Time IS NOT the 4th dimension

>"Degree of freedom" is not a sufficient definition for "dimension"

What do you imagine is missing from that definition?

It's way too wide.
There are many cases where there is less freedom of movement that is not related to having less dimensions

If you mean you can't always move freely along a given dimension then obviously. If you mean something else, I have no clue what you mean.

Which "way" does the hypercube extend from a cube?

Into a fourth spatial dimension orthogonal to the existing three.

I would define dimension as:
"The amount of Axis you can possibly move in"

It's similar to your definition, but it's more specific

What do you think a degree of freedom is? It is a axis of possible movement, nothing more, nothing less.

Degree of freedom can be limited in many ways that are not related to how many axis you got.

An object has less degree of freedom if other physical objects block it's way, for example

So there's a direction which can't be expressed in terms of the other 3? How do i envision it?

You can't, your brain only groks three dimensions. The closest you can come is to imagine Flatland, a Universe with only two spatial dimensions, and then try to explain to a Flatlander where a three dimensional cube "goes".

You don't have to be able to travel along a dimension freely for it to count as a degree of freedom. For example humans can't move along time freely but it still counts as one of our four degrees of freedom.

I mean there was that one lady who was able to intuit 5th and 6th dimensional shapes if I recall correctly. Humans believe and envision lots of impossible things, like you ever getting a girlfriend.

Yeah, no she couldn't. It's easy to model them mathematically, but imagining them is literally impossible.

It is just a perspective projection of a wire-frame form 4D to 3D

Imagine you had a wire-frame 3D cube above a flat 2D surface and held a light source above it to project the shadow of the cube onto the surface.

Add color and it is possible
Your eyes already do this (binocular vision actually gets you to 5D)
Vertical, Horizontal, Hue, Brightness

Useful for functions from C to C

en.wikipedia.org/wiki/Complex_analysis

the order of the pole or zero is represented by how many times you cycle through the color wheel when winding around (note that poles cycle through the color wheel in the opposite direction of the zeros)

It's possible to imagine differently colored three dimensional objects, it is impossible to imagine a four dimensional object. Your brain simply doesn't work like that, you might as well try to imagine a married bachelor.

Analogy to knot diagrams
"where does the string go when it disappears then reappears?"

Maybe >Your brain

>HURR I'm capable of literally impossible things!

Sure you are sweetie.

It's like hearing a blind person tell a sighted person that "seeing" doesn't exist because they, themself, cannot see.

Time is the fourth dimension. Think about "Interstellar" (2014) when Cooper enters the black hole and goes into "The Tesseract" where he can see into different windows where events are being repeated over and over. So, time can be seen a non-physical dimension where things that will happen are already happening. The proof I have for that is death. Everyone is dying, but why?

the tesseract is an object in 4D Euclidean space and the fourth Euclidean dimension is certainly not "time".

There is no "the" fourth dimension.

The concept of dimension is just a helpful way of talking about the number of pieces of information necessary to fully describe something. For most physical purposes, we only need three dimensions because our world can be efficiently modeled with only three pieces of information (length, height, width or x, y, z, whatever you want to call them). But in some cases, it is necessary to mention a fourth piece of information. You do this everyday without realizing it. For example, if you need to take an exam, you need four pieces of information: the physical location of the test-taking room, which can be represented through three physical dimensions, and the time of the exam, which you need an additional dimension to represent.

If you want something a little more formal, I always though the definition of dimension I got from linear algebra was helpful. In that sense, the dimension of a vector space is just the number of elements in a basis for it, though I'm not sure how well this definition translates to other more advanced fields of math.
This is useful to keep in mind as well, Euclidean 4-space is one example of a four dimensional space where the fourth dimension is not time, whereas Minkowski space is a four dimensional space where the fourth dimension is time.

the fourth dimension is duration, dumbass. what a pathetic attempt to troll, you know google exists right?