Values explorer

The short version: Each value gets a “personality profile” across 10 psychological dimensions derived from decades of psychology research. We measure how similar two values are by comparing their profiles using cosine similarity—basically checking if they point in the same psychological direction.

The 10 Dimensions

These dimensions come from established psychological frameworks—primarily Moral Foundations Theory (Haidt) and Schwartz’s Values Theory:

Example Value Vectors

Here are the actual coefficients for 8 arbitrarily selected key values:

Reading the table: Positive values (green conceptually) mean the value strongly expresses that dimension. Negative values (red conceptually) mean the value conflicts with that dimension. Values near 0 are neutral.

How Similarity Works: Cosine Similarity

When you click on values, the system calculates how similar they are using cosine similarity—a measure of how much two vectors point in the same direction:

similarity = (A · B) / (|A| × |B|)

Where:

• A · B is the dot product (sum of dimension-by-dimension products)

  A₁×B₁ + A₂×B₂ + ... + A₁₀×B₁₀

• |A| and |B| are the magnitudes (lengths) of the vectors, or the square root of sum of squares

  √(A₁² + A₂² + ... + A₁₀²), √(B₁² + B₂² + ... + B₁₀²)

Range: -1 (perfectly opposite) to +1 (perfectly aligned)

Example: Why “Obedience” and “Freedom” Repel

Let’s calculate their similarity step by step:

Vectors:

• Obedience: CARE: -0.10, FAIR: 0.00, LOY: 0.20, AUTH: 0.85, LIB: -0.65, AGEN: -0.10, OPEN: 0.50, STAB: 0.80, TRAN: -0.20, ENH: 0.00
• Freedom: CARE: 0.05, FAIR: 0.05, LOY: -0.20, AUTH: -0.30, LIB: 0.90, AGEN: 0.30, OPEN: 0.20, STAB: -0.30, TRAN: 0.10, ENH: 0.25

Step 1: Calculate the dot product (A · B)

Dot product = (CARE: -0.10 × 0.05) + (FAIR: 0.00 × 0.05) + (LOY: 0.20 × -0.20) + 
              (AUTH: 0.85 × -0.30) + (LIB: -0.65 × 0.90) + (AGEN: -0.10 × 0.30) +
              (OPEN: 0.50 × 0.20) + (STAB: 0.80 × -0.30) + (TRAN: -0.20 × 0.10) + 
              (ENH: 0.00 × 0.25)
            = -0.005 + 0.00 + (-0.04) + (-0.255) + (-0.585) + (-0.03) + 
              0.10 + (-0.24) + (-0.02) + 0.00
            = -1.075

Step 2: Calculate the magnitudes

|Obedience| = √(CARE² + FAIR² + LOY² + AUTH² + LIB² + AGEN² + OPEN² + STAB² + TRAN² + ENH²)
            = √((-0.10)² + (0.00)² + (0.20)² + (0.85)² + (-0.65)² + (-0.10)² + 
                (0.50)² + (0.80)² + (-0.20)² + (0.00)²)
            = √(0.01 + 0 + 0.04 + 0.7225 + 0.4225 + 0.01 + 0.25 + 0.64 + 0.04 + 0)
            = √2.135
            ≈ 1.46

|Freedom| = √(0.0025 + 0.0025 + 0.04 + 0.09 + 0.81 + 0.09 + 0.04 + 0.09 + 0.01 + 0.0625)
          = √1.2375
          ≈ 1.11

Step 3: Calculate cosine similarity

similarity = -1.075 / (1.46 × 1.11)
           = -1.075 / 1.62
           ≈ -0.66

Result: Strong negative similarity (-0.66) → These values strongly repel in the visualization, which matches the well-documented tension between authority/hierarchy and personal freedom in psychological research.

Example: Why Compassion and Empathy Attract

Vectors:

• Compassion: CARE: 0.95, FAIR: 0.15, LOY: 0.10, AUTH: -0.20, LIB: 0.00, AGEN: -0.25, OPEN: 0.05, STAB: 0.00, TRAN: 0.70, ENH: -0.40
• Empathy: CARE: 0.90, FAIR: 0.10, LOY: 0.05, AUTH: -0.20, LIB: 0.00, AGEN: -0.35, OPEN: 0.10, STAB: -0.05, TRAN: 0.65, ENH: -0.40

Step 1: Calculate the dot product

Dot product = (CARE: 0.95 × 0.90) + (FAIR: 0.15 × 0.10) + (LOY: 0.10 × 0.05) + 
              (AUTH: -0.20 × -0.20) + (LIB: 0.00 × 0.00) + (AGEN: -0.25 × -0.35) +
              (OPEN: 0.05 × 0.10) + (STAB: 0.00 × -0.05) + (TRAN: 0.70 × 0.65) + 
              (ENH: -0.40 × -0.40)
            = 0.855 + 0.015 + 0.005 + 0.04 + 0.00 + 0.0875 + 
              0.005 + 0.00 + 0.455 + 0.16
            = 1.6225

Step 2: Calculate the magnitudes

|Compassion| = √(0.9025 + 0.0225 + 0.01 + 0.04 + 0 + 0.0625 + 0.0025 + 0 + 0.49 + 0.16)
              = √1.6895
              ≈ 1.30

|Empathy| = √(0.81 + 0.01 + 0.0025 + 0.04 + 0 + 0.1225 + 0.01 + 0.0025 + 0.4225 + 0.16)
          = √1.5795
          ≈ 1.26

Step 3: Calculate cosine similarity

similarity = 1.6225 / (1.30 × 1.26)
           = 1.6225 / 1.64
           ≈ 0.99

Result: Very strong positive similarity (0.99) → These values cluster tightly together, as expected for values that both strongly emphasize care and concern for others.

Known Psychological Tensions Encoded

The vectors capture documented value conflicts from research:

Physical Forces in the Visualization

The system applies three types of forces:

1. Similarity Links (attraction/repulsion)
   • Threshold: |similarity| > 0.3
   • Strength: similarity × 0.1
   • Distance: 80 × (1 - |similarity| × 0.5) pixels
2. Relevance Positioning (when you select values)
   • High-relevance values move toward center
   • Low-relevance values pushed to periphery
   • Strength increases with anchor selections
3. Boundary Forces
   • Keeps all values visible in viewport
   • Prevents nodes from escaping screen

Limitations & Context

What this IS:

• Theory-driven encoding of established psychological frameworks
• Hand-crafted based on decades of empirical research
• Captures documented value trade-offs and conflicts

What this ISN’T:

• Learned from actual survey data
• Validated against individual responses
• Culture-specific (these are Western psychology frameworks)
• Precise to the decimal point (0.85 vs 0.80 is somewhat arbitrary)

Think of it as: A research-informed interactive model that helps you explore value relationships, not a precise psychological assessment tool.

Want to dive deeper? The full vector dataset (120 values × 10 dimensions) is embedded in the code. The frameworks are primarily from Jonathan Haidt’s Moral Foundations Theory and Shalom Schwartz’s Theory of Basic Human Values.