Seeing in the 4th Dimension

[Rudy Toody]

Article is here.

Videos are here.

This is so cool!

 

[lxskllr]

Very cool, thanks for the links :^)

 

[Molondo]

I just finished the first chapter. I wish when i was learning vectors in 3d space (matrices, algebra, etc), they had a visual representation of the things they were teaching. It was difficult at first to visualize and conceive what a cross product, or dot product, or subspace, or any of those did or are at first. Then i was introduced to matlab... life became easier.

In other words, thanks for the videos.

 

[Rudy Toody]

Chapter 6 has an incredible zoom-in on a fractal!

I can't wait for their next edition where they explore the Riemann Hypothesis!

 

[DrPizza]

Next, he draws the three-dimensional ?shadows? of the four-dimensional objects. This turns out to be much better: Rotating the objects around to see different facets of them can give a pretty good feeling for their shapes.

Nothing new That's exactly what my senior thesis was when I received my bachelor's in applied mathematics. I wrote a bunch of software that operated on Mathematica to do just that. It was a lot easier to conceive of the mathematics than it was to "see" 4-dimensional objects in my mind. My work was inspired by my professor's work, Flatland (Abbott), and the work of Thomas Banchoff (Brown University.)

Thanks very much for the link though. I'm required to have "emergency" sub plans in my school's office. I think I'll just get a copy of the DVD & toss that in my sub folder.

 

[BrownTown]

TBH though you are getting screwed over here trying to imagine 4D with only a 2D screen. At the very least you would want a series of 3D object in order to visualize the 4D object. All this is very good and all, but its like trying to visualize a 3D object based entirely on looking at a bunch of 1D objects (lines of different lengths)

 

[Rudy Toody]

Question:

They state that there is no 4 dimensional sphere. Could you approximate a sphere by creating a very large Bucky Ball? One that has many edges to form many shadows?

 

[SsupernovaE]

Originally posted by: BrownTown
TBH though you are getting screwed over here trying to imagine 4D with only a 2D screen. At the very least you would want a series of 3D object in order to visualize the 4D object. All this is very good and all, but its like trying to visualize a 3D object based entirely on looking at a bunch of 1D objects (lines of different lengths)

I agree. For me, it would probably be better if I close my eyes and felt the 3-D objects and imagined them as the faces of the 4-D parent object.

 

[Omegachi]

neat

 

[BW86]

sweet

 

[Gannon]

It's interesting how they chose to do the projections, I wonder if they should get into contact with the game industry to do it better.

Does anyone here remember falling outside of the world in a shooter / FPS / RPG? and you get smeared mirror/images all over?

I'm thinking that might be a good aproach to exploring the 4th dimension, in terms of super imposed images on top of one another with the smear of the object itself in time.

It'd be neat to see what the game industry coders could do with something like that, the art and stuff was neat but I bet with some expert coding from the entertainment / art industry they could take it too the next level (cool shader effects, etc).

 

[hasu]

Here is another tool to help your imagination of higher dimensions...
http://www.tenthdimension.com/medialinks.php

 

[DanPonjican]

Wow! My brain hurts!