Why doesn't rotation count as the fourth dimension?

Question

I noticed I can hold a object such as a pen in my hand and move my hand in all 3 dimensions, BUT the pen is still facing up the entire time. I have to rotate the pen in order for it not to face up, but I can rotate it without using any of the other 3 dimensions becuase my hand doesn't move along any axis it only rotates.

Answer 1

In a way, rotation IS a dimension. "Dimension" implies a system of measurement, and rotation can be measured in degrees. But it is not as simple as describing motion in a cartesian plane or 3-D reference.

One would have to describe the axis of rotation, describe the relationship of the object to that axis (certainly there is more than one axis about which an object can be rotated), and then state the rotation of the object. But, once that is done, you might certainly be able to describe a change in "rotation", or a rate of change over time -- much like any one of the other, more common, dimensions.

But then, what about when the axis of rotation itself is changing over time -- as the earth does when rotating around the sun? Well, then it gets hairy really quick, and it's simpler to just imagine the "Earth" as a dot going around the Sun -- we can model that mathematically as an ellipse quite simply. :P

Answer 2

If you take the time to rotate the pen ... then you have used the fourth dimension. Time!

Doesn't matter how many times you rotate the pen it's rotation exists within three dimensions the time you take to rotate it is the fourth.

Jonnie

Answer 3

Because when you rotate something, you only rotate it in one or more of the first three physical dimensions. When you rotate your hand, you rotate it around one, or a combination of two or more, of the axes of the first three dimensions.

Answer 4

In some systems of coordinates, like cylindrical or spherical rotation is along the dimension theta or phi. In the Cartesian system of coordinates, the vector of rotation must have components in at least two dimensional directions. In Cartesian coordinates, rotation is the vector sum of two or more dimensional vectors.