Necessary precision

Pete Reigel posted thoughts on this years ago. Maybe he can repost?

Mathematician Bob Thurston informs me that 5 places are sufficient. When you look at the distance conferred by that 5th decimal place in most of our applications, you can barely see it.

In SI (metric) units, it's a centimeter. In US measurements, 5/8". You can see it but you can't measure to that precision.

(I got the "5 places" advice from a surveyor, A.J. Vanderwaal, who I think got it from Ted Corbitt.)

The problem with 5 digits after the decimal point is most hand held calculators only can handle 8 total digits. Hence, if you have 11,115.58121 the calculator would only handle 11,115.581.

I feel two decimal places is enough for one to use.

Oh, I see now that I didn't state all the conditions. Five digits after the decimal place applies to when you are using MILES or KILOMETERS as the unit. If meters or feet, I would agree that 2 places after the decimal are sufficient. I doubt if an 8-digit display would run out of space in our work if we are talking about kilometers or miles, as 999.99999 (kms or miles) would still fit!

Right, Bob. Thanks for clarifying this.

quote:

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5 digits makes sense. For a typical 5,000 meter course, 5 digits would get down to 5 cm (<2"). That's less than one count on a 30 counts per rev J-O rig on a nominal 26" bike: 24ish k counts per mile = 2.64 inches per count.

While a smaller distance than 3" can be huge in track, I suspect it has little meaning in our road course measurements. As Bob says, we can't reliably measure to sufficient accuracy to justify anything more stringent.

However - I can guess most of us have encountered two measurements of a single course that have come out to the exact number of counts when measuring under constant temperature and favorable traffic conditions. My best was a 10K on a cloudy day in February with no wind, on car-free rural roads. The counts were exactly the same.

I'd like to hear from everyone out here who has had two back-to-back rides come out to exactly the same count. Longest distance measurement on the same day with identical counts gets a prize - a huge enthusiastic virtual pat on the back!

I would hold the applause until we look at the breakdown of segments along the course. It's not too rare for total measurements to come out with really close numbers, but underneath this "neat" result you often find variations in the individual miles or other segments.

And it's worth remembering that 2 consistent measurements could both be wrong.

You are analyzing this from a mathematical perspective, Bob. I get your points. If breakdowns of the segments of a measured course vary a little, but the total count comes out the same, a pure probability/statistics view would say that the exact same total counts are a coincidence. I contend that such "fortuitiveness" tends to increase with more meticulous measuring.

I don't know how to quantify how unlikely it might be that two total measurements in exact agreement could both be wrong. Assuming no issues with calibration, or with the process of measuring itself, I can guess the probability is small. If this happens to you, I would say the probability of both being wrong is nil! I could say the same for most of the measurers out here that I know.

I know that some examples of "same overall not equal to correct" occur when a measurer doesn't take note of significant differences in individual segments. I've reviewed quite a few that were very close in total counts overall but evidenced much less consistency when compared by parts. (Almost always I can still justify the results by using average constant.)

The other way this can happen is in our interpretation of the correct path to be measured. I have a hunch that once we've measured through a section we may not always look at it with fresh eyes the next time through-- we may instead partially rely on what we've "learned" on the first ride.

Not trying to belabor the point, just trying to remember Emerson ("A foolish consistency is the hobgoblin of little minds").

I wonder if others besides me just didn't take in the first part of Oscar's post: "I wish the manual included a completely filled out App with some explanation of the thinking behind what goes on each line. For instance: how many figures right of the decimal are necessary."

I think I jumped to the for instance and forgot about the opening point. I do think that could be a good idea-- maybe some cautions needed but overall would help. Thoughts?