# Very weird thought

i was wondering if anyone knows how to model fourth dimension stuff. i read up about some of it and its completely twisting my brain.

Use Cinema4D

hahahaha =D

the fourth dimension is time. Maybe you were thinking of the fifth dimension

4 spacial dimensions cannot be modelled, but you can model a 3d projection of a 4d object like a tesseract (4d cube) fairly easily. Making it rotate and stuff requires a bit of jiggery pokery with constraints, but a standard one is easy (in wireframe).

Make 2 cubes and join an edge between each corresponding vertex. Thats it.

A common thought. We just interpret the fourth dimension as time - probably based on the well known Theory of Relativity and it’s Spacetime…(how would you explain that a Tesseract has 16 vertices using time as the fourth dimension?)

But IanC is right. More than 3 dimensions are hard to visualize and the only possibility you have, is to use projections into lower dimensions. Yet it obviously doesn’t really show you what the the fourth dimension really “is”. The Tesseract is almost boring when projected to our 3D…but anyway, maybe it’s easier when you show us, what you have read about it and what you want to do!

And the reason why I actually reply is simple…I’m currently working on something heavily based on the Tesseract - quite a coincidence, huh?

The Tesseract is almost boring when projected to our 3D.

Yeah, though interesting to see it rotate. Gordian knots are funky in 4d.

Ever tried 4d puzzles? 4D sudoku is tricky, and I recall a problem of solving n-queens on a 4-d toroidal coordinate system.

There’s a sudoku here:
http://www.mathpuzzle.com/25Dec2006.html
You have to scroll down.

i think shape keys show 4D. in Frame 1 ObjectA is a cube. in Frame 11 ObjectA is notacube, but a sphere. The same object, along a different axis, is something else, but the same (it is still an object). So, 0D a vertex, 1D a line, 2D a square, 3D a cube, 4D a shape-shifting object.

I am taking multidimensional calculus right now.

I find that the best way to envision the fourth spacial dimension (i consider time the 0th dimension) is to think of a room.

In that room there is air, and that air has temperature. Consider the temperature of the air to be the fourth dimension.
Now you can envision level surfaces, and objects that move in the fourth dimension just heat up or cool down.
Heck, even half an object can go down in the 4th dimension and half can go up.

Why doesn’t it “look like” the other dimensions? Because there are only three major dimensions. It isn’t mathematically possible to project more motion dimensions than there are onto the three we have.

i guess my example is more like parallel universies, since the object exists in two different forms at any one time. When you look (observe) the univers through your magic window called frame 1, it is one way, but if you switch to frame 11 window it looks different, even though at that time a parallel universe exists; to confirm you just look through frame 2, 3, 4, 5, or 1 and see the multi-state universe for that state. So you could represent like 9999 different parallel universes with Blender. Great for a physics class assignment - you’d get an “A”.

So could you use changing colors to represent the 4th dimension?

I find that the best way to envision the fourth spacial dimension (i consider time the 0th dimension) is to think of a room.

In that room there is air, and that air has temperature. Consider the temperature of the air to be the fourth dimension.

Temperature is a good example of a possible dimension, but it’s not a spacial dimension.

Why doesn’t it “look like” the other dimensions? Because there are only three major dimensions.

Slight quibble. Not “major”. “Spacial”. There are three spacial dimensions.

A “dimension” can be any value that can change independently of the other values in a vector. In 3D, its possible to change X without changing Y or Z, and likewise with the other two dimensions. But it’s not possible to go in any other direction without changing more than one coordinate. To map a point in space in the universe we live in and can comprehend, you need three coordinates. To map a point in space and time, you need four. In this case, you can move along the time “axis” without moving along any other axes. That doesn’t mean time is the fourth dimension, it’s just a posssible fourth coordinate for a state that requires four coordinates to describe. Temperature likewise. Temperature and time plus space will require 5 “dimensions”.

More than 3 spacial dimensions are mathematically describable, but not intuitively visualizable because our minds are optimized for dealing with the real, 3 spacial dimensional world. Certain kinds of machine learning and information retrieval methods make a lot of use of “high-dimensional spaces.” All this means is that they represent data in the form of vectors which can have hundreds of orthogonal values, or “dimensions”.

There are a lot of possible ways to represent multiple spacial dimensions in something like Blender. You could color code the axes. You could have them displayed at non-right angles even if they were actually right angles, etc, or display straight axes as curved. The more dimensions you’re trying to represent, the more distorted it’s going to be when you try to project it into a 3D representation.

Certain kinds of machine learning and information retrieval methods make a lot of use of “high-dimensional spaces.” All this means is that they represent data in the form of vectors which can have hundreds of orthogonal values, or “dimensions”.

True, I’m running one I’ve written for a client that has well over 4000 dimensions.

Temperature is a good example of a possible dimension, but it’s not a spacial dimension.

But a reasonable visual aid. You can’t visualise rotation with it, but still it’s useful to explain it.

The more dimensions you’re trying to represent, the more distorted it’s going to be when you try to project it into a 3D representation.

True, though you could show a 3d slice (particularly good for 4d, probably awful for higher), in which case you are losing information.

I remember a program on the Acorn that rotated geometric shaped in 4 dimensions. It was both facinating and bazare. :eek: As for MODDELING in 4 dimensions…

There’s something similar here… http://web.meson.org/4drotations/ but it doesn’t show 3D models rotating in 4D, which I think explains more about 4D rotations rather than jumping straight to the hypercupe. (an object that exists in 4D dimensions).

That’s pretty cool! The page he links to is even better.

http://members.aol.com/jmtsgibbs/draw4d.htm

My eyes hurt, but at least now I know what life’s like in the fourth dimension…

@silverfish: no, the fourth dimension is colour :eek:
seriously, it’s obvious that he means the fourth spatial dimension…

Don’t want to comment