Surveying as a Liberal Art

Several years ago, I wrote an article on the art of surveying. At least one reader took issue with the notion, while others instinctively took to it. In this article I want to show that surveying encompasses the liberal arts taught in medieval universities—and further discombobulate those who suppose me to be an enemy of academics.


Etymological Observations
"Art" is the Latin word for any activity that requires manual skill. It is the substitute for the Greek word techne. This word is evidently the root of "technology," but it doesn't mean the same. Techne is any activity that requires the use of tools or instruments, while technology is the design of these instruments by the application of (modern) science. "Technical" is essentially synonymous with "mechanical."

That is the sense it still has in the name of some of our state universities, such as Texas A & M. These universities were founded to teach the agricultural and mechanical skills needed by society. While other institutions of higher learning, such as Harvard, were founded to replenish the ministry, these had a decidedly practical purpose. Although their model was not the medieval university, they propagated some of its courses.

The arts, then as now, were distinguished from the sciences. Only back then the sciences (-ologies) we know today didn't exist, and the sciences developed in ancient Greece were largely lost (Euclid's work on geometry, for instance, was not translated into English until 1570). What passed for science was erudite argumentation.

|The arts flourished, both the useful and the liberal. The useful arts consisted of the skills employed in satisfying the basic needs of life and the wants of a tasteful life (trades). The liberal arts were the skills practiced by those whose needs and wants were already taken care of, mostly the nobility. They had the time to engage in public affairs, for which the study of the liberal arts prepared them.

Trivium and Quadrivium
The trivium ("threefold way") included grammar, rhetoric, and logic. "Trivial" comes from this word, which indicates the disrepute into which the trivium fell at some point. Now, it is being resurrected as "communication." Surveyors, it has been realized, must be able to write and speak well. They must be able to write good business letters and reports, and speak properly to clients, professionals, government officials, and the agents of the law in and out of court. They must also be able to think a survey through, as if making an argument for its correctness.
The quadrivium ("fourfold way") included arithmetic, geometry, music, and astronomy.

Arithmetic and geometry are theoretical subjects, music and astronomy their applications.
Actually, the quadrivium has only one subject, quantity, that comes in two forms, discrete quantity or numbers and continuous quantity or figures. (Consult Ben Buckner's series of articles about the difference of the two quantities.) Arithmetic can be broadened to include algebra (the rules of arithmetic extended to unknown numbers represented by letters), as well as statistics (the analysis of masses of numerical data). Geometry has by now been further developed into analytic geometry (the basis of the grid system of plane surveying) and various non-Euclidean geometries (notably, the spherical geometry underlying geodetic surveying). If we also include calculus, we have all the math necessary for even the most advanced adjustment computations.

What about their applications? Music? Remember music has tempo—a one and a two—and those notes have a numerical relation that manifests itself in scales and chords. Astronomy? The constellations, the movement of the planets, eclipses, and all the other celestial phenomena have intrigued mankind from the beginning, and "astrometry" surely preceded geometry (the Great Pyramid and Stonehenge apparently served as astronomical observatories). Of course, these were not their only applications. Commerce in the middle ages was brisk and required accounting. Construction in peace time and destruction in war time required measurements of land and buildings.

To teach these measurements—one-, two-, and three-dimensional—there appeared a slew of texts on "practical geometry." The earliest texts collated material already known to the Roman agrimensores. The later ones included the rediscovered work of Euclid and inventions of Arab mathematicians. These texts set the stage for an overhaul of astronomy (from the geocentric to heliocentric theory) during the Renaissance, and the rise of modern science thereafter (Newton, explaining both the fall of an apple from a tree and the rotation of planets around the sun by the law of gravity).

Land measuring also grew by leaps. The astrolabe gave way to the theodolite, ropes to chains, cumbersome calculations to logarithms. It takes little imagination to fill in the steps that lead to the present, although the recent speed of the development may strain it (but still less than the attempt to impress on us the rate and the inevitability of the developments with that outdated symbol of progress, the onrushing train!)

These developments have given the teaching of surveying a new dominance. But what do we gain by thinking of it as an updated version of the liberal arts? That its impetus is technical, rather than theoretical. The "geometry" is already centuries old; only the "astronomy" is new.
The stars of this astronomy, of course, are the satellites of the global positioning system. Before it was put in place, geodetic surveying relied on the instruments and procedures of plane surveying—to the extent of establishing state plane coordinate systems. Now, the reverse is true: plane surveying is subsumed into geodetic surveying. The system is revolutionary for surveying.

The "stars" of surveying, it goes without saying, are those who know the theory and its application. For most of us, the application of the mathematics is mechanical. All we really need is the proper training. But we cannot claim to be professionals, if we do not know the math at all. Besides, we won't pass the exam!

About the Author

  • Wilhelm A. Schmidt, PLS
    Wilhelm A. Schmidt, PLS
    Wilhelm Schmidt is the former owner of the surveying firm Bascom and Sieger in Allentown, Pennsylvania. You may contact him at

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