Friday, 7 March 2014

Dimensions

I am going back to basics with dimensions. Many page viewers will not need to read this post.

On the flat surface of a blank sheet of paper, there are two dimensions: horizontal and vertical. Each dimension has two directions. Horizontal: left and right. Vertical: up and down. Each dimension is at right angles to the other. Thus, it is possible to move up or down without moving left or right and vice versa.

We can let the horizontal dimension represent the temporal dimension. In that case, the vertical can represent either one of the three spatial dimensions or a second temporal dimension. In this post, it will represent the latter. A temporal dimension has a direction or "arrow" defined by causality, memory and entropy whereas a spatial dimension does not.

If the horizontal represents our familiar temporal dimension, then a horizontal straight line represents a history or "timeline" from beginning to end. Each point on the line represents a moment of time. To an observer located in one of these points, every point to the left is earlier or past and every point to the right is later or future whereas, to an external observer looking down on the sheet, the points coexist with each other simultaneously.

A second straight line drawn above and parallel to the first line can represent a second timeline existing later then the first timeline in the second temporal dimension which extends up the page. If a time traveler, reversing his arrow of time, "travels" leftwards, then he moves pastward in the first temporal dimension (T1). If he travels upwards, then he moves futureward in the second temporal dimension (T2).

The hero of Ward Moore's Bring The Jubilee leaves a timeline in which the South won the American Civil War and enters a timeline in which the North won. He moves left/pastward in T1 to a decisive battle but also up/futureward in T2 to the second timeline. Thus, he can say, from the point that he has reached in T2, that the first timeline no longer exists. However, it is still visible to an external observer of the sheet of paper. Further, it is of no concern to the inhabitants of the first timeline that they will no longer exist according to an observer in the second timeline.

Contradictions only occur when we try to cram all of these diverse events into a single temporal dimension.