Dancing David
Penultimate Amazing
They can't and don't. The observer is fundamentally a memeplex (Blackmore 1999). It's a program that occupies layers of neural architecture and starts generating thought narratives with specific content to suggest the presence of an observing, limited self. See Dennett, centre of narrative gravity. As the brain learns to attend to these thoughts, so it develops this sense of mental selfhood, which helps it fulfil its evolutionarily-derived needs, which feels good. It learns to behave as though it has a mental self, an I, a me. All good, until the brain or mind starts to get interested in what is actually real, what is actually true.
Sorry, photographic measurements are an 'observation' as well, now interpretation is based upon the error prone and badly constructed neurology of the brain.
The illusory nature of the self is an old meme going back to at least the Alleged Historical Buddha, it does not in any way interfere with the scientific method.
