Comments on: Seeing in four dimensions

Seeing in four dimensions

Surfin' Bird — Sun, 24 Aug 2008 02:56:53 -0800

Mathematicians create videos that help in visualizing four-dimensional objects. Science News writes about it: seeing in four dimensions.

By: jouke

jouke — Sun, 24 Aug 2008 03:57:56 -0800

Older instructions, from 1904, on visualizing the fourth dimension. The rare book is available online thanks to vacapinta and rajbot.

By: stbalbach

stbalbach — Sun, 24 Aug 2008 05:35:52 -0800

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.

By: billybobtoo

billybobtoo — Sun, 24 Aug 2008 06:26:35 -0800

i like his voice.

By: Roger Dodger

Roger Dodger — Sun, 24 Aug 2008 07:05:46 -0800

Love this. Watched the first one and is very well done. Guess I will be sitting in front of the computer for awhile.

By: dilettanti

dilettanti — Sun, 24 Aug 2008 07:08:50 -0800

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....

By: languagehat

languagehat — Sun, 24 Aug 2008 08:12:13 -0800

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!

By: languagehat

languagehat — Sun, 24 Aug 2008 08:13:58 -0800

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.

By: WolfDaddy

WolfDaddy — Sun, 24 Aug 2008 09:27:48 -0800

Dudes, is all the animation done with POV-Ray? RIGHT ON!

By: vacapinta

vacapinta — Sun, 24 Aug 2008 09:44:07 -0800

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.

By: Flunkie

Flunkie — Sun, 24 Aug 2008 10:01:47 -0800

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?

By: jouke

jouke — Sun, 24 Aug 2008 10:05:11 -0800

Just add a 'w' along with your x,y,z and the same equations apply. But what about the visualizing?

By: Flunkie

Flunkie — Sun, 24 Aug 2008 10:06:53 -0800

jouke, soon after that they note that it doesn't really help visualize the situation, and they start showing you how to visualize it.

By: Flunkie

Flunkie — Sun, 24 Aug 2008 10:09:48 -0800

Oh, I'm sorry, you were quoting vacapinta. I thought you were referring to a similar statement in the video.

By: cj_

cj_ — Sun, 24 Aug 2008 10:29:30 -0800

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.

By: psyche7

psyche7 — Sun, 24 Aug 2008 11:09:15 -0800

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)

By: vacapinta

vacapinta — Sun, 24 Aug 2008 11:41:46 -0800

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.

By: CrunchyFrog

CrunchyFrog — Sun, 24 Aug 2008 11:45:14 -0800

One thing I found very useful in visualizing higher dimensions is the novel Flatland.

By: XMLicious

XMLicious — Sun, 24 Aug 2008 12:02:45 -0800

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.

By: XMLicious

XMLicious — Sun, 24 Aug 2008 12:08:46 -0800

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.

By: Flunkie

Flunkie — Sun, 24 Aug 2008 12:43:13 -0800

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.

By: bilgepump

bilgepump — Sun, 24 Aug 2008 18:43:37 -0800

awesome video. the narrator reminded me somewhat of salad fingers.

By: Hactar

Hactar — Mon, 25 Aug 2008 21:17:06 -0800

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.

By: twoleftfeet

twoleftfeet — Tue, 26 Aug 2008 01:06:56 -0800

Very nicely done. If only this level of visualization was available to every high school student before they learn to hate mathematics.

By: vacapinta

vacapinta — Tue, 26 Aug 2008 07:24:08 -0800

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.

By: XMLicious

XMLicious — Tue, 26 Aug 2008 11:27:32 -0800

The thing you linked to just says what year the subject is taught in, not that it's compulsory or universal.

By: vacapinta

vacapinta — Tue, 26 Aug 2008 12:37:28 -0800

Cool! Thanks for pointing that out.