# Introduction to the Primel Metrology

**Primel** is a proposed **system of measurement units**, or "metrology", which is

- "
**dozenal-metric**" **coherent**- derived from so-called "
**mundane realities**" of human experience on Earth, including Earth's**day**, Earth's**gravity**, the properties of**water**, and so forth - similar to Tom Pendlebury's
**Tim-Grafut-Maz**(TGM) metrology, though arguably even more "dozenal" and "coherent" - providing base units that tend to be "smallish" but that scale up nicely using a set of systematic dozenal scaling prefixes

# A Dozenal-Metric Metrology

**Primel** is a proposed "**dozenal-metric metrology**." This means that it is a **system of measurement units**, comparable to the **metric system** or **SI**, but grounded in **dozenal (base twelve) arithmetic**, rather than decimal.

It can be argued that dozenal would be a more practical base for human use than decimal. The number twelve is highly factorable, being cleanly divisible by four different whole numbers (apart from 1 and itself), namely 2, 3, 4, and 6, whereas ten is only divisible by 2 and 5. Of these, 2, 3, and 4 constitute the subitizing numbers, which are the most frequently encountered by human beings, and the most directly perceived by human number sense. This makes their fractions (½, ⅓, ⅔, ¼, ¾) the most frequently-used by humans and thus the most important in practical settings. In dozenal, these fractions all have simple, one-digit, non-repeating representations (½=0.6_{z}, ⅓=0.4_{z}, ⅔=0.8_{z}, ¼=0.3_{z}, ¾=0.9_{z}) whereas in decimal most of these do not (½=0.5_{d}, ⅓=0.3333..._{d}, ⅔=0.6666..._{d}, ¼=0.25_{d}, ¾=0.75_{d}). This factorability also means that the dozenal multiplication table has more repeating patterns in it than the decimal one. This would make everyday arithmetic easier for children to learn, and simpler to use on a daily basis.

It is no surprise that factors of twelve appear in so many places in traditional systems of measurement, since they make it simpler to divide up measurements into subunits. However, traditional systems only applied such factors in an haphazard and piecemeal way. What a dozenal-metric system like Primel does is to rigorously and systematically apply factors of twelve to all levels of scale, in the same fashion that SI applies factors of ten.

This wiki compares many values using decimal numbers of conventional units to dozenal numbers of Primel units. This wiki will use a subscript "d" to indicate when the base is decimal, and a subscript "z" to indicate when the base is dozenal: For instance, ᘔ_{z} = 10_{d}, Ɛ_{z} = 11_{d}, 10_{z} = 12_{d}, 100_{z} = 144_{d}, etc.

- See also: Dozenal (Base Twelve) Arithmetic

# Coherent Units and Quantitels

Like the metric system, Primel is a **coherent** system of measurement. This means that for each type of physical quantity, Primel defines a specific primary unit of measure, known as its "coherent" unit for that quantity. In a perfectly coherent system, the coherent units for all types of physical quantity would bear direct 1-to-1 relationships to each other based on physical law, without any arbitrary extraneous factors.

To refer to such coherent units, Primel makes use of **quantitels**, a set of generic unit names each formed transparently from the name of the physical quantity it measures, plus the suffix ‑**el**, short for "element of" (by analogy with "pixel" being an "element of" a picture). Such generic names are meant to be reusable across potentially many systems of measure, and even to refer the concept of coherent units in the abstract.

For instance, a coherent unit of time in some system (such as the second in SI) can be classified as a **timel**. A coherent unit of length (such as the meter in SI, or the centimeter in CGS) can be termed a **lengthel**. A coherent unit of mass (such as the kilogram in SI, or the gram in CGS) can be termed a **massel**. A coherent unit of force (such as the newton in SI, or the dyne in CGS) can be classified as a **forcel**. And so forth.

Quantitels eliminate the need to use "derived unit" formulas as coherent units for many types of quantity. For instance, a coherent unit of velocity (such as the meter per second in SI, or the centimeter per second in CGS) can simply be termed a **velocitel**. If one can name the quantity being measured, one can instantly name the quantitel for it.

Quantitels are far more transparent than so-called "honor names", i.e., units named in honor of some "dead scientist" who happens to bear some connection (often obscure or tenuous) to the science surrounding the quantity. For instance, it is not self-evident that a pascal in SI is a unit of pressure, but it would be if we referred to it as a **pressurel**.

In addition to their generic use, quantitels can be used as formal names for the units of any specific metrology, as long as some adjective or "brand" mark is attached as a disambiguating prefix. "Primel" derives its name in part from the fact that it happens to be the first (or "prime") system of measurement to do this. It makes use of the "die-face-1" ( ⚀ ) character (Unicode U+2680_{x}) as the common branding mark for all its units. This may be pronounced "prime" or "primel", or optionally left silent, depending on whether the context requires disambiguation. So Primel's coherent units are formally defined as the **⚀timel**, the **⚀lengthel**, the **⚀massel**, and so forth.

- See also: Coherence of measurement units
- See also: Quantitels
- See also: Branding

# Auxiliary Units, Scaling Prefixes, and Colloquial Names

Beyond the coherent units, Primel defines many auxiliary units for each type of physical quantity. First, it scales its quantitels to any power of dozen, and sometimes to convenient factors of dozen, using a system of dozenal scaling prefixes called **Systematic Numeric Nomenclature: Dozenal** (SNN_{z}). These are comparable to the decimal scaling prefixes defined for the metric system, but are much more comprehensive, taking full advantage of the high factorability of base twelve.

- See also: Systematic Numeric Nomenclature: Dozenal

Second, Primel also introduces many so-called "colloquial" names for its units, as alternatives for the formal names derived from quantitels and SNN_{z} prefixes. Each colloquial name attempts to provide an intuitive sense of scale by relating the given Primel unit to a customary unit that it might approximate, or to some physical object known to human experience, that might be comparable in size. Primel colloquial names usually end in a noun indicating the kind of quantity being measured, often the noun from which the associated quantitel is derived. So for instance, the **⚀unqua·lengthel**, being comparable to a customary hand unit, gets the colloquial name **⚀hand·length**. Such colloquial names themselves become amenable to scaling using SNN_{z} prefixes.

- See also: Colloquial Names

# A Dozenal Day/Gravity/Water System

Primel can further be classified as a "**dozenal day/gravity/water**" system, based on the manner in which it derives its coherent units. Instead of basing its **⚀lengthel** on some grand-scale phenomenon such as the circumference of the Earth (the way the metric system derived its meter), Primel instead uses more "mundane" physical phenomena that human beings experience relatively directly within their environment:

- Primel begins with the mean solar day, the most important periodic cycle affecting human life, and divides it by six powers of dozen to yield the
**hexcia·day**(10^{−6}_{z}day) which it uses as its**⚀timel**. - Then it takes a value for gravitational acceleration on Earth's surface, and uses it as the
**⚀accelerel**. - Multiplying that by the
**⚀timel**, yields the**⚀velocitel**. - Multiplying again by the
**⚀timel**, yields the**⚀lengthel**. - Squaring the
**⚀lengthel**yields the**⚀areanel**. - Cubing the
**⚀lengthel**yields the**⚀volumel**. - Primel uses the (maximum) density of water as the
**⚀densitel**. - Multiplying the
**⚀densitel**by the**⚀volumel**, yields the**⚀massel**. - Multiplying the
**⚀massel**by the**⚀accelerel**yields the ⚀**forcel**. Since the**⚀accelerel**is Earth's gravity, the**⚀****forcel**ends up being equivalent to the weight of one**⚀massel**in Earth's gravity. In other words, the ⚀**forcel**and ⚀**weightel**are synonymous. (Compare this to how SI, not being a gravity-based metrology, must distinguish the newton versus the kilogram‑force.) - Multiplying the
**⚀forcel**by the**⚀lengthel**yields the**⚀energel**. Since work, heat, and "potential" are just forms of energy, this unit is also known as the**⚀workel**, the**⚀heatel**, and the**⚀potentialel**. - Dividing the
**⚀energel**by the**⚀timel**, yields the**⚀powerel**. - Dividing the
**⚀forcel**by the**⚀lengthel**yields the**⚀tensionel**. - Dividing the
**⚀forcel**by the**⚀areanel**yields the**⚀pressurel**. - Primel takes a value for the massic heatability (aka specific heat capacity) of water, and uses that as the
**⚀masselic·heatabilitel**. - Multiplying the
**⚀masselic·heatabilitel**by the**⚀massel**yields the**⚀heatabilitel**. - Dividing the
**⚀heatel**by the**⚀heatabilitel**, yields the**⚀temperaturel**.

Primel is similar to the **Tim-Grafut-Maz (TGM) metrology**, a coherent dozenal-metric system developed in the 1970_{d}'s=1180_{z}'s by Tom Pendlebury, who was a member of the Dozenal Society of Great Britain.

- However, TGM does not arrive at its timel by dividing the day by pure powers of a dozen. Instead, it first does a
*binary*division of the day, into two**semi·days**, and then divides each of those into a dozen customary**hours**, and then divides those by four more powers of dozen, to yield the**semi·pentcia·day**, or**quadcia·hour**, which it uses as TGM's timel, the**Tim**. - TGM then uses a (slightly different) value for Earth's gravity as its accelerel, the
**Gee.** - Multiplying the
**Gee**by the**Tim**yields the**Vlos,**TGM's velocitel. - Multiplying the
**Vlos**by the**Tim,**yields the**Grafut**, TGM's lengthel. - Squaring the
**Grafut**yields the**Surf**, TGM's areanel. - Cubing the
**Grafut**yields the**Volm**, TGM's volumel. - TGM uses the maximal density of water as its densitel, the
**Denz**. - Multiplying the
**Denz**by the**Volm**yields the**Maz**, - Multiplying the
**Maz**by the**Gee**yields the**Mag**, TGM's forcel. - Mutliplying the
**Mag**by the**Grafut**yields the**Werg**, TGM's energel. - Dividing the
**Werg**by the**Tim**yields the**Pov**, TGM's powerel. - Dividing the
**Mag**by the**Grafut**yields the**Tenz**, TGM's tensionel. - Dividing the
**Mag**by the**Surf**yields the**Prem**, TGM's pressurel. - TGM takes a (slightly different) value for the massic heatability (aka specific heat capacity) of water, and uses that as the
**Calsp**, TGM's masselic·heatabilitel. - Multiplying the
**Calsp**by the**Maz**yields the**Calkap**, TGM's heatabilitel. - Dividing the
**Werg**by the**Calkap**yields the**Calg**, TGM's temperaturel.

As it stands, the Grafut is a fair approximation of a customary foot, and so consequently the Volm approximates a cubic foot. For those used to United States Customary (USC), or previously used to British Imperial (BI) units, this correspondence with the foot may seem attractive. And the fact that a dozenal power of the Tim is a conventional hour, is also an attractive result. However, at nearly 26_{d} kilograms, or nearly 57_{d} avoirdupois pounds, the Maz makes a somewhat unwieldy mass unit, and its dozenal powers do not resemble any familiar units. And the fact that the day itself is not a dozenal power of the Tim means that switching between short durations in multiples of the Tim and longer durations in multiples of days is not a simple matter of adjusting a radix point.

In contrast, the **⚀lengthel** is centimeter-like at slightly over 8.2_{d} millimeters or at about a third of an inch (exactly 31/96_{d}=27/80_{z} inch, by a judicious choice of the **⚀accelerel**). This is rather small, but its dozenal powers turn out to be quite convenient: The **⚀****unqua****·lengthel** resembles a customary hand measure, or a decimeter. The **⚀biqua·lengthel** resembles an old English ell measure. The **⚀volumel**, at about 5/9 milliliter, and the **⚀massel** at about 5/9 gram, are also smallish, but when scaled up by three dozenal powers, the **⚀****triqua·volumel** and **⚀triqua·massel** happen to quite closely resemble a liter and a kilogram, respectively. As one proceeds deeper into the derivation of Primel units, other interesting coincidences pop up that help make Primel a rather convenient system of measure.

- See also: Mundane Realities

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