TGM: An Overview
TGM is different from any other metric system in history, and it is different in two ways: first, it is completely consistent; and second, it is completely dozenal. No other metric system in use today can claim to match TGM's consistency (no, not even SI metric, which is full of illogicalities, inconsistencies, and improperly measured base units); and of course, no other system can claim to take full advantage of the superiorities of the dozenal system.
Why a New Metric System?
Metric systems in the past have been based on two things: the simple development of units over long history of practical use, or extrapolation from an arbitrarily chosen set of base units.
An example of the former is the so-called "English sytem," which is more properly called customary-imperial (since it is not really English, being using primarily in the United States; and since it is not the same in every country where it is used, being significantly different in America as opposed to Commonwealth countries). The foot, pound, and gallon that most Americans are used to aren't based on anything in particular (legends about "the foot of this or that king" to the contrary), but rather upon lengths that people found convenient for given tasks. For this reason, there is a bewildering array of these traditional units, even for single physical quantities; for example, distances can be measured in lines, points, picas, mills, barleycorns, inches, hands, feet, yards, furlongs, and miles, just to name a few; this ignores certain special lengths such as links and chains (used by surveyors), and doubtlessly others. People simply came up with lengths which seemed convenient for particular purposes. In later times a system of sorts was applied to these units; a pint of water, for example, was determined to weigh one pound (though a later imperial reform, never adopted in America, made a pint equal to a pound and a quarter), but the system is ad hoc by its nature, and indeed that is precisely its strength, and is the reason that it has always been extremely difficult to prevail upon a people to adopt a non-traditional system.
An example of the latter is the so-called "metric system" (the current incarnation of which is le Système international d'unités (SI), originally introduced in France during the Revolution and gradually, primarily due to the Napoleonic Wars and subsequent colonization, spread throughout large parts of the world. (English colonies, of course, all used the customary-imperial system, specifically the imperial branch, until well after the Second World War; and England herself used it until the 1970s, and still does use some of its units.) This system, at least in principle, is based entirely on the meter, a unit of length which is defined as one ten-millionth of one quarter of the circumference of Earth. Of course, in the 1790s the circumference of Earth could be measured with only limited accuracy, resulting in a meter that is significantly different from this particular ideal; so as a practical meter, the meter is the length of a specific platinum bar sitting in a vault in Paris. That bar has since been measured by laser, and the meter defined in terms of the distance light traverses in the length of time it takes for light to traverse the distance of that bar; but as a practical matter, it's the bar that counts.
Other units were defined in terms of that bar. For example, the basic unit of mass (amount of matter, or physical stuff) is the mass of one cubic centimeter of water. (In SI, the kilogram, or one thousand grams, is the basic unit, being the mass of one cubic decimeter of water.) The basic unit of volume was formerly the liter, the volume of one cubic decimeter of water; in SI, we are no longer supposed to use liters, and the basic unit of volume is simply the cubic meter. Other units are derived in the same general way from the meter, at least in principle; in reality, there are seven basic units: the meter (length), the kilogram (mass), the second (time), the ampere (electric current), the kelvin (temperature), the candela (luminous intensity), and the mole (amount of substance), from which other units are derived in a more or less regular manner.
The problem with this system is threefold: first, there are many irregularities in the system (the mole, for example, is based on twelve grams of carbon, and is based on the gram when the basic unit of mass is the kilogram); second, it is completely arbitrary, with no explanation of why some fraction of the circumference of Earth should be so important; and third, it is decimal, ignoring the many superiorities of the dozenal base.
This last is really fatal. The dozenal base could conceivably simply take over either one of these systems, or it dozenalize them but retain their basic units; but neither of these situations really remedies the fact that neither of them are fully dozenal. Dozenalizing customary-imperial units doesn't change the fact that they're ad hoc and inconsistent; dozenalizing SI metric units doesn't change the fact that they're derived from one other in a thoroughly decimal way.
What is needed, then, is a new system, one which is consistent and rational (so avoiding the faults of the customary-imperial system), yet which is not arbitrary and irregular (so avoiding the faults of the SI metric system), and above all one that is dozenal.
Enter TGM
TGM is not random, like customary-imperial; it wants to base itself upon something and consistently derive its units from that. It also wants that something to be present and familiar to its users, not arbitrary and unfamiliar like the basis for SI metric. And above all, it wants to be consistently dozenal.
This overview of TGM can be broken into two parts: first, how we write and talk about TGM; and second, TGM itself.
Writing Units
SI metric is legendary for its conglomeration of strange prefixes. Everything from "deka" for the base unit multiplied by ten, to "kilo" for the base unit multiplied by a thousand, to "yotta" for the base unit multiplied by X20, are provided by SI. Yet these prefixes, while sometimes being based in Greek or Latin roots, aren't always easy to remember or read, as witnessed by the fact that some (such as "deka" and "hecta") are rarely if ever used, despite being low multiples that one would expect to encounter frequently. TGM can offer a better way.
All of SDN's words can be affixed to TGM units without change in order to express multiples. Let's use the unit "second," which is not a TGM unit, as an example. To refer to twelve times one second, we simply say "unquaSecond," the same way that we say "unqua" when we refer to twelve. To refer to one biqua seconds, we can say "biquaSeconds," and to two biqua seconds, we can say "two biquaSeconds." If we're dealing with very short times, we could also say "two biciaSeconds."
We are thus using the very same words that we use for counting as prefixes for the multiples of our units, rather than devising an entirely different set of more or less arbitrary prefixes which must be remembered anew. This is not, strictly speaking, TGM; but it is an immense improvement on the current way of doing things.
One will notice that, when adding these prefixes to units, the unit "second" was always capitalized. This is another convention in TGM, in order to keep the unit and the prefix clearly separated. This makes it perfectly clear that we're dealing with multiples of a unit rather than new units; there can be no mistakes or confusing base units like SI metric's "kilogram."
TGM units all begin, therefore, with a capital letter, and they all have canonical abbreviations that also begin with a capital letter. One such unit is the Tim, for example, the abbreviation of which is "Tm." This makes the capitalization convention, an enormous improvement in itself, completely effortless, which is itself another improvement.
The last improvement in notation introduced by TGM is the numeric system of indicating multiples. We use words, of course, when we're talking about units; we'll say "biquaSeconds" for 100 (decimal 144) seconds. However, this gets rather wordy when we're writing them down, particularly when we're writing them in equations. SI solves this problem by providing canonical abbreviations for its prefixes; e.g., "kg" for "kilogram" (this despite the fact that the kilogram is supposedly the base unit, yet has a prefix meaning "times a thousand). However, this potentially causes confusion; what if some unit were abbreviated "kg"? Also, it's difficult to read quickly; one must translate the leading "k" into "X3," which can be done but which is harder than necessary. Essentially, SI represents numeric facts alphabetically, a complication we can all do without.
TGM expresses numeric facts numerically; in other words, by using numbers. A leading superscripted number indicates a positive power of the unit; a leading subscripted number indicates a negative power. So, using the Tim as an example, "2Tm" means biquaTim, while "2Tm" means biciaTim. When working in text, one can use the traditional notation for superscripting and subscripting: "2^Tm" or "^2Tm" for biquaTim, "2_Tm" or "_2Tm" for biciaTim.
These improvements reviewed, we can now consider the TGM system itself.
The TGM System
TGM stands for "Tim, Grafut, Maz," the three most basic units of the system, which are the units for time, length, and mass respectively. TGM maintains an exact 1:1 relationship between its basic units, the only exceptions being in the transition to electrical unit and light units, where a 1:1 relationship is not desirable. While most measurement systems begin with the unit of length, TGM begins with the unit for time, the Tim.
Time
The most basic unit of time, for all of us, is the day.
It's the day that governs our habits, the cycles of our
bodies, and the activities of our lives. Other units of
time, like the week and the month, are important; but these
are primarily important in terms of the number of days they
are. And shorter units, like the hours and the minute, are
chiefly important due to the number of them in the day.
TGM, then, takes the day (specifically, the mean solar day)
as the basis of its system.
This day, imagined as a large circle, is then divided into
two, exactly as it is now; and each half of the day is
divided into twelve equal parts, exactly as it is now. This
give us two unqua hours (20
hours; decimal 24 hours). Further subdividing the hour into
divisions of twelve gives us unciaHours (units of five
minutes long), biciaHours (units of twoqua one (21) seconds
long), triciaHours (units of 2;1 seconds long), and finally
quadciaHours (units 0;21 seconds long). This unit, one
quadciaHour, a little more than a sixth of a second, was
found to be the most convenient unit to serve as the basis
for the system. It was therefore made the fundamental unit
of time, and given the name Tim, abbreviated "Tm."
Space
Once the Tim is defined, we are ready to define our unit of length: the Gravity Foot, or Grafut. The fundamental reality on which TGM's units of space is based is the mean pull of gravity on the surface of Earth. This, again, is something which is ever-present and ever-familiar to us.
If we assume that our unit of time is the Tim, and that our unit of distance is called the Grafut, then the unit for acceleration (and thus for the pull of gravity) will be Grafut per Tim per Tim, or Gf/Tm2. If we set the acceleration of gravity equal to 1 Gf/Tm2 (in SI metric it is about 9.8 m/s2, and in customary-imperial it is about 32.2 ft/s2), then the length of the Grafut is a little bit shorter than the normal English foot. This gives us, then, the Gravity Foot, or Grafut:
From the Grafut we can derive our units of speed or velocity, the Vlos; and our unit of acceleration, the Gee:
Gee (G) = Gf/Tm2 = 28;2280 ft/s2 = 9;9879 m/s2 = mean acceleration of gravity
From the Grafut we can also derive our unit of area, the Surf, and our unit of volume, the Volm:
Volm (Vm) = Gf3 = 0;XE56 ft3 = 0;0388 m3
Mass, Weight, and Density
TGM also derives its units of mass, weight, and density from the Grafut. "Mass" is the amount of matter which an object contains; "weight" is the pull of gravity on a given object; and "density" is how tightly packed the object's mass is in a given volume. The unit of mass is the Maz:
In the traditional manner, this is defined in terms of the mass of water, the most common and necessary substance for human life. Specifically, the Maz is the mass of 1 Volm of air-free water a pressure of one standard atmosphere and at the temperature of maximal density. And based on that, we can define our unit of density, the Denz:
This brings us to our unit of force, or weight, which is really the same thing. Weight is simply the force with which gravity pulls on a given mass, so the unit of force is the same as the unit for weight (but not necessarily the same as the unit for mass; in TGM these have a 1:1 correspondence, but in the two traditional systems they do not). The unit of force is the Mag:
The customary-imperial and SI system's confusion of mass and weight results in the different units here. Both systems have two series of force units: the basic units (poundals and newtons) and the mass-based units (pounds-force, lbf; and kilogram-force, kgf). TGM has no such confusion; mass is mass, and weight is weight.
Related to force is pressure or stress, which is force per unit area. The TGM unit of pressure is the Prem; there is also the TGM standard atmosphere, slightly different from the SI standard atmosphere, the Atmoz:
Atmoz (Atz) = 2E Pm = 1;0033 atm
The TGM standard atmosphere is well within the worldwide averages for actual atmospheric pressure; it is slightly different from the SI standard atmosphere so that it will equal precisely 2E Prem.
Work and Energy
Work is force over distance; or, in TGM terms, it is Mags over Grafut. Maintaining the 1:1 correspondence of all TGM units, the unit for work or energy is the Werg:
Heat and Temperature
Scientists draw distinctions between these two things, but for our purposes we may consider them the same. Heat is just energy applied by anything other than work done. It so happens that raising one Maz of water from freezing to boiling requires 6E7;7 biquaWergs (2Wg), assuming a pressure of 1 Atz (2E Pm); deriving from this, one Werg of energy raises one Volm of water through a certain range of heat, which we will name the Calg:
The Calg is, obviously, a very small unit of heat; and it so happens that a biquaCalg is so close to 0.1 K that TGM sets the two as being exactly equal, which makes conversion of data very easy. We work much more often with biquaCalg and triquaCalg than with Calg; these two are given the name decigree and tregree respectively, for conveniences sake, but that are really simply 2Cg and 3Cg.
Conclusion
We have not gone through the whole of TGM in this brief summary of some of the most important parts of the system; this document is meant merely to whet the appetite, to show the reader how beautiful and harmonious a truly consistent dozenal system of measurement can be. For more information on the system, explore more of this site.