Ajat basket, Penan people. Borneo 20th century, 20 (cm) diameter by 35 (cm) height. Hornbill motif. From the Teo Family collection, Kuching. Photograph by D Dunlop. |

Consider a particle P characterized by some repetitive chain of events

$\Psi ^{\sf{P}} = \left( \sf{\Omega}_{1} , \sf{\Omega}_{2} , \sf{\Omega}_{3} \ \ldots \ \right)$

where each orbital cycle is a bundle of quarks

$\sf{\Omega} = \left\{ \sf{q}_{1}, \sf{q}_{2}, \sf{q}_{3 } \ \ldots \ \right\}$

that are described by their internal energies $U$ and some quark coefficients $n$. Definition: the **magnetic radius** of P is

$\begin{align} \rho_{ m} \equiv \frac{ {\Delta}n^{ \mathsf{A}} U^{ \mathsf{a}} - {\Delta}n^{ \mathsf{M}} U^{ \mathsf{m}} }{ k_{\sf{F}} } \end{align}$

the **electric radius** is given by

$\begin{align} \rho_{e} \equiv \frac{ {\Delta}n^{ \mathsf{G}} U^{ \mathsf{g}} - {\Delta}n^{ \mathsf{E}} U^{ \mathsf{e}} }{ k_{\sf{F}} } \end{align}$

the **polar radius** of P is defined as

$\begin{align} \rho_{z} \equiv \frac{ {\Delta}n^{ \mathsf{U}} U^{ \mathsf{u}} - {\Delta}n^{ \mathsf{D}} U^{ \mathsf{d}} }{ k_{\sf{F}} } \end{align}$

where $k_{\sf{F}}$ is a positive constant. An ordered set of these three numbers defines the **radius vector** of particle P as

$\overline{\rho} \equiv \left( \rho_{ m}, \rho_{e}, \rho_{ z} \right)$

Components of $\overline{\rho}$ are conserved because they are defined from sums and differences of quark coefficients, and quarks are indestructible. So if some generic particles $\mathbb{X}$, $\mathbb{Y}$ and $\mathbb{Z}$ interact like $\mathbb{ X } + \mathbb{ Y } \leftrightarrow \mathbb{ Z }$ then by the associative properties of addition and subtraction$\overline{\rho}^{ \mathbb{X}} + \overline{\rho}^{\mathbb{Y}} = \overline{\rho}^{\mathbb{Z}}$

Also $\rm{\Delta} \it{n} ^{\sf{Z}} \left( \sf{P} \right) = - \rm{\Delta} \it{n}^{\sf{Z}} \left( \sf{\bar{P}} \right)$ for any sort of quark, so particles and anti-particles have symmetrically opposed radius vectors

$\overline{\rho} \left( \sf{P} \right) = - \overline{\rho} \left( \sf{\overline{P}} \right)$

The norm of a radius vector is written without an overline $\rho \equiv \left\| \, \overline{\rho} \, \right\|$. Definition: If P is described by a chain of events $\Psi$ where each cycle $\sf{\Omega}$ has the same radius vector, then we say that P is **rigid**. This condition is obtained if there are no changes to the quark content of P.

*net*magnitude. Coefficients of baryonic quarks do not appear in these definitions, only dynamic quarks. So the radius does not depend on thermal sensation, only somatic and visual sensations. Also the null value for energy is referred to down-quarks which are objectified from black sensations. So overall the radius vector is interpreted as a description of the magnitude of somatic and visual sensations, relative to black sensations, net right from left.

Summary |

Noun | Definition | |

Magnetic Radius | $\begin{align} \rho_{ m} \equiv \frac{ {\Delta}n^{ \mathsf{A}} U^{ \mathsf{a}} - {\Delta}n^{ \mathsf{M}} U^{ \mathsf{m}} }{ k_{\sf{F}} } \end{align}$ | 5-1 |

Noun | Definition | |

Electric Radius | $\begin{align} \rho_{e} \equiv \frac{ {\Delta}n^{ \mathsf{G}} U^{ \mathsf{g}} - {\Delta}n^{ \mathsf{E}} U^{ \mathsf{e}} }{ k_{\sf{F}} } \end{align}$ | 5-2 |

Noun | Definition | |

Polar Radius | $\begin{align} \rho_{z} \equiv \frac{ {\Delta}n^{ \mathsf{U}} U^{ \mathsf{u}} - {\Delta}n^{ \mathsf{D}} U^{ \mathsf{d}} }{ k_{\sf{F}} } \end{align}$ | 5-3 |

Noun | Definition | |

Radius Vector | $\overline{\rho} \equiv \left( \rho_{ m}, \rho_{e}, \rho_{ z} \right)$ | 5-4 |

Noun | Definition | |

Rigid | $\overline{\rho} \ \ {\sf\text{has the same value for all events} }$ | 5-5 |