A dimension is “simply” a direction that can be changed without changing any of the other directions.
What people often mean is a spatial dimension in “normal” geometry, where “up” is independent from “left” and “forward”.
A square is a two dimensional shape. It can have points on it specified in two coordinates.
When you hold a block, you’re holding a 3 dimensional shape. It takes 3 coordinates to specify a point in it.
When you draw a 3d cube, you’re drawing the 2d “shadow”, or projection, of that 3d shape into 2d.
A tesseract has the same relationship with a cube as the cube has to the square. What we often see represented is the 2d shadow of the 3d shadow of the 4d object.
On it’s own it doesn’t tell you much about the shape. What tells you more is seeing how the lines and points change as you rotate in 4d.
This seems like a fine little tool for seeing stuff.
The 3d shadow of the tesseract isn’t the tesseract though. We can’t actually see them, only the shadow. Thinking hard and looking at the shadows changes as we move the 4d points can let’s us intuit how they work though.
A dimension is “simply” a direction that can be changed without changing any of the other directions.
What people often mean is a spatial dimension in “normal” geometry, where “up” is independent from “left” and “forward”.
A square is a two dimensional shape. It can have points on it specified in two coordinates.
When you hold a block, you’re holding a 3 dimensional shape. It takes 3 coordinates to specify a point in it.
When you draw a 3d cube, you’re drawing the 2d “shadow”, or projection, of that 3d shape into 2d.
A tesseract has the same relationship with a cube as the cube has to the square. What we often see represented is the 2d shadow of the 3d shadow of the 4d object.
On it’s own it doesn’t tell you much about the shape. What tells you more is seeing how the lines and points change as you rotate in 4d.
https://www.geogebra.org/m/mzycqzgt
This seems like a fine little tool for seeing stuff.
The 3d shadow of the tesseract isn’t the tesseract though. We can’t actually see them, only the shadow. Thinking hard and looking at the shadows changes as we move the 4d points can let’s us intuit how they work though.