So far here we have only limited ourselves to a single time dimension.
It is easy to imagine the concept of multidimensional spatial objects. Even if imagining the actual objects is a challenge, extrapolating their existence and properties is trivial.
- 0 dimensions are a point.
- 2 points delimit a line of 1 dimension. It has a length s.
- 4 points or 4 lines delimit a square of 2 dimensions. It has an area s2.
- 8 points or 12 lines or 6 squares delimit a cube of 3 dimensions. It has a volume s3.
- 16 points or 32 lines or 24 squares or 8 cubes delimit a tesseract of 4 dimensions. It has a hypervolume s4.
- 32 points or 80 lines or 80 faces or 40 cubes delimit a hyper-hypercube of 5 dimensions. It has a hyper-hypervolume s5.
It is easy to handle arbitrary dimensions in mathematics, it is just difficult to visualise a 4d object like a tesseract because our world is limited to 3 space dimensions.
If time and space is the same thing apart from the complexity gradient then what would a multidimensional time world look like?
This is easy to imagine from the outside, but harder from the inside as an inhabitant of the world.
In a 2D world with 1 space and 1 time dimension, this is a representation of order against time:
Now let’s consider a 3-dimensional world with one space and two time dimensions. Here we have another diagram of order, but this time plotted against 2 time axes. We get a slope again, but this time it is cone shaped.
Even though there are only two time dimensions there are many timelines, which are the possible downhill paths. Here in the diagram we have marked two, A and B.
As in the single dimensional case we notice that the complexity gradient appears smooth only at a distance, zooming into a small area (circular inset) we see a bumpy landscape.
Make the thought experiment of considering the slope to be real, and place a ball bearing onto the slope to represent the present. In the first 2-dimensional world case the ball bearing would roll down into the direction of the future.
If we place a ball bearing on the cone shaped 3-dimensional slope, it still rolls downhill, even though the direction ‘downhill’ is not universal, but depends on where we place the ball bearing. In a 2+1 dimensional slope there is also less chance that the ball can get stuck in a local minimum. If it hits something like a bump on the slope it will often be able to route past it to the left or to right.
At each point there is a direction where the slope is steepest, which points into ‘future’ of our time dimension. However there are other directions still going downhill where the slope is not as steep.
The complexity gradients of the multiple time dimensions do not need to have the same steepness. Here are pictures of the same two cones from three different angles. One cone is flatter than the other; the slope of one axis is three times steeper than the other.
The interesting question is how it would feel to be inside a world where the time is 2-dimensional. The answer is surprising.
Let us consider some events A, B and C in a one-dimensional time case:
In this representation event A causes event B which in turn causes event C. An observer looking at event C will remember B and A as well.
In a two dimensional case the flow from event to event is more like a tree: (The labels A,B,C etc have nothing to do with the labels of the 1D case above.)
An observer at point D will remember the events B and A, but not for example the events C or E because they have had no direct influence on the state of the world at D. Interestingly, an observer at event E shares the same memories of B and A as the observer at event D.
So if time were multidimensional when looked at from the outside vantage point, it would appear to be 1 dimensional to observers inside the world.
The effect that appears strange is that each observer, i.e. you and me, continuously spawns off copies of itself, each of which share the history (and memories) of the other up to the spawn off point.
Most of the bizarre and counter-intuitive seeming quantum effects can be explained by the multi dimensionality of time if one bears the two different viewpoints in mind; how does the world appear from the outside and how does it appear to a being that lives inside it.