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<channel>
	<title>Centripetal Notion &#187; Math</title>
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	<link>http://centripetalnotion.com</link>
	<description>miscellaneous badassery</description>
	<lastBuildDate>Wed, 25 Aug 2010 01:26:24 +0000</lastBuildDate>
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			<item>
		<title>Twenty&#160;Ten</title>
		<link>http://centripetalnotion.com/2010/01/01/20:25:55/</link>
		<comments>http://centripetalnotion.com/2010/01/01/20:25:55/#comments</comments>
		<pubDate>Sat, 02 Jan 2010 01:25:55 +0000</pubDate>
		<dc:creator></dc:creator>
				<category><![CDATA[Culture]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[World]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/?p=763</guid>
		<description><![CDATA[

Numeral
Slang Numeral
Vernacular
Slang Vernacular


2000
&#8216;00
&#8220;Two Thousand&#8221;
&#8220;two-thousand&#8221;


2001
&#8216;01
&#8220;Two Thousand One&#8221;
&#8220;oh-one&#8221;


2010
&#8216;10
&#8220;Twenty Ten&#8221;
&#8220;twenty-ten&#8221;


2013
&#8216;13
&#8220;Twenty Thirteen&#8221;
&#8220;thirteen&#8221;


2020
&#8216;20
&#8220;Twenty Twenty&#8221;
&#8220;twenty-twenty&#8221;


2021
&#8216;21
&#8220;Twenty-One&#8221;
&#8220;twenty-one&#8221;


2030
&#8216;30
&#8220;Twenty Thirty&#8221;
&#8220;twenty-thirty&#8221;


Here is my stance on the debate, if &#8220;debate&#8221; is the proper term. I&#8217;ve only included the pivotal years: the ones where some type of grammatical shift occurs.
I think perhaps saying the years of 2001-2009 as &#8220;Two Thousand One&#8221; and so on will break down somewhat [...]]]></description>
			<content:encoded><![CDATA[<table>
<tr>
<th>Numeral</th>
<th>Slang Numeral</th>
<th>Vernacular</th>
<th>Slang Vernacular</th>
</tr>
<tr>
<td>2000</td>
<td>&#8216;00</td>
<td>&#8220;Two Thousand&#8221;</td>
<td>&#8220;two-thousand&#8221;</td>
</tr>
<tr>
<td>2001</td>
<td>&#8216;01</td>
<td>&#8220;Two Thousand One&#8221;</td>
<td>&#8220;oh-one&#8221;</td>
</tr>
<tr>
<td>2010</td>
<td>&#8216;10</td>
<td>&#8220;Twenty Ten&#8221;</td>
<td>&#8220;twenty-ten&#8221;</td>
</tr>
<tr>
<td>2013</td>
<td>&#8216;13</td>
<td>&#8220;Twenty Thirteen&#8221;</td>
<td>&#8220;thirteen&#8221;</td>
</tr>
<tr>
<td>2020</td>
<td>&#8216;20</td>
<td>&#8220;Twenty Twenty&#8221;</td>
<td>&#8220;twenty-twenty&#8221;</td>
</tr>
<tr>
<td>2021</td>
<td>&#8216;21</td>
<td>&#8220;Twenty-One&#8221;</td>
<td>&#8220;twenty-one&#8221;</td>
</tr>
<tr>
<td>2030</td>
<td>&#8216;30</td>
<td>&#8220;Twenty Thirty&#8221;</td>
<td>&#8220;twenty-thirty&#8221;</td>
</tr>
</table>
<p>Here is my stance on the debate, if &#8220;debate&#8221; is the proper term. I&#8217;ve only included the pivotal years: the ones where some type of grammatical shift occurs.</p>
<p>I think perhaps saying the years of 2001-2009 as &#8220;Two Thousand One&#8221; and so on will break down somewhat the further we get from them, but ultimately will be much more common than saying &#8220;Nineteen Hundred One&#8221; as it&#8217;s simply easier to say, and there is so much cultural significance in the turn of the millennium to weigh down this usage.</p>
<p>My logic for saying &#8220;twenty-thirty&#8221;, &#8220;twenty-twenty&#8221;, and so on, instead of just &#8220;thirty&#8221; or &#8220;twenty&#8221; is a little fuzzy, and mostly based on my own usage. I don&#8217;t notice a clear pattern in other people&#8217;s usage, or at least haven&#8217;t bothered to notice. I think generally I say &#8220;nineteen-ninety&#8221; instead of &#8220;ninety&#8221;, as the latter is a little ambiguous. The same applies to &#8220;ten&#8221;, &#8220;eleven&#8221; and &#8220;twelve&#8221;: all grammatical orphans. &#8220;Fifteen&#8221; can stand alone as &#8220;-teen&#8221; provides some kind of context that seems sufficient, as does &#8220;thirty-&#8221; for &#8220;thirty-one&#8221;, or &#8220;ninety-&#8221; for &#8220;ninety-six&#8221;. Am I alone in thinking it feels better to say &#8220;back in ninety-six&#8221; than &#8220;back in ninety&#8221;?</p>
<p>As for decades, I&#8217;ll wager the following: &#8220;Two-thousands&#8221; (2000&#8217;s), &#8220;Tens&#8221; (10s), &#8220;Twenties&#8221; (20s), etc. We won&#8217;t use &#8220;Two-Thousands&#8221; to refer to the entire century until we&#8217;re safely in the 22nd century, much like we don&#8217;t say &#8220;The Nineteen-Hundreds&#8221; but rather &#8220;The Twentieth Century&#8221; for 1900-1999, but we <em>do</em> say &#8220;The Eighteen-Hundreds&#8221; for 1800-1899. This is largely because referral to specific decades becomes less common the further you&#8217;re removed from them, and we more often refer to the whole of the 1800&#8217;s than we do the years 1800-1809 specifically. This is not currently true for the 1900&#8217;s, and won&#8217;t be until some ambiguous region of time well into this century.</p>
<p>For more, see <a href="http://en.wikipedia.org/wiki/English_numerals">Wikipedia&#8217;s article on english numerals and their usage</a>.</p>
<p>Thoughts?</p>
]]></content:encoded>
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		<slash:comments>3</slash:comments>
		</item>
		<item>
		<title>An Exceptionally Simple Theory of&#160;Everything</title>
		<link>http://centripetalnotion.com/2007/11/15/22:28:48/</link>
		<comments>http://centripetalnotion.com/2007/11/15/22:28:48/#comments</comments>
		<pubDate>Fri, 16 Nov 2007 03:28:48 +0000</pubDate>
		<dc:creator>Justin Ruckman</dc:creator>
				<category><![CDATA[Chemistry]]></category>
		<category><![CDATA[Geometry]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Physics]]></category>
		<category><![CDATA[Science]]></category>
		<category><![CDATA[Universe]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/2007/11/15/22:28:48/</guid>
		<description><![CDATA[His explanation traces the seemingly erratic nature of fundamental particles to the symmetries of E8, a simplified representation of an even more complex 248-dimensional object. "My brain exploded with the implications and the beauty of the thing," he told New Scientist, recalling when he first made the connection between his theories and the shape of E8. "I thought: 'Holy crap, that's it!'" Thus far all the particle interactions predicted by his model correspond with observations in the real world. (...)]]></description>
			<content:encoded><![CDATA[<p><img src="http://centripetalnotion.com/images/e8full.jpg"/></p>
<p>By most measures the shape <em>E8</em>, shown above (<a href="http://centripetalnotion.com/2007/03/22/22:31:00/">and previously</a>), is the most elegant and complex figure known to mathematics. It is also the inspiration for one man&#8217;s comprehensive theory of everything.
<p>Garrett Lisi is 39. He splits his time between surfing in Hawaii and snowboarding in Lake Tahoe, Nevada. He has a doctorate but is not affiliated with any university. &#8220;It&#8217;s hard to figure out the secrets of the universe when you&#8217;re trying to figure out where you and your girlfriend are going to sleep next month&#8221; he told the <em>Telegraph</em>. Yet he published a paper this month, &#8220;An Exceptionally Simple Theory of Everything,&#8221; and his ideas are provoking interest around the world.</p>
<p>His explanation traces the seemingly erratic nature of fundamental particles to the symmetries of E8, a simplified representation of an even more complex 248-dimensional object. &#8220;My brain exploded with the implications and the beauty of the thing,&#8221; he told <em>New Scientist</em>, recalling when he first made the connection between his theories and the shape of E8. &#8220;I thought: &#8216;Holy crap, that&#8217;s it!&#8217;&#8221; Thus far all the particle interactions predicted by his model correspond with observations in the real world.</p>
<p>
<blockquote>
<p>It is one of the most compelling unification models I&#8217;ve seen in many, many years.</p>
<p class="source">Lee Smolin, Perimeter Institute for Theoretical Physics</p>
</blockquote>
<p>When the <a href="http://en.wikipedia.org/wiki/Large_Hadron_Collider">Large Hadron Collider</a> opens in May of next year, Lisi hopes his theories will help lead to the discovery of some 20 particles he predicts must exist, particles that so far live only as gaps in a kind of periodic table of particles, all of his construction.</p>
<p class="links"><a href="http://www.telegraph.co.uk/earth/main.jhtml?view=DETAILS&#038;grid=&#038;xml=/earth/2007/11/14/scisurf114.xml"><strong>ARTICLE</strong></a> ["Surfer dude stuns physicists (...)"]<cite> (Telegraph)</cite><br /><a href="http://www.newscientist.com/article/mg19626303.900"><strong>ARTICLE</strong></a> ["Is mathematical pattern the theory of everything?"]<cite> (New Scientist)</cite></p>
<p class="links"><a href="http://arxiv.org/abs/0711.0770"><strong>PAPER</strong></a> [Garrett Lisi - "An Exceptionally Simple Theory of Everything"]</p>
]]></content:encoded>
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		<slash:comments>3</slash:comments>
		</item>
		<item>
		<title>How to Turn a Sphere Inside&#160;Out</title>
		<link>http://centripetalnotion.com/2007/11/15/05:00:11/</link>
		<comments>http://centripetalnotion.com/2007/11/15/05:00:11/#comments</comments>
		<pubDate>Thu, 15 Nov 2007 10:00:11 +0000</pubDate>
		<dc:creator>Justin Ruckman</dc:creator>
				<category><![CDATA[Geometry]]></category>
		<category><![CDATA[Math]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/2007/11/15/05:00:11/</guid>
		<description><![CDATA[(video)]]></description>
			<content:encoded><![CDATA[<p><object width="500" height="411"><param name="movie" value="http://www.youtube.com/v/R_w4HYXuo9M"></param> <embed src="http://www.youtube.com/v/R_w4HYXuo9M" type="application/x-shockwave-flash" width="500" height="411"></embed></object>
<p class="links"><a href="http://centripetalnotion.com/media/video/OutsideIn.mov"><strong>VIDEO</strong></a> [high quality version of clip above]<br /><a href="http://video.google.com/videoplay?docid=-6626464599825291409"><strong>VIDEO</strong></a> [full version, more detail, about 20 min. long]<cite> (via <a href="http://www.kottke.org/remainder/07/11/14469.html">Kottke</a>)</cite></p>
]]></content:encoded>
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		<slash:comments>1</slash:comments>
<enclosure url="http://centripetalnotion.com/media/video/OutsideIn.mov" length="5513583" type="video/quicktime" />
		</item>
		<item>
		<title>Largest Island in a Lake on an Island in a Lake on an&#160;Island</title>
		<link>http://centripetalnotion.com/2007/06/22/23:45:04/</link>
		<comments>http://centripetalnotion.com/2007/06/22/23:45:04/#comments</comments>
		<pubDate>Sat, 23 Jun 2007 04:45:04 +0000</pubDate>
		<dc:creator>Justin Ruckman</dc:creator>
				<category><![CDATA[Environment]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[World]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/2007/06/22/23:45:04/</guid>
		<description><![CDATA[Vulcan point in Crater Lake on Vulcano Island in Lake Taal on Luzon, Philippines. It only gets easier from here.]]></description>
			<content:encoded><![CDATA[<p><img src="http://centripetalnotion.com/images/islandlake.jpg"/></p>
<p>Vulcan point in Crater Lake on Vulcano Island in Lake Taal on Luzon, Philippines. It only gets easier from here.</p>
<p class="links"><a href="http://www.elbruz.org/islands/Islands%20and%20Lakes.htm"><strong>LINK/IMAGES</strong></a> [The Island and Lake Combination]<cite> (via <a href="http://www.kottke.org/remainder/07/06/13848.html">Kottke</a>)</cite></p>
]]></content:encoded>
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		<slash:comments>16</slash:comments>
		</item>
		<item>
		<title>Statistical Analysis of World Flag&#160;Colors</title>
		<link>http://centripetalnotion.com/2007/06/04/11:17:53/</link>
		<comments>http://centripetalnotion.com/2007/06/04/11:17:53/#comments</comments>
		<pubDate>Mon, 04 Jun 2007 16:17:53 +0000</pubDate>
		<dc:creator>Justin Ruckman</dc:creator>
				<category><![CDATA[Art/Design]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[World]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/2007/06/04/11:17:53/</guid>
		<description><![CDATA["Using a list of countries generated by The World Factbook database, flags of countries fetched from Wikipedia (as of 26th May 2007) are analysed (...) to calculate the proportions of colours on each of them. That is then translated on to a piechart (...). The proportions of colours on all unique flags are used to finally generate a piechart of proportions of colours for all the flags combined."]]></description>
			<content:encoded><![CDATA[<p><img src="http://centripetalnotion.com/images/worldflagcolors.jpg"/></p>
<p>
<blockquote>
<p>Using a list of countries generated by The World Factbook database, flags of countries fetched from Wikipedia (as of 26th May 2007) are analysed (&#8230;) to calculate the proportions of colours on each of them. That is then translated on to a piechart (&#8230;). The proportions of colours on all unique flags are used to finally generate a piechart of proportions of colours for all the flags combined. (note: Colours making up less than 1% may not appear)</p>
</blockquote>
<p>Shown above is the world aggregate, on the site there are individual charts for all the countries analyzed.</p>
<p class="links"><a href="http://shaheeilyas.com/flags/"><strong>LINK/IMAGES</strong></a> [Flags By Colors]<cite> (via <a href="http://feeds.infosthetics.com/~r/infosthetics/~3/120185505/flags_by_colors.html">infosthetics</a>)</cite></p>
]]></content:encoded>
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		<slash:comments>2</slash:comments>
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		<item>
		<title>Lee Byron: Last.fm&#160;Visualization</title>
		<link>http://centripetalnotion.com/2007/05/18/19:24:07/</link>
		<comments>http://centripetalnotion.com/2007/05/18/19:24:07/#comments</comments>
		<pubDate>Sat, 19 May 2007 00:24:07 +0000</pubDate>
		<dc:creator>Justin Ruckman</dc:creator>
				<category><![CDATA[Art/Design]]></category>
		<category><![CDATA[Information Design]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Music]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/2007/05/18/19:24:07/</guid>
		<description><![CDATA[After letting Last.fm track his music listening habits for over a year, Lee Byron took the data generated and through some clever math and plotting, produced this beautiful, organic representation of his history. Artists ebb and flow as the seasons and his preferences change.]]></description>
			<content:encoded><![CDATA[<p><img src="http://centripetalnotion.com/images/lastfmviz1.jpg"/><br /><img src="http://centripetalnotion.com/images/lastfmviz2.jpg"/><br /><img src="http://centripetalnotion.com/images/lastfmviz3.jpg"/></p>
<p>After letting <a href="http://last.fm">Last.fm</a> track his music listening habits for over a year, Lee Byron took the data generated and through some clever math and plotting, produced this beautiful, organic representation of his history. Artists ebb and flow as the seasons and his preferences change.</p>
<p>
<blockquote>
<p> After thinking about how I could show this whole sum in a presentable form, I decided on a sort of layered histogram. Each colored sliver represents a different artist listened to in the last 18 months. The sliver moves through time left to right growing thicker where it was more popular and thinner where it was less. The color indicates the first time the artist was listened to, warmer colors being more recent and cooler being further back. As a new artist is listened to it is put onto the outsides of the graph. The result is a wiggling tour through your listening history past.</p>
<p>While this is interesting to look at, it is more significant on a personal level. When viewing your own music listening history you are reminded of past events that caused the trends to emerge.</p>
</blockquote>
<p>There&#8217;s a lot more interesting data visualization at his portfolio site, check it out.</p>
<p class="links"><a href="http://megamu.com/lastfm/"><strong>LINK/IMAGE</strong></a> [Last.fm visualization]<cite> (via <a href="http://infosthetics.com/archives/2007/05/music_listening_history_graph.html">infosthetics</a>)</cite><br /><a href="http://megamu.com/"><strong>LINK/IMAGES</strong></a> [Lee's portfolio]</p>
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		<slash:comments>3</slash:comments>
		</item>
		<item>
		<title>The Dot and the Line: A Romance in Lower&#160;Mathematics</title>
		<link>http://centripetalnotion.com/2007/05/17/00:45:57/</link>
		<comments>http://centripetalnotion.com/2007/05/17/00:45:57/#comments</comments>
		<pubDate>Thu, 17 May 2007 05:45:57 +0000</pubDate>
		<dc:creator>Justin Ruckman</dc:creator>
				<category><![CDATA[Animation]]></category>
		<category><![CDATA[Geometry]]></category>
		<category><![CDATA[Math]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/2007/05/17/00:45:57/</guid>
		<description><![CDATA[(video)]]></description>
			<content:encoded><![CDATA[<p><object width="500" height="394"><param name="movie" value="http://www.youtube.com/v/OmSbdvzbOzY"></param><param name="wmode" value="transparent"></param><embed src="http://www.youtube.com/v/OmSbdvzbOzY" type="application/x-shockwave-flash" wmode="transparent" width="500" height="394"></embed></object>
<p class="links"><a href="http://www.youtube.com/watch?v=OmSbdvzbOzY"><strong>VIDEO</strong></a><cite> (via <a href="http://www.fecalface.com/SF/index.php?option=com_content&#038;task=view&#038;id=564">FecalFace</a>)</cite><br /><a href="http://en.wikipedia.org/wiki/The_Dot_and_the_Line"><strong>ARTICLE</strong></a> [The Dot and the Line]<cite> (Wikipedia)</cite></p>
]]></content:encoded>
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		<slash:comments>0</slash:comments>
		</item>
		<item>
		<title>Archimedes Palimpsest: New Aristotle Text&#160;Found</title>
		<link>http://centripetalnotion.com/2007/05/04/11:51:40/</link>
		<comments>http://centripetalnotion.com/2007/05/04/11:51:40/#comments</comments>
		<pubDate>Fri, 04 May 2007 16:51:40 +0000</pubDate>
		<dc:creator>Justin Ruckman</dc:creator>
				<category><![CDATA[History]]></category>
		<category><![CDATA[Literature]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Philosophy]]></category>
		<category><![CDATA[Science]]></category>
		<category><![CDATA[Technology]]></category>
		<category><![CDATA[World]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/2007/05/04/11:51:40/</guid>
		<description><![CDATA["At first glance, the manuscript appears to be a medieval Christian prayer book.

But on the same pages as the prayers, experts using a high-tech imaging system have discovered commentary likely written in the third century A.D. on a work written around 350 B.C. by the Greek philosopher Aristotle."]]></description>
			<content:encoded><![CDATA[<p><img src="http://centripetalnotion.com/images/palimpsest.jpg"/></p>
<p>
<blockquote>
<p> At first glance, the manuscript appears to be a medieval Christian prayer book.</p>
<p>But on the same pages as the prayers, experts using a high-tech imaging system have discovered commentary likely written in the third century A.D. on a work written around 350 B.C. by the Greek philosopher Aristotle.</p>
<p>The discovery is the third ancient text to emerge from the layers of writing on the much reused pages. In 2002 researchers had uncovered writings by the mathematician Archimedes and the fourth-century B.C. politician Hyperides.</p>
<p>Last year one of the pages was found to contain a famous work by Archimedes about buoyancy that had previously been known only from an incomplete Latin translation.</p>
<p>Project director William Noel, curator of manuscripts at the Walters Art Museum in Baltimore, Maryland, called the latest discovery a &#8220;sensational find.&#8221;</p>
</blockquote>
<p class="links"><a href="http://archimedespalimpsest.org/"><strong>LINK/IMAGES</strong></a> [website: more info &#038; image bank]<br /><a href="http://news.nationalgeographic.com/news/2007/04/070426-aristotle-book.html"><strong>ARTICLE</strong></a> ["New Layer of Ancient Greek Writings  (...)]<cite> (National Geographic)</cite></p>
]]></content:encoded>
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		<slash:comments>2</slash:comments>
		</item>
		<item>
		<title>Stacey Whaley: Intergalactic&#160;Art</title>
		<link>http://centripetalnotion.com/2007/04/08/17:03:38/</link>
		<comments>http://centripetalnotion.com/2007/04/08/17:03:38/#comments</comments>
		<pubDate>Sun, 08 Apr 2007 22:03:38 +0000</pubDate>
		<dc:creator>Justin Ruckman</dc:creator>
				<category><![CDATA[Art/Design]]></category>
		<category><![CDATA[Geometry]]></category>
		<category><![CDATA[Math]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/2007/04/08/17:03:38/</guid>
		<description><![CDATA[(images)]]></description>
			<content:encoded><![CDATA[<p><img src="http://centripetalnotion.com/images/whaley1.jpg"/></p>
<p><img src="http://centripetalnotion.com/images/whaley2.jpg"/></p>
<p class="links"><a href="http://intergalacticart.blogspot.com/"><strong>LINK/IMAGES</strong></a><cite> (via <a href="http://sprott.physics.wisc.edu/pickover/pc/realitycarnival.html">RealityCarnival</a>)</cite></p>
]]></content:encoded>
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		<slash:comments>1</slash:comments>
		</item>
		<item>
		<title>E8</title>
		<link>http://centripetalnotion.com/2007/03/22/22:31:00/</link>
		<comments>http://centripetalnotion.com/2007/03/22/22:31:00/#comments</comments>
		<pubDate>Fri, 23 Mar 2007 03:31:00 +0000</pubDate>
		<dc:creator>Justin Ruckman</dc:creator>
				<category><![CDATA[Geometry]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Technology]]></category>
		<category><![CDATA[Universe]]></category>

		<guid isPermaLink="false">http://centripetalnotion.com/2007/03/22/22:31:00/</guid>
		<description><![CDATA[Essentially, if I understand it correctly, it's like a 2-D shadow of a 248-D sphere, an object so symmetrical you could theoretically rotate it in any direction in up to 248 dimensions and it still appear the same.]]></description>
			<content:encoded><![CDATA[<p><img src="http://centripetalnotion.com/images/e8.jpg"/></p>
<p>This is a 2-dimensional projection of E<sub>8</sub>, a 248-dimensional object seen here simplified into only 8-dimensions to help preserve sanity. Essentially, if I understand it correctly, it&#8217;s like a 2-D shadow of a 248-D sphere, an object so symmetrical you could theoretically rotate it in any direction in up to 248 dimensions and it still appear the same. Talk about a stick in the mud. It took 18 mathematicians four years to produce the calculation for this object, its formula weighing in at 60 gigabytes. The computation was announced at MIT by David Vogan this Monday, the 19th of March, 2007.</p>
<p class="links"><a href="http://www.aimath.org/E8/"><strong>LINK/IMAGES</strong></a> ["Representations of E<sub>8</sub>"]<cite> (AIM)</cite><br /><a href="http://www.aimath.org/E8/images/e8plane2.eps"><strong>DOWNLOAD</strong></a> [E<sub>8</sub> projection, 200kb EPS]<br /><a href="http://en.wikipedia.org/wiki/E8_(mathematics)"><strong>ARTICLE</strong></a> [E<sub>8</sub>]<cite> (Wikipedia)</cite></p>
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