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Counting Quarks by the Bundle

The frequency of observation, classification and rotation is suggested by this gear-like French egraving.
Jean-Baptiste Lamarck, Asterias. Tableau Encyclopédique et Méthodique des Trois Règnes de la Nature, Paris 1791. Photograph by D Dunlop.

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

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

where each repeated cycle  \mathsf{\Omega} is a bundle of  N quarks written as

\mathsf{\Omega} = \left( \mathsf{q}^{1}, \, \mathsf{q}^{2}, \,  \mathsf{q}^{3}  \, \ldots \, \mathsf{q}^{N} \right)

Depending on the level of objectification, each bundle \mathsf{\Omega} may be thought of as a set of sensations, or an orbit, 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.

Solar clocks are like this radiant icon.

The chain  \Psi 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_{\mathsf{\Omega}} by making the description relative to a reference sensation provided by seeing the Sun. Let  N_{\mathsf{\Omega}}^{\mathsf{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 P is an ordinary clock noted by  \mathbf{\Theta}. If this clock  \mathbf{\Theta} is calibrated so that its cycles are in seconds, then

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

This number comes to us from the Sumerian and Babylonian peoples of ancient Mesopotamia1George Sarton, A History of Science, page 74. Harvard University Press, Cambridge 1952.. 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.

Oddness is illustrated by this heartbeat icon for binary somatic sensations.

For EthnoPhysics, we also associate  N_{\mathsf{\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_{\mathsf{\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

\omega \equiv \dfrac{\, 2\pi N_{\mathsf{\Omega}}^{\mathsf{P}} \, }{N_{\mathsf{\Omega}}^{\mathbf{\Theta}}}

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. And since all physical particles are supposedly made of quarks, we can also define a very general expression of the frequency as

\nu \equiv N \dfrac{\omega}{2\pi}

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

1George Sarton, A History of Science, page 74. Harvard University Press, Cambridge 1952.