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Orbits

Orbits are sequences of events that are repeated over and over again in some longer chain of events. Chains like these are used to mathematically describe phenomena that are repetitive or cyclical. More exactly, let \sf{\Omega} be some finite selection of events written as

\sf{\Omega} ^{\mathsf{P}} = \left( \mathsf{P}_{1} , \mathsf{P}_{2} , \mathsf{P}_{3} \; \ldots \; \mathsf{P}_{\mathit{N}}  \right)

Let this selection be repeated over and over again to establish a longer chain of events called \Psi as

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

where \mathsf{\Omega}_{1} =     \mathsf{\Omega}_{2}   =    \mathsf{\Omega}_{3} etc. The repeated sequence of events \sf{\Omega} is called a single orbit or an orbital cycle of P. The long chain \Psi is generically called an orbital chain-of-events. And sometimes, \sf{\Omega} is also called a bundle of sensations because physical events have been defined from sensations.

Orbits and cycles are exploding from a student's head in this 17th century engraving.
Robert Fludd (1574-1637) Utriusque cosmi maioris scilicet et minoris metaphisica. Oppenhemii 1619.

Earlier, it was suggested that any chain of events could be thought of as something like a movie. To illustrate this notion, here is an example of using orbits to make a boring movie. Consider that \sf{P}_{ \it{k}} might be a somatic sensation, and perhaps that \sf{\Omega} is a single-frame within the motion picture. The first thing that happens in this example is some sort of sound that is heard on the right-side

\mathsf{P}_{1} =

{

}

Then the next event is a somatic sensation on the left

\mathsf{P}_{2} =

{

}

These two sensations are bundled together into an orbit

\mathsf{\Omega^{P}} =

(

,

)

= \left( \mathsf{P}_{1} , \mathsf{P}_{2} \right)

and then repeated, over and over again

\Psi ^{\mathsf{P}}

=

(

,

,

,

,

,

... )

= \left(     \mathsf{\Omega}_{1} ,     \mathsf{\Omega}_{2}   ,    \mathsf{\Omega}_{3}  \;   \ldots      \;    \right)

Right, left, right, left, right, left and so on … nothing else happens. So this movie is called The Almost-Dead March. Orbits like this might seem a little tedious, but as we add more detail, they provide a basic structure for describing more complicated happenings in space and time. Describing orbits becomes scientific as we stop talking about sensations, and shift to a discussion of particles. So next we consider how to treat orbits as objects.