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=0.6z, ⅓=0.4z, ⅔=0.8z, ¼=0.3z, ¾=0.9z) whereas in decimal most of these do not (½=0.5d, ⅓=0.3333...d, ⅔=0.6666...d, ¼=0.25d, ¾=0.75d). 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, ᘔz = 10d, Ɛz = 11d, 10z = 12d, 100z = 144d, etc.

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+2680x) 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.

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 (SNNz). 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.

Second, Primel also introduces many so-called "colloquial" names for its units, as alternatives for the formal names derived from quantitels and SNNz 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 SNNz prefixes.

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 is similar to the Tim-Grafut-Maz (TGM) metrology, a coherent dozenal-metric system developed in the 1970d's=1180z'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, TGM's massel.
  • 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 26d kilograms, or nearly 57d 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 8.2d millimeters or at about a third of an inch (exactly 31/96d=27/80z 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.

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