This is probably way too late to get seen, but:
We think of dimensions in terms of shapes and space, but really a dimension should be thought about as some *independent* feature that can be changed. So you can think of a piece of clothing: say, a shirt. That shirt might have a dimension for material, a dimension for size, and a dimension for color. There would be more dimensions if size were broken into length, width, height, like we think of for more traditional geometric shapes, but we can assign any number of dimensions as long as we agree that the new dimension is *independent* from the others. In this case, it is true that we can change the color of the shirt without changing its size or fabric (at least when we are designing it).
Another way we can think of dimensions is with a circle. Traditionally we think of a circle as a 2D geometric shape with width and length (or height, whatever). However, a circle *really* only has one “side,” because its width and length are the same. This “side” is its radius. You change the radius, the size of the circle changes. We can completely control the size of the circle by changing the length of the radius. In this sense, it really only has one dimension.
Time is a dimension because it is a variable that can change independent of what we think of as the “traditional” dimensions of position (e.g. length, width, height, or x, y, and z coordinates). In classical Newtonian physics, the 3 dimensions of space are the most important and the ones we discuss and experience most readily. They are highly *visual* dimensions because they affect shapes and relative positions of objects and we are highly visual animals so this carries a lot of significance. As technology grew in the 80s and 90s we talked about “3D” graphics for computers, games, and movie effects, so this idea of “3 dimensions” is anchored strongly in our collective psyche, but these aren’t the only dimensions.
Mathematics can describe any number of dimensions. Again, a “dimension” is really just a feature that can be changed independently of others. Time is the “4th” to the traditional 3 dimensions of space, but there are many more dimensions we can assign to objects and there are even advanced scientific concepts that observe and study more dimensions.
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