WikiMechanics

To extend an earlier discussion about counting quarks, consider a particle P characterized by a repetitive chain of events

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

where orbital cycles are composed of $N$ quarks

$\sf{\Omega} = \left\{ \sf{q}_{1}, \sf{q}_{2} \; \ldots \; \sf{q}_{\it{N}} \right\}$

Depending on the level of objectification each bundle $\sf{\Omega}$ may be thought of as; a set of sensations, or an orbital cycle, or an aggregation of seeds, or perhaps a compound quark. But for any interpretation we can make a mathematical description of P just by counting bundles.

The chain Ψ is a sequence of an indefinite number of bundles, there may be two or two-billion of them. But we can specify a definite quantity $N_{\sf{\Omega}}$ by making the description relative to a reference sensation provided by seeing the Sun. Let $N_{\sf{\Omega}}^{\sf{P}}$ be the number of P's bundles observed during one solar day. This quantity has units of bundles-per-day or cycles-per-day. Solar clocks are historically important, but not much used anymore. So consider evaluating $N_{\sf{\Omega}}$ where the particle is an ordinary clock noted by $\mathbf{\Theta}$. If $\mathbf{\Theta}$ is calibrated so that its cycles are in seconds, then

$N_{\sf{\Omega}}^{ \mathbf{\Theta}} =$ 86,400 (seconds per day)

This number comes to us from the Sumerian and Babylonian peoples of ancient Mesopotamia.¹ About four thousand years ago their astronomical observations and sexagesimal mathematics established what we mean by a second. Namely that one day is parsed as twenty-four hours of sixty minutes, each of sixty seconds.

For WikiMechanics, we also associate $N_{\sf{\Omega}}^{ \mathbf{\Theta}}$ with the reference sensation of hearing a human heartbeat because the heart rate of human adults usually pulsates between forty and one hundred beats-per-minute when resting. So $N_{\sf{\Omega}}^{ \mathbf{\Theta}}$ gives an order-of-magnitude account of the number of heartbeats-per-day for most people, thereby relating celestial and human-scale events. The foregoing tallies of bundles are used to define the angular frequency of P as

$\begin{align} \omega \equiv \frac{ 2 \pi N_{\sf{\Omega}} ^{\sf{ P}} }{ N_{\sf{ \Omega}}^{ \mathbf{\Theta}} } \end{align}$

This angular frequency has units like bundles-per-second. As descriptions are objectified, we associate $2 \pi$ radians with each bundle and speak more generally of radians-per-second. Since all physical particles are supposedly made of quarks, we can also define a very general expression of the frequency as

$\begin{align} \nu \equiv N \frac{ \omega }{ 2 \pi } \end{align}$

where $N$ is the number of quarks in $\sf{\Omega}$. This generic frequency characterizes the flux of quarks associated with P. It has units like quarks-per-second, or more generally of hertz, and is abbreviated by (Hz). Sensory interpretation: Frequency describes the flow strength in a stream of consciousness. It is proportional to the quantity of Anaxagorean sensations experienced per second.

Summary

Nouns		Definition
Heart Constant	${\sf{\text{Time Units Conversion Factor}}} \\ N_{\sf{\Omega}}^{ \mathbf{\Theta}} \equiv 86,400 \; \; \sf{\text{(seconds/day)}}$	1-8