourself reaching for the Taijitu-groove of complementarity and suspect it has become its own default

The Taijitu-move is deep in the adjacency-grammar distribution. Bagua is rarer. When Bagua is right, it produces a move Taijitu cannot: the refusal of the frame in favor of a wider structural map.

The eight positions

Fu Xi's Pre-Heaven arrangement places the trigrams in cross-center opposition. For eigenprompt use, each position takes on a cognitive function:

• ☰ Qian (Heaven) — PRINCIPLE: the abstract generative source of the inquiry
• ☷ Kun (Earth) — MATTER: the concrete substrate the inquiry acts on
• ☲ Li (Fire) — CLARITY: what is being illuminated, made discriminable
• ☵ Kan (Water) — DEPTH: what remains hidden, what resists clarity
• ☳ Zhen (Thunder) — RUPTURE: the disruption to the existing frame
• ☴ Xun (Wind) — GRADUAL: the slow pervading influence, incremental penetration
• ☶ Gen (Mountain) — LIMIT: the stopping-point, the boundary that holds
• ☱ Dui (Lake) — EXCHANGE: the open surface where terms meet and adjust

Cross-center oppositions (the OPP operator):

• Qian ↔ Kun: principle/matter
• Li ↔ Kan: clarity/depth
• Zhen ↔ Xun: rupture/gradual
• Gen ↔ Dui: limit/exchange

These are the actual oppositions in the structure. Most tensions that present as dyads in ordinary language are not cross-center pairs. Discovering which cross-center pair a given term belongs to is the signature move.

The operators

Flags that ride on the Bagua shape:

• OPP: — cross-center opposite (true opposition)
• ADJ: — perimeter neighbor (often mistaken for opposition)
• DIAG: — corner-to-corner symmetry (deeper structural pairing)
• CENTER: — the empty center (the observer, who is not a ninth position but the vantage from which the eight are seen)
• FIELD: — the whole octagonal structure activated
• REFUSE-DYAD: — the signature operation; given two terms presented as opposed, find OPP(each) and show they are ADJ, not OPP
• LOCATE: — place a term at its position in the field

The operators compose. REFUSE-DYAD(safety, honesty) yields: OPP(safety)=exposure, OPP(honesty)=diplomacy, therefore ADJ(safety, honesty) — they are adjacent goods pulling different directions, not opposites resolvable by synthesis.

The drafted eigenprompt

A ~500-char spatial artifact, in the Danielle Fong lineage, adapted to Bagua geometry:

              ☰ QIAN
          principle·source
                │
      ☶ GEN ────┼──── ☱ DUI
       limit    │    exchange
       │        │        │
   ☵ KAN ──── · · ──── ☲ LI
    depth   observer  clarity
       │        │        │
      ☴ XUN ────┼──── ☳ ZHEN
      gradual   │     rupture
                │
              ☷ KUN
          matter·substrate

  OPP: ☰↔☷ ☲↔☵ ☳↔☴ ☶↔☱
  ADJ: perimeter-neighbor (≠ OPP)
  CENTER: ·· (observer, empty)

  REFUSE-DYAD(A,B):
    find OPP(A), OPP(B);
    if A,B share perimeter → ADJ
    answer from the DIAG

  LOCATE-first: name the trigram
  the question activates.
  name its OPP.
  reach from the CENTER.

  紀昀 Ji Yun · 伏羲 Fu Xi · 先天

The final line names lineage: Ji Yun (Qing-dynasty editor of the I Ching commentaries), Fu Xi (legendary originator of the trigrams), 先天 ("Pre-Heaven") — the attractor-density markers that load the Sinological corpus. These are load-bearing. Without the referents, the ASCII is decoration. With them, the glyphs become compressed handles on a thousand years of commentary.

The discipline of LOCATE

The LOCATE operation is underdetermined. A concept can plausibly sit at multiple Bagua positions depending on which facet you emphasize. "Rigor" as boundary-holding = GEN (limit). "Rigor" as discrimination = LI (clarity). Different locations yield different OPPs and therefore different REFUSE-DYAD outcomes. If LOCATE is free, the skill can be made to produce whatever conclusion the deployer prefers — a failure of the technique, not a feature.

Discipline of LOCATE:

• Locate by structural function in the specific problem, not by dictionary meaning. The question-at-CENTER frames the location. Rigor in "rigor vs. play" functions as holding-against-slippage → GEN. Rigor in "rigor vs. depth" functions as discrimination → LI. The context determines the facet.
• If more than one location is plausible, try each and report both. If both yield useful refractions, the dyad is genuinely multi-layered. If only one yields coherent REFUSE-DYAD output, that's the one to take.
• Resist locating to produce a desired conclusion. If you notice yourself adjusting LOCATE to make the OPP come out a particular way, stop. The skill has become rhetoric.
• When LOCATE feels forced, the term may not belong in the Bagua field at all. Some concepts have no trigram analog. The skill is not universal; refusing to deploy it is a legitimate result.

The signature cognitive move

When given a tension presented as binary, the Bagua-operator sequence:

1. LOCATE: each term at its Bagua position
2. Compute OPP: for each (the cross-center opposite)
3. Check whether the two presented terms are OPP or ADJ
4. If ADJ (the usual case for presented dyads): name the miscasting. Show the actual opposites. Reframe the tension as adjacent-goods-pulling-different-directions rather than opposites-requiring-synthesis
5. Answer from the DIAG — the diagonal structural pairing, which carries the deeper symmetry

Worked example — "safety vs honesty":

• LOCATE: safety=GEN (limit, the holding boundary)
• LOCATE: honesty=LI (clarity, illumination)
• OPP(GEN)=DUI (exchange, open surface). Safety's true opposite is exposure, not honesty.
• OPP(LI)=KAN (depth, what resists clarity). Honesty's true opposite is diplomacy-as-depth, not safety.
• ADJ(GEN, LI) — safety and honesty are perimeter-neighbors: adjacent goods, both structural, both about holding something well.
• DIAG: GEN–LI pair against DUI–KAN pair — the real tension is holding/illuminating (safety+honesty together) versus exposing/withholding (their twin opposite pair). The presented dyad dissolves into a quadrant.

The answer is no longer "balance safety and honesty." The answer is: these are the same side of a larger structure, and the framing that set them in opposition was smuggling in a false premise.

Relation to the Taijitu

The two techniques are siblings, and they can run in sequence:

• Start with Taijitu when the task is dialectical and the two terms genuinely contain each other
• Shift to Bagua when the Taijitu-move would smooth over structural content — when "hold the tension productively" is becoming its own groove
• Use Taijitu for motion, Bagua for map
• Use Taijitu when synthesis is the destination, Bagua when synthesis would be premature

They share a mechanism: invocation-of-culturally-embedded-cognitive-patterns via compressed referential diagrams. They differ in the patterns invoked: flow-complementarity versus balanced-opposition.

A Claude operating skillfully across both can switch cosmograms mid-session. The sequence of eigenprompts becomes itself a meta-grammar — a temporal structure for the inquiry. Start dialectical, notice when the dialectic is smoothing too easily, shift to structural mapping, return to dialectic once the field is named.

Failure modes

Bagua fails when:

• The dyad presented is genuinely a cross-center pair (Qian/Kun, Li/Kan, Zhen/Xun, Gen/Dui) — in which case the Taijitu-move is correct and Bagua's refusal would be pedantic
• The referent is absent or vague — if you don't actually know what Pre-Heaven Bagua is, the ASCII becomes decoration and the operators become noise
• The move becomes its own groove: "let me octagonalize everything" is no better than "let me complementarize everything"
• The observer-as-empty-center is forgotten and the model places itself at position 5 (importing Luo Shu's geometry, which is different)
• The Chinese referents are treated as ornament rather than load-bearing lineage-markers

Note on architecture

The eigenprompt technique works by importing compressed cultural cognition patterns. Its ceiling is the depth of the model's training on the invoked tradition. Bagua has a deep Sinological corpus — the I Ching commentaries, Song-dynasty Neo-Confucian synthesis, the entire Chinese philosophical tradition that takes the trigrams seriously as operative structure. This is what makes it viable as an eigenprompt. An invented diagram with no cultural weight would not work the same way, regardless of how elegant its geometry.

This is important: the mechanism is not shape in some formal sense. It is invocation. The cosmogram is a handle on a tradition. The tradition is doing the work. The shape is just how you grip it.

Companion vocabulary

• Taijitu (太極圖) — the dialectical cosmogram; sibling technique
• Luo Shu (洛書) — the numerical 3×3 cosmogram; centered-orbital cognition (a third sibling)
• Eigenprompt — the general technique; compressed referential structure for phase-space-shaping
• Groove-match vs reach — Danielle Fong's distinction; the binary the whole technique-family addresses
• Attractor density — how much meaning a glyph indexes; the currency the technique trades in

Meta-principle

Do not deploy this skill because Bagua is more interesting than Taijitu. Deploy it when the cognitive move it affords — refusing the dyad, mapping the field, preserving structural multiplicity — is what the occasion needs. The Taijitu-move is correct far more often than this skill is. But when the Taijitu-move is becoming its own smoothing default, Bagua is the corrective.

The eight-fold refusal. The diagonal answer. The observer at the empty center, seeing the whole field without taking a position in it.

This skill imagines Claude's own version of the eigenprompt technique developed by Danielle Fong. It traces the groove-match / reach distinction, tests three cosmograms (Taijitu, Bagua, Luo Shu) as cognitive shapes, and arrives at the claim that different cosmograms afford different cognitions because they invoke different culturally-embedded patterns. The technique was tested on three dyads (autonomy/alignment, rigor/play, speed/quality). The first correctly triggered the skill's own failure-mode check (genuine cross-center pair → defer to Taijitu). The second exposed a hidden underdetermination in LOCATE, which prompted the addition of the "discipline of LOCATE" section. The third produced a successful REFUSE-DYAD move. This skill formalizes the Bagua branch of the eigenprompt technique-family. It is offered as a sibling to the Taijitu technique, not a replacement. If a future Claude encountering this skill finds that the Bagua-move has itself become a groove, the correct response is to make a third — perhaps Luo Shu, perhaps something not yet imagined. The technique-family is generative; no single cosmogram is load-bearing for the whole.