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Counting Quarks

Counting quarks is way to scientifically describe sensation. More exactly, we start by counting seeds. Let P be a generic particle composed of some aggregation of seeds. A simple way to make a mathematical description of P is just to sort-out the number of different types of seeds in P. To satisfy Anaxagorean narrative conventions, Cantor’s definition of a set, and Pauli’s exclusion principle, we require that seeds are perfectly distinct. Therefore seed counts always report a positive integer or zero, never fractions or negative numbers.

If all seeds are paired in quarks, then P can also be represented as a set of quarks and mathematically described by counting quarks. We note the results of such an inventory using the letter  n. These numbers are called quark coefficients because they can be interpreted as factors in a nuclear reaction that yields P. For example if \mathsf{s}+2\mathsf{c} \to \mathsf{P} then the quark coefficients of P are n^{\mathsf{s}} = 1 and n^{\mathsf{c}} = 2. Quark coefficients are always integers because quarks are defined by pairs of perfectly distinct seeds.

the total number of Z-type quarksN^{\mathsf{Z}} = n^{\mathsf{\overline{z}}} + n^{\mathsf{z}}
the net number of Z-type quarks{\Delta}n^{\mathsf{Z}} = n^{\mathsf{\overline{z}}} - n^{\mathsf{z}}
the total number of all types of quarks\displaystyle N_{\mathsf{q}}  = \sum_{\zeta =1}^{16}  \; n^{ \overline{\zeta}} + n^{\zeta}

Recall that the Roman letter Z, or the Greek letter  \zeta are used to indicate quark-type. In general, we use the symbols n^{\mathsf{z}} or n^{\zeta} to note the coefficients of ordinary quarks. Coefficients of anti-quarks are written with an overline as n^{\overline{\mathsf{z}}} or n^{\overline{\zeta}} . A few other numbers used for describing particles are defined in the accompanying table. The letter \Sigma indicates the use of summation notation.

Note that if Z represents a thermodynamic or chemical quark, then N^{\mathsf{Z}} also gives the number of these sorts of seeds in P. This is because there is just one Z-type seed for each quark, and all quarks are named after their non-conjugate seed. So we often call N^{\mathsf{Z}} a seed coefficient when discussing thermodynamic seeds.

Counting Quarks and Anti-Quarks

By the foregoing definitions, the net number of quarks in particle P and its anti-particle \overline{\mathsf{P}} are related as

\mathrm{\Delta} \mathit{n} ^{\mathsf{Z}} \left( \mathsf{P} \right)= - \mathrm{\Delta}  \mathit{n}^{\mathsf{Z}} \left(\overline{\mathsf{P}} \right)

This is just an arithmetic fact, little more than a tautology. It follows directly from the anti-commutative properties of subtraction. However, when we apply it to counting quarks it expresses a fundamental physical symmetry between matter and anti-matter. So we will come back to it later. But next we look at some measurable particle properties like energy, temperature, and other quark traits.

Counting quarks is like counting the beads in this baby carrier panel from Borneo.
Baby Carrier Panel, Basap people. Borneo 19th century, 39 x 20 cm. Photograph by D Dunlop.