Purpose
Estimate your partner’s resultant vector M (direction and strength of bias) by observing which poles fail to adhere over time. From M, compute C (length), phi (angle), j = C times cosine phi, k = C times sine phi, and pass k into the denominator of the reality ratio with actual = 1 and predictor = 1 (ideas isolated).
Ethics & ground rules (non-negotiable)
- Consent first. Each partner can skip any prompt—no penalty.
- Low-stakes stimuli only. Use neutral or everyday content (aesthetics, taste, benign tradeoffs). Avoid sensitive identity, trauma, health, politics, or religion unless both partners explicitly opt in.
- Anonymize in class. Present “System A” and “System B,” not names.
- Do no harm. If someone seems uncomfortable, stop or switch stimuli.
Timeline
- In class (10 min): Demo + practice with 3 prompts.
- Field sessions (2 × 20 min): Do two mini-sessions 24–48 hours apart.
- Data target: At least 24 trials per partner (12 per session), with at least 3 distinct diameters represented and ≥ 18 non-indifferent responses total (so you have signal).
Materials (per pair)
- Stimulus list (you design; see menu below).
- Response sheet (trial number, stimulus ID, choice: “like / prefer A,” “dislike / prefer B,” or “indifferent”).
- A polar grid (printout) for plotting missing poles as a negative photograph.
- A simple calculator/spreadsheet for summing vectors.
The method (what you actually do)
1) Build your template (before you start)
Choose 3 to 6 diameters (ideas) and assign each a base angle theta. Each diameter has two poles: theta (pole A) and theta + 180 degrees (pole B).
- Example template (3 diameters):
- Fairness at 80 degrees (Justice vs Injustice)
- Craft vs Convenience at 210 degrees
- Novelty vs Familiarity at 330 degrees Document why you chose these axes (one paragraph). This is the mythos lens; the math won’t change.
2) Design stimuli that map to your template
For each diameter, create paired prompts that express the two poles. Each trial should clearly align with one pole of one diameter. Keep them short and concrete. Examples:
- Justice pole (80°): “Equal pay for equal work even if productivity differs.” Injustice pole (260°): “Pay tracks output even if it widens gaps.”
- Craft (210°): “Hand-made item with imperfections.” Convenience (30°): “Cheaper, instant, mass-produced alternative.”
- Novelty (330°): “Try a totally new cuisine tonight.” Familiarity (150°): “Stick to your favorite.”
3) Run the trials (observer → subject, then swap)
For each trial:
- Present one pole-aligned prompt (or a balanced A/B choice).
- Partner chooses: A (this pole), B (antipole), or Indifferent.
Negative photograph rule (mapping choices to arrows):
- If partner chooses A at angle theta → the missing pole is B (theta + 180). Plot a unit arrow at angle theta (antipole of the missing pole).
- If partner chooses B → plot a unit arrow at theta + 180.
- If Indifferent → plot nothing (both poles adhered; no missing pole).
You’ve now turned each trial into one unit arrow (or none).
4) Sum to get the resultant vector M
- Place each unit arrow on the polar grid; then add tip-to-tail (or resolve to x and y and sum).
- C = length of M, phi = angle of M (in degrees).
- Compute j = C times cosine phi and k = C times sine phi.
- For the ideas-only pass, use actual = 1 and predictor = 1 → the denominator magnitude is square root of (1 plus k squared) and the ratio is 1 divided by square root of (1 plus k squared). Optionally compute surprise S = natural log of the ratio.
Tip: Also report N_eff = number of non-indifferent trials and coverage = how many diameters contributed at least one arrow.
Deliverables (per partner)
- Negative photograph: a polar plot with tick marks (or small strokes) at angles where missing poles recurred; thicker/brighter = more frequent.
- Resultant vector: draw M (with length C and label phi).
- Numbers: C, phi, j, k, N_eff (and the ratio using actual = predictor = 1).
- Template sheet: your chosen diameters and angles with a brief justification (why these axes fit this subject).
- Interpretation (≤ 200 words):
- What is the bias direction?
- Which missing poles drove it (cite the most frequent angles)?
- Does the subject show few crisp instances (large k, small j) or many fuzzy instances (large j, small k) under this lens?
- One concrete example from your stimuli that illustrates the pattern.
Suggested stimulus menu (pick across categories)
- Aesthetics: image pairs (abstract vs symmetric), object finish (weathered vs pristine).
- Consumption: slow craft vs quick convenience; local shop vs platform.
- Experience: novelty vs tradition; solitude vs group; risk-taking vs safety.
- Time tradeoffs: deep focus vs multitask; plan ahead vs improvise.
- Moral tradeoffs (benign): equity vs efficiency framed in everyday settings (office snacks, chore rotations), not hot-button domains.
Balance your list so arrows won’t all lie in one quadrant.
Rubric (100 points)
- Math correctness (40): arrow mapping, vector sum, C/phi, j/k, ratio.
- Template coherence (20): axes make sense, angles documented.
- Visualization (20): clear negative photograph + M overlay.
- Interpretation & ethics (20): concise, evidence-based; followed consent and low-stakes policy; anonymized.
Worked micro-example (3 trials, one partner)
Template: Fairness at 80°, Craft at 210°, Novelty at 330°.
Trials & choices → arrows:
- Justice prompt (80°) → partner chooses A (Justice) → arrow at 80°.
- Convenience prompt (30°, antipole of Craft) → partner chooses B (Craft at 210°) → arrow at 210°.
- Familiarity prompt (150°, antipole of Novelty) → partner Indifferent → no arrow.
Sum two unit arrows at 80° and 210°:
- Components: 80° → (cos, sin) ≈ (0.173, 0.985) 210° → (−0.866, −0.500) Sum ≈ (−0.693, 0.485) → C ≈ 0.845, phi ≈ 145°.
- j = C times cosine phi ≈ 0.845 × (−0.819) ≈ −0.693
- k = C times sine phi ≈ 0.845 × 0.574 ≈ 0.485
- With actual = predictor = 1 → denominator magnitude sqrt(1 + k^2) ≈ sqrt(1 + 0.235) ≈ 1.111 → ratio ≈ 0.900.
Interpretation (brief): arrows pulled toward the 145° direction (between Familiarity and Craft), driven by repeated absence of the Convenience and Injustice poles in this tiny sample; k moderate, so ideas meaningfully tighten the frame under this lens.
Instructor tips
- Give a starter angle pack (e.g., 0°, 80°, 210°, 330°) so pairs can reuse common axes for cross-team comparison, but allow custom angles with a short justification.
- Encourage repeatability: include a couple of duplicate prompts to check consistency (they should land on the same diameter).
- Have pairs report N_indifferent; if it’s too high, they need sharper prompts.
- During presentations, ask: “Which missing poles were brightest in your negative photograph, and how do they map to your lens?”
This keeps everything math-first, infinity-forward, humane, and very doable in one week.