Time, Gravity and Mass

a review by Arthur Whillock

The publication of TGM brings to fruition Tom Pendlebury's Herculean task of compiling a completely coherent dozenal system of metrology encompassing all aspects of science and technology, yet which is compatible with the measures, and their arrangements, appropriate to everyday experience and use. This is a conjunction singularly lacking in any proposal so far.

Measuring systems established in the past arose out of the real needs of their times and invariably started with a unit of length taken from familiar natural objects such as grains of corn or parts of the body. A length standard could then be reproduced by anyone, with sufficient accuracy for laying-out plots for cultivation or building. It would have been acceptable to all concerned but was quite arbitrary for any higher use.

When the time came to consider wider applications for measurement the real implications of the nascent technical era were scarcely realised. It was hoped to bypass chauvinistic variations of previous methods by adopting an Earth-based length "pour tous les peoples, pour tous les temps" but the result was still a misfit for scientific purposes by not allowing the value of any important constant to become a whole number. Naturally-evolved measures - arranged as they were in divisible groups - were at least well-suited to our understanding and physical needs. Those founded on the metre, with strict obedience to an inflexible numbering scale, failed both the scientific and social requirements of elegance together with comprehension and utility.

In TGM an initial unit of length is still required, but it is derived by insisting that the most important and widely-used physical relationship on this planet - the acceleration due to its gravitational attraction (g) - should be represented as simply as possible, i.e. by unity. For the person who is 'non-technical' there can thus be no numerical distinction between weight and mass, and the inclusion or omission of the constant, g, in dynamic calculations involving forces and the movement of masses becomes unimportant. Within a small unit of time - the Tim - being the hour divided by twelve to the fourth power (just over a sixth of a second), the acceleration under an average value for g will be a little less than a foot per Tim per Tim. This length then becomes the fundamental unit for the system and is known appropriately as the Gravity Foot, or Grafut. With this, TGM has a practical and efficient spatial measure which, for good reason, appears in all national measures in one form or another.

Coincidentally, the Gratut is very close to the original Roman foot of *E·72 inches which in turn was based on sixteen Egyptian digits. Pendlebury modestly disclaims any credit for its discovery, saying that it comes to light when dealing with natural phenomena. Perhaps the Ancients were wiser than they knew!

With a length unit thus obtained, a volume is defined and its mass of pure water at maximum density becomes the unit of mass. The Maz is precisely one cubic Grafut, whereas a small error in constructing the initial decilitre cube means that metric weighs were, and still are, not exactly related to volumes obtained from the length unit: the kilogramme is a little more massive than intended. Mechanical, physical, electro-magnetic, chemical and astronomical data are all restructured into TGM with strict coherence maintained in dozens between units for scientific work. There is, however, good correspondence with familiar, practical measures - either directly or as auxiliary units - by virtue of the divisible arithmetic base which allows a branching-off at useful levels.

Doubing-up and halving-down are perhaps the commonest arithmetical operations we do and there are many ways of expressing them, from book sizes to musical notation. In TGM, logarithms to base two in dozenal notation provide a unique means for handling all ordinary ratios with a simplicity not found in other methods. Each chapter has interesting and sometimes refreshing comments on its subject-matter. Some will say that these are too simplistic, but it is difficult to decide on a level for wide appeal when presenting novel ideas. Students will be enlightened, especially as comparisons are made with Imperial and Metric methods. Those who know should not eschew different viewpoints which may help to transmit understanding to those less fortunate.

A minor disappointment is that is that the Grafut does not quite coincide with the slightly longer metric foot of 30cm which, with its twelve 25mm "inches", is in common use in all but name. Even with points of contact it is not expected that TGM will be welcomed by science and industry to solve their problems, in view of the commitment to the present rival systems. It is offered by its author for the dozenist to use as appropriate and to demonstrate the value of a dozenal approach in all fields of enquiry. If the effort expended on developing an international measurement system had worked with more socially- acceptable material, we might now be in possession of an arrangement that would not only clarify scientific thought but forge links between all classes of use in lieu of the barrier that the decimal-metric method so often becomes; but, as Professor Aitken observed, "It is very early in the history of the world...... anything that is inefficient, even relatively so, will not last for ever."