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October 1, 2004
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Are you using "junk math"?

In the early 1960s the term "junk food" was introduced. Items such as candy bars and sodas were the main examples. The term was expanded in later years to describe any type of fast food. The original application of this expression was to describe food that carried little or no benefit for the human body. The argument against junk food is this: you eat it and are full, but did it provide a balanced set of nutrients?

In the past 20 years, a new term has been introduced: "junk science." Similar to "junk food," the expression is used to refer to data reported or studies performed as if based on solid scientific research, but in reality they are filled with assumptions, innuendos and biases. One prominent example of junk science is the report that eggs are high in cholesterol, and therefore should be avoided. It turned out that the "study" quoted was so full of holes that few accepted its results. Later studies revealed that the egg's reputation was besmirched by this practice of junk science, but today major health groups encourage the eating of all the eggs one wants!

Many of us have been fooled by junk food, junk science and other forms of junk at some time in our lives. But I wonder if the professional surveyor has considered the possibility of being fooled by "junk math" in his daily operations. I think we do junk math every day because we're fooled by it.

At times, the onset of computers and other technologies have caused the surveying profession to lose sight of some basic mathematical principles. The fact that we can compute something to some degree of precision is often unrelated to the reality, necessity, or even the honesty of the data being used. I offer you four simple examples:

1. The record data for a property line in a deed and/or plat is "20 chains." Most of us will quickly convert this number to "1320.00 feet." Even if we do not do it ourselves, our COGO software will. We then find a monument claiming to be the corner at the other end of this line, but it is not at exactly that distance. (Frankly, I am usually suspicious of any line that measures exactly as the record.)

Now we must determine if the monument is an acceptable representation of that corner position. A growing percentage of our profession will not accept the monument, even if called for in the deed, if it is not at the exact record distance. This of course flies in the face of some of the most basic boundary law on the planet. Somehow these folks have decided that supposed precision is superior to boundary law.

Further, if the monument is not called for in the deed, and it is therefore subject to our review, many will still only accept it if it is exactly at the record distance. Others will improperly apply some state measurement standard to it, which is a completely erroneous application of measurement standards. Your standards are about your measurement capabilities, not the acceptance or rejection of evidence!

The problem with this entire picture is one of junk math. The assumption made by most of us, including our COGO software, is that 20 chains equals 1320.00 feet. It does not! Have we forgotten some basic math principles, like significant figures and/or rounding? Dropping the ".00" from 1320.00 does not solve this either. If the record is measured in chains and links, our recognition of the link being the smallest unit of reporting the measurement requires us to allow at least 0.33 feet in either direction as an absolute minimum of our acceptance strategy. In other words, if your measured distance is 1320.31 feet, you are not missing the point by 0.31 feet, you have hit it right on the nail! You might consider adopting this reasoning to bearings as well.

2. The advent of the EDM and GPS has brought many positive benefits to the precision and efficiency of our field operations. That being said, has junk math invaded our use of these everyday surveying tools? The belief by many that whatever the EDM displays is in fact the true distance is sadly mistaken. Increasingly, I find places where a second rebar was set 0.05' away from an existing one, simply because the existing one did not measure to the record. Yet, the measurement capabilities of the EDM itself were plus or minus more than that difference! I know surveyors who argue over a few hundredths, whose rods, tribrachs and other equipment have never been adjusted or checked. Some mix prisms of varying offsets as if they were all the same.

How precise are the measurements from your GPS unit? What factors could be affecting the inverse you get between two GPS-derived coordinates? Or do we treat that inverse as an absolute? Perhaps the comfort level of an LED-displayed measurement has muted our understanding of all the other sources of error. That qualifies as junk math.

3. The latitudinal curve is an issue on certain lines (primarily in the Public Lands Survey System) of which we must be concerned when setting lost corners. The formulae for such computations are found in various textbooks, as well as the BLM Manual. And while for certain situations it is an issue, I am amazed at those who are computing this "correction" for very short distances. Perhaps they do it "just because they can."

Similar to item No. 1 above, we need to get a grip on reality. If the record was reported to the nearest link, or the tables used in the GLO computations were rounded to the nearest link (which they were), we must realize that any adjustment for the curve for a line less than a mile long (in the lower 48 states) is simply junk math. In other words, there is no adjustment for the curve where the record would not have made that adjustment to begin with. You cannot do more precise computations in a resurvey than the record itself allows!

4. You are writing a legal description for a deed. The parcel has been carved out of a larger one, and your legal description software has provided the numerical data. Some in our profession do not recognize that the way we survey today provides no true closure. The legal description is generated from forced inverses between points. We assume, as does our software, that the parcel closes perfectly; there are no sources of error.

So now we produce a legal description with bearings to the second and distances to the hundredth of a foot. Is there anyone out there who honestly believes they can report this data to that level of precision? The ultimate junk math is an area quoted at the end of the legal description, shown to the 100,000th of an acre. And to add insult to injury, they add the words "more or less" to that precision, creating a junk math oxymoron.

Have you ever computed how much error in your survey is allowed when providing an area to that level of precision? But the computer spits it out, the plat and legal look good, the client pays the bill, and off we go into another recording of our own ignorance of basic math and reality. I call that junk math.

So just as the dieticians warn us about junk food, and just as many true scientists warn of "studies" that only confirm already defined biases, we professional surveyors must also recognize that junk math is both a testament and a warning of the ignorant arrogance that has gripped our profession.

While I would like to write more about this, I must attend to a very important matter. It seems another surveyor has disagreed with my position of a corner set from an 84-inch bearing tree. He did a detailed topo of the outline of the tree and computed a center point in his software. I just guessed the center of the tree like the GLO surveyor did on the then 22-inch tree in 1866. We are a whopping 0.24 feet different in corner position.

See what I mean?

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