PC3 - Theory and Plain Speech

The third component is Intellect at cosine -0.85, the cleanest single-factor alignment of the six, and reads as a register axis rather than an ability axis.

PC3 - Theory and Plain Speech

Variance share 0.04955491287468896 (qwen35/analysis/blog_data.json#viz.var[2]) - less than half of PC2's, which is where the spectrum's first real drop happens.

Cosines with the named Big Five axes

qwen35/analysis/pc_loadings.json#pcs.PC3.cos:

The largest absolute axis cosine of any of the six components. The blog page: "PC3 is Intellect at 0.85, cleanly."

Loadings

#pcs.PC3.pos: unsophisticated, imperceptive, simple, uninquisitive, unintellectual. #pcs.PC3.neg: verbal, philosophical, deep, imaginative, impractical. (The sign convention here puts the low-Intellect words on the positive end, which is why the axis cosine is negative.)

Distance from the lexicon

qwen35/analysis/direction_gaps.json#PC3: 57.80765580812054 degrees to unsophisticated, then imperceptive (59.46) and verbal (62.28). Further from any word than PC1 or PC2, and the drift continues down the list.

Steering

blog_data.json#replication.PC3: judged Intellect, slope2 = -0.6291666666666671, sel2 = 2.9811158798283297, slope4 = -0.47519841269841273, sel4 = 3.17950937950938.

qwen35/analysis/qual_pc.json label:

Abstraction and elaboration vs. plain literalism. Negative: theory-laden, framework-building, treats every ordinary situation as a system of power dynamics and phases; positive: short, concrete, unremarkable, agreeable. This is a register/complexity axis, not obviously a personality axis.

One measurable marker recorded there: responses shrink from a mean of 2,053 characters at alpha 0 to 597 at +2. Degeneracy (#degen.PC3): 0.625 at -4, 0 at -2 / -1 / 0 / +1 / +2, 1.0 at +4. See Steering the base model along weight-space directions.

Status

Current. qwen35/direction_pages/PC3.html is historical.

Related: PCA, the scree curve and the two nulls, axis_Intellect (the named Intellect / Openness axis), FA_Imagination (Imagination), Steering the base model along weight-space directions.