**That Dozenal Transcends Metrology**

There are and have been many collections of unrelated units of measurement and more structured systems of units of measurement that have been used at the same time and with one and the same base of numeration for representing the numbers without regard to the way units have been multiplied or aggregated into larger units or subdivided into smaller units of measurement. For example, there have been units of weight that increased as binary powers although their numbers were written decimally. For a number to be the default and only base of numeration used, a single unified, standardised, legally mandatory or obligatory, and conventional system of measurement is not necessary. While a fully global and international system of measurement would be desirable, the aim to design and introduce such a system of measurement should not be used as the main motivation for setting the default base of numeration. Just as having a single system of measurement throughout the world is advantageous, having a single base of numeration for all computations would be convenient. The argument for dozenal being as much as possible the exclusive base of numeration should be founded almost entirely in the advantages inherent from its mathematical and practical merits dissociated from any particular metrological proposal.

**On Computational Conversion**

It must be emphasised that having multiple bases of numeration being used concurrently in public interaction would be inconvenient and disruptive because of the computational conversion between their numbers that would be necessary. At the moment, some of the inconvenience of the use of more than one base is hinted at by the decimal scales being contary to the sexagesimal subdivisions of time and angle, though their numbers are all written with the same decimal digits. Thus, a complete replacement of decimal by dozenal should be desired. Lingering of decimal in a dozenalised society should be discouraged and eventually stamped out.

**On Metrological Conversion**

Since dozenal is to be the only base, there should not be permitted any contexts in which the decimal base persists. Thus, all measurements regardless of their original units should be converted to dozenal. To reduce the proliferation of units in the dozenal world, a scheme should be worked out to make these conversions towards a dozenal derivation as far as possible. To achieve this is proposed that all measurements in a quantity of the same kind and system of measurement should be converted to a single unit within that system which will then in turn be converted to a dozenal unit of measurement. For example, all measurements of the quantity length, whether they be parts of inches, feet, or yards, insofar as they are commensurate without the involvement of factors containing large prime numbers, from the Imperial or Customary systems could be converted first to inches, which then could be converted to be in terms of some unit of length that fits into a dozenally derived metrological system.

**On Money**

Replacement of decimal by dozenal may be begun with national currencies. Only denominations of notes and coins that are legal tender in a country are permitted to be used. Thus, making ultimately one base of numeration alone legal on denominations of national currency would not encroach upon commercial freedoms that are currently enjoyed. Furthermore, there would be no extra cost to changing the base of numeration in currency from decimal to dozenal, because the only cost is of replacing decimalised denominations by dozenalised denominations, which is nothing more than a matter of design and printing or minting, processes that are regularly renewed to counteract counterfeiting and replenish notes and coins withdrawn from circulation because of disrepair from wear and tear anyway. Other supposed costs such as of training and education or informing need not be entertained, because once there is only one system of legal tender, people will be able to suss out for themselves what to do and teach each other free of charge by word of mouth. All worthy independent news media would advertise the transition in the ordinary course of reporting. Enacting dozenal as the base for currency is merely a matter of being signed into law by elected representatives and heads of legislating government. This is really very easy to do once the decision has been made, as for the facile changing of laws generally where the populace do not object. There should only be one set of legal tender. If dozenal is to be allowed freely, decimal must by law be phased out.

**On Numeration**

Once the currency has been adopted and become familiar for some time, the mode of writing or printing numerals in documents regulated by the country may be impelled to be changed from decimal to dozenal. This may be done at no cost, as the emergence of freely available electronic converters and downloadable software to devices can be expected. Contents of textbooks are controlled by syllabuses or curriculums set by educational authorities. There would be no loss of freedom therefore from a demand to print all numbers in school books in dozenal notation. These books are reprinted very frequently, so there would be no extra cost to the printing or publishing house or consumer. Numerals extended to the full dozenal range can be supplied free to the printers on condition that they be used. If it is supposed that Indo-Arabic numerals from zero to nine be retained in expressing numbers dozenally, then the decimal numbers do not co-exist well and their use in decimal ought to be phased out to accommodate dozenal. This should be done through consumer protection, health and safety, and accountability legislation, to which in their current form citizens are already bound, among other acts.

**On Priorities**

By far, the most important agendas for dozenalists to start creating a dozenal world are probably dozenal currency as the only legal tender and dozenal notation. Nevertheless, many purporting to be dozenalists have devoted an inordinate amount of time and energy to less urgent matters, such that milestones of dozenal calendrical dates have come and gone while those dozenalists appeared to have not been ready with a contingency. They are still debating and arguing among themselves and against each other, and refuse as a matter of principle to decide on perhaps the single most important necessity for dozenal notation. And when some purporting to be dozenalists do come to an agreement, it often involves a strategy that makes being a dozenalist more difficult than it was before, which makes one wonder whether they are in fact scheming to hinder dozenalism. A tell-tale sign of those not committed to dozenalism is the advocacy of other bases than base twelve with invention in unnecessary detail of names for numbers and units in systems of those other bases not just in a way of investigation to prove the supremacy of base twelve, and ignoring the clear mathematical superiority of base twelve, while exaggerating alleged perks of other bases.

**On Time**

Many metrological systems proposed for dozenal have begun with the unit of time. Some have claimed that in a dozenal world, the multiplication and division of units of measurement, such as of time, would be consistently dozenal, such that larger and smaller units than the base unit would appear as dozenal powers of the base unit. This claim of consistency in the case of time cannot be true. There cannot be only one base unit of time, because the periods of time by which people reckon their lives are not commensurate with each other. The period of the day governs the light by which work and sleep are scheduled. The solar year governs the seasons by which the production of food is regulated. The lunar month governs the tides by which porting and sailing of ships in harbours are controlled. Yet the day does not divide exactly into the month or year, and the month does not divide by a whole number into the year. The number of times by which the day divides into these larger periods is not even a dozenal power. Hence, the supposition that the division of time can be strongly and consistently dozenal, or indeed any other base, is a fallacy.

One period of time, such as the day, in isolation from the other periods may be multiplied and divided dozenally. Preferentially, this would be done consistently at powers of the base twelve. However, the base ten is used in the represention of all numbers whether they be for divisions at decimal powers of the unit or otherwise. Hence, dozenal can instead be used as the only base of numerical notation for all divisions, whether they be at dozenal powers of the base unit of measurement or not. Ideally, it would be better if all subdivisions were as powers of the base twelve, as this would enable the easiest manner of notation and computation.

However, the concern is introduction of dozenalism in the world rather than in the fantasy of minds, and realistically the better way to introduce dozenal in time may be to retain as much as possible the current most common mechanisms of clocks, which divide the day into two halves and each half into twelve hours. There is then a way to be dozenal with time while keeping all major civic clocks that do not use a second hand unchanged except for the painting of their faces. One may relatively easily achieve such a dozenal clock hands-on by scrubbing off any tick marks between the hourly positions and writing new graduations between them. This makes the clock a measurement device for the dozenal unit of time that is fifty seconds in duration, the same as from completely consistent division at dozenal powers of the day.

A problem with the proposals of consistent division of the day by powers of twelve is that doing so would involve too many hands for the reading of the time. Hands must be distinguished by length, thickness, and design, but if there be too many hands, they would be liable to be less distinct from each other and would involve more mechanical complexity than desirable.

From a language point of view, to have a newly named or prefixed unit at each power of twelve is too frequent. By analogy, for the prefixes to units in the decimal metric system of measurement, prefixes appear at each power of the cube of the base ten, and not more frequently except for powers near the base unit, although even then a prefix for the square power is rarely used, such that the prefixes deca or deci are not often encountered, and the word decimetre is hardly seen outside of the context of discussing certain dozenal metrological proposals. Thus, for example, if there is a word, such as minette, for the dozenal temporal period of fifty seconds, then a word for a duration twelve times that or a twelfth of it should be discouraged. Instead, the named unit has derivative words at its multiples by powers of the square twelve or square twelfth, hence making a consistent division of scale by the square dozen base, rather than its subbase twelve.

Names or prefixes for units should only appear at intervals of the square power of the dozen. This being achieved on the clock face with a square dozen tick marks gives half as many hands, a simplification and an improvement.

Having as many as a square dozen tick marks on a watch face may be too many to be distinguished easily for reading the time. A lesser number such as half a square dozen of tick marks may be preferable. It is better to have as many tick marks as can be readily discriminated, as using fewer would waste space and energy.

Thus, the day can be divided into two dozen hours, each of which is divided into half a square dozen periods of fifty seconds, each of which would be divided into another half square dozen periods of the square of five sixths of a conventional second. An advantage of using this as the fundamental base unit of time is that its square and cubic powers approximate to simple rational portions of the conventional second, enabling easier mental rules of thumb for conversion between the units of the dozenal metrological proposal and the decimal metric, the most commonly used metrological system that should be eradicated by dozenal from the world.

**On Length**

Having selected a unit of time, some have derived with it a unit for length by using the acceleration due to gravity of the Earth set to some constant. However, the graviational acceleration on Earth is not constant, but varies with latitude and density of the geological formations underground. Nevertheless, it has been claimed that the deviation is small enough that such accelerational metrological systems are appropriate worldwide regardless of latitude. Using this logic, the gravitational acceleration at any particular latitude could be used as the constant for the purposes of the definition of units in the system of measurement.

In this proposal, the unit of length is derived ideally as the length of a pendulum with a period of the unit of time already selected for being a dozenal division of the day. The gravitation is chosen so as to make this resulting length of the pendulum exactly equal to a whole number of an existing unit of length in one of the legal standards.

Setting the unit of time to half a square dozenth of fifty seconds and the gravitation at \(2^{6} 3^{5} \pi^{2} /5^{6}\) ~= 9.8235 decimal metric metres per square second gives the unit of length \(L\) through the formula for the period \(T\) of the pendulum in terms of its length and gravitation \(g\):

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Hence, the length of the pendulum becomes twelve centimetres. A twelfth of this as a decimal metric centimetre is constructed as the base unit of length.

From this length, units of area and volume by the second and third powers are constructed.

The combinations of the units of time and length determine the kinematic units in the system of measurement.

**On Mass**

The unit of mass is set as the amount of matter in a unit volume of water under specified conditions, equal to one gram.

The combinations of the unit of mass with the kinematic units determine the mechanical units of the system of measurement.

**On Temperature**

A theoretical consideration might involve Boltzmann's constant.

However, here a much more practical strategy will be proposed.

Temperature is measured by the height of liquid through a narrow bore in a tube of glass. The minimum height for water occurs at the temperature of its maximum density. The temperature of maximum density of water may be set as four degrees Celsius. This temperature in the dozenal scheme is set at zero. The size of the dozenal degree of temperature is set as being equivalent to the size of a degree in Celsius and Kelvin. Hence, the temperature, being a hundred degrees Celsius, of boiling of water at a specified pressure then becomes eight dozenal units of temperature. The conversion from degrees Celsius to the dozenal temperature involves only a subtraction of four degrees. In mathematics, the Greek letter delta is often used to indicate a difference or change in a quantity. In the Greek alphabetical order, the fourth letter is delta. Thus, the resulting dozenal unit of temperature may be called a delta degree, notated \(^{Δ}C\).

**On Electromagnetics**

Ideally, a natural system devised from theoretical physics employing something akin to Planck units and a Lorentz-Heaviside expression would be used for electromagnetic units.

Using a Lorentz-Heaviside type of system, a unit of charge may be derived from the physical constants and the kinematic and mechanical units.

$$Charge = \sqrt{ε_{0} L^{3} T^{-2} M}$$

Ignoring any unspecified constant of proportionality that may be hidden by the metric system of units, a unit for current may be derived as the flow of unit charge per unit time. This gives a unit of current near 2 * 10^-10 Amperes, allowing an easy rule-of-thumb for conversion from metric current to dozenal. That is, simply shift the decimal jot, divide by a factor of two, and write the number dozenally.

The most commonly used electrical units of measurement for ordinary people have been Amps and Volts. It is preferable that these more than any other electrical units should be easily convertible to a dozenal system of units.

**On Molar Units**

The Avogadro constant is little more than a conversion factor between two different units of mass, the gram and the atomic or Dalton. The atomic mass is set as a twelfth of the mass of a carbon-twelve isotope. One mole is then the mass number of an element in grams.

**Luminous Intensity**

It would seem that luminous intensity ought to be derived in terms of energy and spatial considerations.

Setting the base units is sufficient to define the system, as a physicist competent in these matters can simply put these base unit quantities into a spreadsheet and get the derived units as outputs.

**On Unit Symbols**

The symbols T, L, M used above were

*variables*for quantities or numbers as well as their units.

In the specification of a particular amount of a unit, the number is followed by the unit in word form or by a letter symbol abbreviating the unit word form.

The letter symbol abbreviating the unit of time may be

**.**

*s*The letter symbol abbreviating the unit of length, the centimetre, may be

**.**

*l*The letter symbol abbreviating the unit of mass, the gram, may be

**, as in decimal metric.**

*g*The letter symbol abbreviating the unit of temperature may be

**.**

^{Δ}CThe letter symbol abbreviating the unit of charge may be

**.**

*c*The letter symbol abbreviating the mole may be

**, as in the decimal metric system.**

*mol***Reference**

https://en.wikipedia.org/wiki/Lorentz%E2%80%93Heaviside_units

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