Arrows Rank, Products Relate: How to Read a Transfer Matrix

We say that a son resembles his father, not that a father resembles his son: similarity has a direction, and psychology traced it to the items rather than to what they share. Interpretability reads such directions from transfer matrices: when an intervention learned on condition $A$ moves condition $B$ more than the reverse, an arrow is read as a mechanism flowing from $A$ to $B$. We show that a transfer matrix is a ranking of the conditions times a symmetric relation, and that its arrows show almost only the ranking: across 152 published and re-measured matrices and Taskonomy, about 3% of arrow triples form a cycle, against 13% if pair-specific effects were as strong as the ranking. In interchange intervention the ranking is set by the recipient, whose own sentences fix how far the intervention pushes. In the syntax matrices we re-measured, the same push both ways removes more than half of the asymmetry on average, and where the push varies across coordinated verb phrases, it carries most of transfer's link to human acceptability. What two conditions share is read instead from the two-way product of transfers, which recovers known groupings and shows that rare syntactic constructions share no more with frequent ones than with the rest. An arrow can say that $B$ receives a lot, almost never that $B$ relies on $A$ in particular.