In the introduction to this section, we ended with the suggestion to visualise time like a movie reel.

We will now extend this to two dimensions.

In order to show the complexity gradient visually we will sum up the complexity of each space at a certain time as a colour. We can then show a complexity gradient either as a brightness gradient:

or as a colour gradient like in this picture.

Now let’s see how this could look in a universe with 2 time and 3 space dimensions. This is this 5-dimensional universe near the origin.

If t1 and t2 are interchangeable then their complexity gradients must be equal; so the red arrow showing the direction of steepest order decrease is diagonally between t1 and t2.

Now we move really, really far away from the origin as shown in the next diagram.

This is at the microscopic level. You can see the diamond shaped areas for individual time coordinates. There is a very gentle brightness gradient up/down and a much stronger colour gradient across.

At this level both time dimensions are apparent and you can see how each diamond depends on its predecessors.

Now let’s zoom out to a large scale view.

At this level we can see a very gentle complexity gradient up/down but horizontally the spaces change dramatically fast. An observer at this macroscopic level would experience a single time dimension heading down in the direction of the brightness gradient. In that direction the contents of the space only changes gradually and the observer can make sense of cause and effect and have a memory of the past.

We have called these effectively parallel vertical lines time-lines.

We have marked two time-lines in red and blue. Because we are so far from the origin, they can now be considered parallel. These two are just examples; there are many more time-lines next to them and between them, which are also parallel; running down, the direction of steepest order decrease.

We can look at each time-line in isolation and it looks like a one dimensional “movie reel”, with each frame looking very similar to the previous.

If we select a time-line that is too far off the vertical direction, the frames differ too rapidly for observers to make sense of cause and effect as discussed in Chapter 2.4. Look around you. Things will look pretty much as they did a few minutes ago. These are immense time-scales for the particles.

Still at the microscopic level, each frame interacts as much with predecessors “sideways in time” as with predecessors on the same time-line.

Later we will discuss how it appears when particles travel through our time-lines from “sideways in time”.

At the microscopic level our diamond shaped grid looks like a Japanese Pachinko game, or Quincunx.

The shape that is formed is called Pascal’s triangle.

Point p depends on 2 immediate predecessors, one generation previously. We have marked the influence of these predecessors as 1 in the circle. Each of these has 2 predecessors each so the influence on p from 2 generations previously is 2^{2}=4, but there are only 3 actual predecessors because the central one is shared. This is indicated by a 2 inside the circle; it has twice the weighting of the other two predecessors.

At generation g away from p the total influence on p is 2^{g}, which is the sum of each row in the diagram, but they weighting of the fewer than 2^{g} points is uneven, favouring the central ones. It is easy to see how at the microscopic level p is influenced by points sideways, but macroscopically, at large generational distance, most of the influence will come from the central points, diagonally preceding p.

This is not multiple-world theory [[i]], where the universe splits at ill defined decision points and for unexplained reasons into new worlds that don’t interact.

This is a natural consequence of multidimensional time, and neighbouring universes certainly do interact, in fact neighbouring universes share most of their points. In a 6-dimensional model of our universe we have multiple parallel time-lines through 3 time dimensions and with 3 space dimensions. We don’t split off entire copies of the whole universe at each point.