Before explaining, Google magic cube and look at Wikipedia's description of a magic cube.
What was done there is Wiki took a twodimensional object and projected it into a threedimensional object.
Clearly though what you're looking at is neither twodimensional nor threedimensional and I would describe the object as inbetween, 2.5 dimensional.
Now I'm ready to describe a 3.5 dimensional object. Immerse yourself in VR (virtual reality). Take a threedimensional object and project it into a fourdimensional object. Since what results won't be completely three nor fourdimensional, then for me, this object is 3.5 dimensional.
Math can be that strange (btw if I had the right tools, I could do a better projection of a twodimensional object
into a threedimensional object).
PhilX
What 3.5 dimensions means to me

 Posts: 5035
 Joined: Sun Aug 31, 2014 7:39 am
Re: What 3.5 dimensions means to me
There's a welldeveloped theory of fractal dimension.
The Wiki writeup is pretty clear. Imagine a line or a curve traveling through the plane. It has topological dimension 2. The plane itself has dimension 2. I hope we all agree on that.
You've heard of those space filling curves that are lines that snake around so deviously that they fill up the plane.
The fractal dimension of a curve is a number between 1 and 2 that says how close the curve is to being like a plain old wellbehaved curve of dimension one, and a crazy spacefilling curve of dimension 2. You can have curves that take on any value between 1 and 2 inclusive.
Likewise there are fractal dimensions between 2 and 3 to measure how close a 2D figure in three space is like a regular old 2D surface and how much it's like a 3space filling surface.
Fractal dimension 3.5 would be measure of how some 3space fills up 4space in the analogous way.
This notion of fractal dimension is due to Felix Hausdorff, a brilliant German mathematician of the 1930's who worked in topology, set theory, and functional analysis. In 1942 Hausdorff, his wife, and his wife's sister were ordered to a concentration camp. Rather than go, the three of them committed suicide.
The Wiki writeup is pretty clear. Imagine a line or a curve traveling through the plane. It has topological dimension 2. The plane itself has dimension 2. I hope we all agree on that.
You've heard of those space filling curves that are lines that snake around so deviously that they fill up the plane.
The fractal dimension of a curve is a number between 1 and 2 that says how close the curve is to being like a plain old wellbehaved curve of dimension one, and a crazy spacefilling curve of dimension 2. You can have curves that take on any value between 1 and 2 inclusive.
Likewise there are fractal dimensions between 2 and 3 to measure how close a 2D figure in three space is like a regular old 2D surface and how much it's like a 3space filling surface.
Fractal dimension 3.5 would be measure of how some 3space fills up 4space in the analogous way.
This notion of fractal dimension is due to Felix Hausdorff, a brilliant German mathematician of the 1930's who worked in topology, set theory, and functional analysis. In 1942 Hausdorff, his wife, and his wife's sister were ordered to a concentration camp. Rather than go, the three of them committed suicide.
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