This came up as a thread in the “Off-Topic Observatory” of the Cloudy Nights discussion board for amateur astronomers. People have all kinds of hobbies and among the stargazers are skiers, rally racers, runners, and rock climbers, though understandably many more bird watchers, radio hams, and numismatists. Several of us collected slide rules accidentally or on purpose. In response to the topic, one poster just bought a circular slide rule to add to the collection. Aside from the engineer’s slipstick, my circular calculators are all for publishing to reduce or enlarge images and paper pages.
Calculators - and I do use my phone, holding it sideways for the technical functions - give us a false sense of precision, when all you need is accuracy. In other words: will it fly? will it overflow the container? will it carry the load? For backyard stargazing, given that the atmosphere is a roiling ocean, what is the (approximate) limit of observable stellar magnitude with a 115 mm versus 102 mm refractor? The difference between pi=22/7 and pi=3.141 is 0.0018: two thousandths. Not much in life is that close.
 |
| The one at the bottom was special because about 1988 or so, Pickett (or their inheritors) found a large number of them in a warehouse and in a publication (Scientific American or Science News or similar) announced that they would give one (one) to everyone who sent in a letter asking for one. (Email was not common back then), after which, the instruments would be no longer available. The one down from topmost came in a leather scabbard with a fastener on the back so that you could wear it on your belt. Long after those days, I wore it in to work. "What's that?" "This is the formal computing device of a Jedi, from a simpler, more elegant time." |
Clearly, the slide rule has been eclipsed by devices with storage and memory. Back in the 70s, I joined a round-robin newsletter called The Libertarian Connection, which was based on the medium known to science fiction fanzines. We sent in mimeograph stencils; the editors ran them off, collated the magazine, and mailed it out. Back when one ounce first class was 3 cents the saying was “a penny a day from coast to coast.” Then they went to photo-offset, which I enjoyed immensely. And here we are in the age of George Jetson, with a somewhat better BBS via integrated fiber optics into the house instead of a telephone dial-up at 300 baud.
The device is based on logarithms which allowed the transformation of multiplication and division into addition and subtraction. With a five-place or six-place tables of logarithms and trigonometric functions, you could achieve 100 times the precision of daily life. (Consider common retail pricing, for example.) That, in turn, allows efficiencies in engineering and production. Compared against working with tables, the slide rule traded speed for precision. You only get three places, but it is much easier, with the likelihood of errors reduced. If you need more precision, there were the books of tables, and an adding machine, then, later a comptometer.
The slide rule shows ratios and proportions so that you do not need to recursively enter numbers 4.1, 4.2, 4.3,… And it is designed to address basic problems involving circles and square roots.
Even in the 1990s, engineers had AutoCAD and its competitors that let you draw something and the program would show the calculations off to the side. Would you rather start a fire with a BiC lighter or two sticks? Still, it is nice to get away from the computer, sit on a couch or chair, and move the numbers and see what is under the cursor or at the index
 |
| 23 squared times Pi. Set the Index to 23 on the D scale and read the square at the Index on the A scale. Set the cursor to Pi on the B scale and read the answer on the A scale. |
For the telescope of diameter 115 mm, set the index on the D scale, read the square on the A scale and then set the cursor to pi, and you get 417 or close to. The calculator says 41,547.562843725015579. Ignoring all the noise, 415 is within half a percent. The 102-mm refractor has an area of about 327. Set either the AB or CD scales to 415/327 and the larger telescope has 127% the area of the smaller—and the calculator agrees: 1.27114… But you could do most that in your head anyway.
In astronomy, the paradigm shifts in understanding the so-called “expansion of the universe” i.e., the Hubble Constant has been measured in orders of magnitude, not decimal places.
PREVIOUSLY ON NECESSARY FACTS
The Rational Optimist and The Grand Complication
Measuring Your Universe: Alan Hirshfeld’s Astronomy Activity Manual
No comments:
Post a Comment
Note: Only a member of this blog may post a comment.