[A typically wordy introduction, de rigueur for anyone brought up on Asimov non-fiction.]
The advent of computers in engineering has been, on the whole, a remarkably good joining of capabilities; this goes without saying, as many feats of engineering in our modern world would be difficult to impossible without the speed and reliability of computers. But computers have also created a crisis in engineering, or at least one in engineering education.
In the old days before computers and hand calculators were available, the computations in engineering problems were done, of course, mostly by hand. A "slipstick" (slide rule) could be used to do rough computations but they were never more accurate than three decimal places at best, and even that depended upon the experience of the engineer. If more accuracy was required, then laborious pencil-and-paper computations were required, shortcut now and then by the consultation of massive tables of function values and the occasional, cranky, expensive mechanical calculator. Critical applications required multiple derivations in order to assure reliability. Indeed, one of the foremost topics in undergraduate engineering courses was how to measure, interpolate and average to get good, accurate measurement values.
Of course, when deriving a value by hand, a knowledge of the accuracy required for the value was presupposed. It does no good to derive a value to ten decimal places when only four are needed, but if six are required, then stopping at four places is just as bad as not doing them in the first place. Engineers had a very sharp idea of what accuracy and precision implied for the task at hand.
Then along came computers. The same computations that took days before were done almost instantly, and the computations were utterly reliable - providing the program is correct and the input data is accurate. "And look at all the decimal places!" The architecture of computers makes it as easy to do sixteen digits of accuracy as four, and usually all those digits were displayed. Trouble is, the numbers displayed are no more accurate than the input values are, and may be even less so. "All those decimal places" are generally just visual garbage. Now-a-days, most engineering students are exposed to a different lesson on accuracy than their forefathers - mostly concerning the need to ignore all those impressive numbers pouring out of computers.
American Punch! users, burdened with a measurement system that even the English have abandoned, have the ability to place walls and other objects in their plans with great accuracy, expressed in inches and decimal fractions of an inch. Traditional drafting uses feet, inches and power-of-2 fractions - fractions with denominators like 2, 4, 8, 16 and 32. Since a 32nd of an inch is .03125, it takes five digits of accuracy to handle 32nds of an inch without rounding errors. Metric users sneer at all that, easily sliding from meters to centimeters to millimeters as needed. Indeed, standards in metric construction mandate the exclusive use of millimeters, just to avoid using a decimal point at all.
Computers can handle increasing accuracy in numbers, but generally only do so in fairly large chunks. A PC has two kinds of numbers it can commonly use for measurements. The smaller version can hold a decimal number of at least six digits of accuracy, the larger has at least sixteen digits of accuracy. The larger numbers require twice as much space to store and slightly more time to process. Punch! and most PowerTools use the smaller version to store measurements, though they usually process values with the larger numbers in order to preserve accuracy during operations.
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