Halliday & Matthiessen (1999: 572):
As designed semiotic systems emerge, both the registers of everyday language and the original specialist registers continue to exist and to develop; folk models of the world will co-exist alongside the scientific ones. A certain degree of intertranslatablity is likely to be maintained — linguistic renderings of logical or mathematical formulas, for instance; and this constitutes one of the contexts in which ordinary language is brought into explicit contact with more scientific varieties.
There will always be some complementarity of function between the more designed varieties and those that are naturally evolving. They may be allocated to different spheres of activity: for example, the language of bird-watchers vs. the language of ornithologists.
But in other cases the two are closely integrated as submotifs within a single sphere: for example, the use of both natural language and mathematical expressions side by side in the learning and practice of mathematics. This kind of interpenetration still entails a semiotic complementarity, but of a very sensitive kind, requiring a delicate interpretation of the context in order to bring it out.