

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.






You’re more right than you might have expected, but not because it’s a fallacy or misleading. You noticed something important in how it all works: time is a dimension, but it doesn’t act like “up” or “forwards”.
This doesn’t make it less of a dimension or a hindrance to understanding, it’s an observation that leads to: there are different types of dimensions.
Typically called time like and space like, they can also be thought of as “one directional” and “two directional”, although a physicist somewhere is (correctly) coughing politely and glaring at some of the shit photons get up to at the thought of one directional time.
You’re thinking of time as a parameter, which is how it is in classical mechanics. It’s a different category of thing, but it technically makes the system 4d.
When you start looking at how light moves and relativity you find that you actually need time to act much more like another direction because it no longer defined an order or sequence, and you get stuff like “time slows down when move faster in space because acceleration shifts your movement vector in space time”.
It’s even simpler in math, because a dimension is simply a number required to specify a point in a space. If you cared to you could use “left” as your parameter and talk about how a thrown ball changes position in time, up, and forward as a function of left.
Then you could do some real math and use that function as a point in some space and talk about how the different components are different dimensional aspects of the infinite dimensional polynomial function space.