  In this article we discuss an approach to database optimisation in which a
conceptual schema is optimised by applying a sequence of transformations. By
performing these optimisations on the conceptual schema, a large part of the
database optimisation can be done before actually sliding down the software
development waterfall. When optimising schemas, one would like to preserve some
level of equivalence between the schemas before and after a transformation. We
distinguish between two classes of equivalence, one based on the mathematical
semantics of the conceptual schemas, and one on conceptual preference by
humans. As a medium for the schema transformations we use the universe of all
(correct) conceptual schemas. A schema transformation process can then be seen
as a journey (a schema-time worm) within this universe. The underlying theory
is conveyed intuitively with sample transformations, and formalised within the
framework of Object-Role Modelling. A metalanguage is introduced for the
specification of transformations, and more importantly their semantics. While
the discussion focusses on the data perspective, the approach has a high level
of generality and is extensible to process and behaviour perspectives.
