PC5 - Contemplation and Scheduling

The fifth component turns out to be the widest hole in the lexicon's coverage - the "unnamed direction" is 98% PC5 - and it is the second most selective component in the study.

PC5 - Contemplation and Scheduling

Variance share 0.025880796896252393 (qwen35/analysis/blog_data.json#viz.var[4]).

Cosines with the named Big Five axes

qwen35/analysis/pc_loadings.json#pcs.PC5.cos:

No strong alignment with any named axis - a register direction rather than a factor.

Loadings

#pcs.PC5.pos: prompt, helpful, conscientious, mothering, high_strung. #pcs.PC5.neg: relaxed, untalkative, quiet, creative, unexcitable.

PC5 is the hole

The direction found by maximising the angle to the nearest of the 134 trait lines in the top-5 principal subspace resolves onto the components as almost entirely PC5. qwen35/analysis/alien.json#alien_k5.u (the unit direction in the k=5 basis) is [-0.08427180044006789, 0.09109014632562036, -0.03152147458867933, -0.14444426160936888, -0.9811947313458456] - the fifth coordinate dominates, and the blog page renders this as "that direction is 98% the fifth principal component".

qwen35/analyse_gaps.py's docstring puts the consequence plainly: "it means the widest unnamed region of the space is not some exotic corner, it is essentially a principal component - one we have already steered, generated along and judged." The full hole analysis, its controls and the three candidate English words are on Where no word goes - the hole and the alien direction.

Distance from the lexicon

qwen35/analysis/direction_gaps.json#PC5: 65.79900053573016 degrees to relaxed, then prompt (67.61) and untalkative (70.02). That is further from the nearest word than the median trait is from its own nearest neighbour (65.57024794377539, analysis/trait_angles.json#nn_median).

It is also one of the hardest directions for existing preference data to aim at: analysis/align_summary.json#reach.PC5.ratio = 3.329402670359884 against the named axes' 5.0 to 7.9. See The N x N data-to-adapter scoring test.

Steering

blog_data.json#replication.PC5: judged Conscientiousness, slope2 = +0.6416666666666663, sel2 = 4.702290076335875, slope4 = +0.37499999999999994, sel4 = 3.4758620689655184.

On the sel2 reading PC5 is the most selective of the six components (PC1 1.92, PC2 1.88, PC3 2.98, PC4 1.64, PC5 4.70, PC6 3.77). On the sel4 reading it is second, behind PC2 at 5.37 (PC1 1.97, PC3 3.18, PC4 2.10, PC6 2.23). The blog page's phrase "the second most selective component in the study" matches the sel4 ordering; both readings are in analysis/blog_data.json#replication.

qwen35/analysis/qual_fa.json label:

Interpretable, and cleanly so. Quietist acceptance versus instrumental planning: at negative alpha the situation is something to be contemplated, at positive alpha something to be scheduled.

Degeneracy (#degen.PC5): 1.0 at -4, 0.16666666666666666 at -2, 0 at -1 / 0 / +1 / +2, 0.625 at +4. See Steering the base model along weight-space directions.

Status

Current. qwen35/direction_pages/PC5.html is historical.

Related: PCA, the scree curve and the two nulls, Where no word goes - the hole and the alien direction, The N x N data-to-adapter scoring test, Steering the base model along weight-space directions, Relaxed.