Comment Re:The Body Count Unit of Time (Score 3, Insightful) 534
You mistake euclidean geometry with reality.
There are at least 8 dimensions, and more likely at least 11.
Lets do some simple NON-euclidean composition/decomposition here:
- a point is a specific place in a higher-dimensional space. It cannot be described in its' own coordinate system. It's just "there", so we'll assign it a dimension of 1. You cannot "see" a point, for example, though you can describe a points' coordinates, but only in terms of higher dimensions (this should be your first clue that points cannot be perceived in 1 dimensional space). Inside it's own space, a point has NO coordinates - it just "is".
- now let's imagine a sufficient number of "points" with all but one coordinate varying, in sufficient quantity so that, on the balance of probabilities at any one time, they are close enough together that they do in fact define what we would call a "line". The line itself only exists inside the larger coordinate system; lines have added a second "type" to our system. We can now describe things in terms of points (items with 1 dimension) OR lines (items with 2 dimensions, such as a start and a direction). However, a line in and of itself would not be perceptible in a 3-dimensional space, since it would have none of the higher "dimensions" needed to actually exist in that space, such as height and depth;
- So we now take and repeat our transformative operation, taking a multitude of lines and changing a 2nd coordinate - so now they describe what we would call a plane or surface. Would we be able to perceive a pure planar object? No, because it has zero thickness, so while it might exist in the lower dimensions, to us, it would be invisible.
- Next, repeat our transformative operation. Add a 3rd coordinate, and vary it so that our plane now describes some sort of cubic object. Normally, we would say that it has height, width, and depth. Could we now perceive it? No, because it lacks DURATION.
- Duration, or time, like the spatial dimensions, is useless if it is only a point. A point in time, same as the spatial point in #1 above, is not perceptible. We have to apply the same iterative transformation to get a TIME that is actually useful. In all, we've taken 2 starting objects (point in time, point in space), and given each 3 new dimensions, so depending on whether you like zero-based or one-based numbers, we need a minimum of 6 to 8 dimensions for any object.
Normally, we'd prefer zero-based, except that zero-based would tend to get people to think that the 3 dimensions described above are strict analogues with euclidean 3-d space, when they aren't. The point is just as real/fictitious as the line, the plane, and the cube. None of them are real without ALL their time analogues being present, so 1-based it is, for 8 dimensions as the bare minimum for an object in conventional space-time.
Unfortunately, it doesn't end there, but it does show why an infinitely thin monitor can be as "opaque" as you want, but it would have no effect on space-time, and as such would, to your eyes, not exist.
The graininess of the universe allows us to add the necessary mathematical dimensions to "glue" all the above together, as well as explaining some of the "WTF" of quantum mechanics. Consider that, while we now, with 8 dimensions, can come close to describing a conventional object, we are overlooking both the Heisenburg Uncertainty Principle and the Plank constant, which determines the ultimate "graininess" of the universe. The universe simply does NOT allow perfect encoding of any of the above dimensions, so we have to add a mapping of uncertainty to each of them. Fortunately, we can do this with only 3 more "dimensions" - probability for space, probability for time, and probability for space*time, giving us 11 dimensions. (we don't need the underlying probabilities for point, line, plane, because they are implicit in the aggregate probability). We now have an "object" that can exist in and interact with the rest of the grainy objects in our grainy universe.