Suppose that on going to bed at home and falling asleep you found yourself to all appearances waking up in a hut raised on poles at the edge of lake. A dusky woman, whom you realise to be your wife, tells you to go out and catch some fish. The dream continues with the apparent length of an ordinary human day, replete with an appropriate and causally coherent variety of tropical incident. At last you climb up the rope ladder to your hut and fall asleep. At once you find yourself awakening at home, to the world of normal responsibilities and expectations. The next night life by the side of the tropical lake continues in a coherent and natural way form the point at which it left off. Your wife says, “You were very restless last night. What were you dreaming about?” and you find yourself giving her a condensed account of your English day. And so it goes on. ('Spaces and Times', Philosophy 37 (1962), pp. 130–47).
Quinton suggested that one world could be spatially disconnected from the other, without breaking the unity of the individual's consciousness. Intriguingly, though, Mr Proudfoot also proposed that the individual's experience of time across the two worlds was 'topologically, but not metrically connected'. I didn't understand what this meant, because I didn't know what topology was, but my curiosity was definitely piqued, and I set about finding out exactly what it was.
Combined with an interest in cosmology, this brought me, some years later, to a fascination with the topology of space. And here, I'd like to recommend a couple of introductory articles to the subject. First, Jeffrey Weeks's article, 'The Poincare Dodecahedral Space and the Mystery of the Missing Fluctuations', which won the American Mathematical Society's 2007 Conant prize for expository articles. Secondly, the article which Weeks co-wrote with Neil Cornish in 1998, 'Measuring the Shape of the Universe'. Both articles explain the possibilities available for the shape of space, and the proposals for inferring the shape from the cosmic microwave background radiation.