Kir-Sey Fam

Pose Space

An interactive visualization tool for analyzing yoga sequences through linear algebra and vector space geometry. Models each pose as a vector in high-dimensional joint-mobility space, comparing how different traditions navigate this space.

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Pose Space
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After completing 300HR Universal Yoga Teacher Training under Andrey Lappa (2026), I wanted to quantify just how balanced his sequences were compared to others. His systematic approach to mobility and sequencing — combined with my background in mathematics — naturally led me to Pose Space: applying linear algebra and vector space geometry to analyze the structures underlying different yoga traditions.

Pose Space models yoga sequences as paths through high-dimensional joint-mobility space. Each pose becomes a vector spanning 14 joint regions — neck, waist, L/R shoulder, elbow, wrist, hip, knee, and ankle — with sign conventions distinguishing opening (+1) from closing (−1) movements.

p∈R72(14 joints×6 mobilities, except elbows & knees×3)\mathbf{p} \in \mathbb{R}^{72} \quad \text{(14 joints} \times \text{6 mobilities, except elbows \& knees} \times \text{3)}

The cumulative state vector tracks the sequence's aggregate effect on each joint as you move through the practice. Balance is measured as its L₂ norm — a perfectly balanced sequence returns to the origin.

S(k)=∑i=0kpibalance=∥S(n)∥2→0S(k) = \sum_{i=0}^{k} \mathbf{p}_i \qquad \text{balance} = \|S(n)\|_2 \to 0

Sequence similarity is computed via cosine similarity, Shannon entropy measures how evenly a sequence distributes effort across all joint-directions, and PCA projections reduce the 72-dimensional paths to 2D for visualization.

cos⁡θ=A⋅B∥A∥ ∥B∥H=−∑pilog⁡2pi\cos\theta = \frac{\mathbf{A} \cdot \mathbf{B}}{\|\mathbf{A}\|\,\|\mathbf{B}\|} \qquad H = -\sum p_i \log_2 p_i
Explorer view — step through sequences pose-by-pose with body heatmap, trajectories, and balance bars

Explorer view — step through sequences pose-by-pose with body heatmap, trajectories, and balance bars

The tool compares three sequences: Ashtanga Primary Series (Yoga Chikitsa), Ashtanga Intermediate Series (Nadi Shodhana), and Andrey Lappa's Universal Yoga 8-Directional Cross. Visualizations include body heatmaps, cumulative trajectories, practice mandalas, PCA projections, sequence fingerprints, and Panca Kosha five-sheath mappings.

Balance comparison — open/close ratios, L/R symmetry, and residual imbalance polygons across all three sequences

Balance comparison — open/close ratios, L/R symmetry, and residual imbalance polygons across all three sequences

Practice mandalas and pose scatter — geometric fingerprints revealing each tradition's structural identity

Practice mandalas and pose scatter — geometric fingerprints revealing each tradition's structural identity

The analytical framework draws on Neo-Riemannian music theory (Lewin, Cohn, Tymoczko) — a group-theoretic approach to analyzing sequential transformations in tonal space, here adapted for movement through joint-mobility space.

These are preliminary findings — research is ongoing. Built with React and pure SVG, deployed on Vercel. Paper in progress.

next project —→

Yoga Teaching

Kir-Sey Fam