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	<title>Sys--Talk &#187; N-Grams</title>
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		<title>The Enneagram</title>
		<link>http://www.systalk.org/2009/math/n_grams/the-enneagram/</link>
		<comments>http://www.systalk.org/2009/math/n_grams/the-enneagram/#comments</comments>
		<pubDate>Sat, 11 Apr 2009 03:51:09 +0000</pubDate>
		<dc:creator>sigurd</dc:creator>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[N-Grams]]></category>
		<category><![CDATA[Self Development]]></category>
		<category><![CDATA[Systematics]]></category>
		<category><![CDATA[body type]]></category>
		<category><![CDATA[enneagram]]></category>
		<category><![CDATA[personality]]></category>

		<guid isPermaLink="false">http://www.systalk.org/?p=63</guid>
		<description><![CDATA[The Enneagram is a figure that has been appropriated to model all sorts of things - a personality model, a body type model, and as a form for nine-facet systems within the larger topic of Systematics.]]></description>
			<content:encoded><![CDATA[<p>The Enneagram is a figure that has been appropriated to model all sorts of things. Most current books on the Enneagram are about a personality model based on the work of Oscar Ichazo of Arica Institute, Chile. Claudio Naranjo was instrumental in bringing his take on Ichazo&#8217;s work out of Chile. Many Jesuits picked up the ideas and wrote books, as did others. There may be hundreds of titles by now.</p>
<p>There&#8217;s a similar application of the Enneagram, but to body types. Rodney Collin is a source for these ideas. Joel Friedlander and Susan Zannos have written books on this version of the Enneagram.</p>
<p>Another application of the Enneagram is as part of a pantheon of systems &#8211; from monads, dyads and triads through to larger systems. John Godolphin (J. G.) Bennett was key in developing these ideas and their application to life situations. He used the term Systematics (also used in Biology, but with a different meaning). Two of his books that are relevant are <em>Elementary Systematics / A Tool for Understanding Wholes</em> and <em>Enneagram Studies</em>. Bennett had ties to Gurdjieff, who introduced the Enneagram to his students.</p>
<p>Bennett&#8217;s ideas on Systematics have been applied in business situations. See Saul Kuchinsky&#8217;s <em>Systematics / Search for Miraculous Mangement</em> and Richard Knowles&#8217; <em>The Leadership Dance / Pathways To Extraordinary Organizational Effectiveness</em>. Saul died some years ago; go to <a href="http://www.centerforselforganizingleadership.com/" target="_blank">www.centerforselforganizingleadership.com/</a> to contact Richard and his wife. Tell them I sent you.</p>
<p>Here&#8217;s a picture of the Enneagram, with a red circle at the top that I added to fit it into the N-Gram diagrams I developed. They are based on the way the patterns of repeating digits in base ten for n/7 (.00, .142857, .99) and n/3 (.oo, .33, .66, .99)  are represented in the Enneagram, but with other divisors in addition to 3 and 7, and applied in other bases in addition to ten.</p>
<div id="attachment_54" class="wp-caption aligncenter" style="width: 214px"><img class="size-full wp-image-54" title="Enneagram" src="http://www.systalk.org/wp-content/uploads/2009/04/enneagram0.gif" alt="Enneagram with top point emphasis" width="204" height="195" /><p class="wp-caption-text">Enneagram with top point emphasis</p></div>
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		<title>N-Grams</title>
		<link>http://www.systalk.org/2009/math/n_grams/n-grams/</link>
		<comments>http://www.systalk.org/2009/math/n_grams/n-grams/#comments</comments>
		<pubDate>Fri, 10 Apr 2009 02:35:20 +0000</pubDate>
		<dc:creator>sigurd</dc:creator>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[N-Grams]]></category>

		<guid isPermaLink="false">http://www.systalk.org/?p=36</guid>
		<description><![CDATA[You can find some of what I wrote about a decade ago on N-Grams at www.solbakkn.com/math/n-grams.htm . Click on the links for tables to see what N-Grams look like. In my last post I described them as &#8220;a collection of diagrams formed using the same mathematical / diagrammatic rules / conventions as the Enneagram, but [...]]]></description>
			<content:encoded><![CDATA[<p>You can find some of what I wrote about a decade ago on N-Grams at <a href="http://www.solbakkn.com/math/n-grams.htm " target="_blank">www.solbakkn.com/math/n-grams.htm </a>. Click on the links for tables to see what N-Grams look like. In my last post I described them as &#8220;a collection of diagrams formed using the same mathematical / diagrammatic rules / conventions as the Enneagram, but applied to varying number bases and divisors.&#8221; Here are the N-Grams for base ten. Note that the circles for 2, 4, 5, 8 and ten &#8211; all with only the prime factors (2 and 5) that make up the base, ten. The circle for 6 is partially gray, because the prime factor 3 generates a repeating pattern, whereas the prime factor 2 does not.</p>
<div id="attachment_77" class="wp-caption aligncenter" style="width: 430px"><img class="size-full wp-image-77" title="Base Ten N-Grams" src="http://www.systalk.org/wp-content/uploads/2009/04/base10div-sm.png" alt="Base Ten N-Grams" width="420" height="58" /><p class="wp-caption-text">Base Ten N-Grams</p></div>
<p>I&#8217;ve corresponded with Shane Roberts who has taken the same idea in a similar direction, calling his diagrams Rotagrams. Shane has a web page at <a href="http://www.myspace.com/systemlover" target="_blank">www.myspace.com/systemlover</a> and said I could share his email, systemlover at hotmail dot com. His diagrams include non-repeating patterns, e.g., .125 for 1/8 (base ten), mine do not.</p>
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