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 . These numbers are called **quark coefficients** because they can be interpreted as factors in a nuclear reaction that yields P. For example if then the quark coefficients of P are and . Quark coefficients are always integers because quarks are defined by pairs of perfectly distinct seeds.

Characteristic | Definition |
---|---|

the total number of Z-type quarks | |

the net number of Z-type quarks | |

the total number of all types of quarks |

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

Note that if Z represents a thermodynamic or chemical quark, then 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 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 are related as

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.