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in all the examples just given, than is its closest rival, accuracy. “Accurate Laser Tattoo Removal” sounds not nearly as convincing or effective; a car with merely “Accurate Parking Technology” might well be assumed to bump occasional fenders with another; “Accurate Corn” sounds, at best, a little dull. And it surely would be both damning and condescending to say that you tie your tie accurately—to knot it precisely is much more suggestive of élan and style.
THE WORD precision, an attractive and mildly seductive noun (made so largely by the sibilance at the beginning of its third syllable), is Latin in origin, was French in early wide usage, and was first introduced into the English lexicon early in the sixteenth century. Its initial sense, that of “an act of separation or cutting off”—think of another word for the act of trimming, précis—is seldom used today:* the sense employed so often these days that it has become a near cliché has to do, as the Oxford English Dictionary has it, “with exactness and accuracy.”
In the following account, the words precision and accuracy will be employed almost but not quite interchangeably, as by common consent they mean just about the same thing, but not exactly the same thing—not precisely.
Given the particular subject of this book, it is important that the distinction be explained, because to the true practitioners of precision in engineering, the difference between the two words is an important one, a reminder of how it is that the English language has virtually no synonyms, that all English words are specific, fit for purpose by their often very narrow sense and meaning. Precision and accuracy have, to some users, a significant variation in sense.
The Latin derivation of the two words is suggestive of this fundamental variance. Accuracy’s etymology has much to do with Latin words that mean “care and attention”; precision, for its part, originates from a cascade of ancient meanings involving separation. “Care and attention” can seem at first to have something, but only something rather little, to do with the act of slicing off. Precision, though, enjoys a rather closer association with later meanings of minuteness and detail. If you describe something with great accuracy, you describe it as closely as you possibly can to what it is, to its true value. If you describe something with great precision, you do so in the greatest possible detail, even though that detail may not necessarily be the true value of the thing being described.
You can describe the constant ratio between the diameter and the circumference of a circle, pi, with a very great degree of precision, as, say, 3.14159265 358979323846. Or pi can happily be expressed with accuracy to just seven decimal places as 3.1415927—this being strictly accurate because the last number, 7, is the mathematically acceptable way to round up a number whose true value ends (as I have just written, and noted before the gap I have placed in it) in 65.
A somewhat simpler means of explaining much the same thing is with a three-ring target for pistol shooting. Let us say you shoot six shots at the target, and all six shots hit wide of the mark, don’t even graze the target—you are shooting here with neither accuracy nor precision.
Maybe your shots are all within the inner ring but are widely dispersed around the target. Here you have great accuracy, being close to the bull’s-eye, but little precision, in that your shots all fall in different places on the target.
Perhaps your shots all fall between the inner and outer rings and are all very close to one another. Here you have great precision but not sufficient accuracy.
The image of a target offers an easy means of differentiating precision and accuracy. In A, the shots are close and clustered around the bull: there is both precision and accuracy. In B, there is precision, yes, but insofar as the shots miss the bull, they are inaccurate. C, with the shots widely dispersed, shows neither precision nor accuracy. And in D, with some clustering and some proximity to the bull, there is moderate accuracy and moderate precision—but very moderate.
Finally, the most desired case, the drumroll result: your shots are all clustered together and have all hit the bull’s-eye. Here you have performed ideally in that you have achieved both great accuracy and great precision.
In each of these cases, whether writing the value of pi or shooting at a target, you achieve accuracy when the accumulation of results is close to the desired value, which in these examples is either the true value of the constant or the center of the target. Precision, by contrast, is attained when the accumulated results are similar to one another, when the shooting attempt is achieved many times with exactly the same outcome—even though that outcome may not necessarily reflect the true value of the desired end. In summary, accuracy is true to the intention; precision is true to itself.
One last definition needs to be added to this mass of confusion: the concept of tolerance. Tolerance is an especially important concept here for reasons both philosophical and organizational, the latter because it forms the simple organizing principle of this book. Because an ever-increasing desire for ever-higher precision seems to be a leitmotif of modern society, I have arranged the chapters that follow in descending order of tolerance, with large tolerances of 0.1 and 0.01 starting the story and the absurdly, near-impossibly tiny tolerances to which some scientists work today—claims of measurements of differences of as little as 0.000 000 000 000 000 000 000 000 000 01 grams, 10 to the -28th grams, have recently been made, for example—toward the end.*
Yet this principle also prompts a more general philosophical question: why? Why the need for such tolerances? Does a race for the ever-increasing precision suggested by these measurements actually offer any real benefit to human society? Is there perhaps a risk that we are somehow fetishizing precision, making things to ever-more-extraordinary tolerances simply because we can, or because we believe we should be able to? These are questions for later, but they nonetheless prompt a need here to define tolerance, so that we know as much about this singular aspect of precision as about precision itself.
Although I have mentioned that one may be precise in the way one uses language, or accurate in the painting of a picture, most of this book will examine these properties as far as they apply to manufactured objects, and in most cases to objects that are manufactured by the machining of hard substances: metal, glass, ceramics, and so forth. Not wood, though. For while it can be tempting to look at an exquisite piece of wooden furniture or temple architecture and to admire the accuracy of the planing and the precision of the joints, the concepts of precision and accuracy can never be strictly applied to objects made of wood—because wood is flexible; it swells and contracts in unpredictable ways; it can never be truly of a fixed dimension because by its very nature it is a substance still fixed in the natural world. Whether planed or jointed, lapped or milled, or varnished to a brilliant luster, it is fundamentally inherently imprecise.
A piece of highly machined metal, however, or a lens of polished glass, an edge of fired ceramic—these can be made with true and lasting precision, and if the manufacturing process is impeccable, they can be made time and time again, each one the same, each one potentially interchangeable for any other.
Any piece of manufactured metal (or glass or ceramic) must have chemical and physical properties: it must have mass, density, a coefficient of expansion, a degree of hardness, specific heat, and so on. It must also have dimensions: length, height, and width. It must possess geometric characteristics: it must have measurable degrees of straightness, of flatness, of circularity, cylindricity, perpendicularity, symmetry, parallelism, and position—among a mesmerizing host of other qualities even more arcane and obscure.
And for all these dimensions and geometries, the piece of machined metal must have a degree of what has come to be known* as tolerance. It has to have a tolerance of some degree if it is to fit in some way in a machine, whether that machine is a clock, a ballpoint pen, a jet engine, a telescope, or a guidance system for a torpedo. There is precious little point in tolerance if the machined object is simply to stand upright and alone in the middle of a desert. But to fit with another equally finely machined piece