Halliday & Matthiessen (2014: 505-6):
(2) Projections: we saw that the boats had been turned. If I say I can see the boats turning, this is an event. A process ‘the boats are turning’ is being treated as a single complex phenomenon – a ‘macrophenomenon’. If I say I can see that the boats are turning, this is a projection. The process ‘the boats are turning’ is being treated as the projection or idea of a phenomenon – a ‘metaphenomenon’, something not just bigger but of a different order of reality. So we can say I can see that the boats have been turned but not I can see the boats having been turned – because you cannot see a past event. You can see the state of affairs resulting from that past event; but the past event itself can only be treated as a projection. In the present, both are possible; but the meaning is slightly different. If the ‘seeing’ is understanding, or what is seen is a report in writing, then again the relationship must be one of projection.