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The individual, in framing and dealing with reality, can be understood as being at the centre of a field of consciousness offering a range of possibilities. This field can be understood as organized in many ways. The

In the accompanying exploration of the *9-fold Higher Order Patterning of Tao Te Ching Insights*, much attention was given to their possible disposition in a 9x9 matrix -- as an array of insights (disposed in a peacock's tail in some cultural symbolism). Crudely this could then be seen as constituting a kind of setting for a children's game. As with hopscotch, for example, an individual might move from one cell to another -- with each cell being associated with a different perspective, insight or mode of awareness. And with each cell offering different kinds of connectivity to other cells. The challenge in that exploration was to find more powerfully integrative ways of ordering such an array -- hence the exploration of magic squares, and the possible relevance of mathematical objects of higher dimensionality, such as hypercubes. The emphasis however was on how any such order was to be comprehended.

For mathematicians the exploration of hyperspace (according to the admirable description of Michio Kaku: *Hyperspace*, 1994) is based on the "field" theory originated by Faraday -- inspired by an agricultural metaphor. For him, a field occupies a region of three-dimensional space such that at any point in the space a collection of numbers can be assigned that describes the magnetic or electric force at that point. In its development by Georg Riemann (1854), a collection of numbers at every point could be introduced to indicate how much the space was bent or curved. On a two-dimensional surface, a collection of three numbers at every point completely described the bending of the surface -- whereas in four spatial dimensions a collection of 10 numbers was required at each point to describe its properties.

Riemann's metric tensor in 4 dimensions with the information necessary to describe a curved space. In this case, 16 numbers are required to describe each point. 6 of them are redundant (eg g _{12} = g_{21}) leaving 10 independent numbers. These can then be arranged in a square array | |||

g_{11} | g_{12} | g_{13} | g_{14} |

g_{21} | g_{22} | g_{23} | g_{24} |

g_{31} | g_{32} | g_{33} | g_{34} |

g_{41} | g_{42} | g_{43} | g_{44} |

With this device Riemann could then describe N-dimensional space with a metric tensor that would then resemble a chess board that was NxN in size. In the quest to provide a unified description, the metric tensor could be expanded to N-dimensional space then portions of it -- in the form of rectangular pieces -- could be identified as corresponding to different forces embodied in the unified description. Whereas Maxwell's classical field equations for electricity and magnetism are 8 in number, these collapse into a single relativistic equation when time is treated as the fourth dimension -- because they then possess a higher symmetry. The development of theoretical physics over the past century has essentially been based on the search for the field equations of the forces of nature.

Riemann's metric tensor in 5 dimensions as expanded by Kaluza (adding a fifth column and row) so that the 4-dimensional metric of Einstein could be unified with the electromagnetic field of Maxwell -- unifying the theory of gravity with that of light. | ||||

g_{11} | g_{12} | g_{13} | g_{14} | g_{15} |

g_{21} | g_{22} | g_{23} | g_{24} | g_{25} |

g_{31} | g_{32} | g_{33} | g_{34} | g_{35} |

g_{41} | g_{42} | g_{43} | g_{44} | g_{45} |

g_{51} | g_{52} | g_{53} | g_{54} | g_{55} |

This approach was then extended by Kaluza, as indicated above, to provide a basis for unifying Einstein's metric with that of Maxwell. Further expanding the metric tensor in this way subsequently allowed all known forces (gravity, electromagnetism, weak and strong nuclear forces, and most fundamental particles) to be integrated into the unified description. Note that by slicing the metric tensor into its rectangular components, these are respectively descriptive of particular forces.

Super Riemann tensor expanded with the addition to the fifth dimension of supersymmetry to deal with (some) fundamental particles (adapted from Kaku, 1994) | |||

Gravity (Einstein) | Light (Maxwell) | Weak+Strong nuclear force (Yang-Mills) | Quarks-leptons (Matter) |

Light (Maxwell) | . | ||

Weak+Strong nuclear force (Yang-Mills) | . | ||

Quarks-leptons (Matter) | . |

**The question is whether it is fruitful to consider the magic square disposition of the 81 insights of the Tao Te Ching (in the accompanying paper) as in anyway corresponding to such a metric tensor. **Each numbered insight would then hold an aspect of the information which -- with that associated with other numbers -- would define how much the "communication space" was bent or curved at that point. Recall that the

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