TGM units of measurement (note: unfamiliar notation used)

The units of measurement of the SI (System International) are commonly used around the world ·· they form a coherent system usable for a variety of branches of science.

But.. there's another coherent metric system that may be a better fit for many applications in chemistry and physics. The base units are defined in a way to eliminate much of the arbitrariness that is present in the SI and many other systems of measurement by using physical realities that we experience on a consistent basis. Also, unlike SI, this system uses base twelve for orders of magnitude rather than base ten of SI. The notation used here is probably unfamiliar to most, so I made notes to briefly explain the notation. Basically, a number shown with an asterisk '*' or a semicolon ';' or TGM unit is dozenal. The full stop '.' or a SI unit marks a decimal number.

Please note, I did not invent any of the names given below. The TGM system was devised many years ago by a member of the Dozenal Society of Great Britain, Tom Pendlebury. He claims no credit for this devision, stating that it arises from properties of nature that we experience constantly.

The first unit to be defined is that of time. The 'T' in 'TGM' stands for 'Tim', the unit of time. Each cycle day and night is two dozen hours in length; divide an hour by a dozen, the result is five minutes. Divide again by a dozen and we have a length of time about 25 seconds long. The fourth dozenal division of the hour has a special name; it is known as the 'Tim'. This is a bit longer than one-sixth of a second of the SI and is the base unit of time for the TGM system. As a result, one hour is *10000 Tim (decimal, 20736) that is, a dozen to the fourth power of 'Tim'. The mean solar day, the ''first reality of TGM'', is therefore *20'0000 Tim. (In decimal, that's 497'664) In terms of the SI second, the 'Tim' is about 0.176311 s

Next, the unit of length ·· The Earth's gravitational acceleration isn't constant but the variation is small enough that it is generally perceived to be constant. By setting a mid-latitude value for g as the unit of acceleration, the units of velocity and length can be derived. g is around 9.8 m/s^2; given the value of the Tim stated above, the unit of velocity is about 1.7 m/s and the unit of length about 29 to 30 cm. This length is the ''Gravity foot'' or 'Grafut', the 'G' of 'TGM'. Ergo the gravitational acceleration is one Grafut per Tim squared, a nice convenient value to remember whenever the Earth's gravity is involved! This has the neat property that mass and weight of an object have roughly the same number in TGM units. But to define a unit of mass without the use of a specific object, one way to do it is to use the density of a well known material alongside the Grafut.

That material is pure, distilled water in the case of the 'Maz', the 'M' in 'TGM'. Pure water has a maximum density about 999.972 grams per Litre under standard pressure. The density changes little with pressure so the temperature can be set so that the density of water is greatest. This is the standard density of TGM, one Maz per Grafut cubed. This means the Maz is about 25 to 26 kilograms, quite massive compared to the objects often used in laboratory experiments. But we won't stop there... what about force? Work? Power? Pressure? And more? Well, as mentioned before, the standard gravitational acceleration is one Grafut per Tim per Tim, so how much does one Maz of something weigh? The answer is, of course, one 'Mag' (~250 N), the unit of force. A person of 2;6 Maz (this is two and six parts per dozen, or two and a half ·· about 63~65 kg) weights 2;6 Mag (~630 N). See that the 'Maz' and 'Mag' numbers are the same? How useful is that, at least at this coarse level of precision?

Force carried over a distance is work, so for example, I push a box with a force of 0;16 Mag (31~32 N) across 9;0 Grafut (2.6~2.7 m). The work done is 0;16·9;0 Mag·Grafut = 1;16 Werg (~84 J). One 'Werg' is about 75 Joule, not so bad idea given that the joule is in many cases quite small for a unit of energy. One Werg per Tim is one 'Pov' the unit of power, about 430 Watt.

Pressure is force per unit area. 'Prem' is Mag per Grafut squared, *2E Prem is the standard atmospheric pressure. (I can't type an inverted '3' for the digit eleven so I use 'E' as substitute) That is, two dozen eleven Prem to the TGM standard atmosphere, which in decimal SI is 35·2900 Pa ~= 101 kPa.

So that's the basic explanation of TGM in terms of elementary physics. Each base unit has a physical basis, i.e. mean solar day, gravitational acceleration and density of water. The SI based the second on one part in 86'400 of the mean solar day, a strange number for a mostly decimal system. The metre was at one time based on one part in 10^7 of the equator-pole distance, too difficult to conceptualize! And the kilogram already has the prefix for thousand, yet it is based on the mass of one-thousandth of a cubic metre of water! TGM has none of that 'strangeness': the relation between the Tim and half a day-night cycle is strictly dozenal, no irregularity at all. The Grafut is the distance based on the Tim and the Earth's gravitational acceleration, easy to see how it works with a simple experiment! And the Maz has no prefix, it's based on the mass of one cubic Grafut of air-free distilled water, no prefactor there! So anyone think that TGM may serve as alternative to SI?

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