For two millennia, brilliant minds have been trying to find a logical system of measuring the world that everyone can agree upon. The stubborn persistence of yards, gallons and pounds in a world that mostly works in meters, liters and grams suggests how deep the disagreement has been.

While this doesn't bother British architect Robert Tavernor, it does fascinate him. In ''Smoot's Ear,'' he offers a brief history of humanity's effort to measure the world by scientific principle, even as science itself has changed our knowledge.

Over the centuries, the search for a rational basis of measurement moved outward from the human body and its component parts, including the foot and the hand, to the distances of the known world, notably the curvature of the planet.

The discovery that Earth isn't a perfect sphere made it impossible to use the globe as an unerring standard of measure. Then for more centuries scientists and other savants fixed on the pendulum's consistent swing as the source of a scheme to measure.

Finally, in the late 18th century, a radical idea came to the fore. It accepted the arbitrariness and fallibility of any measure and embraced a convention of sheer convenience. The 20th- century artist Marcel Duchamp gave it the charming name of ''canned chance.'' We know this as the metric system.

Tavernor's fact-charged and occasionally dense narrative delves into the physics, mathematics and anthropology of the debate, as well as the national politics that have ruled it.

Dueling Meridians

The British and the French, for example, struggled to codify a standard of terrestrial curvature based on a global meridian through their capital cities. The British won the battle of the meridian for purposes of telling time; the French prevailed in conceiving the system that today governs -- by law and custom -- every country except the U.S., Liberia and Myanmar.

The triumph of the metric system is, considering the anarchy that it replaced, no less impressive than the acceptance of English as the world language. Yet Tavernor asks us to appreciate what's behind the Babel of measurements.

The Enlightenment argument, in essence, was between those who saw numbers as sheer abstract quantities and those who favored numbers with human qualities. The author, who teaches architecture and urban design at the London School of Economics and Political Science, places himself in the latter camp.

''Metric truths are measures -- human conceptions --stripped bare by reason,'' he writes. ''Our bodies require a positive relation with the natural world, and measuring the world with and through our bodies is essential to civilized -- human -- existence.''

MIT Frat Brother

Tavernor goes on to praise the U.S. for its anti-metric ''obstinacy'' and to celebrate Duchamp's equally obstinate suspicion about ''pseudo-purposeful superficial lines drawn over the deeper conventions of form, culture and meaning.''

And Smoot's Ear? The title refers to one Oliver R. Smoot and a gentle hazing two generations ago.

As the shortest freshman in his fraternity at the Massachusetts Institute of Technology, Smoot was selected by his fellow classmates in the autumn of 1958 to embody a new standard of measure, the smoot. Using his body as a ruler, his fraternity brothers carried him, smoot by smoot, across Harvard Bridge to determine its length: 364.4 smoots and one ear. There's a plaque to this effect on the bridge today.

''Smoot's Ear: The Measure of Humanity'' is published by Yale (249 pages, $25.00, 18.99 pounds).