  It was recently shown that the computably enumerable (c.e.) degrees that
embed the critical triple (Downey, Greenberg, Weber 2007) and the M3 lattice
structure (Downey, Greenberg 2015) are exactly those that change their minds
sufficiently often. Therefore the embeddability strength of a c.e. degree has
much to do with the degree's mind change frequency. Nonlowness is another
common measure of degree strength, with nonlow degrees expected to compute more
degrees than low ones. We ask if nonlowness and frequent mind changes are
independent measures of strength. Downey and Greenberg (2015) claimed this to
be true without proof, so we present one here. We prove the claim by building
low and nonlow c.e. sets with an arbitrary number of mind changes. We base our
proof on our direct construction of a nonlow low2 array computable set. Such
sets were always known to exist, but also never constructed directly in any
publication.
