A common experience, when some colleague would try to explain some piece of mathematics to me, woud be that I should listen attentively, but almost totally uncomprehending of the logical connections between one set of words and the next. However, some guessed image would form in my mind as to the ideas that he was trying to convey- formed intirely on my own terms and seemingly with very little connection with the mental images that had been the basis of my colleague’s own understanding- and I would reply. Rather to my own astonishment, my own remarks would usually be accepted as appropriate, and the conversation would proceed to and fro in this way. It would be clear, at the end of it, that some genuine and positive communication had taken place.