Golden basis

Someone (Paul?) mentioned that Kornerup wanted a sort of basis for
everything based on phi--or at least, that's what I got out of it,
after it passed through my weird filter. One sort of basis idea is
that the algebraic integers Z[phi] are dense, so that you can
approximate log2(3) etc as closely as you like; for instance we can
approximate 3 by 2^(21-12 phi) and 5 by 2^(-98 + 62 phi). The ring of
integers is preserved under multiplication by phi, which is a unit,
so a shrinking and expanding process keeps us in the same sort of
basis.

I don't know if this is what Kornerup meant, of course.