In this response to the target article by Law, Power, and Quinto-Pozos, I draw attention to the fact that ‘sound change’ in sign languages does not seem to follow the Neogrammarian regularity principle and that, as a consequence, synchronic phonologies of sign languages do not have productive, obligatory phonological rules (whether allophonic or allomorphic rules). For example, the sound change that introduced aspiration for voiceless stops at the beginning of stressed syllables (when not preceded by /s/) is reflected as a regular, so-called allophonic rule in the synchronic phonological grammar of Modern English. Sign languages do not appear to have such regular allophonic rules or regular allomorphic rules.

The quartimax and varimax algorithms for orthogonal rotation attempt to maximize particular simplicity criteria by a sequence of two-factor rotations. Derivations of these algorithms have been fairly complex. A simple general theory for obtaining “two factor at a time” algorithms for any polynomial simplicity criteria satisfying a natural symmetry condition is presented. It is shown that the degree of any symmetric criterion must be a multiple of four. A basic fourth degree algorithm, which is applicable to all symmetric fourth degree criteria, is derived and applied using a variety of criteria. When used with the quartimax and varimax criteria the algorithm is mathematically identical to the standard algorithms for these criteria. A basic eighth degree algorithm is also obtained and applied using a variety of eighth degree criteria. In general the problem of writing a basic algorithm for all symmetric criteria of any specified degree reduces to the problem of maximizing a trigonometric polynomial of degree one-fourth that of the criteria.