So, my understanding is that you can have a 4 dimensional object, with time being the 4th dimension.

An example given to me of this is a passing window in sports, specifically football. A QB has a 3 dimensional target he most throw the ball to in order for a receiver to catch it. But, due to the nature of pass defense, the ball has to be there within a certain constrained time, less the receiver run past the window, or the defenders close the window.

But, what about something like the feasible window for shooting a flying clay target in skeet? There is a 3 dimensional space that you need to shoot, and it expires after a time as the target goes out of range, but the space moves and shrinks to nil as time elapses. Are these additional dimensions, especially the size / shape of the window? You should be able to model / express them (the size of the window related to time, the location of a window related to time) as a function.

Am I thinking about this correctly? Genuinely uninformed here and looking for analysis and / or references.

Since no one else has chimed in:

I think it's a bit more complicated than that. Zero dimensions is just a single point with no width, depth or anything. One dimension is a line with no width. You can move back and forth along the line but you can't "stick out" from the line. Two dimensions is a flat surface. Three dimensions is what we have with length, width and height. That's the easy stuff.

It's hard to understand anything higher than that except using math. Time acts like a 4h dimension in some ways but not others. For instance, it is independent from all other length, width and height, and according to Einstein they all get warped similarly by acceleration. However, time only moves in one direction, and it keeps moving forward with stopping. So imagine dropping from orbit to the earth. From the moment you jump, you can move longwise or widthwise, but you are pretty much going to keep moving down at a more or less constant rate until you aren't anymore. During your fall, height is acting like time, always moving in a single direction at a predictable rate.

In a true 4th dimension, objects would be able to move back and forth in that dimension or stand still. If you could freeze time and move back and forth through time, then it would be a full 4th dimension. A fourth dimension would also be able to interact with every point in 3 dimensions. A 1 dimensional person would see a 1 dimensional line as a point. A 2D person would see the line as a wall. A 2d person could see only the outer edges of a shape, but a 3d person can see inside a 2d shape. Similary, a 3d person can only see the surfaces of objects, but a 4d person could see inside a 3d object without any effort. if a 3d person saw a 4d person, we'd only see the surface that overlapped with our 3 dimensions. However, a 4d person wouldn't have to overlap with any 3d volume, just like we don't have to overlap with any 2d piece of paper.

Anything higher than 4d and you're better just sticking to math, IMHO

Quote:

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Time acts like a 4h dimension in some ways but not others. For instance, it is independent from all other length, width and height, and according to Einstein they all get warped similarly by acceleration.

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Gotta start with a Sagan classic:


For folks who want to be mind blown by a genius math type about the topic at length;

TLDW: exotic manifolds are tough to comprehend. I'm not the poster/person to do it.