A colleague of mine (a numerical analyst) and me (a statistician) once had a PhD student physicist telling us that a computer was broken because the output from a program matched theory to only 3 sig. fig. The input came from a 4 digit data logger, but he kept saying the numbers were accurate because they were measured by a machine. After 90 minutes, we decided he was ineducable, and threw him out. I rather tentatively rang his supervisor and, as soon as I mentioned his name got the response "Oh, God, what has he done NOW?"
]]>Say rather if you're doing 5.3 x 8.7 on an abacus, calculator, or with pencil and paper. You'll get lower precision on an N600, the slide rule carried on Apollo landings, just because it's a five inch pocket rule. (It's a joy to use, though; magnificent engineering.) The slide rule closest at hand when I read this was a plastic 10" Aristo made for students and frankly it has terrible accuracy - I just got it recently and need to lubricate the slide if it's to be useful.
Yes, I pulled out a slide rule to check 5.3 x 8.7...
]]>An accurate computer-generated set of log, trig and root tables would be more useful. They could be engraved on enduring stone in various places for post-apocalyptic rediscovery, with rubbings taken to make copies rather than transcriptions which might introduce errors in the copying process. I can imagine, in my mind, a computer-controlled robot driving a high-pressure water-cutting jet engraving such tables on prepared granite and basalt outcrops across the world...
Slide rules are good for quick-and-dirty number crunching but errors accumulate, four-figure tables are more accurate. Five-figure tables would be better of course.
]]>I'd hope anyone assembling a library would include some basic math and science books. More critical than a big list of numbers is the explanation of why someone collected all these numbers and what they're good for; given an understanding of logarithms or square roots, anyone with time and nothing better to do can work out the numeric values.
An underground transit station in my city has, among other wall decorations, pi to 100+ digits. I remember thinking I'd have put up even more information than that...
]]>Doing it accurately without computers is the problem -- Charles Babbage among others spent an inordinate amount of time cross-checking various logarithm table books and identifying errors, discovering by forensic means why an error occurred (in one case he proved that a "4" and a "2" had fallen out of the printer's type plate and been put back in the wrong place) and that a Chinese logarithm table book had been copied from an Italian book produced a couple of hundred years before since the errors were identical.
In the end he decided that making the calculations by machine was the way to go hence his development of the Difference Engine which included a printing mechanism to reduce the possibility of transcription errors. Leaving a legacy of accurate log and trig tables to our post-apocalyptic brethren is better than letting them make the same mistakes again.
]]>SS @ 656 Yes, well, the book I just mentioned ....
]]>The point is that automation is a lot faster, and does not need an expert to concentrate on the matter for weeks or months, NOT that it is significantly more reliable (it may be, or may not be).
My 5-figure log tables are 3 feet to the left of me now ....
]]>Digital computer generation of log tables and trig functions can be done without exhaustion, eye strain, dyslexia etc. Cross-checking of results produced from different algorithms and program versions on different hardware is simple and the final results can go to press on paper without manual intervention or transcription. It's also a lot faster -- I expect, if I ran a program to generate log tables on the computer I'm typing this on I could replicate years of effort by dozens of human "computers" in a few minutes or, if working to 15 significant digits or more, hours. Returning the theme to SF see "The Nine Billion Names of God" by Arthur C. Clarke for a worked example of the process.
]]>I've got a Casio FX-100D calculator. 10 displayed digits, a further 4 (IIRC) digits of precision, and 2 digits exponent. I bought it for my final year at uni (1996) after I broke my previous calculator. As an engineer, I probably use it most days, because I find it more convenient than the PC calculator app.
Last year I changed the battery. For the first time. Yes, a single AA battery powered this calculator without a hitch for 21 years.
So as neat as slide rules are, I'm going to say you're wasting your time. Get yourself an old-school Casio calculator and a four-pack of Duracells, and you can reasonably guarantee that you'll die before the calculator. Or swap the Duracells for some zinc and copper wire, and plant a row of lemon trees.
]]>Most volumes of log tables were produced long before copyright was a legal and enforceable concept. The copier was limited by the cost and effort required to typeset a book, not a trivial thing in those days and not helped by the fact the numbers had to be accurate to be of serious use to a purchaser of the copied volume.
Nowadays photocopying such a book of tables is cheap and producing a run of such books using offset litho and other modern printing tech is not expensive either. Distributing a PDF or ebook is comically cheap and simple given the original files.
]]>"Stop" in the sense of "cease to exist" or—more to the point—"go to hell"? ;-) No, I don't think we should do that now.
Thus I'm taking a step above and beyond an arbitrary number that only had a particular meaning in a specific context roughly 1930 years ago—and nobody today is even certain what that particular meaning was, although there are some reasonable hypotheses.
I should note, however, that the context—a scathing critique of imperialism—is indeed no less relevant today than it was back then. It is even related to the discussion in this blog post!
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