Historical Order
//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.
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 $\Psi ^{\sf{ Earth}}$. Compare these events with any other chain

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

using $\delta _{ t}$ the temporal orientation. Definition: The direction-of-time for the events in $\Psi ^{ \sf{P}}$ is given by

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

The widespread practice of using the Earth as a frame of reference is deeply embedded in our use of language. We recognize this with a nomenclature that applies to an arbitrary pair of events in $\Psi ^{ \sf{P}}$ that are noted by $\sf{P}_{\it{i}}$ and $\sf{P}_{ \it{f}}$. Let $\epsilon_{t}^{\, \sf{P}} = 1$. Then if $\it{i} < \it{f} \;$ we call $\sf{P}_{ \it{i}}$ the initial event, and $\sf{P}_{ \it{f}}$ the final event of the pair. Thus the chronological order of events is locked into the numerical order of the event-index $k$.

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Sensory Interpretation: To consistently establish names for initial and final events, consider using a thermal reference process 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 other particles that are thermally similar to the Earth because a warming process is the time-reversed experience of a cooling process. Accordingly, we make the following definition. If

$\epsilon_{t}^{\, \sf{P}} = 1$

then we say that P's events are in historical order. When we call a chain-of-events a history, we imply that it is historically ordered and P is going forward in time. However, if $\epsilon_{t}^{\, \sf{P}}= -1$, then a cooling process for most terrestrial particles could be a 'warming' process for P. And it might seem like $\Psi ^{ \sf{P}}$, which we have likened to a movie, was running backward through the movie-projector. So this number $\epsilon_{t}$ is used later when we make a formal definition of time.

Right.png Next step: Describing vibrations.
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
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