Asterias, Jean Baptiste Lamarck. Tableau Encyclopédique et Méthodique des Trois Regnes de la Nature, Paris 1791-1798. Photograph by D Dunlop. |

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 each cycle is some bundle of quarks

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

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.

$N_{\sf{\Omega}}^{ \mathbf{\Theta}} =$ 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 or orbits-per-second. As descriptions are objectified, we speak more generally of radians-per-second.