Seeing in four dimensions


	Seeing in four dimensions

Silkweaver

8-29-2008 8:20 PM

1096 views

tags:

mathematics, visualization

Silkweaver says:

The videos are all available free at www.dimensions-math.org. The videos go on to show how we can visualize imaginary numbers geometrically, how fractal patterns emerge in the Mandelbrot set and Julia sets, and how beautiful and complex shapes can be built up from circles.

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8-30-2008 4:23 AM

abailart

A wonderful, beautiful site. How especially inspiring to see: <<<Commentary in Arabic, English, French and Spanish.
Subtitles in Arabic, Dutch, Chinese, English, French, German, Hebrew, Italian, Japanese, Portuguese, Spanish and Russian.>>>

9-1-2008 4:43 AM

Silkweaver

I think it has to do with the number of dimensions one would allow himeslef to see

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<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/1f05d0bb-8603-40bc-baec-0b5662495b29/4F09A365-7400-4733-9459-4B580721F4E0/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions" href="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions" style="font-size: 11px;">www.sciencenews.org</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions">Mathematicians create videos that help in visualizing four-dimensional objects</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions">Three dimensions can be so limiting.</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.sciencenews.org/img/1A32D84E-BE41-4AE2-9C14-C99E1F3154C1" alt="access" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions">There is the minor difficulty that our nervous systems are only equipped to conjure images in three dimensions. But that doesn’t stop Étienne Ghys of the École Normale Supérieure in <ST1:PLACE w:st="on"><ST1:CITY w:st="on">Lyon</ST1:CITY>, <ST1:COUNTRY-REGION w:st="on">France</ST1:COUNTRY-REGION></ST1:PLACE>, from visualizing the four-dimensional dynamical systems he studies: “I live in dimension four,” he says.</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions"><div align="center"><img src="http://content9.clipmarks.com/blog_cache/www.sciencenews.org/img/18D40016-F01B-456E-A547-43CA28F75BA6" alt="access" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions">And you can too. Ghys has now created a <A href="http://www.dimensions-math.org" linkindex="42" target="_blank" set="yes">series of video</A>s teaching others to visualize four dimensions the way he does.</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions"><div align="center"><img src="http://content6.clipmarks.com/blog_cache/www.sciencenews.org/img/EAC39748-E46F-45A6-9137-F26A96369E8C" alt="access" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions">in four dimensions, there are six regular solids, including one with 600 faces! Each of those 600 faces is itself a three-dimensional tetrahedron, and 20 of them meet at each vertex.</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions">How on earth can we visualize such a thing?</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions"><div align="center"><img src="http://content7.clipmarks.com/blog_cache/www.sciencenews.org/img/68E9782B-E12A-4D00-BE34-1A5F1C753611" alt="access" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions">Still, they could try. We depict three-dimensional objects on a page all the time, essentially by drawing their outlines.</blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions">a third method called “stereographic projection,” which is less intuitive but much more helpful. </blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://www.sciencenews.org/view/generic/id/35740/title/Seeing_in_four_dimensions"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/www.sciencenews.org/img/4256C992-1224-4E37-906B-09224206CFD4" alt="access" /></div></blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/4F09A365-7400-4733-9459-4B580721F4E0/blog/" title="blog or email this clip"><img src="http://content9.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>

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