I was a nerdy 10 year old kid who liked doing arithmetic in 1970, but didn't know anything particularly advanced. I convinced my parents to get me a slide rule as a Christmas present that year; a basic white Post model 1447 - I know that because I'm looking at it right now. It's been in my desk drawer forever as I could never convince myself to throw it away, even though I've long since lost the sliding cursor.
Anyway, I got the slide rule, had fun with basic multiplication/division, but didn't understand what the S, T, and L scales on the back were for. Sine/Tangent/Logarithm? What are those?
Off to the library, where I picked up a Tutor-Text book  on trigonometry, discovered I'd better first learn some algebra, picked up another Tutor-Text book on that, and began a two-year tear teaching myself algebra to integral calculus. Which meant I tested out of a couple years of math in high school, ran out of courses to take, and in my junior year was allowed to walk to the local college to take 2nd year Calc classes.
At that college, they started letting me play with the computers, both an IBM 5100 APL machine over one summer, and hands-on access to the IBM 11/30 clone minicomputer that was the main machine. The math prof pointed me at Knuth's "The Art of Computer Programming", and that began my transition from pure mathematics to computer programming/science instead. I even wrote a MIXAL assembler/MIX simulator for the minicomputer that the college ended up using to teach an assembly language course.
So thank you, Post, Pickett, K&E! And Tutor-Text as well.
True story: my son took an AP physics class in high school, (LASA) taught by sokeone with a PhD in physics. They had an oversized teaching sliderule hanging from the ceiling, where nobody could use it. It had become decoration, as nobody was left to teach with it.
When I was at the school for a “meet your student’s teachers” night, one of the other parents asked about the side rule. Instructor didn’t know how it worked.
So I explained it.
My wife still has her grandfather’s slide rules from when he was the state engineer in the 50s and 60s.
Neither of my parents were mathematically inclined, but they were content to let me forage for information on my own, with lots of trips to the library. Amazing how clear are my 50-year-old memories of 10-year-old me sitting on the floor with a trig book, drawing random triangles on paper, measuring them as carefully as I could with ruler and protractor, and verifying the law of sines and cosines with paper and slide-rule. God, I was such a nerd. Paid off well in the end, though :-)
Now I'm retired, and for fun, I work my way through the problems at Project Euler. Four years in, and only two more problems to go to hit 90% complete! It'll probably take me another year+ to finish them all (hopefully).
I'm sure the way schools look made a lot of sense in the time of industrialisation and the manual labour of the factory worker, but it's crazy we still shape students by that mould when it's so far removed from the creative pursuits we expect them to go on later in life.
“Please excuse <name>, I am tardy.” <signature of name>”
I didn't even grow up in this era and I keep buying stuff from eBay purely out of fascination for old ways of doing things. These names on all kinds of things I have horded - architectural templates, drafting machine, cutting mat, compass set, lettering templates, etc.
Thanks for sharing your story!
Still have a few slide rules, includingn Pickett and K&E.
This is also great when you have a bunch of resistors and capacitors, and you need to build a circuit where the two are at a particular ratio. Set the ratio you want, then you can take whatever resistor you have, and see if you have a cap that is "close enough" to what you need.
So if the primary ingredient is chevre cheese, the recipe calls for 180 grams, but you can only buy it in 250 gram packages, you can set the slide rule to "180 over 250" and then just mechanically read off the proportionally correct amounts of all other ingredients.
Slide rules are indispensable in the kitchen to me and I'm surprised they're not part of standard kitchen equipment like e.g. scales.
Edit: Similarly, if the recipe is expressing ingredients in US units and you would want to know the international amounts, you can set the slide rule to the conversion ratio and again, mechanically read off the correct amounts as you go.
Yes! This is the sort of thing my Dad used them for (see my other comment here for the context)
He asked me what I use to lubricate it, and when I said "Pencil graphite" he got even more excited. Apparently a lot of the other astronauts had used fancy light lubrication oils, but he always used a pencil and never had any problems.
He was a lovely man, and it was fabulous to enthuse with him over this wonderful piece of technology.
The main benefit of introducing this friction, rather than allowing calculators, is that it (a) encourages one to do simple calculations by hand, and (b) gets one in the habit of quickly double checking that log-table-based results fall in the correct ballpark. Calculators induce a sort of mindlessness where glaring orders-of-magnitude errors pass us by since we expect the machine to get it right.
With all that said, I don't know that I would recommend the use of log tables to high schoolers in the 21st century. That effort might be better utilized on more pressing needs e.g. statistical literacy. Many folks (including me) got entirely through STEM-focused high school knowing not even the slightest basics of statistical inference or causality.
Really? According to Wikipedia, the Fahrenheit scale (https://en.wikipedia.org/wiki/Fahrenheit#History) is about 18 years older than the Celsius scale (https://en.wikipedia.org/wiki/Celsius#History), and I'm surprised that human body temperature wasn't included as a calibration. (But of course the fact that I'm surprised by it doesn't mean it isn't true!)
However after the introduction of Celcius, Fahrenheit was redefined slightly (with the freezing and boiling point of water being the fixed "nice" values for the scale -- to match the model used by Celcius) which resulted in human body temperature no longer having such a nice value. This also moved the 0°F value. So while technically Fahrenheit does predate Celcius and it did have a "nice" value for body temperature when invented, it was soon afterwards redefined such that arguably the value is just a conversion from Celcius.
In short, you're both correct. :D
Now imagine making a thermometer by marking off the 32° and 96° points (64° apart). Now delineate the 2° intervals.
Considering those two tasks, 64 seems a much better number to me (only have to divide unit lengths in half) than 100 (have to divide something by 5).
Where it comes from, I think, is that cow body temperatures are about 100°F, and someone assumed that the scale must have been calibrated using 0° and 100° as specific endpoints.
According to Wikipedia, Fahrenheit seems to have chosen 32°F as the reference point for the freezing of water [it's not clear why this number specifically], and found the body temperature of a human to be 64° more than 32°F [i.e., 96°F]--it being much easier to divide a unit distance in 64 = 2⁶ than to divide it in 100ths.
That does bring up an interesting point, though: while we modern people may think of the metric, base-10 system as being much easier to work with since it's all about lopping off digits, trying to divide a unit length into tenths with high precision is actually far more difficult than halves or thirds. This is why pretty much every customary system involves a lot of units that are twice or three times the next smaller unit. The metric system isn't really feasible until you get the dividing engine , which doesn't show up until about the 1760s.
> This is why pretty much every customary system involves a lot of units that are twice or three times the next smaller unit.
I think easily of units that step up by a multiple of 6 (inches and the various time steps), but nothing immediately occurs to me where one unit is directly twice or thrice another. (Oh, except tablespoons, which are three teaspoons.) What examples am I missing?
Anyway, I started playing with ratios, and noticed that the thing is inaccurate! Further inspection and hypothesizing led me to discover that the scales were not printed concentrically with the mechanism. It's very slight, and not critical to my work in any way, so I treat it as part of the learning experience.
A 5-function calculator was about $100 in 1974 (so about $350 in current dollars) and an HP scientific calculator was 3 or 4x as much. By about the next year, a TI scientific calculator was about the same and by a year or two later you could get an HP--which was the gold standard for about the same amount.
And that was around the price point where making them not just OK to use but mandatory was reasonable at least in higher ed. I was one of the first classes in college where calculators were the norm and slide rules were maybe something you brought for backup at exams. (Calculators were still LEDs so you had to keep them charged.)
With a calculator, you get precision. With a slide rule, you get a value and its sensitivity.
You are allowed to bring a calculator to ham radio license exams in the US, but you have to clear its memory (both data and program memory for programmable calculators) first. If the examiners aren't sure you have done so, they are supposed to disallow the calculator.
Unlike many other standardized tests, there is no specific list of what calculators are allowed. I brought my HP-15C, but wasn't sure that the examiners would be familiar with it and so wasn't sure I'd be able to convince them that I had cleared it.
I also brought a slide rule. That way if the examiners disallowed my HP-15C I'd still be covered.
They did allow the HP-15C, and it turned out that even though I took all three exams (Technician, General, and Extra) that day, I only actually used the calculator once. The questions are all multiple choice, and there was only one where a quick mental approximation wasn't enough to identify the right answer.
It also is fairly hard to hide the fact that the memory isn’t cleared.
Many slide rules also have some read-only memory, for example ’storing’ the constant π.
It's really fascinating, I will show my nephews when I am back in the home country :)
Thanks for posting!
After graduating high school I spent two years in Germany. Whenever I found a flea market or an antique store, I'd search for slide rules. I found two that were in pretty good condition. People always seemed a little confused as to why I wanted these. I guess they just didn't see the beauty in these simple, elegant devices.
Most of us didn't use them, except the fancy-pantses who also insisted on using mechanical pencils. But we all knew how to use them.
I'm graybeard enough that even through college, electric calculators were prohibited in class because they would give you answers without helping you understand the problem.
This is my problem with common core math. It shows how to get to an answer, but I feel it bypasses fundamental understanding on why the answer is what it is.
The main thing that seems to be lacking in K-12 math today, is proofs. Those were my favorite part of math.
With that said, K-12 math teaching in my generation wasn't all that successful.
It's natural to lump these together as if they are a unit, but I think it's important to be explicit about the fact (which of course you know) that they are all too easily separable: it is incredibly easy, given sufficiently powerful tools, to get correct answers with little to no understanding. True understanding (not just "oh, I think I get it") that doesn't help to get answers is not nearly as common, but of course it exists, too.
"...But in the new approach,
As you know, the important thing is to understand what you're doing,
Rather than to get the right answer."
I suspect that part of the problem is that teaching math concepts is at least somewhat orthogonal to drilling kids on being able to perform basic arithmetic operations fluently. Of course, these days I assume at least some of the debate probably gets into the fact that being able to do, say, long division quickly has about the same utility as learning Palmer script.
This definitely looks like a great tool, and I'm kind of sad I don't have one or understand how it works, but this kind of complex learning and memorization up against dropping a needle on a record you like isn't really a great comparison.
C and D are plain log scales, where one decade is the length of the rule. They're sort of the default scales to use.
Multiplication is commutative, so you put either number on either scale. The important thing is that the distance from the left index of the scale is proportional to the log of the number (reading the scale as 1 to 10), so you want to arrange the scales to add the lengths corresponding to your numbers such that the lengths add up. (Or so that you subtract the length of the divisor from the dividend, if you're dividing).
You can get by without the approximation if you're willing to set up the multiplication, see that the product is out there in thin air, then move the slide to put the right index where you originally put the left index. (3 times 5: on the d scale find 3 and put the left index of the C scale there; opposite 5 on the C scale read nothing because there's no D scale there; try again using the right index of the C scale, which is the same thing as having another copy of the D scale out there to the right where the air was).
A and B are each 2 copies of a log scale. You can absolutely use the left side of A and B for your numbers to multiply, and the product will always be on the scale.
People normally use(d?) C and D because the precision is better and because the rest of the scales (like the trig and log-log) are constructed to work with them.
> In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
Are you saying you disagree?
The A/B/C/D names are from Amédée Mannheim, who in 1851 designed the "modern" slide rule & give those scales those names. In practice, you normally just use the C & D scales when you want to multiply. Here's a history of the "cursor" on a slide rule, that also provides a clear history of the slide rule itself: https://www.nzeldes.com/HOC/Cursors.htm
I've never had a practical reason to use a slide rule over a calculator. But I've had fun with them, & that means something.
And slide rules don't do addition or subtraction.
So they were useful in the absence of calculators as a way to avoid using log and trig tables but you wouldn't realistically use them in place of calculators today. (But then I think vinyl records are pretty silly too; and I say that as someone who grew up with them and actually owns a turntable.)
One thing that struck me was that it does require a good instinct for the magnitude of numbers to use. Lots of fun though and surprisingly quick to use.
I did take a technical math class that involved programming a desktop calculator. Basically the first programming class I had.
I wish I remembered what brand it was, I'd like to try to pick one up if I could find one.
Given how you could forget and inadvertently reverse the scales, etc, you have to think whether the answer you're getting makes sense by looking at the trend of the numbers. Plug and chug into a calculator takes some of that away.
I'd like to get one now, mainly for fun, but if you want to buy one on Ebay in good condition, you have to pay quite a bit of money.
It seems around 35 EUR is a normal price.
The game of Go also redecorates my thinking, in a way I cannot put into words.
My children all seem to prefer video.
> My children all seem to prefer video.
When I ask for text transcripts of our training videos, in place of having to sit through 20 minutes of poorly acted out skits (that, re-certification being a periodic thing, I have sat through some 5 or 6 times already in my 10 years on the job), I am always told "but people enjoy the videos"—as if providing transcripts were somehow exclusive of providing videos.
A well-written and illustrated explanation like this one? I can't imagine preferring a video unless someone just wants some background noise and they don't really care about understanding the subject.