Seeing in four dimensions

August 24, 2008 2:56 AM

Mathematicians create videos that help in visualizing four-dimensional objects. Science News writes about it: seeing in four dimensions.
posted by Surfin' Bird (26 comments total)

Older instructions, from 1904, on visualizing the fourth dimension.
The rare book is available online thanks to vacapinta and rajbot.
posted by jouke at 3:57 AM on August 24, 2008 [1 favorite]

This looks very very cool. Watching the first video I was already lost about half way though, and it is only "the first stage of our journey to the 4th dimension." Hope I make it to the 4th.
posted by stbalbach at 5:35 AM on August 24, 2008

i like his voice.
posted by billybobtoo at 6:26 AM on August 24, 2008

Love this. Watched the first one and is very well done. Guess I will be sitting in front of the computer for awhile.
posted by Roger Dodger at 7:05 AM on August 24, 2008

There are some very nice animations here - thanks for the link! It's a bit odd to be trying to visualize 4-dimensional solids by watching 2-d projective animations of 3-d projections of them. Maybe someday we'll have holographic projections in 3-space that will make things a bit easier still....
posted by dilettanti at 7:08 AM on August 24, 2008

Great post and film! But I've watched the first five and am losing interest because I already know about complex numbers and want to get back to the good four-dimensional stuff. Can someone who's watched the whole thing let me know when it gets back there? Thanks!
posted by languagehat at 8:12 AM on August 24, 2008 [1 favorite]

A minor annoyance: the guy doing the English version occasionally slips up, saying "four" when it should be "two" and "i" when it should be "minus i"—I don't know whether he got a bum script to read or is just reading sloppily, but I'm worried that he might be misspeaking when it's not so easy to tell.
posted by languagehat at 8:13 AM on August 24, 2008

Dudes, is all the animation done with POV-Ray? RIGHT ON!
posted by WolfDaddy at 9:27 AM on August 24, 2008 [3 favorites]

To be honest, I'd always thought that higher spatial dimensions should be part of math education in early secondary school. Kids are ready for it and who wouldn't be interested in "higher dimensions"? Its really not that difficult - an extension of basic geometry. Just add a 'w' along with your x,y,z and the same equations apply.

As can be seen by every breathlessly stupid science article these days (which always abuse the terminology), it is also a fundamental part of modern science - both relativity and modern physics.

The website here already mentions that complex numbers are taught to kids in secondary school in France. Sadly, I'm not sure thats the case in the United States.
posted by vacapinta at 9:44 AM on August 24, 2008

The website here already mentions that complex numbers are taught to kids in secondary school in France. Sadly, I'm not sure thats the case in the United States.

Huh? It certainly was for me. Why do you think it wouldn't be?
posted by Flunkie at 10:01 AM on August 24, 2008

Just add a 'w' along with your x,y,z and the same equations apply.
But what about the visualizing?
posted by jouke at 10:05 AM on August 24, 2008

jouke, soon after that they note that it doesn't really help visualize the situation, and they start showing you how to visualize it.
posted by Flunkie at 10:06 AM on August 24, 2008

Oh, I'm sorry, you were quoting vacapinta. I thought you were referring to a similar statement in the video.
posted by Flunkie at 10:09 AM on August 24, 2008

The website here already mentions that complex numbers are taught to kids in secondary school in France. Sadly, I'm not sure thats the case in the United States.

Assuming "secondary school" maps to high school here, then yes -- at least when I went there ~15 years ago. Although I may have learned it in pre-calc, which isn't compulsory. Not everyone makes it that far. I wouldn't be surprised if the math curriculum has been dumbed down since then so no child gets left behind, though.

Also, good videos, thanks for the post.
posted by cj_ at 10:29 AM on August 24, 2008

Need more help with higher-dimensional visualization?

4D Visualization
Thinking 4-d - visualizing 4-space
Visualizing the Hypercube
V3d+ Equations
how How Does One Obtain the Ability to "See" in Four Spatial Dimensions?
Polytope Visualization: Peek N-dimensional polytope visualization
4th Dimension: Selected Course Notes
Applet to see 4D shapes - Ken Perlin Seeing into four dimensions
Hyperdimensional Java Applets
Surfing Through Hyperspace
The Tesseract - a 4-dimensional cube from Interactive Mathematics Miscellany and Puzzles
Hyperspace structures Exploring the fourth dimension
enter the fourth dimension
Fleischfilm

Hyper Dimensia HyperDimensional Viewing
Russell Towle's 4D Star Polytope Animations
Four Dimensional Figures Page Uniform Polytopes in Four Dimensions
Fourth Dimension: Tetraspace
Stereographic projection of 4D rotating cube
N-Space
Why the Rhombic Dodecahedron is a Shadow of the 4-Dimensional Hypercube
Hyperspace structures

Thomas Banchoff's Home Page
The Fourth Dimension Thomas Banchoff
Beyond 3D *

MagicCube5D

From : Dimensions and Dimensionality (self-link)
posted by psyche7 at 11:09 AM on August 24, 2008 [8 favorites]

Huh? It certainly was for me. Why do you think it wouldn't be?
posted by Flunkie at 6:01 PM on August 24

Where I went to high school (San Diego) it wasn't compulsory. I think most people go up to pre-Calc and I dont think complex numbers are part of the curriculum.
posted by vacapinta at 11:41 AM on August 24, 2008

One thing I found very useful in visualizing higher dimensions is the novel Flatland.
posted by CrunchyFrog at 11:45 AM on August 24, 2008

I wouldn't say that the videos in the OP are strictly to "help in visualizing four-dimensional objects". That's somewhat secondary - note that they really only cover visualizing 4D Pythagorean solids. And for example their favorite method for visualizing, the stereographic projection, wouldn't be very useful for visualizing the 4D analogs of a cone, cylinder, or sphere. (Demonstrating what a 4D hypersphere would look like via the "slicing" method is quick and easy but they don't touch on that.) They're just making a basic pass through explaining four dimensions because it's intimately connected to the other topics they cover, seems to me.

But I think it's a great post and a quite valuable video series in that it's taking a Connections-type approach to a cluster of pure math topics. The authors also did well in putting a good balance on it so that it can appeal and be rewarding to someone at almost any level of math knowledge.

Good list of resources psyche7, I look forward to picking through them. One thing I'll add is that the book mentioned in the Escher-themed video segment, Edwin Abbot's Flatland, is very much a classic and is available in several online versions.
posted by XMLicious at 12:02 PM on August 24, 2008

On complex numbers - in public school in New England it was definitely introduced as a topic well before pre-calc, covered in-depth with high-school level Algebra IIRC.
posted by XMLicious at 12:08 PM on August 24, 2008

Where I went to high school (San Diego) it wasn't compulsory.

I don't remember whether it was compulsory or not for people in my school. Regardless, you didn't say that whatever page you were looking at says that it is compulsory in France, either.
posted by Flunkie at 12:43 PM on August 24, 2008

awesome video. the narrator reminded me somewhat of salad fingers.
posted by bilgepump at 6:43 PM on August 24, 2008

This is really cool stuff. I worked with a lot of this in college, but it's really fun to see it again. I wonder now about trying to use this in a pre calculus or calculus class.
posted by Hactar at 9:17 PM on August 25, 2008

Very nicely done. If only this level of visualization was available to every high school student before they learn to hate mathematics.
posted by twoleftfeet at 1:06 AM on August 26, 2008

Regardless, you didn't say that whatever page you were looking at says that it is compulsory in France, either.

The guide page, referring to Chapters 5 and 6.
posted by vacapinta at 7:24 AM on August 26, 2008

The thing you linked to just says what year the subject is taught in, not that it's compulsory or universal.
posted by XMLicious at 11:27 AM on August 26, 2008

Cool! Thanks for pointing that out.
posted by vacapinta at 12:37 PM on August 26, 2008