Yup, this is one of the more interesting old threads to resurrect.

The question, as posed in the thread title, cannot be answered definitively, although I think it's fair to say we've got quite a lot of insight relating to it.

First of all, we can show that clear relationships exist between space and time, hence the emergence of the concept of a unified space-time. However, while we these relationships indicate that space and time are essentially the same, our personal perspective indicates that they are fundamentally different, and I think this is where and why the entire issue arises.

The most obvious difference seems to be that we can move in any direction through space but can only move forward through time.

One way that this can be explained is to look at the phenomenon of time dilation due to spatial movement i.e. the way that time appears to slow down as one moves faster. Now the Lorentz solution that describes time dilation due to spatial movement is a simple adaptation of Pythagoras's right-angle triangle solution, where Lorentz uses it to sum the movement vectors through space and time. The solution indicates that the sum of the two vectors is always equal to the speed of light 'c', so that the rate of movement through time reduces as the rate of movement through space increases, and visa-versa (when you normalise the rates of movement along both axis to the range 0 - 1 and then plot the curve you end up with a quadrant of a circle [

]).

It also seems that, in accordance with Relativity, it is not possible for anything with a non-zero rest mass to be accelerated to 'c'.

The consequence of this is that anything with non-zero rest mass must always exist on the circular arc between the two axis but can never actually reach either axis and just as nothing can be accelerated to 'c', so that the rate of movement along the time axis reaches zero, the implication is that the same holds true at the other end of the arc and nothing can ever be absolutely stationary and move at the temporal equivalent of 'c' through time.

In short then, to change our direction in time would need us to cross the axis, which we can't because we can only ever approach it.

Just going back to that circular plot is also instructive; we seem to only exist along that arc in the quadrant between the two +ve value axis, but the implication of a complete circle is clear.

Also consider how what we view as three spatial dimensions and one temporal dimension may well be transformed into, let's say two spatial axis and two temporal axis.

Imagine a cylinder: we perceive it as a three spatial-dimensional object that exists in a single temporal dimension but we could just as easily define it as being a two dimensional disk that exists for a period of time where the length of the cylinder represents its temporal duration i.e. its life time, but because it has two temporal dimensions we can see its entire life time all at once instead of serially.

So no definitive answer, but I don't think we're entirely devoid of ideas and insights.