Someone is showing a photo of a soybean plant on a screen then asking an audience what they are looking at. He corrects anyone who offers “soybean plant” … it is a photograph of a soybean plant. Better still – the digital rendering of a picture onto a screen through software used to make a presentation. Software version? Picture metadata? Too pedantic?
Sometimes extreme specificity is necessary, sometimes not. If you are winging your way to Mars and ground control suggests you make a minor adjustment to your flight path… extreme specificity might be worth your attention. If you are buying a tomato for a recipe that wants a half cup of chopped tomato… you might be forgiven if your selection comes in a bit out of range.
How then do you know where and when you must pull out the micrometer or the gram scale to get to the necessary precision? Not always an easy call. It’s further complicated by personal expectations in relation to accuracy. Still further down that rabbit hole – the significance of the two terms: Precision and Accuracy. Back to the tomato deal. Pick one out and weigh it for the grocer to know how much to charge. The scale you’ll use to weigh it likely wouldn’t be used to weigh a diamond to determine the latter’s mass for commercial purposes. These extremely different situations don’t confound us; but consider situations of less extreme comparison and add on the complication of many thousands of rough estimates summed up over time.
When a farmer sells grain these days we are usually talking about the sale of a fairly large quantity; many tons in one go. The scale to weigh her grain will first weigh her whole tractor, trailer, and grain (and the scale operator will also note whether she is on board). Next the grain is dumped from the truck to a facility prepared for such. Then finally the whole truck system (plus or minus the driver as originally weighed in) is reweighed so that the net weight of grain can be determined. Recall our tomato – if it were placed on such a scale it likely wouldn’t even register.
It is possible for a scale to be improperly calibrated and to over or under estimate all loads measured while out of calibration. This will of course lead to difficulty at some point. But even a properly calibrated scale, one with random over or under small mismeasurements, can lead to difficulty over time. Our farmer from above likely doesn’t care if the tomato goes missing on the scale. But a government warehouse inspector will get concerned when an audit of the grain facility which has handled thousands of such transactions is unable to balance their receipts to within a few bushels. I should acknowledge here that there are many more factors that go into balancing the receipts to within a few bushels. The curious may inquire in the comments below. But the weighing piece is where I want to focus now.
State governments here in the US, watched over by the federal government, are responsible for weights and measures. This enormous scale we’re talking about will be audited annually to make sure it is properly calibrated. The little scales at the grocer are likewise audited to make sure customers really get a pound of tomato when that is what they’re paying for. With all this attention to detail one might imagine there should be no difficulty. But what about rounding error? At what point do we dive into the rabbit hole so far as to ponder if the grain facility with a balance sheet off by three bushels is somehow better or worse than another facility off by six bushels? Does it matter – or are we being too pedantic? Consider facility A which buys and sells 2.5 million bushels of grain in a year (which for the curious is about 2,800 of those truck loads mentioned above) and at the end of the year shows a balance offset of 50 bushels (an error of 0.002%). Note too that at today’s price of about $9 a bushel for soybeans this is a “mistake” worth $450. Much more than the value of a tomato, but pretty insignificant compared to the $22.5 million value for all the product involved. Note also that for our example we’ve not indicated whether the difference was a plus or minus offset – it was merely out of balance. Next look at the books for facility B which buys and sells one million bushels and has an offset of 72 bushels. The math is easy enough, B has a bigger problem than A. Is it too big a problem?
I have oversimplified this example – perhaps by too much. I don’t want to start a criminal investigation into commercial scale manufacture. These behemoth scales are pretty incredible when you get right down to it. There is a moisture tester involved in the measuring, a test weight bucket, people, ambient temperature and humidity (influencing rates of grain drying) – and a long list of other possible sources of mismeasurement that factor in [all the weighing, moisture testing, people etc. are involved in the outgoing sales as well]. Indeed, the facility that can balance its books as accurately as ‘A’ might be doing a better job than a jeweler who sells 1,000 carats of diamonds in a year.
For a little reference – the 2018 US soybean crop is estimated at 4.693 billion bushels. If this entire crop were loaded into the typical hopper bottomed grain trailer one will see on the highways, at a load size of 880 bushels, it would require 5,332,955 such loads*. This 4.7-billion-bushel crop will be measured at least a couple times (through points of sale and processing). One can be rather certain a few mistakes will be made. How many – to be specific?
*And just for fun, if these tractor trailer loads were lined up on the freeway (at an average length of 65 feet per load) the line would be 65,652 miles long or could circle the earth almost three times at the equator (2.64 times – to be specific).