My main complaint here is that the “much more” hasn’t really made it into the k-12 curriculum. As in: my 10 year old daughter has a Scratch book that more-or-less had her write an ode solver so that the little cat can jump with a bit of realistic physics. It wasn’t all that hard and it has a nice outcome on the screen, but you can’t find any trace of it in the standard curriculum. The only thing that people seem to want to do with these new found powers is less.
2 Likes
I’m a collector of calculators (mostly focusing on HP models), but recently I was given an entire box filled with 25 slide rules by an older engineer who just wanted them not to have to be thrown away.
Right here at my desk I have one from Keuffel & Esser in its original box. This thing is over 20 inches long with inches and centimeter scales on the edges. It’s a marvel of precision, but I still don’t have the hang of how to make use of it.
5 Likes
See my comment re estimating. You have learned well, Grasshopper.
1 Like
That’s the kind of gorgeous device that makes it clear how scientists could be confused for witches. It just looks powerful and mystical to me, a calculator generation kid.
3 Likes
My Dad taught me how to use a slide rule back when I was in junior high or high school, I think? Anyway, I pretty much said, “Oh cool,” and never touched it again. Technology advances. I don’t know why people get hung up on thinking the older ways are better. They almost never are. There’s a reason we don’t use abaci (abacuses?) anymore. I got an HP 15C calculator when I graduated high school in 1987. I used it all through college and throughout my 15+ years as an engineer. I still have it, but I actually don’t know where it is. In a box in the attic, probably. I no longer use it. Why? Because the stupid free calculator app on my phone does everything I need it to do. Technology advances. The old ways aren’t better. They’re just comfortable.
4 Likes
They were around, but definitely on their way out. I graduated in 1988, and our physics teacher gave us a lecture on how to use a slide rule, but I don’t think he really expected us to use one outside of that lesson – just to inform us that there were ways to do scientific math before electronic calculators.
As for the abacus thing, I remember an old guy in a Chinese restaurant even in the 1990s who still used one to calculate the bill. Abacuses were very popular in Asia before the electronic era, and even in the 1970s there were “John Henry” style competitions where expert abacus users beat users of the new electronic calculators in speed tests.
3 Likes
I’ve had a slide rule since my high school days – currently tucked away in a box somewhere – and I’ve used it less than 10 times, mostly as a novelty. (I graduated in 83). I kept it as it’s an interesting piece of kit, but along with my antique drafting tools (example), not for practical use.
Yeah, Buzz Aldrin didn’t need a stinkin’ calculator on the Gemini 12 mission. That’s back when men were men! (And astronauts were apparently allowed to smoke pipes onboard spacecraft??)
15 Likes
I do too, but since William Gibson tipped everyone off to them in Pattern Recognition I’m not optimistic. Working maybe, cheap not so much.
4 Likes
I jumped straight over slide rules from log tables to calculators. The first electronic calculator my school owned cost £200 (a lot of money in the mid-1970s) and used Polish notation which no-one understood. A couple of years later I could buy a pocket Casio for £20. They cost about the same now but have a lot more functions.
About the same time my parents got rid of their mechanical adding machine, which was like a huge hand-cranked typewriter for numbers. They also dumped a wonderful clockwork acoustic record player the size of a sideboard. I kind of regret the loss of those old artifacts. They had a physicality which modern gizmos lack.
1 Like
Western countries don’t but Asian countries do. When visited Tokyo a few years ago i even saw an Abacus store
6 Likes
My takeaway from the article and from some of the comments above was explicitly spelled out by Richard Feynman when he told the story about the abacus salesman that he met in a restaurant while he was teaching in Brazil. It’s the important notion that there is a difference between being able to compute an arithmetic operation… and having intuition about numbers and about the relationships between them. A way to compute arithmetic operations - be it a slide rule, an abacus, or even a way to write the numbers on a piece of paper to calculate the answer - can be seen by someone with numerical intuition as a way to gain that intuition if only the student is paying attention to what they’re doing, to how the solution process works, to how things go a little differently if the input is a little different… or, it can be seen (as it is, in practice, by most students) as a tedious machine where you unthinkingly follow some steps and a number falls out. It’s easy for people with good numerical intuition to make the mistake of believing that exposing students to the inner workings of the machinery will help the students develop those intuitions. Often, it won’t.
The first time I was in Brazil, I was eating a noon meal at I-don’t-know-what-time - I was always in the restaurants at the wrong time - and I was the only customer in the place. I was eating rice with steak (which I loved) and there were about four waiters standing around.
A Japanese man came into the restaurant. I had seen him before, wandering around; he was trying to sell abacuses. He started to talk to the waiters, and challenged them: He said he could add numbers faster than any of them could do.
The waiters didn’t want to lose face, so they said, “Yeah, yeah. Why don’t you go over and challenge the customer over there?”
The man came over. I protested, “But I don’t speak Portuguese well!”
The waiters laughed. “The numbers are easy,” they said.
They brought me a paper and pencil.
The man asked a waiter to call out some numbers to add. He beat me hollow, because while I was writing the numbers down, he was already adding them as he went along.
I suggested that the waiter write down two identical lists of numbers and hand them to us at the same time. It didn’t make much difference. He still beat me by quite a bit.
However, the man got a little bit excited: he wanted to prove himself some more. “Multiplicação!” he said.
Somebody wrote down a problem. He beat me again, but not by much, because I’m pretty good at products.
The man then made a mistake: he proposed we go on to division. What he didn’t realize was, the harder the problem, the better chance I had.
We both did a long division problem. It was a tie.
The bothered the hell out of the Japanese man, because he was apparently well trained on the abacus, and here he was almost beaten by this customer in a restaurant.
“Raízes cúbicas!” he says with a vengeance. Cube roots! He wants to do cube roots by arithmetic. It’s hard to find a more difficult fundamental problem in arithmetic. It must have been his topnotch exercise in abacus-land.
He writes down a number on some paper— any old number— and I still remember it: 1729.03. He starts working on it, mumbling and grumbling: “Mmmmmmagmmmmbrrr”— he’s working like a demon! He’s poring away, doing this cube root.
Meanwhile I’m just sitting there.
One of the waiters says, “What are you doing?”.
I point to my head. “Thinking!” I say. I write down 12 on the paper. After a little while I’ve got 12.002.
The man with the abacus wipes the sweat off his forehead: “Twelve!” he says.
“Oh, no!” I say. “More digits! More digits!” I know that in taking a cube root by arithmetic, each new digit is even more work that the one before. It’s a hard job.
He buries himself again, grunting “Rrrrgrrrrmmmmmm …,” while I add on two more digits. He finally lifts his head to say, “12.01!”
The waiter are all excited and happy. They tell the man, “Look! He does it only by thinking, and you need an abacus! He’s got more digits!”
He was completely washed out, and left, humiliated. The waiters congratulated each other.
How did the customer beat the abacus?
The number was 1729.03. I happened to know that a cubic foot contains 1728 cubic inches, so the answer is a tiny bit more than 12. The excess, 1.03 is only one part in nearly 2000, and I had learned in calculus that for small fractions, the cube root’s excess is one-third of the number’s excess. So all I had to do is find the fraction 1/1728, and multiply by 4 (divide by 3 and multiply by 12). So I was able to pull out a whole lot of digits that way.
A few weeks later, the man came into the cocktail lounge of the hotel I was staying at. He recognized me and came over. “Tell me,” he said, “how were you able to do that cube-root problem so fast?”
I started to explain that it was an approximate method, and had to do with the percentage of error. “Suppose you had given me 28. Now the cube root of 27 is 3 …”
He picks up his abacus: zzzzzzzzzzzzzzz— “Oh yes,” he says.
I realized something: he doesn’t know numbers. With the abacus, you don’t have to memorize a lot of arithmetic combinations; all you have to do is to learn to push the little beads up and down. You don’t have to memorize 9+7=16; you just know that when you add 9, you push a ten’s bead up and pull a one’s bead down. So we’re slower at basic arithmetic, but we know numbers.
Furthermore, the whole idea of an approximate method was beyond him, even though a cubic root often cannot be computed exactly by any method. So I never could teach him how I did cube roots or explain how lucky I was that he happened to choose 1729.03.
21 Likes
I guess I missed the slide rule era, but my dad used to have one kicking around in a desk drawer, and I could never make heads or tails of it. To no one’s surprise I’m sure, there are plenty of slide rule simulators online, complete with tutorials, for anyone interested in trying to decipher them.
2 Likes
Yeah but you never know a garage sale or estate sale someone selling grandpa’s old junk…
1 Like
I used a proportion wheel at work, which is a simplified Slide rule. People thought I was a weirdo, but it was often faster than tabbing over to the online version.
We were allowed to use slide rules in high school in the late 60s and early 70s. I had what was considered a pretty nice model, a Faber Castell Reitz. It’s still kicking around in my stuff somewhere.
One of the most useful skills I developed in college getting my engineering degree was to get in the practice of approximating answers in my head. I had a professor who all but insisted on it. And the reason he did this wasn’t so that we could quickly come up with rough answers, it was so that we could come up with rough answers before actually solving the problem, so that when we did the actual solution, we could compare that to our rough approximation as a check. It helped to prevent stupid math errors. If you came up with a solution that was two orders of magnitude off from the rough approximation, you knew you probably made a stupid mistake somewhere. That’s why it’s really important to actually understand numbers, a la Richard Feynman.
6 Likes
3 Likes
I’m using log tables RIGHT NOW!
Actually I’m not. I just had them next to me as a mousepad, so I guess maybe I am using them?
20 Likes
I used to keep an abacus and a slide rule next to my computer at work. I never touched them - their purpose was to remind me that no matter how frustrating software could be, the alternatives were worse.
We also had a prof who insisted on this, but it came with the caveat: “agreement between the rough approximation and the detailed calculation does not necessarily mean either is correct.” 
5 Likes
