In metaphysics, extension signifies both 'stretching out' (Latin: extensio) as well as later 'taking up space', and most recently, spreading one's internal mental cognition into the external world.
The history of thinking about extension can be traced back at least to Archytas' spear analogy for the infinity of space. How far can one's hand or spear stretch out until it reaches the edge of reality? "If I arrived at the outermost edge of the heaven, could I extend my hand or staff into what is outside or not? It would be paradoxical [given our normal assumptions about the nature of space] not to be able to extend it."[1]