Four Dimensions: A Simple Proof
This is a proof that four dimensions is sufficient to contain all possible spaces and times — ten are not necessary.
First, let us remember what a dimension is. Mathematically, a dimension is an axis across which something can change. Space has three dimensions, because you can change along length, width, or height. Time has a dimension because you can change through time. Saltiness also has a dimension, although it’s not particularly useful for most purposes; but even so, my science teacher informed me that oceanographers treat saltiness as a dimension.
One dimensions represents every possible value of some particular thing. A dimension could be represented with a line, which contains every possible location in one-dimensional space. It could be represented as moving through every possible shade of red, or every possible level of saltiness, or any other measurable thing that you can think of. You can also use this line to represent every possible combination of this thing: you can represent one shade of red along the redness dimension, or you can use two points to represent two shades of red, or three points to represent three shades of red, and so on.
What about when you introduce a second dimension? Now you can represent every combination of two things and every possible set of combinations. The most obvious example is length and width. On a spacial plane, you use a single point to represent length and width, and a set of points to represent many different lengths and widths.
You can also extend this into three dimensions, for example with three-dimensional space. Using the axes of length, width, and height, you can represent any point in space.
Next, bring it into the fourth dimension. If the first three dimensions are space and the fourth is time, then we are now able to represent every combination of space and time that can possibly exist. This four-dimensional construct contains all possible universes and all possible timelines.
I have an objection to this proof, as well as a refutation. It is much more complex, so I will be addressing it in an upcoming post. If you still have a problem with my proof, stick around.