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What if there were 5 dimensions?

No! No more maAadness f-f-f-for m-m-m-mwahahaha-m-m-m-eeeeeeeeeee!

Besides, if you were a little line segment living on a line, how much of a three-dimensional object would you be able to see?

Chances are I would only see the space on the line but if a line segment could stand it would probably see a decent amount of space.

To be more specific, a line segment (1) cannot perceive the world outside the line (1). Whichever direction it looks, all it should see is a point (0) of varying brightness. If a three-dimensional object (3) passed through the line (1), what would be seen is a certain amount of fluctuation in the brightness of the point (0).

To be more specific, an area (1+1=2) cannot perceive the world outside the plane (1+1=2). Whichever direction it looks, all it should see is a line (0+1=1) of varying brightness. If a four-dimensional object (3+1=4) passed through the plane (1+1=2), what would be seen is a certain amount of fluctuation in the brightness of the line (0+1=1).

To be more specific, a solid (1+2=3) cannot perceive the world outside the space (1+2=3). Whichever direction it looks, all it should see is a plane (0+2=2) of varying brightness. If a five-dimensional object (3+2=5) passed through the space (1+2=3), what would be seen is a certain amount of fluctuation in the brightness of the plane (0+2=2).

The human mind is not designed to visualize extra dimensions. I wish it were.

But then, a computer (which has essentially 2-dimensional processing) can process three-dimensional objects with decent speed. Suppose a human (which has essentially 3-dimensional processing) acquired experience with four-dimensional objects....

I have no idea how I would perceive the world in. I'm always open to seeing new things though.

Hmm, now that you've said that...

Picture the tesseract, endlessly rotating its inner cell and outer cell forever.

I have the visual in mind, I'm just still wondering how it would be applicable to other objects though.

A simple way to visualize is to imagine an analogue of the 3-4 system in a 2-3 system.

A cylinder (3) can be described as a a rectangle (2) wrapping around the circumferences (1) of two circles (2).

A cylinder (3) can be described as a a tube (3) wrapping around the surface areas (2) of two spheres (3).

The circles that form the bases have every point on their circumferences in contact with one side of the rectangle in the same way the tube's surfaces should be in contact with every point on the surface of the spheres.

And about the cake, there was some frustration about how SketchUp turns polylines into line segments enclosing areas after a while without notification, so it is distorted (it is nearly impossible to select 72 line segments at once, move them a specific distance, 144 segments at once, move them a specific distance, and do the same again).

So it does matter, but maybe my lack of SketchUp skills matter even more.

Did you know that songbirds can sing two songs at once?

That's amazing!

*yawn* I'm so tired from hiking today. I think I'll go to sleep extra early today. G'night everyone, and thanks for the birthday wishes!