QOD #11 — Solution

Solution

This QOD allowed for several answers, especially creative ones, if you defined "dimensions" in the right way. Specifically, "dimensions" are not limited to defining position only. Examples are below.

Example of a creative answer:

If you lived in a different world where "time" was not defined the way it is defined on Earth, and the sky turned different colors at random, or random odors passed through, you could tell your friend, "I'll meet you on E. 53rd Street, 4th floor, purple, (or) onion odor." Combining the "odor" basis with a "color" basis, you can make either one a 4th dimension, and the other one a 5th dimension. As the problem defined, as long as the bases are independent and not definable through combinations of other dimensions, they are valid answers. This example is very similar to an example that Douglas Adams gave in Hitchhikers, where he defined "probability" as a dimension.

Example of a theoretical dimension

This is a picture of a hypercube, or hypersphere:
In theory, as you watch each of the 3-d boxes/cubes "move" or change from one to the other, you are watching 4-dimensional movement. Additionally, you can make the analogy that a 0-d point is the projection of 1-d (a line) onto 0-d space, that a line is the projection of 2-d (a plane) onto 1-d space, that a plane is the projection of 3-d (a cube) onto 2-d space, and finally that a cube is the projection of 4-d (a hypercube) onto 3-d space.

Example of a real-world answer

Humans are multidimensional: 3-d volume (height, girth, etc.), weight (mass), hair color or eye color, etc. are all independent characteristics that can be defined as distinct dimensions according to this QOD. Another real-world example would be the elctron, for which you can describe its position (3-d) and its spin (4-d).

Comments

I regret to say that I think this QOD really sucked. The "answers" were too easy to come up with once given a second of thought (if that much). Admittedly, given Dr. MacCready's lecture, it does inspire thought beyond the restrictions of the "traditional" space-time dimensions, but most of us have already passed that boundary
Why would most people think that "time" is the 4th dimension? It is a "dimension" as defined in the QOD, but, as the second example states, there is a 4th spatial dimension. In fact, if theory is to be believed, there are ten such spatial dimensions. Of course, we are unable to perceive these higher dimensions. And because of that, I believe that these higher dimensions make for poor answers to this QOD
Incidentally, the image might be clearer like this:

At least now, you can see the cubes (or at least, one possible pair)
Ever read Michio Kaku's "Hyperspace"?

Back to the QOD