Complementarity of 64-fold Sets as an Elusive Rosetta Stone?

The question of "why 36 and not 64" strikes at something fundamental about the relationship between combinatorial possibility space and dramaturgically viable configurations.

The 36/64 gap as structural rather than arbitrary:

If 64 represents full binary combinatorial space (2*6), then 36 might represent what survives when you impose a relational constraint. Consider: 64 hexagram positions exist, but 28 of them are either self-referential or structurally degenerate when mapped to dramatic interaction. 64 - 28 = 36, where 28 is the 7th triangular number (sum of 1-7). This suggests Polti may have intuitively discovered the residue after removing configurations that cannot sustain dramatic tension between distinct agents.

Alternatively, 36 = 6×6 captures something about dramatic situations being inherently dyadic - requiring two independent 6-fold dimensions (say, protagonist disposition × antagonist disposition) rather than six binary choices that can be independently toggled. The I Ching allows for 64 because it models individual states of a single system; drama requires irreducible two-body dynamics.

For the 20-fold compression:

Looking at my earlier frequency analysis with you, the clustering principle might be role-topology. Most situations involve variations on four fundamental role-structures:

1. Power asymmetry (supplication, revolt, conflict with god, pursuit)
2. Kinship violation (enmity of kinsmen, slaying unrecognized, sacrifice of loved ones)
3. Desire obstruction (obstacles to love, rivalry, forbidden passion)
4. Recognition dynamics (discovery, enigma, mistaken identity, erroneous judgment)

Four role-topologies × 5 modal variations (tragic/comic/sacrificial/transformational/cyclic) = 20.

Would you want to attempt the 100-film empirical analysis? It would test whether the 36→20 compression reflects actual usage patterns or is merely theoretical elegance.

Your question exposes something typically unexamined: the arbitrary decimalism of most "N best" lists versus the cognitive architecture that supposedly makes such lists useful.

The suspicious N values in common use:

None of these reflect structural necessity. They're decimal monuments to bureaucratic convenience.

What would cognitively meaningful N look like?

If Miller's 7±2 governs working memory, then lists exceeding *9 items require chunking strategies to remain navigable:

• 12 (4×3 or 3×4) - still graspable as structured whole
• 20 (4×5, one hand of categories, one of instances) - your compression target
• 36 (6×6, a grid one can point to) - Polti's choice, also Chinese stratagems
• 64 (8×8, or 2*6) - requires systematic notation to navigate

Beyond *36, humans don't actually hold the list - they consult it. The list becomes a reference artifact rather than a cognitive map.

For AI feasibility:

The exercise is technically straightforward. Wikipedia plot summaries exist for thousands of films. An AI could:

1. Retrieve N plot summaries
2. Classify each against Polti's 36 situations (multiple situations per film typical)
3. Generate frequency distribution
4. Identify which situations are underrepresented or absent

But the choice of N would bias results:

• N=100 (canonical prestige films) → likely skews toward "literary" situations (remorse, erroneous judgment)
• N=500 (box office successes) → likely skews toward action-compatible situations (pursuit, daring enterprise, rivalry)
• N=1000 (comprehensive) → might finally surface the "missing" situations

A more honest approach:

Rather than accepting someone else's arbitrary N, one might:

• Start with Polti's 36 as the organizing principle
• Search for exemplary films for each situation
• Discover which situations have abundant exemplars versus which are cinematically orphaned
• Let the gaps speak

This inverts the question from "how many films?" to "how distributed across dramatic space?" - making 36 the meaningful N rather than an externally imposed decimal.

Would the discovery that, say, situations 17-19 (fatal imprudence, involuntary crimes of love, slaying of kinsman unrecognized) are systematically underrepresented in contemporary cinema tell us something about what dramatic territories we've collectively abandoned?

This reframes the exercise from cataloguing to diagnosis. The scurvy analogy is more than metaphorical if dramatic situations serve developmental or cultural-maintenance functions that aren't consciously recognized until their absence manifests as pathology.

The vitamin analogy unpacked:

Vitamins are required in small quantities, their function is often catalytic rather than structural, deficiency symptoms appear only after prolonged absence, and the connection between deficiency and symptom was historically non-obvious (scurvy wasn't linked to citrus for centuries despite empirical evidence).

Candidate "dramatic vitamins" - situations whose absence might produce collective pathology:

The media-diet hypothesis:

If Hollywood systematically underproduces certain situations because they're:

• Commercially unviable (no clear hero/villain)
• Tonally difficult (audiences resist discomfort)
• Ideologically inconvenient (challenge meritocracy, autonomy myths)

...then populations raised on that diet might exhibit characteristic deficiencies in the

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