I've noticed that my daughter, despite being an engineering student, isn't nearly as comfortable with the properties of logarithms as I am. Of course, she studied them in Calculus classes, but they were just abstract functions to her since she always had computers or calculators to perform calculations. For me, they were a part of the standard education for technical or science related fields. Even in high school we were expected to use slide rules or tables of logarithms to perform calculations.<p>I bought my first slide rule around 1964 (with money I made delivering the Detroit Free Press newspaper every morning before school). It was a bright yellow Pickett like those available on EBay[1]. It was possible to do multiplication, division, roots, trig, exponentials, etc. to just less than 3 significant digits of accuracy. If this wasn't enough accuracy, I had to recast the computation as addition or subtraction of logs from log tables, which could with some interpolation yield around 6 significant digits of accuracy.<p>I just recently pulled out my old slide rule to show my accountant how they worked.<p>At MIT I saw circular slide rules, and some of my fellow students used them (more accuracy on the outer scales, less on the inner most scales). The most interesting slide rules I've seen are cylindrical. The scales wrap around the cylinder in a helix and are much longer giving an extra digit or two of accuracy (but requiring more mental work on the user to figure out which reading of the cursor to use because the cursor was parallel to the axis of the cylinder). See [2]<p>By the time I was finished using my slide rule, I'd started working with computers. Even today, I have a fancy overpriced TI calculator that just sits in a drawer. I'd much rather fire up a Python REPL to do most calculations.<p>[1] <a href="https://www.ebay.com/itm/VINTAGE-1959-PICKETT-DUAL-BASE-SLIDE-RULE-MODEL-N4-ES-WITH-LEATHER-CASE/113321672651?hash=item1a627f7fcb:g:tCMAAOSwWotbwn12:rk:10:pf:0" rel="nofollow">https://www.ebay.com/itm/VINTAGE-1959-PICKETT-DUAL-BASE-SLID...</a><p>[2] <a href="https://ocw.mit.edu/courses/edgerton-center/ec-050-recreate-experiments-from-history-inform-the-future-from-the-past-galileo-january-iap-2010/image-galleries/slide-rule/" rel="nofollow">https://ocw.mit.edu/courses/edgerton-center/ec-050-recreate-...</a>
I grew up long after slide rules went out of fashion, but I really like them. And not only for their signaling value; I genuinely think they make working with specifically ratios easier.<p>For example if you have a recipe calling for 150 g of butter, but you want to use all of your 250 g, you can just align 150 and 250 on the slide rule, and then read off the correct amounts of the other ingredients, without ever touching the slide rule again. No multiplication performed.<p>I understand people don't use slide rules for more things, but I'm baffled they aren't considered standard kitchen equipment, in one shape or another.
"A movable pointer called a 'cursor' was developed to make it easier to read numbers off more precisely. (This is likely the origin of the computer cursor!)" Etymonline corroborates this, <a href="https://www.etymonline.com/word/cursor#etymonline_v_494" rel="nofollow">https://www.etymonline.com/word/cursor#etymonline_v_494</a>. So its cursor was the precursor to our cursor.
I got familiar with a slide rule when I studied for my pilot's license, through the "E6B flight computer"[1]. This is essentially a slide rule for specialised calculations (knots-km/h, gallons-litres, density altitude, etc). The E6B is still a mandatory piece of equipment for student pilots but generally regarded as outdated, even by instructors.<p>As an early millennial I'd never ran into this 17th century marvel called slide rule. When I asked the instructor how it works (rather than how to use it) he answered along the lines of "don't ask, it just does".<p>[1] <a href="https://en.wikipedia.org/wiki/E6B" rel="nofollow">https://en.wikipedia.org/wiki/E6B</a>
The transition was nearly instantaneous. We all used slide rules in high school chemistry and physics. Two years before I entered freshman engineering, “engineering computation” was taught with slide rules. The next year, you could optionally take the traditional course or the new version based around calculators. My freshman year, the calculator-based course was required. As a senior, I bought the most high-end Post slide rule at the campus bookstore at the clearance sale for $3.00.
That IBM ad at the end is priceless on so many levels.
(What did that massive computer do? How many female engineers do you count... etc,)<p>Thanks for the article. My grandfather was an accountant who preferred the slide rule to a calculator. I grew up with slide rules around me, and never could understand the logic.<p>Another tool lost in the past generation is the Abacus (here is a great story with Feynman[1]) and I would love more info as to how those compared in logic or use, if anyone can shed insight.<p>[1]: <a href="https://www.ee.ryerson.ca/~elf/abacus/feynman.html" rel="nofollow">https://www.ee.ryerson.ca/~elf/abacus/feynman.html</a>
Growing up at a time B.C. (before calculators), we learned to use the slide rule in high school trig. I also used it during my freshman year in college. My dad bought me a Pickett trig slide rule that I still have in a drawer at home. I've taken it out occasionally to play with and I am always impressed by how simple and yet powerful it is. Very elegant. Very dated.
There is a fairly good writeup on various slide rule types and scales, on <a href="http://www.quadibloc.com/math/slrint.htm" rel="nofollow">http://www.quadibloc.com/math/slrint.htm</a> (the rest of this guy's site is worth exploring on its own too, there seems to be a huge dump of various bits of knowledge on it).
A nice reference is Clifford Stoll's (author of A Cuckoo's Egg) article in Scientific American 2006:<p><a href="http://www.uvm.edu/pdodds/files/papers/others/2006/stoll2006a.pdf" rel="nofollow">http://www.uvm.edu/pdodds/files/papers/others/2006/stoll2006...</a><p>And a way to make your own sliderule:<p><a href="https://static.scientificamerican.com/sciam/assets/media/pdf/Slide_rule.pdf" rel="nofollow">https://static.scientificamerican.com/sciam/assets/media/pdf...</a><p>The article has the same IBM ad and says it's from 1953.
People on eBay are selling these Soviet pocket-watch style rotary slide rules:<p><a href="https://www.youtube.com/watch?v=Kuzdjy3HpWg" rel="nofollow">https://www.youtube.com/watch?v=Kuzdjy3HpWg</a><p>I think they were made into the 80s.
Another precursor to logarithms was prosthaphaeresis[1], based on trigonometric functions. Of course, like the quarter-square method, this required lookup tables, not a nifty device. But even with logarithms, log tables were pretty commonly used as well.<p>[1] <a href="https://en.wikipedia.org/wiki/Prosthaphaeresis" rel="nofollow">https://en.wikipedia.org/wiki/Prosthaphaeresis</a>
Recently someone posted about a paper-based calculating tool where you had two or three scales and used a ruler to combine the numbers. There was even a Python package for producing them.<p>What was the name?
I have my grandfather's slide rule. I don't often handle it because it has a patina on it from the thousands of calculations he must have carried out on it. It has several rulings on it and a sliding cursor.<p>Studying it, I realized that, once set, it shows the multiplication of the whole continuum. In other words, a given setting of the rule to some <i>n</i> shows <i>nm</i> for all <i>m</i>. (Actually all <i>mnEk</i> for all <i>m</i> and <i>k</i>.)<p>Some slide rules are circular or tubular.<p>See also: <a href="https://en.wikipedia.org/wiki/Nomogram" rel="nofollow">https://en.wikipedia.org/wiki/Nomogram</a>
The intro about Kepler is inaccurate, so I distrusted the claim about Newton too. It seems he did use a kind of slide rule: <a href="http://www.oughtred.org/history.shtml" rel="nofollow">http://www.oughtred.org/history.shtml</a><p>> In 1675 Sir Isaac Newton solves cubic equations using three parallel logarithmic scales and makes the first suggestion toward the use of the cursor.<p>> In 1677, two years after Newton invents the cursor, Henry Coggeshall perfects the timber and carpenter's rule. Newton's cursor fails to catch on at the time.
> The last slide rule manufactured in the US was produced on July 11, 1976<p>Actually, ThinkGeek made a production run a couple years back (though I guess I don't know that they were US-made). Doesn't seem to still be on their website, but I have one so it definitely existed. <a href="https://www.amazon.com/ThinkGeek-Slide-Rule/dp/B003M5B84C" rel="nofollow">https://www.amazon.com/ThinkGeek-Slide-Rule/dp/B003M5B84C</a> still shows a listing.
A practical implementation of a slide rule can be found on watches such as the Breitling Navitimer. I like to use it for quick currency conversions when traveling.
I've got a slide rule to thank for my precocious early math studies. I was always interested in math as a young kid, and my parents got me a Post slide rule for Christmas 1970, when I was in 5th grade/10 years old. I didn't know what the S and T scales on the back side of the main slide were for, so went looking up info in the local library. Turns out they were sine/tangent scales, which led to reading about trigonometry, which led to me realizing I needed to know algebra first. Over the next couple years, those library trips led to teaching myself algebra, geometry, trigonometry, and calculus, thanks mostly to TutorText books. For a nerdy little kid in the early 70s, that was heaven.
Reading about the usefulness of logs reminded me of another spatial math tool: The Triangle of Power!<p><a href="https://www.youtube.com/watch?v=sULa9Lc4pck" rel="nofollow">https://www.youtube.com/watch?v=sULa9Lc4pck</a>
Some of the last people using them for work may have been graphic artists, who called them "proportion wheels". I don't know how many of the folks sizing photos knew that they were using circular slide rules.
> The last slide rule manufactured in the US was produced on July 11, 1976<p>This is bit surprising to me. Does it imply that slide rule production had shifted to other countries, or did it really fall out of fashion so very rapidly? For reference, HP-35 calculator was released only in 1972 (for launch price of $395), and TIs competing SR-50 ("slide rule calculator") in 1974 (at $170). I would expect slide rules to be significantly cheaper and fairly entrenched (especially in colleges etc), so being killed in only few years is remarkable if true.
First, the positive note: This is an awesome, accessible article.<p>Now the error: In the paragraph beginning "By converting numbers into their logarithm", log(4)=2 should be log2(4)=2 - it's been a while since I was in mathematics academically, but isn't it a necessity to show the base of the log if it's not 10?
This reminds of my uncle who had them in his university and later at work (studying in the 70s in the communist Poland). I remember him mentioning that when first calculators came, skilled slide rule users were much much fasters, than anyone using a calculator.