Formula for surveying measurements and...

I heartily agree, but I would point out further that True value merely equals Most Proabable value, since, as you say we are only taking out the observable corrections.

There will always be small errors present that defy detection.

Equally appicable to both life and surveying measurements.

Stephen

> T = R + C, where T = the "true" value, R = the reading, and C = the total of all observable corrections.

The history of the world is the history of statistical outliers.

Assuming that the number of "observable" corrections even begins to approximate the total number of "possible" corrections will lead you to equating the "truth" with the "probable" and that is an epistemologically arrogant recipe for disaster in any endeavor.

Yes, it's unfortunate, but the truth once discovered can never be exactly found again.

The entire paragraph:

The general formula for systematic errors is T = R + C, where T = the "true" value, R = the reading, and C = the total of all observable corrections. On the cover of my book, entitled Surveying Measurements and their Analysis, and on my seminar brochures for Surveyor's Educational Seminars, is the caption, "The truth is equal to one's initial observations plus the corrections discovered through added experience or knowledge." You see, error theory can be applied to affairs outside the world of measurement. A person often is far from possessing the truth of a perceived matter until that person is willing to get rid of biases or prejudices affecting such observation. As has been said, measurement theory is somewhat of a mirror of many things in life. Understanding these concepts helps a person to deal with life and its pitfalls.

The full article can be found at:

http://www.profsurv.com/magazine/article.aspx?i=163

Your theorem fails when you consider you can't actually measure ALL of the values, and that everything is a sample, thereby making N, N-1.

🙂

Could be that "observable" needs emphasis in this context. Systematic vs. random. Interesting that in his book, Buckner states the formula thus: Error = Reading - True Value. (p. 27)

> The general formula for systematic errors is T = R + C, where T = the "true" value, R = the reading, and C = the total of all observable corrections. On the cover of my book, entitled Surveying Measurements and their Analysis, and on my seminar brochures for Surveyor's Educational Seminars, is the caption, "The truth is equal to one's initial observations plus the corrections discovered through added experience or knowledge." You see, error theory can be applied to affairs outside the world of measurement. A person often is far from possessing the truth of a perceived matter until that person is willing to get rid of biases or prejudices affecting such observation. As has been said, measurement theory is somewhat of a mirror of many things in life. Understanding these concepts helps a person to deal with life and its pitfalls.

Thus rendering all the chatter in P&R irrelevant.

Remember too that there is more to a measurement than just the measurement. From part 6 in the series:

Any measurement has three values or numbers associated with it. That's right—not one, not two, but three. First is the estimate (all measurements are estimates) of the size of the quantity. Then, since a measurement is an estimate of a continuous (another statistical term) number, there must be some estimate of the range of error. This range of error is often called the "uncertainty," but more commonly simply the "error."

Next is the third dimension to a measurement—level of certainty. We see it in National Map Accuracy Standards, where it is stated that "90 percent of the well defined horizontal positions shown on the map shall be within 1/50 inch," and "90 percent of the elevations interpolated from the map shall be within 1/2 the contour interval." This is a statement saying we are 90 percent sure of our accuracy, within stated limits. Only nine out of 10 of the points tested would need to pass the test. One could fail and we would meet the standard. GPS standards are on the 95-percent confidence level, as regards the relative positional error between adjacent points. The 95-percent confidence level seems to be emerging as the favored level. Some instrument accuracies are cited by manufacturers at the 68-percent confidence level. You must know the level of confidence attached to any cited errors to properly interpret the accuracy or precision statement.

You would never know by looking at the CAD file generated by the survey data that these other elements are just as important. Lesson - Surveyor's notes need to remain with the design drawing.

A final summary of Buckner's summary in Part 12

Axiom #1: We are responsible for our mistakes.

Axiom #6: Absolute certainty is impossible in the real world. Certainty is delusion, whereas uncertainty is reality.

Surveyors with the science of measurement I believe hold the keys to help humanity not only with matters of land but also with most human efforts including: philosophy, faith, politics, and on and on. I apologize if I've made my own post into something beyond the category of Land Surveying, but in a sense it is not my fault. Buckner made me do it. 🙂

With this thread naturally being pushed down, I know few will read but I think all twelve articles should be stressed and applied. I know I will try.

The Total Of All Observations...?

Could produce a very large number. What is intended is the mean of the total of all observations, and that means at some times the weighted mean because all observations are not the same quality.

Paul in PA