TGM Space

From the unit of time we proceed to the units which govern space: length, area, volume, speed, and acceleration. With time, we selected a fundamental reality as the basis for our basic unit with which we are all intimately familiar: the mean solar day. For space, we select another fundamental reality: the acceleration of gravity.

Length

Accleration is the rate of change of the speed of an object over time; in other words, it's the unit of distance divided by the square of the unit of time. If we use the Tim as the unit of time, then gravity causes an accleration of just under a standard customary-imperial foot each Tim. The most useful upshot of this is that gravitational accleration (affectionately called "gee" even in modern systems) is equal to 1, which we will touch more on in a moment. For now, we'll simply note that this unit is made the basic length unit of TGM, and is called the Gravity Foot, Gravfoot, or Grafut.

Just less than a normal foot, about halfway between a third and a quarter of an SI meter. The Grafut yields a number of very convenient units, some of which can be seen below. Like the units of time, most of these units have acquired colloquial names, which will vary according to language; the canonical TGM and SDN name, of course, is constant across all languages.

On will note that the Gravpalm is in fact a quarter of a Grafut, and the Gravhand a third of a Grafut. Nor are these the only easy correspondences. The Grafut is almost precisely the length of one metric A4 sheet of paper; biciaGrafut are only slightly longer than two millimeters. For microbiologists, the hexciaGrafut is just under a tenth of a micrometer (micron). For printers and typesetters, two triciaGrafut is quite close to a traditional printer's point (which is itself quite close to a Postscript "big point"), and twelve of them (2 biciaGrafut) is more or less equal to a pica, six of which is equal to about one unciaGrafut. And for longer distances, the Gravmile and Gravkay are useful, of course; also useful is simply the quadquaGrafut, about 3;9874 miles, or 6;16XX kilometers.

Area and Volume

While in our current systems we bandy about terms like the "square foot" and the "cubic centimeter" (or "cc"), TGM offers unit names specifically for area and volume. (Metric once had a unit for volume, the liter; but it wasn't a 1:1 ratio, being a cubic decimeter, and it's not really equal to that, either. SI considers the unit deprecated.) In TGM, of course, one can easily speak about the square and cubic Grafut, as well; however, TGM also offers independent names for the units of area and volume.

The Surf is, obviously, a bit smaller than the square foot, and about an uncia (a twelfth) of a square meter. This means that an unquaSurf is about one and a quarter square yards (1;3082), and only a very little bit more than a square meter (1;070X).

The Volm is a uniquely useful unit of measure, and its multiples and divisors are likewise. The Volm itself, of course, is about an uncia (twelfth) less than a cubic foot, and lies about halfway between an imperial and a customary (U. S.) gallon. In metric terms, it's a bit less than twoqua-one (twenty-five) cubic decimeters, which is tolerably close to the same number of liters. The system gets still better, though, with an astonishing number of useful and convenient correspondences.

These correspondences should serve quite well during the transition from customary-imperial and SI systems to TGM. Subsequently, they may continue to be used, because they fit quite well into the dozenal TGM system; or perhaps other fractions of the Volm will become dominant.

Accleration and Velocity

We've already seen that we defined our unit of length by assuming that the acceleration due to gravity was equal to one. This is an extremely convenient assumption; the acceleration due to gravity occurs constantly in all sorts of calculations, and having it equal to one means that multiplying or dividing it wrongly, or forgetting to do either entirely, makes no difference to the result. Furthermore, it prevents having to grapple with the complex numbers which are the accleration of gravity in current system. Since this is the unit of accleration in TGM, it has its own name, the Gee:

Note that this is slightly different from our current idea of the "standard gravity" (9.80665 m/s²). This difference is because the acceleration due to gravity is actually quite variable, and within certain small limits we can choose the exact acceleration of gravity that we will consider "standard." TGM has selected one slightly higher than is currently considered standard.

So much for accleration. For speed or velocity, we have another unit:

The inventor of TGM, Tom Pendlebury, labelled this a "comfortable walking speed." Personally, I think this is a bit optimistic on his part, but it's still a convenient unit for gauging travelling time in both walking and motorized transport.

The image above shows a speedometer delineated in Vlos, in miles per hour, and in kilometers per hour. The advantages of using Vlos should be pretty clear. All normally vehicle speeds are easily contained within the first two dozen Vlos; yet walking speeds can easily be described in terms of Vlos or simple fractions thereof.

So much for the TGM units regarding space; we turn now to the units regarding matter: the units of mass, density, force, and pressure.