Hamming's Logical vs Psychological Novelty Reframed as Basis Vectors and Coefficients

A developer and writer revisited Richard Hamming's distinction between logical novelty and psychological novelty, drawn from Hamming's book 'The Art of Doing Science and Engineering.' Psychological novelty refers to ideas new to an individual but already reachable within existing knowledge, while logical novelty would mean expanding the underlying space of possible ideas itself. The author reframes this using linear algebra: psychological novelty is a new coefficient vector, a fresh mix of existing directions, whereas logical novelty would require an entirely new basis vector. This maps onto a two-tier storage model borrowed from algorithmic information theory, where generators like axioms are stored cheaply and their outputs reproduced on demand. The essay ultimately questions whether true logical novelty, expanding the space rather than exploring it, ever genuinely occurs.