Is Time the 4th Dimension ?

Such a movement in itself implies that there is a change between two time-points. We can be here now and compare this to where we were in the past. So, it appears that without time (or change), a movement cannot be defined and thus we cannot describe the concept of a dimension.

One strategy to deal with this mutual dependency is to force the issue and declare time to be a dimension in itself and place the observer completely outside space. If we could do that we would be able to observe space instantaneously and would be able to define a navigational system that would respect our current understanding of dimensionality. E.g: look at the snapshot of the world and observe what is present at position (x1,y1,z1) and then observe what is present at another position (x2,y2,z2). We would find that the observation at each coordinate becomes more similar the closer those two coordinates come to each other (continuity), and this for each of the individual dimensions of the coordinate system.

Dimensionality in this case defines the structure of the space. It specifies how we can alter the similarity between observations by altering either of the coordinates. In this sense dimensionality is merely an ordering of space such that it forms a continuous space. We could choose any other ordering of space that still acts as a continuum (at a specific scale).


Of course we cannot place the observer outside the universe and as soon as we place the observer within the world, time becomes much more difficult to understand. As a thought experiment, consider Lineworld (next figure), a 1 dimensional world, in which the Linelanders live. They currently observe a point O moving from coordinate 1 to 4. To be able to describe this change, they set out a 2nd dimension and call it A-time. (The fact that they develop time is necessary from their perspective, hence we observe the universe as if it were through their eyes). Consider now that Lineworld was actually moving through Flatland, a 2 dimensional world, inhabited by Flatlanders, and that the movement of point O was directly related to the movement of Lineworld through Flatfland. The Flatlanders also developed the concept of time, called B-time. For them it is a 3th
dimension that accounts for changes in their world. Without their B-time, they cannot model the location change Lineworld seems to be experiencing.

Now, the interesting thing is that from the Linelanders their point of view it does not matter whether Lineworld was solely moving through time (A-time) or through time in another dimension (in which case A-time is the 2^{nd} dimension in Flatland and the time dimension the Flatlanders developed: B-time). In both cases the trick of adding a time dimension makes it possible for the Linelanders and Flatlanders to cope with change. This illustrates that time might as well be a collapse of all remaining dimensions and simply model in-deterministic behavior.

Following the above logic, in both cases the main pinnacle is change. Whether this change is deterministic, non-deterministic matters little. Whether A leads to B, or B happened instantaneously, independent of A, or whether B cause A and we observe them in the wrong order all does not matter. The bottom line is that everything changes. There are however some properties of time and change that are worth discussing.

Time is in comparison to normal spatial dimensions also perceived as a continuum. Things do not suddenly happen, there is always some form of explanation, (It seems humans can come up with any form of explanation, whether this gives us any predictive power is an entirely different matter, but our neural networks/brains are extremely capable of creating explanations that offer no advantage whatsoever.) or rather continuity from one state to the other. A second observation regarding time is that it ties together different dimensions, such that a coordinate change of an object is instantaneous at all other dimensions at the same time. A third observation about time is that it tends not to be viewable. We simply cannot look at the past as we look at a spatial room. We can in the same manner not look into the future as we look into the distance. This of course makes sense since the complexity of the landscape across time is so much more complicated because it is probably a collapse of all remaining dimensions. As such we are stuck with no predictive power and no determinism unless we are able to unravel these dimensions and observe them as they are but even that might not be possible. It is very unlikely that Linelanders can deduce the objects that exist in Flatland simply by sorting the information appropriately.