TITLE: The Measure of All Things AUTHOR: Eugene Wallingford DATE: October 07, 2006 10:34 AM DESC: ----- BODY:

The truth belongs to everyone,
but error is ours alone.

-- Ken Alder, The Measure of All Things

On my trip to the Twin Cities last weekend, I had the good fortune to listen to Ken Alder's entertaining The Measure of All Things on tape. Alder tells the story of the Meridian Project, revolutionary France's effort to define the meter -- the Base du Systeme Metrique, the foundation of the metric system -- in terms of the distance between between the North Pole and the equator. Before happening upon this book, I knew nothing of this project or the scientists involved, and less about the political history of the era than I should have known. In the Meridian Project, two of the finest astronomers of the day set out to measure the line of longitude that runs from Dunkirk on the northern coast of France to Barcelona on the northeast corner of Spain. They used the technique of triangulation, wherein they measured all of the angles in a sequence of coincident triangle running the length of the line and then used the length of a single side to compute the length of the target line. I was surprised by both the quality of the tools and techniques available to 18th century scientists and the fortitude with which they overcame the practical obstacles that stood in their way. Those of us who do science in the 21st century -- and all of us, who enjoy the benefits of science and technology every day -- really do owe a great debt to the men and women who laid our scientific foundation. This was the Golden Age of geodesy, the art of measuring the Earth. The Meridian Project captured public and political interest. Scientists made trips to places as remote as Peru and Lappland in an effort to draw a more complete picture of the size and shape of the Earth. We are in an age of tremendous growth of computing; what is our signature project? What can capture -- or recapture -- the public's real interest? We in the sciences talk a lot about the Human Genome Project, but I don't think that this will ever have universal appeal outside the sciences. Digital media are now woven inextricably into our lives, but so deeply that few people think twice about them as anything special any more. Perhaps the key technical point in the Meridian Project story involves error. Mechain and Delambre, the protagonists of the story, used a repeating circle to take their angle measurements. This tool was designed to help users reduce small observational errors by taking repeated observations, amalgamating the results, and computing the actual value from the amalgamation. This made small values that were otherwise imperceptible to the human observer appear manifold, where they were observable as a group. (Anyone who has tried to time a lightning-fast computer operation is familiar with the CS analog of this technique: write a loop to do the operation a million times, and then divide by a million. Values that would otherwise show up as a 0 on your timer are now computable!) In the course of his measurements in the north of Spain, Mechain encountered a discrepancy between two readings -- and panicked. He didn't want anyone to know about the error, lest it reflect badly on his skill, so he conducted an elaborate cover-up, one that did not alter the ultimate calculation of the length of the meter. Both Delambre and Alder marvel at Mechain's artistry in doctoring his data. However, if Mechain had understood that there are different kinds of error, he may not have worried so much about the discrepancy in his data, or the potential effect on his reputation for exactitude. For, while the repeating circle's multiple readings helped to increase the precision of his results, they did nothing to increase their accuracy, and in fact made his results less accurate. A technique can produce internal consistency without veridicality, and vice versa.

We live on a fallen planet,
and there is no way back to Eden.

-- Jean-Baptiste-Joseph Delambre

In writing up the results of the Meridian Project for publication, Delambre came to appreciate Mechain's dilemma and was quite generous in his treatment of Mechain's error, by keeping the cover-up out of plain sight. Delambre never did anything to impugn the integrity of the study, but by writing with care he was able to preserve Mechain's contribution to the project, and his public reputation. Delambre's work in the decades following the project are a fine example of a scientist acting honorably, with respect for both truth and his fellow man. At the time of the Meridian Project, many scientists thought that error could be handled in a purely rational way, through perfection of tools and techniques. Today we have formalized much of our way of handling error in a social process within the community of scientists. Peer review and open discussion of results are central components in this process. Consider Andrew Wiles's proposed proof of Fermat's Last Theorem. In many ways, our open scientific culture owes much to the democratic revolutions in America and Europe around the time of this project. Another interesting thread running through Alder's book is the story of how definitions and standards are adoption. The US has been discussing the metric system since it was merely a proposal in the French Academy of Science, in our pre-revolutionary days. Indeed, the U.S. Constitution grants Congress the authority to establish national standards of weights and measures, as essential to interstate commerce and the smooth functioning of a national economy. But codifying the metric system ahead of its widespread adoption is in some ways antithetical to democracy, whose primacy was much on the minds of our Founding Fathers. As Benjamin Franklin asked of John Quincy Adams, "Shall we shape the people to the law, or the law to the people?" I see this conflict in many elements of my professional, from trying to set departmental policy as department header, to defining curriculum as a faculty member, to selecting and refining a software methodology as a developer!

Men will always prefer
a worse way of knowing to
a better way of learning.

-- Jean-Jacques Rousseau

Alder writes that, "Science likes to think itself the one human endeavor free of idolatry." But his story, like any complete recount of a real scientific project, points out the many ways in which scientists and their processes elevate some ideas to the status of dogma, both locally within our own programs and globally within the paradigm that dominates science of our time. We have to be on the look-out for these blind spots in our vision. Often, they hide errors in our thinking; sometimes, they hide opportunities to advance our science in a big way.

You're not the only one who's made mistakes
But they're the only thing that you can truly call your own

-- Billy Joel, You're Only Human (Second Wind)

The Meridian Project began in an attempt to anchor "the measure of all things" -- the meter -- to something unassailable in the external world, the size of the Earth. But along the way they helped us to learn the many ways in which the external world is imperfect to this end: the design of our tools, the use of these tools, the setting on approximations in the absence of complete knowledge, the refining of definitions in face of new knowledge and technology, an adoption of standards that is driven by political and social needs, .... Ultimately, the project only reinforced what Protagoras had taught 2500 years ago, that man is the measure of all things. -----