TITLE: The Measure of All Things
AUTHOR: Eugene Wallingford
DATE: October 07, 2006 10:34 AM
DESC: 
-----
BODY:
<P ALIGN="right">
   <EM>The truth belongs to everyone, <BR/>
   but error is ours alone. <BR/><BR/>
   -- Ken Alder, The Measure of All Things</EM> </P>

On my trip to the Twin Cities
<A HREF="http://www.cs.uni.edu/~wallingf/blog/archives/monthly/2006-10.html#e2006-10-01T19_54_32.htm">
   last weekend</A>,
I had the good fortune to listen to
<A HREF="http://www.kenalder.com/">
   Ken Alder</A>'s
entertaining
<A HREF="http://www.kenalder.com/measure.htm">
   The Measure of All Things</A>
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
<EM>triangulation</EM>, 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
<A HREF="http://en.wikipedia.org/wiki/Geodesy">
   geodesy</A>,
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
<A HREF="http://americanhistory.si.edu/collections/surveying/type.cfm?typeid=16">
   repeating circle</A>
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
<EM>kinds</EM> 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.

<P ALIGN="right">
   <EM>We live on a fallen planet, <BR/>
   and there is no way back to Eden. <BR/><BR/>
   -- Jean-Baptiste-Joseph Delambre</EM> </P>

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!

<P ALIGN="right">
   <EM>Men will always prefer <BR/>
   a worse way of knowing to <BR/>
   a better way of learning. <BR/><BR/>
   -- Jean-Jacques Rousseau</EM> </P>

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.

<P ALIGN="right">
   <EM>You're not the only one who's made mistakes <BR/>
   But they're the only thing that you can truly call your own <BR/><BR/>
   -- Billy Joel, You're Only Human (Second Wind)</EM> </P>

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.
-----