tag:blogger.com,1999:blog-91127481288177625592024-02-21T05:36:15.318-05:00shaRQ: Math & MythshaRQ-tank serves as a repository for thesis researchShar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.comBlogger60125tag:blogger.com,1999:blog-9112748128817762559.post-53296000514431792642013-03-03T07:02:00.001-05:002013-03-05T18:44:21.419-05:00Fu Xi and King Wen<span style="font-family: Trebuchet MS, sans-serif;">Fu Xi 's complementary arrangement and King Wen's pairs coincide on the 8 x 8 square</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgK2EIYPqEV9-oogGAPwyLfACzRJWnE-lBUA3jxAaAIGv87jy4LxC95exI46GoPm5iV5C6BIP7J9P-uQlz1o-JpuRp5MEYS33m0kjv8MDA5QLq5gPhtxz3BKuLx4uVsQCIwjVyhliftHq72/s1600/fuxi-wen.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgK2EIYPqEV9-oogGAPwyLfACzRJWnE-lBUA3jxAaAIGv87jy4LxC95exI46GoPm5iV5C6BIP7J9P-uQlz1o-JpuRp5MEYS33m0kjv8MDA5QLq5gPhtxz3BKuLx4uVsQCIwjVyhliftHq72/s1600/fuxi-wen.png" height="263" width="320" /></a></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">Wen's pairs can be said to fall into two categories: 8 pairs that are complementary, and 24 pairs that are figurate inverses.</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">The pairs of the first kind are found along both of the major diagonals which reflect across each other. </span><span style="font-family: 'Trebuchet MS', sans-serif;">The pairs of the second kind are found reflected across the vertical axis of the diagram.</span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">The colors indicate the line-composition of the figures: </span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">Black: 6 YANG 0 YIN</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">Indigo: 5 YANG 1 YIN</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">Blue: 4 YANG 2 YIN</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">Green: 3 YANG 3 YIN</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">Yellow: 2 YANG 4 YIN</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">Orange: 1 YANG 5 YIN</span></div>
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<span style="font-family: Trebuchet MS, sans-serif;">Red: 0 YANG 6 YIN</span></div>
Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-1174808106025267412013-03-03T01:30:00.001-05:002013-03-20T10:44:21.168-04:00Fu Xi's arrangement, Wen's pairs, and the 8 x 8 square<span style="font-family: Trebuchet MS, sans-serif;">This diagram shows the affinity between Wen's pairing and Fu Xi's arrangement of complementary opposites on the 8 x 8 square.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQSY-Vb3_hGFg2Jjse7wBZcjnON7dyFs-GuE-W4i_6vJnBmvFiQk0RgEioDaiLR2dXSAo1NNxWmzxHAEilZE_5q1NcAALS-1usd38t0c_tf6zAH0083VJlOuZVf-4nVM_7i0fTmXShGrAJ/s1600/wen_yarrow_scalar.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQSY-Vb3_hGFg2Jjse7wBZcjnON7dyFs-GuE-W4i_6vJnBmvFiQk0RgEioDaiLR2dXSAo1NNxWmzxHAEilZE_5q1NcAALS-1usd38t0c_tf6zAH0083VJlOuZVf-4nVM_7i0fTmXShGrAJ/s640/wen_yarrow_scalar.png" /> </a> </div>
Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-45123446113540414262013-01-16T21:47:00.001-05:002013-01-19T16:11:45.075-05:00"Heaven and Earth, that is Tao"<span style="font-family: arial; font-size: medium;">In the first chapter of </span><u style="font-family: arial; font-size: large;">The Great Treatise</u><span style="font-family: arial; font-size: medium;"> we find:</span><br />
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<span style="font-size: medium;"><i>The changes and transformations of Heaven are in the symbols of Change<br />The changes and transformations of Earth are in the forms of Change</i></span></blockquote>
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<span style="font-size: medium;">Also:</span></div>
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<span style="font-size: medium;"><i>What moves and completes the symbols is called Ch'ien.<br />What unfolds them into patterns of living is called K'un.</i></span></blockquote>
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<span style="font-size: medium;">Thus, <i>Ch'ien</i> represents enfolded or implicate order, creative, symbolic reality; while <i>K'un</i> is explicated/unfolded, structive, formative reality.</span></div>
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<span style="font-size: medium;">Earth (<i>K'un</i>) is represented by the form of the simple square. </span></div>
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<span style="font-size: medium;">Heaven (<i>Ch'ien</i>) is immaterial or intangible and has no form as such, but we may represent it through an overlaid series of lines that partition the square into four discrete regions:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-ktDh64cenF-2XAg4gZUliAa__jAm02nlXZl2rUjOZiEzNQ-AOzAKFOYbgirmbzRKNQhK87Kg5bNGEXYj4kEmddpNQV_jIvhT8MtHN9azuytT7LRdWp4sFrKzCUdRx5S1qK3LfhfWh6tu/s1600/field_chien.xcf.small.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-ktDh64cenF-2XAg4gZUliAa__jAm02nlXZl2rUjOZiEzNQ-AOzAKFOYbgirmbzRKNQhK87Kg5bNGEXYj4kEmddpNQV_jIvhT8MtHN9azuytT7LRdWp4sFrKzCUdRx5S1qK3LfhfWh6tu/s1600/field_chien.xcf.small.png" /></a></div>
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<span style="font-size: medium;">The resulting figure can be resolved into fractions of sixteen. The respective areas of the four discrete regions are 1/16, 3/16, 5/16, and 7/16, comprising a unity. These four fractions are identical to the probabilities, given by the yarrow oracle, of measuring the four </span><i style="font-size: large;">xiang</i><span style="font-size: medium;"> symbols during divination. </span></div>
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<span style="font-size: medium;">Having received the four symbols by combining Heaven and Earth, we project them onto our figure, yielding a full field to support the existence of the 64 Images:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0Btpis6MPpupVm5qFhiTglt8pSKzc5V5CSuytztLPWv5_d05Vu67xz8KjrNnxBYJfwWjKFd2fB1DeMgcIHHggZBnqxL3wgwUt9IVULHUuUpAi_0pwx-Mb-CMsQp29v-ogqDTV24TReAMe/s1600/field_chien.xcf.small.1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0Btpis6MPpupVm5qFhiTglt8pSKzc5V5CSuytztLPWv5_d05Vu67xz8KjrNnxBYJfwWjKFd2fB1DeMgcIHHggZBnqxL3wgwUt9IVULHUuUpAi_0pwx-Mb-CMsQp29v-ogqDTV24TReAMe/s1600/field_chien.xcf.small.1.png" /></a></div>
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<span style="font-size: medium;"><br /></span><span style="font-size: medium;">From this we can infer that the Eight Diagrams emerge from the </span><span style="font-size: medium;">64 Images</span><span style="font-size: medium;">, consistent with Dr. Stephen Karcher's argument that the 64 Images "preceded" the </span><span style="font-size: medium;">Eight Diagrams</span><i style="font-size: large;"> (Ba Gua)</i><span style="font-size: medium;">, which are used for identification and interpretation of the Images.</span></div>
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<span style="font-size: medium;">The ancients are said to have devised many implements by imitating Change. Here, and elsewhere, I suggest that that the yarrow oracle was devised to imitate the intermingling of Heaven and Earth that reveals the <i>xiang.</i> The figures presented here are purely geometric, hence they are antecedent of human artifice. The <i>xiang</i> are eternal; </span><span style="font-size: medium;">coeval with, and fairly indistinct or inseparable from Change. The ancient sages' far-reaching powers of </span><span style="font-size: medium;">sentience and cognition brought </span><span style="font-size: medium;">forth the <i>xiang</i> into consensus reality for the use of mankind.</span></div>
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<span style="font-size: medium;">The point that I hope to have made is that the <i>xiang</i> are entangled with Change, embedded or encoded in Change by way of this intermingling of the square (representing Earth) and the enfoldment that Heaven represents. Without the enfoldment, we cannot discern the symbols in the square; without the square, the symbols have no basis for existence. Indeed, "Heaven and Earth, that is Tao."</span></div>
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<span style="font-size: medium;">If we accept this line of reasoning, we can posit a natural, mathematical interpretation for Change that can be extended with further investigation.</span></div>
Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-29529175917925776862013-01-01T23:34:00.000-05:002013-02-11T00:26:46.455-05:00Quantum Measurement<div class="separator" style="clear: both; text-align: left;">
<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">Systems exhibiting tangled hierarchy are said to have some degree of self-awareness or 'soul', per the writings of Douglas Hofstadter. </span><span style="font-family: Trebuchet MS, sans-serif;">The following illustrations are provided to demonstrate the tangled hierarchy of the system called Change. </span></span></div>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">Physicist Amit Goswami argues that systems demonstrating tangled hierarchy (plus non-locality and discontinuity) are related to quantum systems. A sub-theme of these illustrations concerns <a href="http://en.wikipedia.org/wiki/Observer_(quantum_physics)">observers</a> and <a href="http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Measurement_from_a_practical_point_of_view">measurement</a>, salient themes of quantum mechanics</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyN9r2SSf6Kl_uJ1-xp0uR2dI-632GYex-2FFtIvmeW7Dj_ApAQttOhmsgIzqxd09koPMPvWVGVCvgd1uZs-iuhyooqjn2qs6KSMO7h356obTbmATXgG2mAzIJN8xHw1-NLjiq7pYqgkId/s1600/1.Field.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyN9r2SSf6Kl_uJ1-xp0uR2dI-632GYex-2FFtIvmeW7Dj_ApAQttOhmsgIzqxd09koPMPvWVGVCvgd1uZs-iuhyooqjn2qs6KSMO7h356obTbmATXgG2mAzIJN8xHw1-NLjiq7pYqgkId/s640/1.Field.png" width="640" /></a></div>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">In the Field diagram above, the four concentric regions </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">indicate four "densities" and </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">represent the four Symbols. </span><br />
<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">The numbers in the diagram indicate the areas of the bounded regions enclosing those numbers. </span><br />
<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">Each quadrant of the diagram encloses an area of 16 units; thus the t</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">wo cardinal axes and four densities enfold 6 dimensions and 64 Elements.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMPVuXZutVySspmpfDvnZD6Liy29WMlkqczH6GaAQ2hwaJTKaIvxtNJ0TjPlA8HfBPP-N00HVilWWU0fQoI79r_wi86wcWPLfsTHWyKg6gdq0Y5eoAL1Rf4xEE-iZcufy8OIXeQUKTYDEh/s1600/2.64_Elements.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMPVuXZutVySspmpfDvnZD6Liy29WMlkqczH6GaAQ2hwaJTKaIvxtNJ0TjPlA8HfBPP-N00HVilWWU0fQoI79r_wi86wcWPLfsTHWyKg6gdq0Y5eoAL1Rf4xEE-iZcufy8OIXeQUKTYDEh/s640/2.64_Elements.png" width="640" /></a></div>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">We never experience any of the 64 elements directly; we perceive them only indirectly by way of the four Symbols, which we can experience probabilistically, through random selection detailed by the measurement Ritual.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2DEQm69WWDL6DrQqAYU8-f7yv1m9NMKXO-2ufUxUdhWq8_XzYWTIchnRrfMjzTuSOFw-xLt-OvnrSpKZtNtUSPBMzYJ0wpyCs9AzLx0NTnw5HYnIw3DfrnCPrNdZCaeJYFUjYefpnSJnc/s1600/3.Four_Symbols.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2DEQm69WWDL6DrQqAYU8-f7yv1m9NMKXO-2ufUxUdhWq8_XzYWTIchnRrfMjzTuSOFw-xLt-OvnrSpKZtNtUSPBMzYJ0wpyCs9AzLx0NTnw5HYnIw3DfrnCPrNdZCaeJYFUjYefpnSJnc/s640/3.Four_Symbols.png" width="640" /></a></div>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">The four Symbols, represented on the Field with colors, give us probability densities represented by their respective bounded areas. The densities reflect the chance of sampling the given Symbol during the measurement Ritual.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXDEMVSyMo_dtbZV4IRThOMcxdhTDFWgt1g44NZRWLJY-rLnkTHIginZqUq7FXFyyUmGIL2Ci-d_Y5KgvOcr_19VwYgsUprz20qjn5G8996mTO7uuiPYsIfyajV8TTRlR1HFyaLyrxv8Ih/s1600/4.Six_Places.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXDEMVSyMo_dtbZV4IRThOMcxdhTDFWgt1g44NZRWLJY-rLnkTHIginZqUq7FXFyyUmGIL2Ci-d_Y5KgvOcr_19VwYgsUprz20qjn5G8996mTO7uuiPYsIfyajV8TTRlR1HFyaLyrxv8Ih/s640/4.Six_Places.png" width="640" /></a></div>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">The Field comprises six dimensions. An object represented on the Field, or by the Field, or which existence depends on the Field, should reasonably comprise 6 dimensions. Likewise, any such object should be expressible in terms of 6 dimensions. </span><br />
<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">The figure above right is a stack made of six Fields; thus, these six Places are means of expressing</span><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: large;"> the 6 dimensions. </span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1EotGtJkaVG1DNMhjYmIdo01eHLi1CxuhAJ1NTUnQu4rTjedsuZ3dvHrys9TaqcexkEnzt_qMsAwX_fOAT2Q0c-v9lwKESwukMv7PdaJ-A6q3YmtzOl0CEtU-1FGXmRrx3R4gjYIN7fPH/s1600/5.Ritual.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1EotGtJkaVG1DNMhjYmIdo01eHLi1CxuhAJ1NTUnQu4rTjedsuZ3dvHrys9TaqcexkEnzt_qMsAwX_fOAT2Q0c-v9lwKESwukMv7PdaJ-A6q3YmtzOl0CEtU-1FGXmRrx3R4gjYIN7fPH/s640/5.Ritual.png" width="640" /></a></div>
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<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">The Ritual is conducted upon the Field </span><span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;">(above left)</span><span style="font-family: Trebuchet MS, sans-serif; font-size: large;"> by randomly sampling a single Symbol from each of its six dimensions, represented by the stack </span><span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;">(above center)</span><span style="font-family: Trebuchet MS, sans-serif; font-size: large;">, then interpreting the ordered collection of samples </span><span style="font-family: Trebuchet MS, sans-serif; font-size: x-small;">(above right)</span><span style="font-family: Trebuchet MS, sans-serif; font-size: large;"> as one of the 64 Elements.</span><br />
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<span style="font-family: Trebuchet MS, sans-serif; font-size: large;"><br /></span><span style="font-family: Trebuchet MS, sans-serif; font-size: large;">Questions:</span><br />
<span style="font-family: Trebuchet MS, sans-serif; font-size: large;">What is the subject of </span><a href="http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Measurement_from_a_practical_point_of_view" style="font-family: 'Trebuchet MS', sans-serif; font-size: x-large;">measurement</a><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">?</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">What is the <a href="http://en.wikipedia.org/wiki/Observer_(quantum_physics)">object</a> of </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">measurement</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">?</span><br />
Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com3tag:blogger.com,1999:blog-9112748128817762559.post-7832261552879531282012-09-20T01:48:00.002-04:002013-02-24T04:49:40.283-05:00Sphere: Squared<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieFU1INvH5ZtOcZrtXseOdXe9XK1jjTY8I40bAEvrZ8T8Ys7NvRkErSvqO5kp6hxOqRHgB0HHbHmUKFHtoP42F6yPDzJJlAYn422hwobVbXsD6vupGzlKYfrQTujmNZUGBoShCN7cXiJyS/s1600/mercury_magic_square.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieFU1INvH5ZtOcZrtXseOdXe9XK1jjTY8I40bAEvrZ8T8Ys7NvRkErSvqO5kp6hxOqRHgB0HHbHmUKFHtoP42F6yPDzJJlAYn422hwobVbXsD6vupGzlKYfrQTujmNZUGBoShCN7cXiJyS/s200/mercury_magic_square.png" width="200" /></a><span style="font-family: 'Trebuchet MS', sans-serif;">In the diagram at right, e</span><span style="font-family: 'Trebuchet MS', sans-serif;">ach figure's cell is identified by two numbers: traditional sequence at upper-right, and </span><span style="font-family: 'Trebuchet MS', sans-serif;">scalar quantity at </span><span style="font-family: 'Trebuchet MS', sans-serif;">lower-left. </span><span style="font-family: 'Trebuchet MS', sans-serif;"><br />This 64-cell grid is arranged so that each cell is placed at 180 degrees of rotation from its logical complement. <br /><br />Other ways of expressing this spatial relationship are that the complementary figures are maximally-separated, that they are antipodally-</span><span style="font-family: 'Trebuchet MS', sans-serif;">positioned</span><span style="font-family: 'Trebuchet MS', sans-serif;">, or that they are </span><span style="font-family: 'Trebuchet MS', sans-serif;">diametrically-</span><span style="font-family: 'Trebuchet MS', sans-serif;">arranged . </span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">Complementary hexagram pairs comprise a symbolic whole when their scalar values are summed, </span><span style="font-family: 'Trebuchet MS', sans-serif;">represented by the number 65</span><span style="font-family: 'Trebuchet MS', sans-serif;">. Seen together, </span><span style="font-family: 'Trebuchet MS', sans-serif;">one figure will have YANG lines where the other figure has YIN lines. </span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">In the diagram following, complementary relationships are also depicted by color pairs: RED with VIOLET, ORANGE with INDIGO, YELLOW with BLUE, or GREEN with </span><span style="font-family: 'Trebuchet MS', sans-serif;">GREEN</span><span style="font-family: 'Trebuchet MS', sans-serif;">. Complementary pairs on the 8 x 8 grid are</span><span style="font-family: 'Trebuchet MS', sans-serif;"> precisely analogous to antipodally-positioned hexagram pairs on any of the thirty-two spherical axes.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgExrwNuODnnKD0qKk4c0SsMttBABAFFe4VXJWnVRljCTQDYRxlUiyMYmwwEUh74zz-Bdd1KbVPriBM0L2kRyoqJ8FyeFfzEumpRvnC9ZLL2mXixN4Hm9nSghWd5GL9U04zhGO_9S1wGMsl/s1600/adinkra.2.xcf.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="338" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgExrwNuODnnKD0qKk4c0SsMttBABAFFe4VXJWnVRljCTQDYRxlUiyMYmwwEUh74zz-Bdd1KbVPriBM0L2kRyoqJ8FyeFfzEumpRvnC9ZLL2mXixN4Hm9nSghWd5GL9U04zhGO_9S1wGMsl/s640/adinkra.2.xcf.png" width="640" /></a></div>
<span style="font-family: 'Trebuchet MS', sans-serif;"><u><br /></u></span>
<span style="font-family: 'Trebuchet MS', sans-serif;"><u>Key</u></span><br />
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<span style="font-family: Trebuchet MS, sans-serif;">RED + VIOLET = 2 polar cells (absolutely polarized)</span><span style="font-family: 'Trebuchet MS', sans-serif;">ORANGE + INDIGO = 12 cells (strongly polarized)</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">YELLOW + BLUE = 30 cells (weakly polarized)</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">GREEN = 20 equatorial cells (non-polarized)</span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><u><br /></u></span>
<span style="font-family: 'Trebuchet MS', sans-serif;"><u>Explication</u></span><br />
<br />
<span style="font-family: 'Trebuchet MS', sans-serif; text-align: justify;">RED and VIOLET figures establish a pole that vertically bisects the grid</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">YELLOW and BLUE figures are located close to GREEN and far from RED and VIOLET, thus they are weakly polarized: young, static, stable</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">ORANGE and INDIGO figures are located close to the </span><span style="font-family: 'Trebuchet MS', sans-serif;">RED and VIOLET polar figures</span><span style="font-family: 'Trebuchet MS', sans-serif;">, thus they are strongly polarized: old, dynamic, changing</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">GREEN figures horizontally bisect the grid, are located between BLUE and YELLOW, and are generally farthest from the poles; thus they are neutrally- or non-polarized</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>
<span style="font-family: 'Trebuchet MS', sans-serif;">Classified per line-type count,</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;">YELLOW and ORANGE have predominantly open lines and have YIN character</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">GREEN have YANG and YIN in equal measure</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">BLUE and INDIGO have predominantly closed lines and are YANG in character</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><u>NOTES</u>:</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">Wen's traditional pairing schema is preserved within the <i>xian tian</i> arrangement. Wen's pairs are defined as </span></div>
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<li><span style="font-size: x-small;"><span style="font-family: 'Trebuchet MS', sans-serif;">a figure pairing with its <i>figurate</i> inversion where such inversion produces a </span><span style="font-family: 'Trebuchet MS', sans-serif;">figure </span><span style="font-family: 'Trebuchet MS', sans-serif;">different from the original; otherwise by</span></span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">a figure mated to its <i>logical</i> negation, as in the case of (#01, #02).</span></li>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-align: justify;">Icosahedral characteristics </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; text-align: justify;"><span style="font-size: x-small;">30 EDGES, 20 triangular FACES, 12 VERTICES</span></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; text-align: justify;"><span style="font-size: x-small;"><br /></span></span>
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-align: justify;">Dodecahedral characteristics</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; text-align: justify;"><span style="font-size: x-small;">30 EDGES, 12 pentagonal FACES, 20 VERTICES</span></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;"><br /></span>
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">xiang::nucleotide bases: adenine + uracil & cytosine + guanine</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">hexagram equivalent in RNA language: three nucleic acids :: codon :: hexagram</span><br />
<span style="font-size: x-small;"><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>
<span style="font-family: 'Trebuchet MS', sans-serif;">xiang::nucleotide pairing schema:</span></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">adenine: (INDIGO, old yang, 9) + uracil (ORANGE, old yin, 6)</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">cytosine (YELLOW, young yin, 8) + guanine (BLUE, young yang, 7)</span><br />
<span style="font-size: x-small;"><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>
<span style="font-family: 'Trebuchet MS', sans-serif;">ROYGBIV Color "octave"</span></span><br />
<span style="font-size: x-small;"><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>
<span style="font-family: 'Trebuchet MS', sans-serif;">Figures #01 and #02, located in the diagram at the high and low corners, are poles of the reference axis. The remaining </span><span style="font-family: 'Trebuchet MS', sans-serif;">62 paths, or 31 axes are "free"</span></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">Human peripheral nervous system comprises 31 nerve pairs</span><br />
<span style="font-size: x-small;"><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>
<span style="font-family: 'Trebuchet MS', sans-serif;">Tun calendar :: 18 * 20 = 360</span></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">Tzolkin calendar :: 13 * 20 = 260</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">20 * (13 + 18) = 20 * (31) = 620</span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-38239532790409085392012-09-19T01:22:00.001-04:002012-09-27T09:19:05.861-04:00Tun, Tzolkin, and XMS<span style="font-family: 'Trebuchet MS', sans-serif;">The Maya are said to have used many calendars, several of which remain unknown to outsiders. </span><span style="font-family: 'Trebuchet MS', sans-serif;">Three of their calendars are fairly-well known; t</span><span style="font-family: 'Trebuchet MS', sans-serif;">hese </span><span style="font-family: 'Trebuchet MS', sans-serif;">calendars are based on the standard 24-hour day, called </span><i style="font-family: 'Trebuchet MS', sans-serif;">kin</i><span style="font-family: 'Trebuchet MS', sans-serif;">. </span><br />
<ul>
<li><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><i><b>Tun</b></i> (literally, stone) is regarded as a prophetic calendar by the Maya people. It comprises 360 <i>kin</i> partitioned into </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">18 <i>uinal (or winal, </i>month), each with </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">20 <i>kin.</i></span></li>
<li><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><i><b>Tzolkin</b></i> is the sacred calendar of the Maya; it comprises 20 periods of thirteen <i>kin</i>, or 260 days. </span><span style="font-family: 'Trebuchet MS', sans-serif;">Together these two form the basis of the Maya timekeeping system.</span></li>
<li><i style="font-family: 'Trebuchet MS', sans-serif;"><b>Haab</b></i><span style="font-family: 'Trebuchet MS', sans-serif;"> (365 </span><i style="font-family: 'Trebuchet MS', sans-serif;">kin</i><span style="font-family: 'Trebuchet MS', sans-serif;">) reflected the Mayan solar year, and was used as a civil calendar, strictly used for accounting, taxation, and perhaps agriculture.</span></li>
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<div style="font-family: 'Times New Roman';">
<a href="http://mayanmajix.com/art011.html" style="font-family: 'Trebuchet MS', sans-serif;">Ian Lundgold's statements</a><span style="font-family: 'Trebuchet MS', sans-serif;">:</span></div>
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<blockquote class="tr_bq">
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">All Mayan calendar dates, including personal birthdays, dedications and most sacred ceremonial events were measured in 360-day periods called, tuns. All dates "carved in stone" throughout the Mayan and Toltec world are tun dates...</span></blockquote>
<blockquote class="tr_bq">
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">This <i>Tun</i>, 360 day calendar is the only Maya calendar directly connected to the Tzolkin and they run together like two gears, each day being a tooth on the respective gears.</span></blockquote>
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><a href="http://www.mesoweb.com/publications/CAA/CAA11.pdf">J. Eric Thompson's paper:</a></span></div>
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<blockquote class="tr_bq">
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">J. T. Goodman wrote of the 360-day period, now called the Tun: “This period is the real basis of the Maya chronological system.”</span></blockquote>
<blockquote class="tr_bq">
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Furthermore, every known unit in the Maya calendar has in its composition the symbol for the 360-day year....</span></blockquote>
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><a href="http://www.calleman.com/content/articles/true_meaning.htm">C. J. Calleman's statements:</a></span></div>
<blockquote class="tr_bq">
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">The real point to get for the study of the Mayan calendar is however that in its prophetic uses it is based on the 260-day tzolkin or the 360-day tun, cycles that do not have an origin in the physical universe.</span></blockquote>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8siH_NQ3MEc4WyKQT81xIVyvxDxy7aI1Qmja4dlWcPDl-QJGsLk5A9bsnXWXR_z0Qw3Bmi2hZlKaEe3I1WeOmW-Ef-BT8CzojK-pu14r6B-MwgIslClDF5-a_O7ZXZ0k3qCE1lustuIcP/s1600/18_spells.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8siH_NQ3MEc4WyKQT81xIVyvxDxy7aI1Qmja4dlWcPDl-QJGsLk5A9bsnXWXR_z0Qw3Bmi2hZlKaEe3I1WeOmW-Ef-BT8CzojK-pu14r6B-MwgIslClDF5-a_O7ZXZ0k3qCE1lustuIcP/s200/18_spells.png" width="191" /></span></a></td></tr>
<tr><td class="tr-caption" style="font-size: 13px; text-align: center;"><span class="Apple-style-span"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;"><i>18 "spells" of xiantian</i> magic square</span></span></td></tr>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><u>Xiantian Magic Square</u></span><br />
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">The XMS arrangement comprises eight columns, eight rows, and two diagonals for a total of 18 groups linearly-arranged. We can also refer to the groups as octets or "spells."</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"> </span><span style="font-family: 'Trebuchet MS', sans-serif;">Each of the eighteen "spells" comprises a unique collection of eight numbers all arranged in a line on the grid. Additionally, e</span><span style="font-family: 'Trebuchet MS', sans-serif;">ach octet sums to 260, the same number of days as in the </span><i style="font-family: 'Trebuchet MS', sans-serif;">tzolkin</i><span style="font-family: 'Trebuchet MS', sans-serif;">.</span><br />
<ul>
<li><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Each octet may stand for a w<i>inal</i> (20-day <i>tun</i> month) since both octets and uinals relate to eighteen</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;">Since an octet represents 20 days (winal) and sums to 260 (tzolkin year), it </span><span style="font-family: 'Trebuchet MS', sans-serif;"> </span><span style="font-family: 'Trebuchet MS', sans-serif;">associates</span><span style="font-family: 'Trebuchet MS', sans-serif;"> each day of an octet with the value 13</span></li>
</ul>
<span style="font-family: 'Trebuchet MS', sans-serif;">Considered this way, XMS can be considered as relating to both</span><span style="font-family: 'Trebuchet MS', sans-serif;"> </span><i style="font-family: 'Trebuchet MS', sans-serif;">tun</i><span style="font-family: 'Trebuchet MS', sans-serif;"> </span><span style="font-family: 'Trebuchet MS', sans-serif;">and</span><span style="font-family: 'Trebuchet MS', sans-serif;"> </span><i style="font-family: 'Trebuchet MS', sans-serif;">tzolkin</i><span style="font-family: 'Trebuchet MS', sans-serif;"> calendars, though our use of metaphor may somewhat exaggerate these </span><span style="font-family: 'Trebuchet MS', sans-serif;">relations. It should be noted that the number 20 is not yet directly discernible within the XMS arrangement, though it is a demonstrable feature of the 64 hexagrams (q.v. yao-groups). The equatorial plane of the spherical representation of Change comprises twenty complementary pairs. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><span style="font-family: 'Trebuchet MS', sans-serif;">Notes:</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: x-small;">Complementary pairs on the XMS grid sum to 65; any four such pairs sum to 260, the same number of days in the tzolkin calendar. Four pair is an octet, an octet is 20 days; therefore one pair is five days (value 65) and one day has value 13. QED</span></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: x-small;"><br /></span></span>
<span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: x-small;">Coincidentally, 13 / 8 * 360 (<i>tun</i>) = 585, a fair approximation to the Venus cycle of 584. Admittedly, 8 / 5 * 365 (<i>haab</i>) = 584; a precise fit. Both fractions (13/8 and 8/5) are common approximations to the golden ratio, <i>phi (~1.618)</i>.</span></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: x-small;"><br /></span></span>
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;"><a href="http://www.nytimes.com/1996/07/09/science/new-gauge-for-shorter-day-of-past.html">Scientists have calculated</a> that approximately 1 billions of years ago, the Moon was ~25% closer than it is today, the Earth having an ~18-hour day and a <a href="http://adsabs.harvard.edu/abs/2010AGUFMEP21A0727C">18 - 20-day month</a> as marked by the Moon's circuit.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;"><br /></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">Linear octants are also called "spells" in acknowledgement of the 18 spells gained by Odin through his self-sacrifice on the World Tree Yggdrasil: two for each day he was hanged.</span></div>
Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com1tag:blogger.com,1999:blog-9112748128817762559.post-78573832462334642982012-09-18T00:04:00.000-04:002013-02-23T02:02:15.134-05:00Axes and Reflections on the 8 x 8<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQlR0Rfhd476Rv-LK-tQfz2hbOXE4Z5bJ33nXWi1vchhruL-fjYAtril4PxojeNd7AZsBUeNRylOnn3T6mFhCToDV2F7o7roXvHIbQSUIRz0L4Ul8TYdrLqSZOch5chdCSnTAC78o5d_NZ/s1600/crossed_axes.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQlR0Rfhd476Rv-LK-tQfz2hbOXE4Z5bJ33nXWi1vchhruL-fjYAtril4PxojeNd7AZsBUeNRylOnn3T6mFhCToDV2F7o7roXvHIbQSUIRz0L4Ul8TYdrLqSZOch5chdCSnTAC78o5d_NZ/s320/crossed_axes.png" width="304" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Verdana, sans-serif;">16 axial figures</span></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><i>Ashtapada</i>, the 8 x 8 field, is here populated with </span><i style="font-family: 'Trebuchet MS', sans-serif;">xian tian</i><span style="font-family: 'Trebuchet MS', sans-serif;"> (complementary opposition) hexagram arrangement. We observe that two pairs of <i>orthogonal </i></span><span style="font-family: 'Trebuchet MS', sans-serif;">axes </span><span style="font-family: 'Trebuchet MS', sans-serif;">(opposed at 90 degrees) cross the field. </span><span style="font-family: 'Trebuchet MS', sans-serif;">These axes include </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">HORIZONTAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> with </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">VERTICAL</span><span style="font-family: 'Trebuchet MS', sans-serif;">, and </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">DIAGONAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> with </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">SLANT</span><span style="font-family: 'Trebuchet MS', sans-serif;">. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">The 48 remaining cells of the field are effectively partitioned </span><span style="font-family: 'Trebuchet MS', sans-serif;">into four </span><span style="font-family: 'Trebuchet MS', sans-serif;">groups of twelve </span><span style="font-family: 'Trebuchet MS', sans-serif;">contiguous </span><span style="font-family: 'Trebuchet MS', sans-serif;">cells </span><span style="font-family: 'Trebuchet MS', sans-serif;">by the </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">SLANT</span><span style="font-family: 'Trebuchet MS', sans-serif;"> and </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">DIAGONAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axes</span><span style="font-family: 'Trebuchet MS', sans-serif;">. The </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">VERTICAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> and </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">HORIZONTAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axes further bisect these four </span><span style="font-family: 'Trebuchet MS', sans-serif;">groups of 12 cells.</span><br />
<ul>
<li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: x-small;">HORIZONTAL</span> axis (unmarked) divides the field into an upper half and a lower half</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: x-small;">VERTICAL</span> axis </span><span style="font-family: 'Trebuchet MS', sans-serif;">(unmarked) </span><span style="font-family: 'Trebuchet MS', sans-serif;">divides the field into left and right halves</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: x-small;">DIAGONAL</span> axis is defined by the eight cells that span the corners lower left to upper right, or conversely. </span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: x-small;">SLANT</span> axis is defined by the eight cells that span the corners lower right to upper left, or conversely.</span></li>
</ul>
<span style="font-family: 'Trebuchet MS', sans-serif;">It should be noted that t</span><span style="font-family: 'Trebuchet MS', sans-serif;">he figures </span><span style="font-family: 'Trebuchet MS', sans-serif;">located </span><span style="font-family: 'Trebuchet MS', sans-serif;">on the </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">DIAGONAL </span><span style="font-family: 'Trebuchet MS', sans-serif;">and </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">SLANT</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axes exhibit the associated relationships when they are folded or reflected across each other. Example: </span><span style="font-family: 'Trebuchet MS', sans-serif;">figures (#52,#53)</span><span style="font-family: 'Trebuchet MS', sans-serif;"> located on the </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">SLANT</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axis (which crosses the </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">DIAGONAL</span><span style="font-family: 'Trebuchet MS', sans-serif;">), are related through transposing and complementing both trigrams. </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEga3Q5ryQC1fm8AcTyui23Yw46aZW36vDtLZQZQziZmSRs_nhTGYuDb33yucpSfkI_dS3RwkjxLLWM1jUqxfHlNlykugA1THUZkWFBKWfcVI-bcTXBNQ21KtrxpdLctAGGYpWjcOU5J3O4N/s1600/crossed_axes_inverted.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto; text-align: center;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEga3Q5ryQC1fm8AcTyui23Yw46aZW36vDtLZQZQziZmSRs_nhTGYuDb33yucpSfkI_dS3RwkjxLLWM1jUqxfHlNlykugA1THUZkWFBKWfcVI-bcTXBNQ21KtrxpdLctAGGYpWjcOU5J3O4N/s320/crossed_axes_inverted.png" width="304" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif;">48 non-axial figures</span></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><u><span style="font-size: x-small;">REFLECTIONS ACROSS AN AXIS</span></u></span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Imagine our grid printed on a square piece of paper which is then folded across length and width, and across both diagonals. An axis is equivalent to any singular fold-line; reflection across an axis results in two cells that "mirror" each other on either side of the fold-line. If the paper were actually folded as described, the mirrored cells would overlap perfectly. </span><span style="font-family: 'Trebuchet MS', sans-serif;">Now with a working definition of axial reflection over our grid, let's look at relationships among the reflected figures.</span><br />
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<ol>
<li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-family: 'Trebuchet MS', sans-serif;">Reflection across the </span><span style="font-size: x-small;">HORIZONTAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axis </span>complements a figure's lower trigram, leaving the upper trigram unchanged; e.g.: (#46,#24)**</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-family: 'Trebuchet MS', sans-serif;">Reflection</span><span style="font-family: 'Trebuchet MS', sans-serif;"> across the</span><span style="font-family: 'Trebuchet MS', sans-serif;"> </span><span style="font-size: x-small;">VERTICAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axis </span><span style="font-family: 'Trebuchet MS', sans-serif;">complements a figure's upper trigram, leaving the lower trigram unchanged; e</span>.g.<span style="font-family: 'Trebuchet MS', sans-serif;">: (#59,#40)</span></span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-family: 'Trebuchet MS', sans-serif;">Reflection</span><span style="font-family: 'Trebuchet MS', sans-serif;"> across the </span><span style="font-size: x-small;">SLANT</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axis </span><span style="font-family: 'Trebuchet MS', sans-serif;">transposes</span><span style="font-family: 'Trebuchet MS', sans-serif;"> OR complements both<span style="font-family: 'Trebuchet MS', sans-serif;"> </span><span style="font-family: 'Trebuchet MS', sans-serif;">trigrams of a figure</span>; e</span>.g.<span style="font-family: 'Trebuchet MS', sans-serif;">: (#28,#61)</span></span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-family: 'Trebuchet MS', sans-serif;">Reflection</span><span style="font-family: 'Trebuchet MS', sans-serif;"> across the </span><span style="font-size: x-small;">DIAGONAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axis </span><span style="font-family: 'Trebuchet MS', sans-serif;">transposes AND complements both trigrams of a figure</span><span style="font-family: 'Trebuchet MS', sans-serif;">; e</span>.g.<span style="font-family: 'Trebuchet MS', sans-serif;">: (#4,#38) </span></span><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: x-small;">** parenthesized numbers indicate the traditional hexagram ordering, located at upper-right corner of cells in white text.</span></span></li>
</ol>
<span style="font-family: 'Trebuchet MS', sans-serif;">Likewise, paired </span><span style="font-family: 'Trebuchet MS', sans-serif;">figures (#11,#12) located <b>on</b> the </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">DIAGONAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axis (which crosses the </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">SLANT</span><span style="font-family: 'Trebuchet MS', sans-serif;">), are related through transposing </span><span style="font-family: 'Trebuchet MS', sans-serif;">trigrams</span><span style="font-family: 'Trebuchet MS', sans-serif;">; alternatively, through complementing </span><span style="font-family: 'Trebuchet MS', sans-serif;">trigrams</span><span style="font-family: 'Trebuchet MS', sans-serif;">.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;">Reflection across a single axis is equivalent to rotating the grid in place by 90 degrees; therefore, reflection across two orthogonal axes </span><span style="font-family: 'Trebuchet MS', sans-serif;">is equivalent to rotating the grid in place by 180 degrees. </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;">For any figure selected, crossing two orthogonal axes </span><span style="font-family: 'Trebuchet MS', sans-serif;">results in complementing the entire figure. </span><span style="font-family: 'Trebuchet MS', sans-serif;">This fact is intrinsic to the </span><i style="font-family: 'Trebuchet MS', sans-serif;">xian tian</i><span style="font-family: 'Trebuchet MS', sans-serif;"> arrangement whereby pairs of </span><span style="font-family: 'Trebuchet MS', sans-serif;">complementary </span><span style="font-family: 'Trebuchet MS', sans-serif;">hexagrams are separated on the field by 180 degrees of rotation, or </span><span style="font-family: 'Trebuchet MS', sans-serif;">two orthogonal axes</span><span style="font-family: 'Trebuchet MS', sans-serif;">. Since </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">DIAGONAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> and </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">SLANT</span><span style="font-family: 'Trebuchet MS', sans-serif;"> axes cross both </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">HORIZONTAL</span><span style="font-family: 'Trebuchet MS', sans-serif;"> and </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">DIAGONAL </span><span style="font-family: 'Trebuchet MS', sans-serif;">axes, the reflections of the figures on those axes are complementary.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;">No matter the combination of axial reflections, any selected figure and its several reflections remain confined within the same concentric band of figures on the field. These are termed xiang probability bands because of their relation to the divinatory probabilities for generating each of the four kinds of lines (<i>xiang</i>) that may appear when consulting the oracle.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><span style="font-family: 'Trebuchet MS', sans-serif;">XMS (<span style="font-size: x-small;">XIANTIAN MAGIC SQUARE</span></span><span style="font-family: 'Trebuchet MS', sans-serif;">, </span><span style="font-family: 'Trebuchet MS', sans-serif;">elsewhere described in detail) is a magic square that is also a </span><i style="font-family: 'Trebuchet MS', sans-serif;">xian tian</i><span style="font-family: 'Trebuchet MS', sans-serif;"> or complementary opposition arrangement; therefore, the relationships described above likely also hold for XMS.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;">This diagram embodies many of the same qualities as the 8 x 8 xiantian diagram</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDdpM0E5gIcsUVh-NbRJi8s5eeI8JkKve_ZNFIGZHjNc7z7OmcFL2iHXU62cF0bPVqPo0XhtYZ-V4-5emqLgbhyphenhyphensvOLoR21DQeSLd2XinbgWzZGwuyQijzY2J8mrIgQvFnrHPVb3niWGPS/s1600/oracular_ashtapada.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDdpM0E5gIcsUVh-NbRJi8s5eeI8JkKve_ZNFIGZHjNc7z7OmcFL2iHXU62cF0bPVqPo0XhtYZ-V4-5emqLgbhyphenhyphensvOLoR21DQeSLd2XinbgWzZGwuyQijzY2J8mrIgQvFnrHPVb3niWGPS/s200/oracular_ashtapada.png" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">xiang probability bands</span></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif;">NB: The two outer bands of the <i>xiang</i> probability square representing static <span style="font-size: x-small;">YIN</span> and static <span style="font-size: x-small;">YANG</span> contain 28 + 20 = 48 cells, the same number as the non-axial cells Therefore, these cells may stand for static <span style="font-size: x-small;">YIN</span> with static <span style="font-size: x-small;">YANG</span>, or a stable condition overall. The same logic represents the axial cells as 12 + 4 = 16, dynamic <span style="font-size: x-small;">YANG</span> with dynamic <span style="font-size: x-small;">YIN</span>, a changing condition.</span><br />
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Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com2tag:blogger.com,1999:blog-9112748128817762559.post-79518095633816731822012-07-19T01:16:00.002-04:002013-01-11T21:08:55.376-05:00I Ching and Bloch Sphere<br />
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<tr><td style="text-align: center;"><a href="http://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Bloch_sphere.svg/256px-Bloch_sphere.svg.png" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Bloch_sphere.svg/256px-Bloch_sphere.svg.png" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif; font-size: small;">Bloch sphere</span></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The Bloch or Poincare sphere seems particularly instrumental to understanding how I Ching may be related to quantum mechanics; perhaps even an ancient depiction of it. I Ching is founded on two principles, <i>Ch'ien</i> and <i>K'un,</i> or the Creative and the Receptive, commonly known as YANG and YIN, and discussed at length in various appendices to I Ching (namely, appendices III and IV). Appendix III, the Great Treatise, is quite clear on the distinction between hexagrams #1 and #2 and the remainder of I Ching. </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Stated clearly in several verses, Ch'ien and K'un are the "pole," "axis, or "gates" of Change, without which Change could not be seen and would cease to exist. (*provide references*). </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">These passages provide support to the intuition that hexagrams #1 and #2 are intended to act as basis vectors and define the </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">spherical </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">system that represents the I Ching. </span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMgkdsgg54ZEdXAFnpC1QjiYMihLmnxA-bgva3IS3QUuKwrV0hoGDp6RdF9Lae6qTrTbX3ySJLUDZmuxYTOS4mPNaummCPf9OZcbnf8972xJwV9-G3y-adojyGGBMPNhp8a2ZKFxoMcVvG/s1600/yao_groups_on_sphere.png" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="" border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMgkdsgg54ZEdXAFnpC1QjiYMihLmnxA-bgva3IS3QUuKwrV0hoGDp6RdF9Lae6qTrTbX3ySJLUDZmuxYTOS4mPNaummCPf9OZcbnf8972xJwV9-G3y-adojyGGBMPNhp8a2ZKFxoMcVvG/s320/yao_groups_on_sphere.png" height="320" title="64 hexagrams on a sphere" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif; font-size: small;">Spherical I Ching</span></td></tr>
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<span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">We now set aside Ch'ien and K'un for consideration of the remaining thirty-one pairs of hexagrams. </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"></span><br />
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<span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">Some effort was made earlier to find meaningful correspondence between the human body's 31 pairs of spinal nerves and the 31 (+1) hexagram pairs, but these efforts have not borne fruit.</span><br />
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<span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">A presentation from the </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;"><b>Vienna Center for Parallel Computing</b></span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;"> shows us that our complementary or <i>xian tian</i> hexagram pairs having scalar values which sum to 65 are regarded as orthogonal and identical states (except for phase/sign) </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">on the Bloch sphere</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">. The model of I Ching presented in these blogs accounts not only orthogonal hexagram pairs, but also the pairs given by Wen, Duke of Chou. </span><br />
<span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">I Ching tradition describes Duke's imprisonment at the hands of the evil tyrant of Shang, and of the pairing scheme he devised during his period of captivity. </span><br />
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<span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">In general, Wen's pairs are distinct figurate inversions </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">(read: 180</span><span style="background-color: white; font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">°rotation) </span></span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">except in the eight cases where inversion does not produce an hexagram </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">distinct from the original</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">: </span><br />
<span style="font-size: large;"><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">[(1,2) (51,57) (29,30) (52,58)]. In those cases, </span></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">the </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">complementary</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> pair </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">is taken as </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">the Wen pair</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">.</span><br />
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<a href="http://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Bloch_sphere.svg/256px-Bloch_sphere.svg.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br class="Apple-interchange-newline" /><img alt="" border="0" src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Bloch_sphere.svg/256px-Bloch_sphere.svg.png" height="200" title="Bloch sphere" width="188" /></a><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The graphic of the Bloch sphere (at left) highlights its important features:</span><br />
<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;"><i>basis vectors</i> |0</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">⟩</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;"> and |1</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">⟩</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">, arbitrary </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">quantum state <i>psi</i> (</span></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Ψ</span><span style="font-size: large;"><span style="background-color: white;"><span style="font-family: 'Trebuchet MS', sans-serif;">), </span></span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">two <i>coordinate systems</i>; <b>polar: </b>denoted by angles theta </span></span><span style="font-size: large;"><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">(</span></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Θ</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">)</span><span style="font-size: large;"><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;"> and phi </span></span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">(</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Φ</span><span style="font-size: large;"><span style="background-color: white;"><span style="font-family: 'Trebuchet MS', sans-serif;">); and </span></span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;"><b>rectangular:</b> denoted by orthogonal axes <b>x,y,z</b>. </span></span><br />
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<span style="font-size: large;"><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">Selecting one of the remaining 56 'non-distinct' hexagrams to approach this question spatially, we see that complementary pairs are opposite and orthogonal points on the Bloch sphere, while Wen pairs lay on the same (or opposite latitude) to the selected hexagram and may also be complementary to the selected hexagram. We see in the graphic above the north and south poles (denoted by </span><span style="font-family: 'Trebuchet MS', sans-serif;">|0</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">⟩</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;"> and |1</span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">⟩) along </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">with <i>psi</i></span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;"> (</span></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Ψ</span><span style="font-size: large;"><span style="background-color: white;"><span style="font-family: 'Trebuchet MS', sans-serif;">) </span></span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">forming an imaginary triangle.</span><i style="background-color: white; font-family: 'Trebuchet MS', sans-serif;"> </i></span><br />
<span style="font-size: large;"><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">Arbitrarily selecting hexagram #41, we get its Wen pair #42, and #31 as its orthogonal point. These three hexagrams form a corresponding imaginary triangle: #41 and #42 analogous to the poles, and #31 as </span><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif;">the surface point. <i>The hexagram, its Wen inverse, and its opposite form a triplet: two hexagrams share a latitude while two share a diameter. </i>Selecting any hexagram from the eight pairs listed above produces just a diametric pair instead of a triplet since the Wen pair is also the opposite hexagram.</span></span><br />
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<span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: large;">If we accept that I Ching is analogous with Bloch's sphere as a working model or depiction of quanta, the question begs, what is to be made of Wen's pairs? We understand that Wen pairs are figurate inverses</span><span style="background-color: white; font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">, but what does this mean in terms of the Bloch sphere and how might this inform us to quanta?</span></span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-83224810352647874852012-05-10T06:26:00.001-04:002012-06-19T00:12:05.542-04:00The Spherical Model of Change<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">As promised at the end of the previous entry, here </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">we </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">present a non-arbitrary arrangement of the hexagrams on the sphere.</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> Our spherical arrangement is based on a construct called "<b>yao-numbers"</b>, the existence of which is attested in an appendix of the Book of Changes known as <i>Ta Chuan</i> (The Great Treatise).</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: small;">Spherical Model</span><br /><span style="font-size: x-small;">(equatorial view)</span></span></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Once the hexagrams were sorted by the size of the yao-group in which they fall [1, 6, 15, or 20], it seemed natural to sort them again by their scalar (<i>xiantian</i>) index. Recall that the xiantian or scalar index of an hexagram is the decimal value of an hexagram figure rendered into binary. Scalar value is a reasonable indicator of an hexagram's magnitude; thus it appears a reasonable choice for placing the hexagrams of a given yao-group (which all lay on a common latitude) at specific meridians.</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: small;">Spherical model</span><br /><span style="font-size: x-small;">(depicted with vectors)</span></span></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Expressed another way, the problem was to determine how to arrange the hexagrams on each latitude of the sphere in such a way that the ordering remained consistent with the complementarity of the 32 antipodal pairs. Scalar value was used as a proxy for angular displacement (</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">PHI</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">) </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">on a latitude, with larger values corresponding to larger angular measures.</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif; font-size: small;">Spherical Model</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">(polar view)</span></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">In the table following, each hexagram is assigned a coordinate pair (<i>theta,phi</i>) on the sphere: THETA is the measure of latitude (declination from the positive vertical) while PHI measures longitude (angular displacement from a given meridian) on a latitude. The hexagrams are </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">grouped, </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">generally speaking, by yao-number and ordered within a yao-group by scalar value (XT).</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirOlx2jZ8Ntc7XumoiTXjneB8NYQVTmcV0-PiwjCm4FnQic2CMHg1SlmOKOuGE0BVY4NwzBf1tH8TZcrp_5qVWy4mPfqqknwmEQkqA17dIgawcgg2ux4xRPzv2f_g_zYjRD8U-Ggl53JrX/s1600/spherical_map.pdf.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirOlx2jZ8Ntc7XumoiTXjneB8NYQVTmcV0-PiwjCm4FnQic2CMHg1SlmOKOuGE0BVY4NwzBf1tH8TZcrp_5qVWy4mPfqqknwmEQkqA17dIgawcgg2ux4xRPzv2f_g_zYjRD8U-Ggl53JrX/s400/spherical_map.pdf.png" width="213" /></a></div>
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">As detailed in other entries, the</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> yao-numbers of the </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">paired hexagrams </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">sum to 360</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">. A</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">dditionally,</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> these pairs </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">have XT numbers summing to 65, thus they are complementary pairs</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">. The spherical model presented here preserves those relationships.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">One unexpected outcome of this effort was the discovery of a natural partition of yao-group[20] which, </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">for lack of a self-consistent way to divide it,</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> had been treated only as a unit. With the aid of the XT index, however, t</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">his group of 20 hexagrams falls naturally into halves: one half with XT less than 32; the XT of the other ten hexagrams exceeding 32. Only yao-group of 20 features this relationship. Indeed, only this group requires additional means to distinguish pair-mates. </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Whereas they were previously presented as seven groups on discrete latitudes, the 64 hexagrams can </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">now </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">be portrayed as four groups of varying sizes, each group with equal-sized halves as shown in the table. These eight sections comprise an octo-partition of spherical space, bringing us full-circle (pardon the pun). </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The model is expected to serve as an anti-</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><a href="http://en.wikipedia.org/wiki/Stereographic_projection">stereographic projection</a> of the xiantian magic square onto the unit sphere and may prove useful for visualizing projections of XMS subsets onto 3-space. For example, how do the </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">XMS </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">main diagonals -- or any of the "18 spells" for that matter -- appear when displayed on the sphere? </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The projection may also help with transforming the XMS field into a magic </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">4x4x4 cube (</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">with magic constant 130).</span><br />
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<span style="font-size: x-small;"><span style="font-family: 'Trebuchet MS', sans-serif;">[NB: Consequently, the yao-groups should perhaps be redefined for the sake of clarity in designation:</span></span><br />
<span style="font-size: x-small;"><span style="font-family: 'Trebuchet MS', sans-serif;">[2 12 30 20]</span><span style="font-family: 'Trebuchet MS', sans-serif;"> with modifiers '+' or '-' to indicate latitudes above or below the equator, respectively. Again, this coincides with the specification of a dodecahedron]</span></span><br />
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</div>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com3tag:blogger.com,1999:blog-9112748128817762559.post-1396137292687607762012-05-08T06:44:00.002-04:002012-05-11T02:44:32.061-04:00Progressing Toward a Spherical Model of Change<div class="separator" style="clear: both; text-align: center;">
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif;">Yao-numbers depicted as radial vectors</span></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Having determined </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">a set of coordinates for e</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">ach hexagram allows us to generate 32 pairs of complementary vectors with which </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">vector-analysis </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">may be performed. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The spherical model also enables us to derive insight from </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">quantum mechanical systems by using </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">the Bloch/Poincare model of the </span><a href="http://en.wikipedia.org/wiki/Qubit" style="font-family: 'Trebuchet MS', sans-serif; font-size: x-large;">qubit</a><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> as an entry-point.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The basis vectors in our model are hexagrams #1 and #2, found at the "poles" of our model; the remaining 31 pairs of hexagram figures are said to derive from these. </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Prior to performing an instance of divination, the answer to the posed question is like a superposition of the basis vectors, entailing 64 x 64 = 4,096 possible results. Once the oracle is consulted, the superposition collapses to a single result. </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Future entries on this topic intend to determine the meridian lines in order to produce a model that fits the 64 hexagrams onto the unit sphere in a non-arbitrary fashion. That is, the particular assignment of hexagrams to points on the surface of the sphere will be based a scheme that preserves the integrity of known relationships.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><br /></span></div>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-56950353356079966632012-05-07T02:50:00.002-04:002012-05-19T02:27:40.344-04:00Subspatial Scaffolding, Aetheric Architecture<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx_0bLqVquHC0FMGc7kbuMC06kbN39u6fQ74Jw4NriDdriGeKlRyPzUOB82_2JCRJ5z9CMkwDyNpgrRoknUvbOzkVqI13yLro6tTA0Q-XloJRkGnPoSTR8WoMJGyZciedRZsUlFWITJ6s/s1600/bagua_hypercube.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br class="Apple-interchange-newline" /><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx_0bLqVquHC0FMGc7kbuMC06kbN39u6fQ74Jw4NriDdriGeKlRyPzUOB82_2JCRJ5z9CMkwDyNpgrRoknUvbOzkVqI13yLro6tTA0Q-XloJRkGnPoSTR8WoMJGyZciedRZsUlFWITJ6s/s320/bagua_hypercube.png" width="320" /></a></div>
<span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">This graphic attempt to convey the notions of subspace, or the </span><span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">architecture of volumetric space</span><span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">. </span><br />
<span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">It is easy to take space for granted, like we assume a fish takes water for granted. Indeed, were there no water, there'd be no fish -- likewise for space and ourselves. </span><br />
<span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">It's not so easy to wrap one's mind around non-volumetric reality, though some are familiar with '<a href="http://www.imdb.com/title/tt0814106/">Flatland</a>,' a fictional 2-D world.</span><span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;"> Space normally provides an habitat for objects to occupy, but under certain conditions, intense gravitation does not allow space to exist as we understand it. Under those conditions, space is presumed to collapse. The Big Bang cosmological theory proposes that </span><span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">the universe as we know it evolved </span><span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">from a singularity; otherwise there was no space nor time. From this we may infer that some 'thing' or force exists that gives space the rigidity to resist gravitationally-induced collapse. Some physicists have proposed that hypothesized (but undetected) "dark energy" fill this function. To this point, physicist David Bohm once remarked in <u>The Holographic Universe</u> that "</span><span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">every cubic centimeter of empty space contains more energy than the total energy of all the matter in the known universe</span><span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">." We propose that this role is fulfilled by an architecture, hypothesized in the above graphic.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibRldKRMgAICcB8GAu70otiGvJxfpK0D0nqHjtUswnqaZGu243MSYkK-XTidEBdikiri7r7halOPJ5D1mRxPlcuGEv4NnsrHz2J5-FtwOOEbtI2bjZsBZFn8Kue5sl2dVM-alekqc20UY/s1600/bagua_hypercube_frame.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibRldKRMgAICcB8GAu70otiGvJxfpK0D0nqHjtUswnqaZGu243MSYkK-XTidEBdikiri7r7halOPJ5D1mRxPlcuGEv4NnsrHz2J5-FtwOOEbtI2bjZsBZFn8Kue5sl2dVM-alekqc20UY/s320/bagua_hypercube_frame.png" width="320" /></a></div>
<span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">In the diagram, mutually complementary elements intersect on orthogonal axes. </span><span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">This arrangement is presumed to produce a framework that 'erects' space and maintains its volume, similar to the way that a balloon maintains its shape from the force exerted by the gas within.</span><br />
<span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">Complementarity is depicted via the axes of 'opposing' color pairs: red and blue, yellow and green. These opposing pairs span opposite corners of the bounding box. </span><br />
<span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">The nexus of the four axes at the center of the figure suggests a combination of the four axes that intersect there. This is perhaps where the proposed structive force emerges.</span><br />
<span style="font-family: 'Trebuchet MS',sans-serif; font-size: large;">We note that the central nexus is adjoined by the apexes of six square pyramids, the bases of which comprise the faces of the bounding box and its enclosed cube.</span></div>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com1tag:blogger.com,1999:blog-9112748128817762559.post-69656844091501707572012-05-05T01:57:00.000-04:002013-02-03T03:27:05.322-05:0011,520: "The Number of All Things"<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">This entry treats the connection between the 8x8 grid and 11,520, the "number of all things," attested in <i>Ta Chuan</i> (the "Great Treatise"). </span><span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">The 64 hexagram are commonly depicted on an 8 x 8 grid, known in Hindu culture as <i>ashtapada</i>. Its metric (generic term for measure) is 2080, and is thus related to 11,520:</span></span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: large;">1) Begin by enumerating its cells beginning with 1, through 64, noting that the cells sum to 2080.</span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgs4HYnODzv2MYbcD4kSISMq-_DocGkfalAG9jnLWEI0woGSHLbSPkj5KPkQPkuL43ouGbp1Sn7vxB_tRgKICIBPREfDVL1t8wM0f6TJRUyRvCyDDT3Y3x7fQhaipmOnVUm-YfwTUY1a4F/s1600/enumerated_ashtapada.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgs4HYnODzv2MYbcD4kSISMq-_DocGkfalAG9jnLWEI0woGSHLbSPkj5KPkQPkuL43ouGbp1Sn7vxB_tRgKICIBPREfDVL1t8wM0f6TJRUyRvCyDDT3Y3x7fQhaipmOnVUm-YfwTUY1a4F/s320/enumerated_ashtapada.png" width="320" /></a></div>
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">2) A</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">rrange</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> the numbered cells such that the numbers within each row, column, and major diagonal sum to 260. </span><br />
<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">Under this arrangement, the 18 columns, rows, and diagonals sum to 4680 = 18 * 260 = 13 * 360 = 18 * 13 * 20. This number seems to link the Mayan</span><span style="font-family: 'Trebuchet MS', sans-serif;"> </span><span style="font-family: 'Trebuchet MS', sans-serif;">360-day </span><i style="font-family: 'Trebuchet MS', sans-serif;">tun</i><span style="font-family: 'Trebuchet MS', sans-serif;"> calendar to the Mayan 260-day </span><i style="font-family: 'Trebuchet MS', sans-serif;">tzolkin</i><span style="font-family: 'Trebuchet MS', sans-serif;"> calendar. </span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1nevppfdXuXE051oWy_UScwflGdzMvPKRx2oMTRmltvr_ZRsppDC3c5nwRRBzlzfisLQ9imFgCjYvN8wU_qBqh7cnnHJYpAEkAa8Oh06EBU2fNJZ858gydXmbMl4gp9WSRkFbGI6YMhuA/s1600/xms_ashtapada.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1nevppfdXuXE051oWy_UScwflGdzMvPKRx2oMTRmltvr_ZRsppDC3c5nwRRBzlzfisLQ9imFgCjYvN8wU_qBqh7cnnHJYpAEkAa8Oh06EBU2fNJZ858gydXmbMl4gp9WSRkFbGI6YMhuA/s320/xms_ashtapada.png" width="320" /></a></div>
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">3) Convert the numbers into hexagrams (6-line binary figures) , the least-valued hexagram valued having the value one (1).</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgs56LZuAx6CsK1176rLJkPI_36p0outu3NhW3Vdu1NM4M2bdwJLMaLFwUGXi38ShGTj3HxifNY_98o8tn7Dh_0XbxksGWcBLO5n-vejFberNJKBwQnGvJMa8M_404U0NCqKs3Lav8woK_Z/s1600/xms_figure_ahstapada.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgs56LZuAx6CsK1176rLJkPI_36p0outu3NhW3Vdu1NM4M2bdwJLMaLFwUGXi38ShGTj3HxifNY_98o8tn7Dh_0XbxksGWcBLO5n-vejFberNJKBwQnGvJMa8M_404U0NCqKs3Lav8woK_Z/s320/xms_figure_ahstapada.png" width="320" /></a></div>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large; text-align: -webkit-auto;">4) Transform e</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large; text-align: -webkit-auto;">ach figure into a <i>yao-number</i> by substituting its lines with the corresponding divination ritual numbers: '6' for YIN lines and '9' for YANG lines, summing the substitutions,</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> then scaling each sum by 4. This step is derived from instructions given in <i>Ta Chuan, </i>and</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> has the effect of:</span></div>
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<li>"flattening" the hexagram (like a logarithm), which may be regarded as a "stack" of binary exponents </li>
<li>shifting the range of values from a continuum of [1..64] to [144..216] in discrete intervals of 12 </li>
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<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">The 18 rows, columns, and diagonals noted above now sum to 1440, and produce a grand sum of 18 * 1440 = 25,920, equal to the duration of a precession cycle.</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifOFg_EtwdDuJqwUCH7xN46MGnL7OFhntuTzPIxWhCVVbosG2FvtJANCLTvGO9bbhagYSS77bjlozGKDoZCJ0ln00wt41vIM54wrLlUljGdjyTGQnGqmnQPkg6NmUSUs_7wbHaSm0shZnE/s1600/yao_xms_ashtapada.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifOFg_EtwdDuJqwUCH7xN46MGnL7OFhntuTzPIxWhCVVbosG2FvtJANCLTvGO9bbhagYSS77bjlozGKDoZCJ0ln00wt41vIM54wrLlUljGdjyTGQnGqmnQPkg6NmUSUs_7wbHaSm0shZnE/s320/yao_xms_ashtapada.png" width="320" /></a></div>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">5) Finally, the hexagrams and their associated </span><span style="font-family: Trebuchet MS, sans-serif; font-size: large;"><i>yao-numbers</i></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> from steps #3 and #4 are sorted to produce seven groups with the following membership and distribution:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhU9tvkopjHKl4v42QNQBE6w71Y6Fttr-E44EXKXVTrn6cL5fD_6DpU968Zs4YVyMHl5A2HRYB68xdURc7vhToDvYDcaweR6-xXbBKyzrg4txKGbOfFTWZSe_340vPOM5L6Fjm2q51AXDp_/s1600/7-yao-groups.xcf.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="252" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhU9tvkopjHKl4v42QNQBE6w71Y6Fttr-E44EXKXVTrn6cL5fD_6DpU968Zs4YVyMHl5A2HRYB68xdURc7vhToDvYDcaweR6-xXbBKyzrg4txKGbOfFTWZSe_340vPOM5L6Fjm2q51AXDp_/s640/7-yao-groups.xcf.png" width="640" /></a></div>
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The 64 resulting </span><span style="font-family: Trebuchet MS, sans-serif; font-size: large;"><i>yao-numbers</i></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> are summed to produce 11,520, the "number of all things."</span><br />
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Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com4tag:blogger.com,1999:blog-9112748128817762559.post-11212249059590836362012-05-03T04:01:00.002-04:002012-09-04T22:05:49.167-04:00XMS and Genetic Code<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">German medical scientist </span><span style="font-family: 'Trebuchet MS', sans-serif;">Dr. Martin Schönberger is attributed with the initial observation that the 64 hexagrams of the genetic code are analogous to the 64 codons of the DNA genetic code. His book, <u><a href="http://www.amazon.com/Ching-Genetic-Code-Hidden-Life/dp/094335837X">I Ching and the Genetic Code: The Hidden Key to Life</a></u>, is regarded as the inaugural work on this topic.</span></span><br />
<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;"> Other authors have convincingly discussed the similarity between the I Ching and the genetic code, including Steve Krakowski</span><span style="font-family: 'Trebuchet MS', sans-serif;">, </span><span style="font-family: 'Trebuchet MS', sans-serif;">whose work borrowed from </span><span style="font-family: 'Trebuchet MS', sans-serif;">Schönberger's</span><span style="font-family: 'Trebuchet MS', sans-serif;">, as well as Mark White M.D. Both these authors' work is cited by the current author.</span></span><br />
<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">Krakowski's work seeks to integrate Hebrew language, 22 Tarot trumps, genetic code, and I Ching. </span><span style="font-family: 'Trebuchet MS', sans-serif;">Dr. White's introduction of "dodecahedral language" brings the discussion squarely into the realm of tangible objects by mapping the 64 hexagrams onto the twelve-faceted, twenty-verticed Platonic solid lovingly-called a "12-tope." </span></span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The figure at right poses a comparison between the XMS (xiantian magic square, at right), and the tzolkin calendar (lower right) of the Maya. The author holds that there is a deep connection between these two objects, and uses math and art in his work to promote said thesis.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The XMS is a particular arrangement of the 64 hexagrams on the 8x8 grid whereby any hexagram is mated to its complementary opposite located at 180 degrees of rotation. Each hexagram on the grid is both indexed, and assigned a scalar value; the scalar values of complementary pairs sum to 65. This relationship is also proven by the fact that when the hexagrams are rendered into their numerical equivalents, all rows, columns, and main diagonals sum to 4 * 65 = 260. The latter number is emblematic of the tzolkin calendar of the Maya people.</span><br />
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<a href="http://1.bp.blogspot.com/-vOIH-byVqws/T6ImU4KNGlI/AAAAAAAABJM/Ua6hosXHdWw/s1600/tzolkin+little.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-vOIH-byVqws/T6ImU4KNGlI/AAAAAAAABJM/Ua6hosXHdWw/s1600/tzolkin+little.jpg" /></a><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Arguelles and "His" Tzolkin</span></h4>
<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">The 260-day tzolkin (at right) is displayed as a 13x20 grid with a </span><span style="font-family: 'Trebuchet MS', sans-serif;">highlighted </span><span style="font-family: 'Trebuchet MS', sans-serif;">subset of 52 days identified by Tony Shearer as galactic "portal days" or by Jose Arguelles as the "Loom of the Maya." [The author is seeking/awaiting an detailed account of their derivation]. Arguelles' greatest achievement, arguably, was the popularization of Mayan calendrics. This was also his greatest folly as well, since his efforts -- even post-mortem -- have taken on the trappings of new-age religion. Nonetheless, Arguelles was possessed of a peculiar spiritual intuition which makes the current author reluctant to throw out the bathwater for fear that the baby may still be in it. References to the <i>Loom of the Maya</i> viz. tzolk'in often involves references to DNA or the genetic code. The pattern formed by the portal days is held by some to resemble the helical shape of DNA. The following passage is from a <a href="http://www.13moon.com/">site</a> that promotes Arguelles' work:</span></span><br />
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This form of the Tzolkin as the "Harmonic Module," (shown above), inclusive of the 52 shaded squares which form what is called the "Loom of the Maya," is based on Dr. Jose Arguelles' presentation in The Mayan Factor, and is distinct from the form of the Tzolkin as taught and followed by the Quiche Maya of Guatemala. For instance, the 52-unit loom is a bi-lateral symmetry pattern which reflects the basic pattern of our DNA double helix, and was passed down from a secret lineage of Yucatec Mayan shamans, received and revealed by the works of Dr. Jose Arguelles. Integrating the galactic code of light into the genetic code of life, this "portal" formation is a resonant structure linked to the activation of our full DNA potential. Find out when these galactic activation portal days occur, and receive indepth descriptions of the 13 Tones of Creation and the 20 Solar Seals by utilizing the <a href="http://www.13moon.com/products.htm#cals">13-Moon Natural Time Calendar.</a></blockquote>
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">So, while the Arguelles camp appears to recognize a connection between time and inner space (body its subtler structures), no evidences are offered to ground its bold assertions.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">DETAILING the XMS and SUBSTANTIATING its RELATION to GENETIC CODE</span></h4>
<span style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: large;">The colored partitions of the XMS grid originate from a simple mathematical transform of the hexagrams that assigns a yao-number to each. </span>[</span><span style="font-family: 'Trebuchet MS', sans-serif;">The origin of the concept of yao-numbers is discussed in greater detail elsewhere; suffices it to say, they were not invented by the author.] </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Yao-numbers range from 144 (hexagram #2, all YIN) to 216 (hexagram #1, all YANG), with intervals of 12 between the seven groupings. The midpoint of the yao-number scale is found at 180. </span><br />
<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">Yao-numbers measure the YIN- or YANG-ness of an hexagram on a continuum. Thus, the 22 YIN-dominant </span><span style="font-family: 'Trebuchet MS', sans-serif;">hexagrams</span><span style="font-family: 'Trebuchet MS', sans-serif;"> (having yao-numbers less than 180) are red-colored, while the 22 YANG-dominant hexagrams (having yao-numbers greater than 180) are blue-colored. The remaining 20 hexagrams that are balanced in terms of YIN and YANG (yao-number 180) are white-colored; they also divide the grid in half.</span></span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">While the similarity of the figures formed by the 20 white-colored cells and that of the 52 portal days forming the <i>Loom of the Maya</i> is superficial and debatable, what is less-debatable is that the 20 white-colored cells partition the grid into 22 pairs, curiously identical to the number of human <a href="http://en.wikipedia.org/wiki/Autosome">autosomes</a>, which are indistinguishable by sex. The uncounted (23rd) pair of human chromosomes is responsible for sex-differentiation, and is necessarily different between males and females. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The white-colored group of 20 hexagrams is fairly representative of the 20 essential amino acids of the human genome.</span><br />
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</h4>
<h4>
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large; text-align: left;">Thus, in a single diagram we have represented salient characteristics of the genetic code:</span></h4>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEeESpH6JeaAHOgaRR5n4wp7Nl-gcFLjdQA5Fs3FHN5ktskCGphkYoOPBYjqdjQCh5YFREQZd9_U9JZkT4pe5FHQfiXky40NwYzYXvvTEdTDlgQVTWo5TGKMpv4zRz7prDNMWfTX0NgdiD/s1600/xms_genetic_code.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEeESpH6JeaAHOgaRR5n4wp7Nl-gcFLjdQA5Fs3FHN5ktskCGphkYoOPBYjqdjQCh5YFREQZd9_U9JZkT4pe5FHQfiXky40NwYzYXvvTEdTDlgQVTWo5TGKMpv4zRz7prDNMWfTX0NgdiD/s200/xms_genetic_code.png" width="200" /></a><b style="font-family: 'Trebuchet MS', sans-serif; text-align: left;">22 yang hexagrams <==> </b><b style="font-family: 'Trebuchet MS', sans-serif; text-align: left;">22 chromosomes contributed by the male</b><br />
<b style="font-family: 'Trebuchet MS', sans-serif; text-align: left;">22 yin hexagrams <==> 22 chromosomes contributed by the female</b><br />
<b style="font-family: 'Trebuchet MS', sans-serif; text-align: left;">20 neutral hexagrams <==> 20 essential amino acids</b><br />
<b style="font-family: 'Trebuchet MS', sans-serif; text-align: left;">An admittedly-vague helical or chromosomal shape</b><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The analogy seems fairly solid so far; Argulles, we're not done with you just yet.</span></div>
<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-12738350556639426622012-04-25T21:07:00.000-04:002015-12-11T13:10:44.100-05:00Hypothetical Structure of Space-time<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRlpEHKqWrEkq_-vwYz5_yChl14ackNMVOEaI8wfnYGkoTKHd4RDRktIz9R9hcSuuZrVBuex0f3l9KwCEF17fCFc9PNNcrg3lf7segN6MPIMThma8h5argzLmTnuhPGV-TEHVbkO0TrtiE/s1600/hypercube_axes.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRlpEHKqWrEkq_-vwYz5_yChl14ackNMVOEaI8wfnYGkoTKHd4RDRktIz9R9hcSuuZrVBuex0f3l9KwCEF17fCFc9PNNcrg3lf7segN6MPIMThma8h5argzLmTnuhPGV-TEHVbkO0TrtiE/s1600/hypercube_axes.png" imageanchor="1"><img border="0" height="195" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRlpEHKqWrEkq_-vwYz5_yChl14ackNMVOEaI8wfnYGkoTKHd4RDRktIz9R9hcSuuZrVBuex0f3l9KwCEF17fCFc9PNNcrg3lf7segN6MPIMThma8h5argzLmTnuhPGV-TEHVbkO0TrtiE/s200/hypercube_axes.png" width="200" /></a></div>
<span style="font-family: "trebuchet ms" , sans-serif;">Our hypercube is used here to model space-time.</span><br />
<span class="Apple-style-span" style="font-family: "trebuchet ms" , sans-serif;">The core of the 4 x 4 x 4 cube is a 2 x 2 x 2 cube. Since each of these are composed of cubes, the entire object is considered an hypercube.</span><br />
<span class="Apple-style-span" style="font-family: "trebuchet ms" , sans-serif;">The core may be regarded as the hypercube's <b>inner</b> dimension, while </span><span style="font-family: "trebuchet ms" , sans-serif;">the corners of the shell may be taken as framing the corresponding <b>outer</b> dimension. F</span><span style="font-family: "trebuchet ms" , sans-serif;">or the sake of clarity, t</span><span style="font-family: "trebuchet ms" , sans-serif;">he remaining 48 cubes are not depicted .</span><br />
<span class="Apple-style-span" style="font-family: "trebuchet ms" , sans-serif;"><br /></span><span style="font-family: "courier new" , "courier" , monospace;"><b><span class="Apple-tab-span" style="white-space: pre;">oracle </span>inner<span class="Apple-tab-span" style="white-space: pre;"> </span>outer<span class="Apple-tab-span" style="white-space: pre;"> </span></b></span><br />
<b><u style="font-family: 'Courier New', Courier, monospace;">prob %</u><span style="font-family: "courier new" , "courier" , monospace;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><u style="font-family: 'Courier New', Courier, monospace; white-space: pre;">color</u><span class="Apple-tab-span" style="font-family: "courier new" , "courier" , monospace; white-space: pre;"> </span><span style="font-family: "courier new" , "courier" , monospace;"><u>corners</u></span><span class="Apple-tab-span" style="font-family: "courier new" , "courier" , monospace; white-space: pre;"> </span><span style="font-family: "courier new" , "courier" , monospace;"><u>corners</u></span><span class="Apple-tab-span" style="font-family: "courier new" , "courier" , monospace; white-space: pre;"> </span><span style="font-family: "courier new" , "courier" , monospace;"><u>remains</u></span><span class="Apple-tab-span" style="font-family: "courier new" , "courier" , monospace; white-space: pre;"> </span><span style="font-family: "courier new" , "courier" , monospace;"><u>dimension</u></span></b><br />
<b><span style="font-family: "courier new" , "courier" , monospace;"> 4/64</span></b><b><span style="font-family: "courier new" , "courier" , monospace;"> </span><span class="Apple-tab-span" style="font-family: "courier new" , "courier" , monospace; white-space: pre;"> </span></b><b><span style="font-family: "courier new" , "courier" , monospace;">red </span></b><b><span style="font-family: "courier new" , "courier" , monospace;"> 2<span class="Apple-tab-span" style="white-space: pre;"> </span> 2<span class="Apple-tab-span" style="white-space: pre;"> </span> 0<span class="Apple-tab-span" style="white-space: pre;"> </span> 0th</span></b><br />
<b><span style="font-family: "courier new" , "courier" , monospace;">12/64</span></b><b><span style="font-family: "courier new" , "courier" , monospace;"> </span></b><b><span style="font-family: "courier new" , "courier" , monospace;">blue</span></b><b><span style="font-family: "courier new" , "courier" , monospace;"> </span><span style="font-family: "courier new" , "courier" , monospace;"> 2<span class="Apple-tab-span" style="white-space: pre;"> </span> 2<span class="Apple-tab-span" style="white-space: pre;"> </span> 8<span class="Apple-tab-span" style="white-space: pre;"> </span> 1st</span></b><br />
<b><span style="font-family: "courier new" , "courier" , monospace;">20/64</span></b><b><span class="Apple-tab-span" style="font-family: "courier new" , "courier" , monospace; white-space: pre;"> </span></b><b><span style="font-family: "courier new" , "courier" , monospace;">green</span></b><b><span style="font-family: "courier new" , "courier" , monospace;"> 2<span class="Apple-tab-span" style="white-space: pre;"> </span> 2<span class="Apple-tab-span" style="white-space: pre;"> </span> 16<span class="Apple-tab-span" style="white-space: pre;"> </span> 2nd</span></b><br />
<b><span style="font-family: "courier new" , "courier" , monospace;">28/64</span></b><b><span style="font-family: "courier new" , "courier" , monospace;"> </span><span style="font-family: "courier new" , "courier" , monospace;"> </span></b><b><span style="font-family: "courier new" , "courier" , monospace;">yellow</span></b><b><span style="font-family: "courier new" , "courier" , monospace;"> 2<span class="Apple-tab-span" style="white-space: pre;"> </span> 2<span class="Apple-tab-span" style="white-space: pre;"> </span> 24<span class="Apple-tab-span" style="white-space: pre;"> </span> 3rd</span></b><br />
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<span class="Apple-style-span" style="font-family: "trebuchet ms" , sans-serif;"><br /></span><span class="Apple-style-span" style="font-family: "trebuchet ms" , sans-serif;">In the table above, the yarrow-stalk divination probabilities are treated in a reductive fashion. The inner and outer dimensions are framed at the corners, and are assumed to be analogues of each other. We observe that the red probabilities are completely consumed by the framework, leaving no remainder for the sides of the hypercube. This suggests that, when regarded as a dimension, the red probability is unmanifest or non-spatial, serving perhaps as the ground/field for the remaining dimensions. Given that there are four dimensions in our model, time may be regarded as the zeroth dimension. </span><br />
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<span class="Apple-style-span" style="font-family: "trebuchet ms" , sans-serif;">The other three colors (blue green, and yellow), a</span><span style="font-family: "trebuchet ms" , sans-serif;">fter contributing to the framework,</span><span style="font-family: "trebuchet ms" , sans-serif;"> leave remainders that are multiples of 8, reinforcing the notion that eight, expressed cubically, is template for dimensional space. Continuing our analogy, these three colors provide for three manifest spatial dimensions. These [sixteen] cubes, comprising fully one-quarter of the hypercube complete the framework, leaving 48 cubes (not shown) to fulfill their respective dimensional spaces.</span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-1719192862010133342012-04-25T20:26:00.001-04:002012-04-25T20:26:20.648-04:00Hypercubes: Strange & Loopy<div class="separator" style="clear: both; text-align: center;">
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Abstract: Hypercubes, or tesseracts, are proposed as instances of, or equivalent to "<a href="http://en.wikipedia.org/wiki/Strange_loop">strange loops</a>," </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">self-referential, paradoxical constructs </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">discussed by Douglas Hofstedter in </span><a href="http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach" style="font-family: 'Trebuchet MS', sans-serif; font-size: x-large;">Gödel, Escher, Bach</a><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> (GEB).</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Strange loops are often characterized as "level-crossing feedback loops" that inexplicably create cycles from hierarchies. On traversing the hierarchy in an </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">apparently</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> monotonic manner, one is returned to the origin, often signaled by a change in context.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7lhAbhbEvJnbmEh_boWATfCq5RxVtPl1j0aWj98d0GNo0PRYSsdMtv0_y-vdJtlr7DuglTxa6fE9HsSSfoU0TBuYrRC-Co-kW2PgYRez1wzq9UnEVLs8DBSrarF1MqTkgNQNBkYg2aWlv/s1600/500px-Dimension_levels.svg.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7lhAbhbEvJnbmEh_boWATfCq5RxVtPl1j0aWj98d0GNo0PRYSsdMtv0_y-vdJtlr7DuglTxa6fE9HsSSfoU0TBuYrRC-Co-kW2PgYRez1wzq9UnEVLs8DBSrarF1MqTkgNQNBkYg2aWlv/s320/500px-Dimension_levels.svg.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">geometric hierarchy</span></td></tr>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">We begin with a geometric hierarchy of </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">points, </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">lines, and areas; these give rise to volume. </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Points or vertices in space give rise to line segments or edges. Connecting line segments end-to-end to form a closed figure yields area.</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Areas connected by their edges can enclose space (think "soccer ball"). </span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Some form of subspace, however, is presumed to permit the very existence of points. The very location of a point begs the question, "where?" What is the position of these points? If points are to be assigned definite locations, axes are also presumed to exist. In the graphic at upper right, the colored arrows denote the axes of extension/projection.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJGFsFzG5dRs5Ort_KcTHS3-ctBvRFIV88echX2He1doemR1Eo9YeEEg9lMG9P96i8JLR8-zNMnsp4b9EGiUWrMJ0yTTt1uUHW3LLs5_yMCo5Pqgpv8w3lEy3IEN-1yOhOUuxR2IO2wSQ/s1600/mjolnir.1.xcf.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJGFsFzG5dRs5Ort_KcTHS3-ctBvRFIV88echX2He1doemR1Eo9YeEEg9lMG9P96i8JLR8-zNMnsp4b9EGiUWrMJ0yTTt1uUHW3LLs5_yMCo5Pqgpv8w3lEy3IEN-1yOhOUuxR2IO2wSQ/s320/mjolnir.1.xcf.png" style="cursor: move;" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">"Seed, Tree, & Fruit"</span></td></tr>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Once space, itself a "container," is enclosed, t</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">he strange loop manifests </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">. A</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> tesseract may be produced</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> by retracing our sample strange loop and substituting cubes for points. Descriptive rhetoric lacks the force of mathematical argument, but compensates for this with simplicity and accessibility.</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The crux of GEB is Hofstedter's proposition that strange loops are the <i>prime material</i> of consciousness itself.</span><br />
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</span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-84843359948803118592012-04-25T20:07:00.000-04:002012-05-31T20:04:49.629-04:00Yao-Numbers: Complementary to 65 and 360<div class="separator" style="clear: both; text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Py4hCmMIGrdCE9nvoSUDww8__0yILtPN_zJGfSLdOxvXpRj1MLoOo42CTDtgQgC5i62Lg1dcUJoljrYflNQxE3_B6IcV0zKgycQI16126mipnBiHAAKGBRLNM3r31AMW58cmHKO9NQi8/s1600/wen_xiang.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="328" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Py4hCmMIGrdCE9nvoSUDww8__0yILtPN_zJGfSLdOxvXpRj1MLoOo42CTDtgQgC5i62Lg1dcUJoljrYflNQxE3_B6IcV0zKgycQI16126mipnBiHAAKGBRLNM3r31AMW58cmHKO9NQi8/s640/wen_xiang.png" width="640" /></a></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">This graph demonstrates how yao-numbers (complement 360) and xiantian (complement 65) and Wen pairing correlate. Wen pairs are </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">consecutively-numbered (</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">odd-even) pairs; e.g., (33,34)</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Five groups, lettered A, C, F, T, and L</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">, have subgroups 1 and 2, according to their yao-number. Group T has no known subgroups.</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Given any group A, C, F, L, or T: </span><br />
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">boxed pairs are binary complements (65)</span><br />
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">boxed pairs constitute a circle (or two triangles) 360 degrees. A</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">n hexagram is 180 degrees or pi, </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">on average. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><br /></span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-79409619684855006902012-04-25T18:22:00.002-04:002012-04-25T18:22:24.424-04:00Heaven is Round, Earth is Square<i><span style="font-family: 'Trebuchet MS', sans-serif;">The numbers that yield THE CREATIVE total 216; those which yield THE RECEPTIVE total 144, making in all 360. They correspond with the days of the year.</span><br style="font-family: 'Trebuchet MS', sans-serif;" /><span style="font-family: 'Trebuchet MS', sans-serif;">--Ta Chuan pt. 1, ch. 9, v. 4</span></i><br style="font-family: 'Trebuchet MS', sans-serif;" /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><span style="font-family: 'Trebuchet MS', sans-serif;">"[N]umbers" in this context refers to the yao-numbers, while ䷀ (CREATIVE) and ䷁ (RECEPTIVE) are the first two hexagrams in the traditional sequence.</span><br style="font-family: 'Trebuchet MS', sans-serif;" /><br style="font-family: 'Trebuchet MS', sans-serif;" /><span style="font-family: 'Trebuchet MS', sans-serif;">Two useful representations of the Book of Changes include the square and the cube since both can be used to represent the 64 figures:<br /><br />64 = 8 x 8<br />64 = 4 x 4 x 4<br /><br />Observe the yao-numbers of Receptive and Creative compared with the representations of 64 (above):<br /></span><div>
<span style="font-family: 'Trebuchet MS', sans-serif;">144 = 12 x 12<br />216 = 6 x 6 x 6<br /><br />In each case we presented two expressions of the form<br /><br />a. X^2<br />b. (X/2)^3<br /><br />144 is a perfect square, 216 is a perfect cube; 64 is both perfect square and cube.</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiN5fomJ6vgNvkWEEIeset_ZxXK_PHZ0dnWAPZHhNggs6K88P3h4kuYQH60f8ktVEvOqUyESJR0iXacD3mLAIVFV2LNPcXFWuegAvODS6QJOCphMqxwgeArlAFEUHFmgzibIftyvDJ07g0/s1600/bagua_hypercube_frame.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="283" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiN5fomJ6vgNvkWEEIeset_ZxXK_PHZ0dnWAPZHhNggs6K88P3h4kuYQH60f8ktVEvOqUyESJR0iXacD3mLAIVFV2LNPcXFWuegAvODS6QJOCphMqxwgeArlAFEUHFmgzibIftyvDJ07g0/s320/bagua_hypercube_frame.png" width="320" /></a><span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">The four colored line segments span opposite corners of the cube and those of its bounding box. The axes presume to represent the traditional three dimensions of space, plus a fourth -- time, or Change. We envision our fourth dimension via notions of expansion or contraction. In this case, the blue cube expands (in the time domain) to fully occupy the bounding frame. </span><span style="font-family: 'Trebuchet MS', sans-serif;">In our simple example, </span><span style="font-family: 'Trebuchet MS', sans-serif;">the time axis is not discrete from three-dimension space, but supplements it. As the blue cube expands along the colored lines, we measure the elapsed time by noting the positional change of the vertices along their respective axes as a function of elapsed time. Is it but coincidence that the two opposed square pyramids (their tips meeting at [0,0,0]) within the bounding box resemble an hourglass?</span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRlpEHKqWrEkq_-vwYz5_yChl14ackNMVOEaI8wfnYGkoTKHd4RDRktIz9R9hcSuuZrVBuex0f3l9KwCEF17fCFc9PNNcrg3lf7segN6MPIMThma8h5argzLmTnuhPGV-TEHVbkO0TrtiE/s1600/hypercube_axes.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-size: large;"><img border="0" height="312" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRlpEHKqWrEkq_-vwYz5_yChl14ackNMVOEaI8wfnYGkoTKHd4RDRktIz9R9hcSuuZrVBuex0f3l9KwCEF17fCFc9PNNcrg3lf7segN6MPIMThma8h5argzLmTnuhPGV-TEHVbkO0TrtiE/s320/hypercube_axes.png" width="320" /></span></a></div>
<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">Deriving a means to integrate the <i>ashtapada</i> and the hypercube representations of the Book of Changes has remained a goal of the author. </span><span style="font-family: 'Trebuchet MS', sans-serif;">A physical model </span><span style="font-family: 'Trebuchet MS', sans-serif;">was fashioned with this end in mind. </span><span style="font-family: 'Trebuchet MS', sans-serif;">While the yellow and green axes represent Earth and Air respectively, the blue and red axes symbolize Fire and Water. Earth and Fire stand for OLD YIN and YOUNG YIN; Air and Water stand for OLD YANG and YOUNG YANG. These four symbols (xiang) are the stuff of existence.</span><span style="font-family: 'Trebuchet MS', sans-serif;">Our model begins with a depiction of the four symbols (xiang) presented in pairs and forming a 2x2x2 cube (the "bagua cube"). A second, exploded bagua cube extends in space beyond the corners of the first along the major diagonals. </span></span><br />
<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">In total, this produces the framework of 4x4x4 tesseract. If the <i>ashtapada</i> is a representation of </span><span style="font-family: 'Trebuchet MS', sans-serif;">planar/areal dimension ("Heaven is Round, Earth is Square") , here, we have "folded" space into a cubical form. </span><span style="font-family: 'Trebuchet MS', sans-serif;">Imagine the outer eight cubes as an expansion of the inner 2x2x2 </span><span style="font-family: 'Trebuchet MS', sans-serif;"> </span><span style="font-family: 'Trebuchet MS', sans-serif;">along the diagonals</span><span style="font-family: 'Trebuchet MS', sans-serif;">, and you will have seen the author's vision of space-time.</span></span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-8416576502580791562012-04-10T17:59:00.001-04:002012-05-31T19:20:59.405-04:00Exploring the Dodecahedral Model<span style="font-size: large;"><span style="background-color: rgba(255, 255, 255, 0.917969); font-family: 'Trebuchet MS', sans-serif;">Per the work introduced at </span><a href="http://www.codefun.com/" style="background-color: rgba(255, 255, 255, 0.917969); font-family: 'Trebuchet MS', sans-serif;">http://www.codefun.com</a> <span style="font-family: 'Trebuchet MS', sans-serif;">(authored by</span> <span style="font-family: 'Trebuchet MS', sans-serif;">Mark White, MD </span></span><span style="background-color: rgba(255, 255, 255, 0.917969); font-family: 'Trebuchet MS', sans-serif; font-size: large;">et al.), the current author has expanded and refined ideas relating to the Book of Changes. Briefly, White invites his readers to reappraise the genetic code (and related constructs) as </span><b style="background-color: rgba(255, 255, 255, 0.917969); font-family: 'Trebuchet MS', sans-serif; font-size: x-large;">language</b><span style="background-color: rgba(255, 255, 255, 0.917969); font-family: 'Trebuchet MS', sans-serif; font-size: large;"> based on </span><b style="background-color: rgba(255, 255, 255, 0.917969); font-family: 'Trebuchet MS', sans-serif; font-size: x-large;">shape</b><span style="background-color: rgba(255, 255, 255, 0.917969); font-family: 'Trebuchet MS', sans-serif; font-size: large;">, rather than through the conventional reductive viewpoint of nucleotides and amino acids.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Here, we adapt the dodecahedral model to the system of Change in an attempt to discern what insights or refinements to extant notions we might derive. Hand-held models are dear to the author, particularly for the practical value they provide in exploring the systems thus represented. This exploration proves no exception. The model displayed below employs color to characterize the faces. Each face is blazoned with McNeil notation (q.v.) to assist in diagramming the model. The blazon allows for quick identification the attached vertices, face, and edges.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7x44SXVR77gfXXvnJCxiUBG0L1qcL3o_SFgLzsvKUNT1O7TitqP5Af-VfpAzwN7gvKfmUEbAyl308EaCXXvPKfvSwM7_9ZUc8v-pz1AxWlITONFBPRYp_ko4dynhyUZ583Cp0AJqhzrEZ/s1600/IMG_20120410_164014.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="color: black; font-size: large;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7x44SXVR77gfXXvnJCxiUBG0L1qcL3o_SFgLzsvKUNT1O7TitqP5Af-VfpAzwN7gvKfmUEbAyl308EaCXXvPKfvSwM7_9ZUc8v-pz1AxWlITONFBPRYp_ko4dynhyUZ583Cp0AJqhzrEZ/s320/IMG_20120410_164014.jpg" width="320" /></span></a></div>
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<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">Faces stand for symbols (xiang). Our symbol set is described by the letters [E W F A], standing for the four elements recognized by the ancients (earth, water, fire, and air). In the "alphabet" of Change, these would be represented by xiang di-grams [</span><span style="background-color: transparent;"><span style="font-family: 'Trebuchet MS', sans-serif;">⚏ ⚎ ⚍ ⚌]. D</span></span><span style="font-family: 'Trebuchet MS', sans-serif;">odecahedral modeling provides three faces per symbol, possibly to provide for each </span><b style="font-family: 'Trebuchet MS', sans-serif;">position</b><span style="font-family: 'Trebuchet MS', sans-serif;"> in a sequence; that possibly being a defining characteristic of a symbol -- where it falls within a sequence. <br />We should like to investigate the possible significance of the pentagon as it relates to the symbols. "Why five sides?" Five does not often appear in the lexicon of Change. The Chinese did have a theory of Five Elements (the four mentioned plus 'Metal'). We further observe that the maximal path length connecting any two vertices on the model is five.</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDw-VXET__0FhIB16k3wm9brssunr_cEQ9p1cJcXlskmPZJAYpmVaUMANIPJbZnvMsNw8hXnSlC4I0REyKlLQql2TsF3_rHAyHeEYKVE5IuKlReJjhotNuNku0g9navMAyz3FaWXzQ2AD3/s1600/IMG_20120410_164001.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="color: black;"><br class="Apple-interchange-newline" /><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDw-VXET__0FhIB16k3wm9brssunr_cEQ9p1cJcXlskmPZJAYpmVaUMANIPJbZnvMsNw8hXnSlC4I0REyKlLQql2TsF3_rHAyHeEYKVE5IuKlReJjhotNuNku0g9navMAyz3FaWXzQ2AD3/s320/IMG_20120410_164001.jpg" width="320" /></span></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDw-VXET__0FhIB16k3wm9brssunr_cEQ9p1cJcXlskmPZJAYpmVaUMANIPJbZnvMsNw8hXnSlC4I0REyKlLQql2TsF3_rHAyHeEYKVE5IuKlReJjhotNuNku0g9navMAyz3FaWXzQ2AD3/s1600/IMG_20120410_164001.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a></div>
<b style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-size: large;">VERTICES</span></b><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">the dodecahedral model of Change places hexagrams at the vertices, where faces (symbol triplets) converge. Since the dodecahedron has twenty vertices, each vertex identifiable by a McNeil symbol triplet, with each of the twenty triplets having six possible symbol sequences, the model appears to allow for 120 possible hexagrams, providing for some redundancy. In the discussion that follows, </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Isochromous (same color) triplets (e.g. <b>AAA</b>) have only one distinct sequence; four such triplet sequences exist:</span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Heterochromous (all different colors) triplets (e.g. <b>AFW</b>) have six valid sequences; twenty-four such triplet sequences exist:</span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Dichromous (two colors) triplets (e.g. <b>AAE</b>) have only three valid sequences, one for each position of the odd symbol; thirty-six such triplet sequences exist:</span></div>
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<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">Author </span></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Mark White, MD proposes that each nucleotide in a triplet is inherently distinct, and </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">that all of the the six possible isochromous sequences, AeAfAw (subscripted for clarity) for example, are meaningfully different from one another. Likewise treating heterochromous and dichromous triplets, we discover that </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">56 (</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">120 - 64 = 56)</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> "isotopic" </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">sequences exist that are generally indistinguishable (unless subscripted) from one of the basic 64 triplet sequences. We should note, however, that this inability to distinguish isotopic sequences derives from our abstraction of the sequence from the physical model and its orientation in space.</span><br />
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<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">Edges define faces, each edge held in common by two adjoining faces. Edges also connect vertices. Thirty distinct edges exist on the dodecahedron. Since vertices stand for hexagrams, edges act as paths connecting vertices. This role suggests that an edge defines a change from one hexagram to another, further implying that the paths are directed, hence numbering sixty in total. We have elsewhere noted that the hexagrams may be understood as forming thirty-two pairs, under at least two schema. Efforts to i</span><span style="font-family: 'Trebuchet MS', sans-serif;">ntegrate edge-as-pairing</span><span style="font-family: 'Trebuchet MS', sans-serif;"> would have to account for the missing paths/edges.</span></span></div>
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<span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">It is arguable that the pentagon, with its vertex angle of 108</span></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">° and central angle of 72</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">°</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">,</span><span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;"> defines the dodecahedron, as its a</span></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">djoining faces meet at the same </span><span style="font-size: large;"><span style="font-family: 'Trebuchet MS', sans-serif;">108</span></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">°</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">angle. A</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> pentagram results w</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">hen the vertices of a pentagon are connected. The diagram at left shows that 36</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">°</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">angle is fundamental to the pentagon (and pentagram), thus to the dodecahedron. In fact, the pentagonal net is fractal of a single 72-36-72 isosceles triangle. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">If a side of the pentagon </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">(purple) </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">is taken as unity (1), a diagonal (blue) measures <i>phi</i>. The red segment equals (<i>phi</i> -1), and the yellow segment equals (2 - <i>phi</i>).</span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The pentagon's relation to </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><i>phi</i></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> is worthy of mention in this section since the author had long-sought a relation between Change and <i>phi,</i> now obtained, albeit indirectly. </span><br />
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</div>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-79869046984312489962012-04-10T17:56:00.001-04:002012-04-11T04:15:55.876-04:00Dodecagonal Depiction of Change<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The author revisited yao-numbers, recalculating them based strictly on the divination ritual values of Ch'ien (9) and K'un (6).</span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihYcKbAnAQiqEbtwkBq3ezI2vEgaMjn6qoFOROGQvtNIFCb08bYgrU2LgLiqOUrnv2z9_qlrhLOeKBdXYdLg8wS9R95AEPO2nMXbMUrDZIi-D_mv9DStbMi6WDC0D7e-eJpPHj2JE3e5rY/s1600/king_wen_12.pdf-2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihYcKbAnAQiqEbtwkBq3ezI2vEgaMjn6qoFOROGQvtNIFCb08bYgrU2LgLiqOUrnv2z9_qlrhLOeKBdXYdLg8wS9R95AEPO2nMXbMUrDZIi-D_mv9DStbMi6WDC0D7e-eJpPHj2JE3e5rY/s640/king_wen_12.pdf-2.png" width="640" /></a></div><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The outcome is a distribution that naturally accords with the combinatorics of a 6-bit system. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">There are seven groups with the following distribution: </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">[1 6 15 20 15 6 1].</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">This is a departure from the prior distribution of yao-numbers, which incorporated 9 groups: </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">[1 3 6 12 20 12 6 3 1]</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">the author had the r</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">ecent</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">fortune to discover a <a href="http://www.codefun.com/">website</a> that treats systems like Change (and the genetic code) in some depth. That author makes the unqualified claim that the genetic code is a </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">dodecahedral</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> system. The Book of Changes, again, is based on the same underlying grammatical components (four basic elements, arranged in triplets). One tremendously useful product of the website is the depiction of the genetic code on a </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">dodecahedron</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> (12-faceted Platonic solid). Several tools and perspectives are additionally presented to facilitate pattern-recognition.</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><br />
</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The current author observes that the array [1 6 15 20 15 6 1] can also be depicted as [2 12 30 20] when that array is "folded" on the central value (20). What we find is that at least three of the values of the resultant array find direct correspondence to attributes of a dodecahedron, perhaps confirming the author's <a href="http://codefun.com/Papers/Dodecahedron.pdf">claim</a></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">.</span><br />
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</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Dodecahedra have 20 vertices, 30 edges, and 12 pentagonal faces. The array value of '2' is not nearly as unambiguous, but could correspond to </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">symmetry axes or</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">polarity. An arrangement suggested by the author of the mentioned <a href="http://www.codefun.com/">website</a></span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">involves four (tetrahedral) poles corresponding to the four genetic nucleotides. </span><br />
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</span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">In the Book of Changes, four corresponding elements exist called symbols (or <i>xiang</i>). When we computed the Wen distribution based on the divination ritual values of <i>xiang</i> (6,7,8,9), no correspondence (to date) is found with any real-world objects. </span><br />
<span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Conversely, when we computed (as described in the open paragraph) the Wen distribution based on 6 and 9 (the ritual values of Ch'ien and K'un), the characteristics of a dodecahedron emerge as just described. This is the rationale for asserting that the value '2' in the array [2 12 30 20] may indicate the number of poles to incorporate in the dodecahedral depiction of the Book of Changes. </span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-12403756826416050612012-02-13T04:26:00.000-05:002012-09-20T02:32:33.941-04:00I Ching in 3-D<div style="text-align: left;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDdpM0E5gIcsUVh-NbRJi8s5eeI8JkKve_ZNFIGZHjNc7z7OmcFL2iHXU62cF0bPVqPo0XhtYZ-V4-5emqLgbhyphenhyphensvOLoR21DQeSLd2XinbgWzZGwuyQijzY2J8mrIgQvFnrHPVb3niWGPS/s1600/oracular_ashtapada.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: 'Trebuchet MS', sans-serif;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDdpM0E5gIcsUVh-NbRJi8s5eeI8JkKve_ZNFIGZHjNc7z7OmcFL2iHXU62cF0bPVqPo0XhtYZ-V4-5emqLgbhyphenhyphensvOLoR21DQeSLd2XinbgWzZGwuyQijzY2J8mrIgQvFnrHPVb3niWGPS/s200/oracular_ashtapada.png" width="200" /></span></a></div>
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The presented diagram depicts the 8 x 8 field known as <i>ashtapada</i>. The colored bands represent the oracular probabilities corresponding to the four <i>xiang</i> (symbols). In this entry, the author extends the notions implied by this diagram into three-dimensions through the use of 64 colored cubes.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR3Jzw_PTpRL91qx6QD0-nxosHScM9rBBamknGmPh5H6eBbgEejqj0PQ_I_uuVkofw1zgEOMoJKyo98QGyn-ix4rYu9JmvWMxAM6zWr2BJvnZhXDGy1aOoLr0b8x_hA0Mlwl_etD0_gZ4Y/s1600/IMG_20111028_030152.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><span style="font-family: 'Trebuchet MS', sans-serif;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR3Jzw_PTpRL91qx6QD0-nxosHScM9rBBamknGmPh5H6eBbgEejqj0PQ_I_uuVkofw1zgEOMoJKyo98QGyn-ix4rYu9JmvWMxAM6zWr2BJvnZhXDGy1aOoLr0b8x_hA0Mlwl_etD0_gZ4Y/s200/IMG_20111028_030152.png" width="200" /></span></a></div>
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The idea is simple: </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">a cube has six faces; while </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">an hexagram has six places, </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">commonly denoted as <b>bottom</b>, <b>2nd</b>, <b>3rd</b>, <b>4th</b>, <b>5th</b>, and <b>top</b></span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">. </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Each cube face, therefore, may represent one place of an hexagram and its associated text.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHLif8Y6Ag4EdGyxxoJ39bE1fuFuW-ikeNgReBx_z9afzIMkicU9JpYrp32o9kVDGBMlAOqeh-hygBMGLNK4dTiRDzese7zXaLiGQqq8CpceDF-_YL5HKrPEiwuk0hY_z99EJNTvZKAaco/s1600/hsiang.4.png" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><span style="font-family: 'Trebuchet MS', sans-serif;"><img border="0" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHLif8Y6Ag4EdGyxxoJ39bE1fuFuW-ikeNgReBx_z9afzIMkicU9JpYrp32o9kVDGBMlAOqeh-hygBMGLNK4dTiRDzese7zXaLiGQqq8CpceDF-_YL5HKrPEiwuk0hY_z99EJNTvZKAaco/s400/hsiang.4.png" width="400" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">representation of xiang</span></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: large;">Tradition asserts that </span><span class="Apple-style-span" style="font-size: large;"><b>bottom</b> <b>place</b> is nascent, and <b>top</b> <b>place</b> is retiring. It follows, therefore, that </span><span class="Apple-style-span" style="font-size: large;">the bulk of a hexagram's meaning or action is found in the middle of the hexagram, sometimes called a 'tetragram'. These four middle places of the hexagram, </span><span class="Apple-style-span" style="font-size: large;">akin the four walls of a room,</span><span class="Apple-style-span" style="font-size: large;"> correspond to the four sides of a cube; corresponding furthermore, to the </span><span style="font-size: large;">four seasons, four cardinal directions (xiang), four elements, four tarot suits, or any other quaternity</span><span class="Apple-style-span" style="font-size: large;">.</span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWXUrpavI-EqH9ndSrXx8d61CzY7b8xvzN10s7CI0K88lOw-5DbO32UYcqKzk1mKeLrKl6LFXHaCzxNC928Ip1r1kofa8qksrOjTn9DeKjtwn1chXqxGrNQf7woFGnR8H4s1261u51URzR/s1600/unit_cube.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><span style="font-family: 'Trebuchet MS', sans-serif;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWXUrpavI-EqH9ndSrXx8d61CzY7b8xvzN10s7CI0K88lOw-5DbO32UYcqKzk1mKeLrKl6LFXHaCzxNC928Ip1r1kofa8qksrOjTn9DeKjtwn1chXqxGrNQf7woFGnR8H4s1261u51URzR/s200/unit_cube.gif" width="200" /></span></a><br />
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Since the oracular probabilities are depicted by the colors, all that remains is to devise unambiguous </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">means of</span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">associating </span><span style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">a particular cube face with an hexagram place. </span><br />
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: large;">We may appropriately mark the six faces, 1) to indicate the relative positions of the faces, and 2) to determine their yin or yang character, and perhaps, 3) with its index (for easy reference). </span></span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">This permits us to determine easily the quality of the upturned face when a cube is selected</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">.</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">P</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">roceeding to </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">appropriately </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">label each of the 384 cube faces, </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">we now have a device whereby the identity of an hexagram is determined by the unique configuration of its faces. Simultaneously</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">, that same cube indicates by its color if the upturned face is a changing line or static. Alternately, six cubes may be selected blindly with replacement to generate an hexagram line-by-line with color alone as an the line-type indicator . </span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Addendum (26April12):</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMtfgKEEwLFefCfsWVXZBh9trRHOknbYqnphLTLTf_55NW4cb6T63JSuxnO_9F6gdAcOMGKLLlZvbH2RHrVc-dvo3cVdnsyfHmo6duoZ5z7SnKexZqsMjbgs1sQXJMxIHI9ahRtuHZaj6v/s1600/IMG_20120426_145236.jpg" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMtfgKEEwLFefCfsWVXZBh9trRHOknbYqnphLTLTf_55NW4cb6T63JSuxnO_9F6gdAcOMGKLLlZvbH2RHrVc-dvo3cVdnsyfHmo6duoZ5z7SnKexZqsMjbgs1sQXJMxIHI9ahRtuHZaj6v/s320/IMG_20120426_145236.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif;">Yarrow Oracle</span></td></tr>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The author has fashioned for himself a compact set of divination cubes that are functionally equivalent to the yarrow oracle. Since the yarrow probabilities reduce to multiples of 1/16, four colors in the proper proportions reproduce the oracle. Six cubes are selected individually and randomly with replacement. Further, the author employs a webcam to film a blind-selection procedure to reduce the possibility of inadvertently influencing the outcome while divining.</span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-37213133413613412052012-02-13T00:18:00.000-05:002015-09-23T11:08:57.242-04:00Human Body: the Field of Action<span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: 'Trebuchet MS', sans-serif; font-size: 12.8000001907349px;">Vastu Purusha mandala over </span><i style="font-family: 'Trebuchet MS', sans-serif; text-align: -webkit-auto;"><span style="font-size: x-small;">ashtāpada</span></i></td></tr>
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<span style="font-family: 'Trebuchet MS', sans-serif;">In the graphic at right, Cosmic Man, <i>Purusha</i>; the "enjoyer of the field of activity" is overlaid on <i>ashtapada,</i> the 8x8 grid. He is
positioned face-down, his head pointing toward North-east. It should be noted that in the <i>Manduka</i> mandala the <i>Vastu Purusha</i> is depicted with the head facing east and the feet facing west. Here, grid-points along the NE-SW main diagonal enjoy congruence with the seven chakras.</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><i>Ashtāpada</i>, the <a href="http://en.wikipedia.org/wiki/Chaturanga#History">uncheckered</a> 8 × 8 board, is presumed to be of Hindu derivation. </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">The literal meaning of <i>ashtapadi</i> is "eight steps." This word is the origin of the word <i>ashtāpada</i>, an Indian board game, the forerunner of chess. The word now </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">primarily </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">refers to the board itself.</span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;">The 8 x 8 grid, <i>ashtapada</i>, <i>manduka</i>, or <i>chandita</i> mandala, is regarded by several sources to represent a "field of action[1]."</span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">Ashtapada is depicted here as four concentric square bands with areas of 28. 20, 12, and 8 units relative to the whole. The areas of the four banded regions are precisely mirrored by the divination probabilities given by the yarrow-stalk oracle commonly used to consult the Book of Changes. </span><br />
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<span style="font-family: 'Trebuchet MS', sans-serif;"><i>Vastu Purusha</i> mandala presents <i>Purusha</i> over the 8 x 8 grid, implying that the grid symbolizes <i>Purusha's</i> dwelling-place, or <i>Prakriti</i>, the material body or world, material contrast to <i>Purusha</i>. Furthermore, when <i>Purusha </i>(Cosmic Man, Universal Soul, or <i>Atman</i>) is positioned on the <i>ashtapada</i>, the grid can be said to represent the human body -- which is itself considered a "field of action," or "<i>kurukshetra</i>[2]." </span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">When the divination ritual numbers (6, 7, 8, and 9) and their respective divinatory probabilities (4, 12, 20, and 28 taken as fractions of the 8 x 8 field) are treated as vectors and the inner-product taken between them, the result is the "perfect" number 496. We can regard this number as a defining characteristic of ashtapada within the context of I Ching divination.</span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">We may again relate 496 to the human body because the body possesses 31 pairs (or 62) of spinal nerves. The prime factorization of 496 is 31 times 16 which is also 62 times 8; thus 62 is the octopartition of 496, which number defines the divination field; the field, in turn, representing the human body.</span></div>
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<span style="font-family: 'Trebuchet MS', sans-serif;">NOTES:</span><br />
<u><span style="font-family: 'Trebuchet MS', sans-serif;">Ashtapada</span></u><br />
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<ul style="text-align: left;">
<li><span style="font-family: 'Trebuchet MS', sans-serif;">Related to the game <i><a href="http://en.wikipedia.org/wiki/Chaturanga">Chaturanga</a>:</i> <span style="font-size: x-small;">(Skt: "four-limbed")</span>, ancestor of modern chess</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;">Related to <i>Manduka/Chandita</i> mandalas </span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;">Populated by the 64 hexagrams, it represents 2080</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;">Overlaid by xiang probability bands, it represents 496, the third "perfect number"</span></li>
<li><i style="font-family: 'Trebuchet MS', sans-serif;">Kurukshetra</i><span style="font-family: 'Trebuchet MS', sans-serif;"> (site of the war in </span><i style="font-family: 'Trebuchet MS', sans-serif;">Mahabharata)</i></li>
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<li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="background-color: white;"><i>kuru</i>, from the Sanskrit root <i>kri</i>="work, material action" and <i>ksetra</i>=</span></span><span style="background-color: white;">"field". This "field of action" is the human body with its physical, </span><span style="background-color: white;">mental and soul faculties, the field (<i>kurukshetra</i>) on which all </span><span style="background-color: white;">activities of one's life take place.</span> </li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;">Characterized as a "field of activity," indicating the body, or even the World, suggesting metaphoric identity relation between these</span></li>
<li><span style="font-family: 'Trebuchet MS', sans-serif;">References</span></li>
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<ul style="text-align: left;"><ul><ul>
<li><span style="font-family: 'Trebuchet MS', sans-serif;"><i>Bhavagad Gita</i></span>: ch. 13, v1-2</li>
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<li><a href="http://vedabase.net/a/arjuna" style="background-color: white; color: black; font-family: 'Trebuchet MS', sans-serif; font-size: small; text-align: justify; text-decoration: none;">Arjuna</a><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-align: justify;"> said: O my dear </span><a href="http://vedabase.net/k/krsna" style="background-color: white; color: black; font-family: 'Trebuchet MS', sans-serif; font-size: small; text-align: justify; text-decoration: none;">Kṛṣṇa</a><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-align: justify;">, I wish to know about </span><a href="http://vedabase.net/p/prakrti" style="background-color: white; color: black; font-family: 'Trebuchet MS', sans-serif; font-size: small; text-align: justify; text-decoration: none;">prakṛti</a><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-align: justify;"> [nature], </span><a href="http://vedabase.net/p/purusa" style="background-color: white; color: black; font-family: 'Trebuchet MS', sans-serif; font-size: small; text-align: justify; text-decoration: none;">puruṣa</a><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-align: justify;"> [the enjoyer], and the field and the knower of the field, and of knowledge and the object of knowledge.The Supreme Personality of Godhead said: This body, O son of </span><a href="http://vedabase.net/k/kunti" style="background-color: white; color: black; font-family: 'Trebuchet MS', sans-serif; font-size: small; text-align: justify; text-decoration: none;">Kuntī</a><span style="background-color: white; font-family: 'Trebuchet MS', sans-serif; font-size: x-small; text-align: justify;">, is called the field, and one who knows this body is called the knower of the field.</span></li>
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<li><span style="font-family: 'Trebuchet MS', sans-serif;"><i>Ta Chuan</i></span> pt.1; ch.11; v.5-6</li>
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<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">Therefore there is in the Changes the Great Primal Beginning. This generates the two primary forces. The two primary forces generate the four images. The four images generate the eight trigrams. The eight trigrams determine good fortune and misfortune. Good fortune and misfortune create the great field of action.</span></li>
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<li><span style="font-family: 'Trebuchet MS', sans-serif;">Foundations of Oriental Art and Symbolism, ch. 9, "Symbolism of Chess" </span></li>
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<li><span style="font-family: 'Trebuchet MS', sans-serif; font-size: 12px; text-align: justify;">The form of the chess-board corresponds to the "classical" type of </span><i style="font-family: 'Trebuchet MS', sans-serif; font-size: 12px; text-align: justify;">Vāstu-mandala, </i><span style="font-family: 'Trebuchet MS', sans-serif; font-size: 12px; text-align: justify;">the diagram which also constitutes the basic layout of a temple or a city. It has been pointed out</span><a href="http://www.studiesincomparativereligion.com/public/articles/The_Symbolism_of_Chess-by_Titus_Burckhardt.aspx#_edn3" name="_ednref3" style="font-family: 'Trebuchet MS', sans-serif; font-size: 12px; text-align: justify;" title="">[3]</a><span style="font-family: 'Trebuchet MS', sans-serif; font-size: 12px; text-align: justify;"> that this diagram symbolizes existence conceived as a "field of action" of the divine powers.</span></li>
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Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-63358211850633282502011-11-08T18:54:00.000-05:002012-09-21T17:42:23.446-04:00Xiantian Cube<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHLif8Y6Ag4EdGyxxoJ39bE1fuFuW-ikeNgReBx_z9afzIMkicU9JpYrp32o9kVDGBMlAOqeh-hygBMGLNK4dTiRDzese7zXaLiGQqq8CpceDF-_YL5HKrPEiwuk0hY_z99EJNTvZKAaco/s1600/hsiang.4.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="186" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHLif8Y6Ag4EdGyxxoJ39bE1fuFuW-ikeNgReBx_z9afzIMkicU9JpYrp32o9kVDGBMlAOqeh-hygBMGLNK4dTiRDzese7zXaLiGQqq8CpceDF-_YL5HKrPEiwuk0hY_z99EJNTvZKAaco/s320/hsiang.4.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><i>depiction of xiang</i></span></td></tr>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Abstract: Investigating ways to derive the 4th-order cube from the <i>ashtapada</i> </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">informed by notions of </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><i>xiang</i> and </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">complementarity.</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">At the center of the diagram following is an 8X8 field with colored bands. This <i>field of action</i> (Sanskrit: <i>kurukshetra</i>) is also known as <i>ashtapada</i>. The bands represent the <i>xiang</i>; alternatively, the oracular probabilities representing them </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: large;">when expressed as fractions of 64</span></span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">. </span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Surrounding that field are four 4 X 4 sections. These are intended to represent <i>xiang</i>. They are presented with the intention of providing a static internal view of the assembled cube. </span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The <i>xiang</i> sit on a 2 X 2 grid with axis labels in <span class="Apple-style-span" style="background-color: white;">white</span>. The labels serve to explain the depiction of the <i>xiang</i> relative to the 2 X 2 grid and 8 X 8 field.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8C9bsMGa3TLAUTRxCpwjrJMhyog_3nWVY0UEiufAa5OmhCTfibd5zNgbtjdYcMxiBE2RssC45fh37Vq5HMb0l8KJWsUMaXMf7D_vi0z7D5P5wEz3D5q7Q0mwDaX0p7tvQI-tHdI_xV-2l/s1600/xiang_cube--20-12.xcf.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8C9bsMGa3TLAUTRxCpwjrJMhyog_3nWVY0UEiufAa5OmhCTfibd5zNgbtjdYcMxiBE2RssC45fh37Vq5HMb0l8KJWsUMaXMf7D_vi0z7D5P5wEz3D5q7Q0mwDaX0p7tvQI-tHdI_xV-2l/s320/xiang_cube--20-12.xcf.png" width="320" /></a></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Labels:</span><br />
<b style="font-family: 'Trebuchet MS', sans-serif;">CREATIVE<span class="Apple-style-span" style="font-size: large;"> </span></b><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">indicates</span><b style="font-family: 'Trebuchet MS', sans-serif; font-size: x-large;"> </b><b style="font-family: 'Trebuchet MS', sans-serif;">YANG</b><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">, while</span><b style="font-family: 'Trebuchet MS', sans-serif; font-size: x-large;"> </b><b style="font-family: 'Trebuchet MS', sans-serif;">STRUCTIVE</b><b style="font-family: 'Trebuchet MS', sans-serif; font-size: x-large;"> </b><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">indicates</span><b style="font-family: 'Trebuchet MS', sans-serif; font-size: x-large;"> </b><b style="font-family: 'Trebuchet MS', sans-serif;">YIN<span class="Apple-style-span" style="font-size: large;">.</span></b><br />
<b style="font-family: 'Trebuchet MS', sans-serif;">STATIC </b><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">&</span><b style="font-family: 'Trebuchet MS', sans-serif; font-size: x-large;"> </b><b style="font-family: 'Trebuchet MS', sans-serif;">DYNAMIC</b><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"> are related to the notion of <i>action</i> or <i>change</i>, and the background against which it must be observed.</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">also: 'event vs. environment,' 'figure vs. ground,' or 'text vs. context,' even 'nature vs. nurture.'</span><br />
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</span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-49581491907560283952011-11-02T04:36:00.004-04:002011-11-08T13:49:30.596-05:00Jörmungandr-Ouroborus, the Tesseract<div><div style="text-align: left;"></div><div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheP83jaQuyIOPqI_2DqTZGybmOfuc6clpFhCmC7-bzGNxGCe6d_Hu0tv8XnVkjoUmLazwQJ_jNbc9ynvF5yTKygyi6yMh0n4bVII-ybQYcNj4OskgwXobfuTtYJqgDVYgT6GNfwMPLI6xI/s1600/240px-Tesseract.gif" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheP83jaQuyIOPqI_2DqTZGybmOfuc6clpFhCmC7-bzGNxGCe6d_Hu0tv8XnVkjoUmLazwQJ_jNbc9ynvF5yTKygyi6yMh0n4bVII-ybQYcNj4OskgwXobfuTtYJqgDVYgT6GNfwMPLI6xI/s1600/240px-Tesseract.gif" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Tesseract</span></td></tr>
</tbody></table><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">According to legend, Odin threw the serpent <a href="http://en.wikipedia.org/wiki/Jormungandr"><i>Jörmungandr</i></a> into the great ocean (primal void or akasha) surrounding the plane called <a href="http://en.wikipedia.org/wiki/Midgard#Old_Norse">Midgard</a>. The serpent grew so large as to surround the Earth. <br />
</span></div><div><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">This tends to confirm the truism that Earth is encompassed by 4-D space-time -- exactly that which is represented by the <a href="http://en.wikipedia.org/wiki/Tesseract">tesseract</a>.</span><br />
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<tr><td style="text-align: center;"><a href="http://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Ouroboros-simple.svg/200px-Ouroboros-simple.svg.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Ouroboros-simple.svg" border="0" height="200" src="http://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Ouroboros-simple.svg/200px-Ouroboros-simple.svg.png" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Ouroborus</span></td></tr>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><i>Jörmungandr</i> is known in the Greek mythic tradition as <i><a href="http://en.wikipedia.org/wiki/Ouroborus">Ouroborus</a></i>. Both are commonly represented by a serpent biting (swallowing) its own tail. Indeed, the name itself means "tail-eating," or self-devouring. This is an apt description of what we see in the animated graphic at top left.</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipPDXgxOYbhYHyKtkBBdvMaO7U-a6WWKjYuiVKluruclSCAYzreHVKgsyW6u3wnL9KxRmKSpYbOasiS1VVyIkpCrjypPcy7Xi9cgsjvq9lkf07vCK3gPwVlMLNLg6jPv6atVJ32JpgdRsI/s1600/2010-09-15-155524-743156.png" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipPDXgxOYbhYHyKtkBBdvMaO7U-a6WWKjYuiVKluruclSCAYzreHVKgsyW6u3wnL9KxRmKSpYbOasiS1VVyIkpCrjypPcy7Xi9cgsjvq9lkf07vCK3gPwVlMLNLg6jPv6atVJ32JpgdRsI/s200/2010-09-15-155524-743156.png" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">hypercube pendant</span></td></tr>
</tbody></table><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The deeper significance, hinted in the opening paragraph, is that our three spatial dimensions, plus the temporal fourth, constitute an </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">eternal </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">self-devouring subject which acts as our existential domain.</span><br />
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">The photograph at left presents a three-dimensional object commonly presented in two-dimensions as a cross within a circle, known as the Sun cross, or <a href="http://www.symbols.com/encyclopedia/29/291.html">Odin's cross</a>. It is used in astrology to represent the planet Earth.</span></div><div><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><br />
</span></div><div><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">"Since each vertex of a tesseract is adjacent to four edges, the <a href="http://en.wikipedia.org/wiki/Vertex_figure">vertex figure</a> of the tesseract is a regular <a href="http://en.wikipedia.org/wiki/Tetrahedron">tetrahedron</a>." </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: x-small;">(<a href="http://en.wikipedia.org/wiki/Tesseract#Geometry">source</a>)</span></div><span class="Apple-style-span" style="background-color: white; color: #333333; font-family: Arial;"><span class="Apple-style-span"><span class="Apple-style-span" style="color: #333333;"></span></span></span></div>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0tag:blogger.com,1999:blog-9112748128817762559.post-5147170611638769642011-10-27T17:12:00.005-04:002012-05-30T18:44:15.896-04:00Treatment of Hexagrams as Trigram Superpositions<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUk2BTtpi90zrOWZJhV4axSn7Ufx2MpGFaqUpFTusIuhgRpo1WRPnsdeQEKa58wsOH-dvkpnPpxrN9_pdJf2sjiz7IxFgLlnfexErE21n67auElLYi_2ywwfD5v_MaU1vsPYtoC_um6HC-/s1600/wen_trigrams.jpg" imageanchor="1" style="clear: left; display: inline !important; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="166" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUk2BTtpi90zrOWZJhV4axSn7Ufx2MpGFaqUpFTusIuhgRpo1WRPnsdeQEKa58wsOH-dvkpnPpxrN9_pdJf2sjiz7IxFgLlnfexErE21n67auElLYi_2ywwfD5v_MaU1vsPYtoC_um6HC-/s200/wen_trigrams.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Legge, 1879</span></td></tr>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Trigrams are composed of three "places" or "positions", each "containing" YIN (0) or YANG (1). The trigrams will be denoted by triplets read left to right as in the diagram below. </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">In the wireframe diagram (below right), the numbered vertices stand for the trigrams.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWXUrpavI-EqH9ndSrXx8d61CzY7b8xvzN10s7CI0K88lOw-5DbO32UYcqKzk1mKeLrKl6LFXHaCzxNC928Ip1r1kofa8qksrOjTn9DeKjtwn1chXqxGrNQf7woFGnR8H4s1261u51URzR/s1600/unit_cube.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWXUrpavI-EqH9ndSrXx8d61CzY7b8xvzN10s7CI0K88lOw-5DbO32UYcqKzk1mKeLrKl6LFXHaCzxNC928Ip1r1kofa8qksrOjTn9DeKjtwn1chXqxGrNQf7woFGnR8H4s1261u51URzR/s200/unit_cube.gif" width="200" /></a><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Hexagrams are composed of a trigram pair arranged in superposition: <b>lower</b> and <b>upper</b>, or <b>inner</b> and <b>outer</b>. The places are numbered 1 through 6 from bottom to top. Therefore, we can depict an hexagram using our unit square wireframe diagram by connecting any two vertices with directed paths. The syntax for this poses the </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">original </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">vertex as lower trigram, the terminal vertex as upper.</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;"><span class="Apple-style-span" style="font-size: small;">For example, the directed path leading from (1,1,0) to (0,0,1) gives ䷨ hexagram #41, Reduction. Reversing the direction of the path produces ䷩ hexagram #42, Increase.</span></span></blockquote>
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Each of the eight vertices has seven outbound paths to each of the other vertices, totaling 56 paths. Half of these paths are duplicates, in the sense that the paths connect the same pair of trigrams; thus, the 56 paths comprise 28 pairs of heterogenous* hexagrams. </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Each vertex can also loop back to itself. </span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span class="Apple-style-span" style="font-size: large;">These 8 loops constitute 4 pairs of homogenous* hexagrams. An outbound path and its reversal constitute a Wen Pair; loops at antipodal corners </span>(e.g. the example given above)<span class="Apple-style-span" style="font-size: large;"> also designate Wen pairs.</span></span><br />
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">*The terms</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"> heterogenous and</span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"> homogenous (applied to hexagrams) refer to the constituent trigrams</span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Given the <a href="http://sharq-tank.blogspot.com/2011/06/yao-numbers-pt-1.html">yao-numbers</a> derived from Wen's hexagram pairs, we are enabled to assign a weighting to each path, and treat the paths as proper vectors.</span>Shar Qaanhttp://www.blogger.com/profile/12437811464432879555noreply@blogger.com0