Friday, March 16, 2007

The shape of space

Michael Proudfoot has a lot to answer for. Some years ago, during an undergraduate philosophy seminar, Michael introduced the seminar attendees to Anthony Quinton's dreaming argument. To counter Kant's claim for the necessary unity of space, Quinton suggested the following scenario:

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.


Susan said...

Gordon, Do you remember an absolutely horrible movie was made based on this concept -- it came out a few years ago and I only watched it because I was on a transatlantic flight and the novel I'd brought was a dud. (This movie was a dud, too -- or, rather, a train wreck.) Demi Moore was the person who had two lives -- one in the dream world, where she lives in the South of France with husband and two kids, one in the real world, where's she's a single woman involved with that actor named Ed (?) Ficht. Both lives unscroll day by day and night by night.

Movie was called "...of Mind" and doubtless went straight to video (or in-flight movie).

Gordon McCabe said...

It was called Passion of Mind, Susan, and Demi Moore's performance in it earned her a Razzie (Golden Raspberry Award) nomination in 2001.

Neil Forsyth said...

Very interesting Gordon. I hadn't come across Quinton and his scenario before. Topologically, but not metrically connected? I'm struggling with that one. The length of his dream-day appears to be the same length as his ordinary, waking day, yet isn't, and cannot be. It's this problem of space and time again. I get really stuck. I can't conceive of time being condensed, somehow, yet be experienced as unaltered in this condensed form. Then again, I could be reading it arseways.