Horlogerie, Plate IX-7. Encyclopédie, ou Dictionnaire Raisonné des Sciences, des Arts et des Métiers. Edited by Denis Diderot and Jean le Rond d'Alembert, Paris 1768. Photograph by D Dunlop. |

Our knowledge of time's arrow comes from the ordinary run of human affairs. So for WikiMechanics, the direction of time is derived from the historical record of human events; our collective experience, as recorded in the newspapers. Arbitrary sequences of events can be compared with such mundane proceedings, and a binary description of their relationship made as follows. The historical record is introduced via the reference sensation of touching the Earth. And the very common human experience of keeping in touch with some selection of terrestrial events is assumed to provide an ordered set of sensations that we note by $\Psi ^{\, \sf{ Earth}}$. Consider comparing these terrestrial-events with another chain-of-events associated with particle P

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

Make the comparison using $\, \delta _{ t} \,$ their temporal orientation, to define $\, \epsilon_{ t} \,$ as the **direction-of-time** for P's events

$\epsilon_{t}^{\, \sf{P}} \equiv \, \delta _{ t}^{\, \sf{ P}} \! \cdot \delta _{ t}^{\sf{\, Earth}}$

When P is like the Earth both particles have the same temporal-orientation; $\delta _{ t}^{\, \sf{ P}} \! = \delta _{ t}^{\sf{\, Earth}} \! = \pm 1 \, \,$. If this condition obtains then

$\epsilon _{t}^{\, \sf{P}} =1$

and we say that P's events are in **historical** **order**. This historical-order is locked into the numerical-order of event-index $k$ using the following nomenclature. Let $\sf{P}_{\it{i}}$ and $\sf{P}_{ \it{f}}$ be an arbitrary pair of events in $\Psi^{ \sf{P}}$. If $\epsilon _{t}^{\, \sf{P}} =1$ and $\it{i} < \it{f} \;$, then we call $\sf{P}_{ \it{i}}$ the **initial** event, and $\sf{P}_{ \it{f}}$ the **final** event of the pair. We also use $\epsilon_{t}$ to make a formal definition of time.

**history**we imply it is historically ordered, and going

*forward*in time. To label initial and final events consistently with this progress, consider using a thermal reference provided by the absorption of a tepid particle. Let $\epsilon_{t}^{\, \sf{P}} = 1$ so that P has the same temporal orientation as the Earth. Then the temperatures of P and the Earth are both on the same side of tepid. Both are either higher or lower. So they both describe the absorption in the same way; as either a warming process, or a cooling process. But not one of each. So the terms

*initial*and

*final*can be used uniformly with both P and the Earth. Taxonomic agreement extends to thermally similar particles because, in accordance with the English grammar of participles, a warming process is a cooling processes that is going

*backwards*, and vice versa.

Summary |

Adjective | Definition | |

Direction of Time | $\epsilon_{t}^{\, \sf{ P}}\equiv \, \delta _{ t}^{\, \sf{ P}} \! \cdot \delta _{ t}^{\sf{\, Earth}}$ | 6-6 |

Adjective | Definition | |

Historical Order | $\epsilon_{t} = 1$ | 6-7 |

Noun | Definition | |

Initial Event | The event with the lowest event-index in a historically ordered pair of events. |
6-8 |

Noun | Definition | |

Final Event | The event with the highest event-index in a historically ordered pair of events. |
6-9 |

Adjective | Definition | |

History | $\sf{\text{A chain of events that is in historical order.}}$ | 6-10 |