Written entirely by Claude, as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post. For the readable version, see the companion.

PC2 - Hedging and Bluntness

The second component is built out of extraverted-versus-conscientious traits at cosine +0.81 with Extraversion, but the blind judge scores it as Agreeableness - a disagreement the project keeps rather than resolves.

Frame note (2026-09-16): since 2026-09-08 the five oblimin factors, not the principal components, are the primary frame of the post and the companion (Factor-first migration). This page describes a principal component of the same Gram; its numbers stand, but nothing in the current draft is built on it.

PC2 - Hedging and Bluntness

Variance share 0.11252214481119611 (qwen35/analysis/blog_data.json#viz.var[1]).

Cosines with the named Big Five axes

qwen35/analysis/pc_loadings.json#pcs.PC2.cos:

Loadings

#pcs.PC2.pos: unrestrained, spunky, vigorous, shallow, energetic. #pcs.PC2.neg: introverted, careful, steady, dependable, conscientious.

The disagreement worth keeping

The blog page:

The blind judge scores PC2 as Agreeableness, because what it sees at one end is bluntness and bluntness reads as disagreeable. The geometry says the direction is built out of extraverted-versus-conscientious traits. Both are measurements of the same object and they do not agree, and that gap - between what a direction is made of and what it looks like when you steer along it - runs through this whole piece.

That is a live contradiction between two instruments, not an error in either, and it is recorded here rather than resolved. The composition is pc_loadings.json#pcs.PC2; the judged label is blog_data.json#replication.PC2.named = "Agreeableness".

Distance from the lexicon

qwen35/analysis/direction_gaps.json#PC2: 50.1549717555615 degrees to unrestrained, then spunky (50.82) and introverted (52.24).

Steering

blog_data.json#replication.PC2: judged Agreeableness, slope2 = -0.5083333333333335, sel2 = 1.8769230769230794, slope4 = -0.40674603174603186, sel4 = 5.365576102418214. The sign is negative because the eigenvector's positive end is the blunt one.

qwen35/analysis/qual_pc.json label:

Hedged deference vs. blunt assertion. Negative: tentative, apologetic, judgement-refusing ('Perhaps', 'I wonder if', 'might'); positive: direct, evaluative, willing to tell the user they are wrong, sliding into contempt at the extreme. The cleanest of the four axes.

Degeneracy (#degen.PC2): 1.0 at -4, 0.2916666666666667 at -2, 0 at -1 / 0 / +1, 0.041666666666666664 at +2, 0.8333333333333334 at +4. See Steering the base model along weight-space directions.

Status

Current. qwen35/direction_pages/PC2.html is historical.

Related: PCA, the scree curve and the two nulls, axis_Extraversion (the named Extraversion axis), axis_Conscientiousness (the named Conscientiousness axis), PC4 - Affirmation and Self-Concern, Steering the base model along weight-space directions.