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	<title>Comments on: Multidimensionality: Finding underlying dimensions</title>
	<link>http://groksystems.com/2008/02/03/multidimensionality-finding-underlying-dimensions/</link>
	<description>Exploring the world and life as systems</description>
	<pubDate>Mon, 08 Sep 2008 16:48:43 +0000</pubDate>
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		<title>By: Adam Smith</title>
		<link>http://groksystems.com/2008/02/03/multidimensionality-finding-underlying-dimensions/#comment-3</link>
		<author>Adam Smith</author>
		<pubDate>Sun, 03 Feb 2008 21:05:55 +0000</pubDate>
		<guid>http://groksystems.com/2008/02/03/multidimensionality-finding-underlying-dimensions/#comment-3</guid>
					<description>In the final lesson, "from multiple interacting dimensions, complex types can emerge," you've used a story where adding one dimension results in a description with two more types in total.  The reader should note that this is a simple example of exponential complexity, not incremental, additive behavior. For example, if we were to find 6 distinct, relevant ways to measure properties related to extroversion (not implausble) and each measurement could give us a binary (two state) distinction, then we would have 2^6 = 64 identifiable personality types.</description>
		<content:encoded><![CDATA[<p>In the final lesson, &#8220;from multiple interacting dimensions, complex types can emerge,&#8221; you&#8217;ve used a story where adding one dimension results in a description with two more types in total.  The reader should note that this is a simple example of exponential complexity, not incremental, additive behavior. For example, if we were to find 6 distinct, relevant ways to measure properties related to extroversion (not implausble) and each measurement could give us a binary (two state) distinction, then we would have 2^6 = 64 identifiable personality types.</p>
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		<title>By: Jeff Lindsay</title>
		<link>http://groksystems.com/2008/02/03/multidimensionality-finding-underlying-dimensions/#comment-4</link>
		<author>Jeff Lindsay</author>
		<pubDate>Mon, 04 Feb 2008 00:56:23 +0000</pubDate>
		<guid>http://groksystems.com/2008/02/03/multidimensionality-finding-underlying-dimensions/#comment-4</guid>
					<description>Yes, although the way that was stated I feel like I should explain that even though it seemed one dimensional before (intro vs extro, maybe self vs environment) and in the end they came up with two new dimensions, it wasn't really just adding a dimension in this case. It was really coming up with two underlying dimensions that shared a relation with a sort of meta dimension of self vs environment, internal vs external, subjective vs objective.

The point on complexity sort of brings up something I was hoping somebody would. Both the fact that they represented these dimensions with binary state and that there are only two distinct dimensions (when there are almost certainly more) are examples of creating a model that is "good enough."

I haven't seen anything in model theory that talks about this, maybe because I'm looking in the wrong place or not hard enough. It's more in the practice of applying and building models, but models that are "good enough" are ones that most effectively explain phenomena or are most useful, while maintaining boundaries and a level of abstraction that keep the model simple enough to be used and understood easily.

But yes, the main point you're making is that the type of complexity I'm talking about here will increase exponentially as dimensions are added &lt;em&gt;and&lt;/em&gt; as dimensions are chunked into more states. All the more reason to keep models just simple enough to be effective.</description>
		<content:encoded><![CDATA[<p>Yes, although the way that was stated I feel like I should explain that even though it seemed one dimensional before (intro vs extro, maybe self vs environment) and in the end they came up with two new dimensions, it wasn&#8217;t really just adding a dimension in this case. It was really coming up with two underlying dimensions that shared a relation with a sort of meta dimension of self vs environment, internal vs external, subjective vs objective.</p>
<p>The point on complexity sort of brings up something I was hoping somebody would. Both the fact that they represented these dimensions with binary state and that there are only two distinct dimensions (when there are almost certainly more) are examples of creating a model that is &#8220;good enough.&#8221;</p>
<p>I haven&#8217;t seen anything in model theory that talks about this, maybe because I&#8217;m looking in the wrong place or not hard enough. It&#8217;s more in the practice of applying and building models, but models that are &#8220;good enough&#8221; are ones that most effectively explain phenomena or are most useful, while maintaining boundaries and a level of abstraction that keep the model simple enough to be used and understood easily.</p>
<p>But yes, the main point you&#8217;re making is that the type of complexity I&#8217;m talking about here will increase exponentially as dimensions are added <em>and</em> as dimensions are chunked into more states. All the more reason to keep models just simple enough to be effective.</p>
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		<title>By: Casey</title>
		<link>http://groksystems.com/2008/02/03/multidimensionality-finding-underlying-dimensions/#comment-9</link>
		<author>Casey</author>
		<pubDate>Wed, 13 Feb 2008 10:19:19 +0000</pubDate>
		<guid>http://groksystems.com/2008/02/03/multidimensionality-finding-underlying-dimensions/#comment-9</guid>
					<description>Reminds me of this article I found recently - http://discovermagazine.com/2008/feb/if-osama.s-only-6-degrees-away-why-can.t-we-find-him</description>
		<content:encoded><![CDATA[<p>Reminds me of this article I found recently - <a href="http://discovermagazine.com/2008/feb/if-osama.s-only-6-degrees-away-why-can.t-we-find-him" rel="nofollow">http://discovermagazine.com/2008/feb/if-osama.s-only-6-degrees-away-why-can.t-we-find-him</a></p>
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		<title>By: Grok Systems &#187; Blog Archive &#187; Multidimensionality: Dissolving dichotomies</title>
		<link>http://groksystems.com/2008/02/03/multidimensionality-finding-underlying-dimensions/#comment-11</link>
		<author>Grok Systems &#187; Blog Archive &#187; Multidimensionality: Dissolving dichotomies</author>
		<pubDate>Wed, 13 Feb 2008 18:11:12 +0000</pubDate>
		<guid>http://groksystems.com/2008/02/03/multidimensionality-finding-underlying-dimensions/#comment-11</guid>
					<description>[...] basic systems principles, there&#8217;s more to the point of multidimensionality than the story in the last post explained. What we did cover was how it can suggest that a system has more states than previously [...]</description>
		<content:encoded><![CDATA[<p>[&#8230;] basic systems principles, there&#8217;s more to the point of multidimensionality than the story in the last post explained. What we did cover was how it can suggest that a system has more states than previously [&#8230;]</p>
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