Positional tolerance is becoming the darling of surveyors searching for an acceptable alternative to traverse "precision" tables for boundary surveys. While not new, the notion is gaining popularity for three reasons: a growing dissatisfaction with traditional "ratio of error" type expressions, the increasing availability of alternative measurement systems—GPS for example—which do not lend themselves to methods anticipated by the old tables, and the proliferation of "least squares" analysis programs capable of determining the reliability of any position, given the potential sources of error.

Positional tolerance has been defined in several ways by different organizations, but all use it to express the maximum likely distance from the computed position of a point to the "true" position of the point. It is usually expressed as either a circular or elliptical value, and it attempts to account for the likely sources of error in the survey. Thus, a location with such an expression attached to it also conveys the reliability of the position. The clear advantage of the idea is that the methods used to achieve the tolerance are irrelevant. Many types of surveys, such as control and topographic surveys, would benefit from positional tolerance specifications. Boundary surveys, however, do not fit the positional tolerance equation.

Specified Positional Tolerance
On the surface, a specified positional tolerance for boundary surveys seems to benefit both client and surveyor. The client receives a product with a tolerance that can be readily understood, and the surveyor maintains the flexibility to decide how best to achieve the tolerance in the most cost-effective manner. In addition, third parties reviewing the survey would have a clear understanding of the reliability of the work. After all, every survey contains error, and it is only fair to the client to state the reliability of the positions that are being rendered. A plat would thus contain a note similar to the following: "Boundary corners shown hereon are accurate to within 0.04 feet of the true boundary corner."

Presumably, the surveyor would compute the positional tolerance of the corners based on the precision of his or her instruments and based on the closure of the control established during the survey. The process of determining the positional tolerance is purely a mathematical one, and several available programs do an excellent job at the necessary computations.

Yet, is a boundary survey purely mathematical? Do control loops and precise instrumentation comprise the information needed by the client in a boundary retracement survey? They contribute to the work, of course, but they are the means to an end, not the end itself. The silence of evidence in the positional tolerance equation is deafening. Where is the sufficiency (or insufficiency) of the evidence used or considered in the boundary analysis factored in? It is not, and never could be.

Some years ago, the United Nations became immersed in controversy when some of its policies inadvertently angered the environmental community. While estimating the assets of countries for the System of National Accounts, damage to natural and environmental resources (something not easily measured) was ignored, while the cost of environmental cleanup (since it can be easily measured) was included as a liability. In the balance sheet for the country then, cleaning up the environment resulted in fewer assets than destroying it. Environmentalists howled that the United Nations thus appeared to suggest that destroying the environment was in a country's best interest. Is a clean environment really worth nothing? Of course not. However, its value is impossible to quantify.

Similarly, one of the regional Bell telephone companies recently declared that henceforth it would evaluate all of its consultants using three factors: quality, timeliness and cost. Each would be given equal weight. Timeliness is easy to measure, as is cost. But how does one measure the quality of a consultant's services? The employees charged with determining the quality of the work have no idea how to go about the task. Therefore, quality is assumed as equal among all the consultants—effectively removing it from the equation.

Omitted from Equation
These examples illustrate that, unless one can attach a number to something, that something must be omitted from any equation—or valued at zero. Accountants, who have been confronted with this problem for centuries, routinely ignore factors impossible to quantify. How much is "being your own boss" worth? No business owner would say zero, but try finding the item on a firm's balance sheet! It simply cannot be measured, and is therefore omitted.

In the same manner, evidence—both its discovery and its subsequent evaluation—must be valued at zero in the positional tolerance equation. No one will be able to determine any sensible value for it. Would that reflect its importance? Hardly.

Those among our brethren who are more mathematicians than evaluators of evidence—and let us not deceive ourselves, there are many of them among our ranks—do not understand the value of evidence. Since measurements are easier to describe (and defend), many surveyors prefer to focus on that aspect of retracement and minimize—either consciously or unconsciously—the impact of evidence. While measurements are essential, they are no longer the primary demons contributing to the error of most retracements. The primary errors now stem either from the failure to discover sufficient evidence of the boundary or from the incorrect evaluation of the evidence that is found.

The likely impact of evidence errors now dwarfs that of measurement errors (blunders excepted). For instance, not honoring a stone, incorrectly, could displace the "measured" corner two feet from the "true" corner. In contrast, an adjusted value with a positional tolerance of two feet must be the result of either one of two things: a project of colossal proportions or a grossly sloppy set of measurements. I suggest the possibility of not honoring that stone is far higher than the possibility of having two feet of measurement error. If the plat contained a positional tolerance statement, it would focus wholly on the measurement error, thus misleading the reader into thinking the survey was more accurate than it really was.

Some will probably argue that a positional tolerance should be reported, even if only applicable to the mathematical components of a survey. For example, the tolerance would apply only to the "determined" corner and not to the "true" boundary corner, which could be determined through a complete, proper evaluation of all the evidence contributing to the corner location.

Yet, who would be interested in that? Such a statement would be worse than no statement at all; it leads to a potentially false conclusion of reliability. Consider this: a surveyor could ignore every scrap of evidence on the ground and could fail to discover essential written evidence at the courthouse and at various other places, and if he or she uses very precise instruments and techniques to locate his incorrect corners, he or she could truthfully state that the corners had a positional tolerance of, say, 0.04 feet (or perhaps even 0.01 feet). Who would be served by this? Certainly not the landowner.

Map With Extremely Limited Value
This would be similar to taking insufficient measurements in a topographic survey to depict the terrain accurately, even though a very precise instrument was used. While the surveyor might truthfully be able to certify as to the positional accuracy of the actual points shown, he or she could not truthfully certify that the terrain was as shown. Such a map would have extremely limited value.

I am not suggesting that the old ratio of error statements are flawless, or that they should be venerated in any way. I merely point out that in this mad rush to develop alternative expressions of precision, accuracy (or closeness to the truth) may be forgotten.

I am afraid that this is yet another example of surveyors missing the point. In fact, this push for positional tolerance, and the ignoring of evidence in the process, may say more about surveyors than anything else. Apparently, the old saying "the more things change, the more they stay the same" is true. Hundreds of years ago, the courts concluded that the mathematical expressions on surveyors' plats were not to be trusted; things that could be seen and touched were of greater certainty than abstract things like measurements. which were prone to error. Those decisions are enough to deflate any surveyor's ego. The courts were correct then, and we threaten to provide them with more evidence of their correctness now.