Space, Time, and SpaceTime
Let's look into some physics.
I've been thinking about SpaceTime and the components thereof for as long as I can remember. It started when I was a boy, I would always wonder about the fourth spacial dimension. I never bought that there were only three spacial dimensions, nor that time was the end all be all fourth dimension. I always believed that to be false.
I do believe that Einstein was correct when he said that Space and Time were interconnected, related, and more or less one thing. I just never believed that Space ended at three, or that Time consisted of only one- dimensions, that is.
Space
In recent years, I've come to hear the name of the Tesseract, which is to the Fourth Dimension as the Cube is to the Third Dimension. I'd always known one was possible, however, never heard it's coined name until less than a year ago. I am vexed by patterns, and so, when faced with the daunting self-assigned task of imagining a Tesseract, I began working out patterns with what little I had to work with.
First, I decided to break down each dimension into a regular object. I have an affinity for squares, and they're the basis of the Tesseract (as opposed to triangles, pentagons, circles, etc), so it made for a good choice.
I then looked to each Dimension and took their component parts. I started with the "Zero" Dimension, the fundamental component thereof is a mathematical point. The First Dimension's component is a line. The Second's a plane. The Third is a 'Three-Dimensional plane', which though aptly named, is not rather creative.
After I'd done that, I looked at each regular object and listed the number of each component found in each. For example:
Number of points per object: 0D(point): 1 1D(line): 2 2D(square): 4 3D(cube): 8
And as you can see, patterns appeared. In this case, the number of points in the regular object of a dimension n can be represented as 2n.
If this formula proves true in the Fourth Dimension, then we can calculate that a Tesseract will contain 16 points or 'vertexes'.
Using similar methods, we can determine the number of lines, planes, and 3D-planes that comprise a Tesseract.
However, Understanding the make-up of a Tesseract does not prove its existance, nor does it allow one to picture it, in their head or otherwise.
Time
So then, on to Time we go.
I do not believe that Time is one-dimensional, as I mentioned above. I believe that it is at least two-dimensional, however, we only have proof of it having one dimension.
I'd like to explain what I think the possibilities are. As well as their effects on free will and the possibility of time travel.
One-Dimensional
I'll admit, it's possible that time is one-dimensional, and if it is, then all time would already be determined. To such an extent that the advent of consciousness in the universe could not affect any outcome. one-dimensional time is pure pre-determination. Not to mention time travel is useless/impossible in this model, as if any detail is changed in the past, a paradox would open up, preventing said time travel from occuring. An exception is made for a case in which one was pre-determined to travel back in time, and does not alter any history. (much like in Harry Potter, by the lake. He was there in the first instance, and in the second).
Two-Dimensional
Then there's two-dimensional time, in which there are two possibilities I consider to be possible. NOTE: once you pass one-dimensional time, time travel can exist without us being aware until discovering it.
2D Time Graph
The first possibility is that, much like a two-dimensional graph, time lies on a plane, and must go from 0 (the bottom of the graph) to 10 (the top), but may take any course to get there. This allows for true free will, as any choice could slightly alter the path time takes. This possibility also allows for time travel, as the line may move backwards and split from the original line at any point, preventing paradoxes by not overwriting the events that caused the change to begin with.
2D timeline idea
A take on the 'timeline' idea, in which there are multiple timelines that coexist, and any decision made either moves you to a new timeline, or creates a new timeline, however, in this example, time travel would be tricky, if possible, as it could potentially require one to pass through many timelines in order to reach their destination.
Three+ Dimensions
There are several possibilities here, but I'll only touch over each one briefly.
3+D time graph
Essentially just like 2D time graph, however on a 3D temporal plane such that time travel has more freedom to play with events (shifting time one way then the other in 2D causes time to cross itself. In 3+D, this would not happen so often.)
3+D timeline
Again, similar to 2D timeline, however, it would allow more free will (an infinite number of possible timelines to move to at any one time, whereas in 2D, you could only shift it in two directions, the only variable being the amount), as well as more options for time travel (not having to cross another timeline to get to the destination timeline).
Multiverse Theory
This theory may not seem to have to do with time, but in reality, it does. If multiverse theory is correct, the number of temporal dimensions doesn't matter, as free will is at its zenith. Time travel would still be dependant upon time itself, however, if traveling between the multiverses were possible, it would/could act as time travel in and of itself.