The Topology of Time

It's natural to think that time can be represented by a line. But a line has a shape. What shape should we give to the line that represents time? This is a question about the topology, or structure, of time.

One natural way to answer our question is to say that time should be represented by a single, straight, non-branching, continuous line that extends without end in each of its two directions. This is the “standard topology” for time. But for each of the features attributed to time in the standard topology, two interesting questions arise: (a) does time in fact have that feature? and (b) if time does have the feature in question, is this a necessary or a contingent fact about time?

Questions about the topology of time appear to be closely connected to the issue of Platonism versus Reductionism with Respect to Time. For if Reductionism is true, then it seems likely that time's topological features will depend on contingent facts about the relations among things and events in the world, whereas if Platonism is true, so that time exists independently of whatever is in time, then time will presumably have its topological properties as a matter of necessity. But even if we assume that Platonism is true, it's not clear just what topological properties should be attributed to time.

Consider the question of whether time should be represented by a line without a beginning. Aristotle has argued (roughly) that time cannot have a beginning on the grounds that in order for time to have a beginning, there must be a first moment of time, but that in order to count as a moment of time, that allegedly first moment would have to come between an earlier period of time and a later period of time, which is inconsistent with its being the first moment of time. (Aristotle argues in the same way that time cannot have an end.)

It is also worth asking whether time must be represented by a single line. Perhaps we should take seriously the possibility of time's consisting of multiple time streams, each one of which is isolated from each other, so that every moment of time stands in temporal relations to other moments in its own time stream, but does not bear any temporal relations to any moment from another time stream. Likewise we can ask whether time could correspond to a branching line, or to a closed loop, or to a discontinuous line. And we can also wonder whether one of the two directions of time is in some way priveleged, in a way that makes time itself asymmetrical.

Suggestions for Further Reading: On the beginning and end of time: Aristotle, Physics, Bk. VIII; Kant, The Critique of Pure Reason, esp. pp. 75ff.; Newton-Smith, The Structure of Time, Ch. V; Swinburne, “The Beginning of the Universe;” Swinburne, Space and Time. On the linearity of time: Newton-Smith, The Structure of Time, Ch. III; Swinburne, Space and Time. On the direction of time: Price, “A Neglected Route to Realism About Quantum Mechanics;”Price, Time's Arrow and Archimedes' Point: New Directions for the Physics of Time; Savitt, Time's Arrows Today; and Sklar, Space, Time, and Spacetime. And finally, on all of these topics: Newton-Smith, The Structure of Time.