Obvious Leo wrote: Minkowski's mathematical chicanery was philosophically bogus from the outset because to represent time as a spatial dimension is metaphysical nonsense.
I find it very sad that I cannot win you over to the idea of higher dimensions of space and how they relate to our subjective perception/cognition of time-motion. You seem very intelligent and I can't understand why you'd oppose this idea. Allow me one more attempt....
In any 'world' of a given number of dimensions of space, you must add one greater dimension of space than exists
within it in order to have a conception of time-motion as pertains to the entire 'world'. As an example, let us take the geometric point. It has zero dimensions of space. In order for the point to move (which implies "moving in time") the point must exist
within a space of one dimension greater than itself. If there are zero dimensions of space, then a point is all that exists, and it cannot move, nor can there be any "time" for it. There simply isn't anywhere else for it to "go", therefore there is no movement and no time. But if we place that point
within a "world" of one dimension greater than itself, like a
line, which has one dimension of space, then we can move the point back and forth within our line. This gives us both motion (of the world itself not just internal to itself) and time.
Now let us take the line which has one dimension. For it to be able to move once again it must exist within a space which has at least one more dimension of space than itself. In this case adding another dimension of space (two) gives us a plane. Now the line can move across the plane and we can cognize "time". Without that extra dimension of space we cannot have any motion-time. We can continue our example by placing a plane within a three dimensional space, such as a cube or sphere. Once again, by placing our world of a given number of dimensions of space (in this case two)
within a space of more dimensions (in this case three), we can now observe and cognize motion. The plane can move
within the cube or sphere, because in the latter we have an extra dimension of space
which allows the former to move
as a whole.
Now let us apply all of the above to the world as we know it --- our world of apparently three dimensions of space. In this world we have a cognition of time, and it applies to the whole. We say that time applies to the
whole Universe of three dimensions of space. Time-motion are not merely going on in one part of the Universe and not in another part, the whole Universe is "moving through time". Our cognition of time applies to the entire Universe as a whole.
Now following the above examples, we can clearly see that another dimension of space is
necessary for us to have this cognition of motion-time-phenomenon
in the first place. Without it, our three dimensional world would be just like the plane, line, or point existing without being within a higher dimension of space --- it would be the only thing in existence and therefore there could not be any cognition of time-motion as applies to it as a whole. Without a fourth dimension of space there could be no time, no motion, and no phenomenon in our three dimensional world at all. It would be a static three dimensional world in which nothing ever happened, nothing ever moved, and nothing ever changed. The reason why we perceive time-motion is because our entire three dimensional world is
moving within a space of greater dimensions than itself possesses, just like the point is moving
within a line, the line is moving
within the plane, and the plane is moving
within the solid. Our Universe is moving
within four dimensions (or more) of space, which accounts for our perception of a "before, now, and after", a "yesterday, today, and tomorrow". Without higher dimensions of space this would be as impossible, just like a point, line, or plane trying to move
within themselves.
For a point to move and therefore have the property of "time" pertaining to its whole, rather than "time" only applying to parts of itself by measuring movements within it, we must have a line. For a line to move we must have a plane. And for a plane to move we must have a solid. For a solid to move we must have a fourth dimension of space (time). The solid can only "move in time", i.e. it can only move if a dimension higher than those within itself are present.
Surely an intelligent man like yourself can grasp this basic geometric (albeit meta) truth. Time is merely how we perceive/cognize our Universe as it moves through a space which has more dimensions than it has within itself (three).