
The Slide Rule - refrigerator
https://tryretool.com/blog/the-slide-rule/?4
======
todd8
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.

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.

I just recently pulled out my old slide rule to show my accountant how they
worked.

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]

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.

[1] [https://www.ebay.com/itm/VINTAGE-1959-PICKETT-DUAL-BASE-
SLID...](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)

[2] [https://ocw.mit.edu/courses/edgerton-
center/ec-050-recreate-...](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/)

~~~
rmason
I bring out the slide rule pretty much these days to give history lessons to
young folks. Last time I showed how it worked to a pair of GenZ kids they
looked at me with a healthy bit of skepticism. Like somehow this was some sort
of fake contraption. I felt a bit like my late father explaining what it was
like to crank a car to start it.

~~~
todd8
I know what you mean. I borrowed a car from a fraternity brother to pick up a
date once. Before departing he explained that if it didn't start I might have
to use the crank! It was a Citroën if I remember correctly. I'm sure it really
impressed my date.

~~~
blattimwind
Extra battery (the one you take inside where it's warm over night) and starter
cables in the footwell :)

------
kqr
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.

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.

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.

~~~
moate
>>For example if you have a recipe calling for 150 g of butter, but you want
to use all of your 250 g,

What a strange way of cooking. I'm not saying it's bad, just that typically
people cook for a result (I want to make X servings) not a reason (I want to
eliminate all of the butter in my house).

~~~
ealhad
Would you understand it better the other way around? A recipe calling for 250
g of butter, but alas, you only have 150 g left.

~~~
moate
Not really? If I have a dinner party involving 6 guests, and my recipe calls
for (<ingredients per portion>*6) then scaling down that ratio may give me 4.5
portions.

I don't cook things without purpose/specific goals. I'm cooking to make enough
for the people I'm expecting.

That's not to say it doesn't make sense, just not how I've tended to see
things cooked.

~~~
eT8AZithxooKei6
OK. What if you have a dinner party for 6 guests, but your recipe is written
to give 8 portions?

~~~
Zancarius
What I'd do in this case (and this is true for most everyone I know) depends
on what "portion" means:

\- If it's something that can be reasonably divided among guests (such as a
soup or something similar), then I eyeball the portions so they're all
approximately even. Optionally, if there's an ample amount, you can simply let
people decide how much they want through self-service.

\- If it's something that's demarcated by physical objects (e.g. dinner rolls,
cupcakes, etc), then you have a few other options: Leftovers to save for
later, split them among people who want extra, or give them away to whomever
wants them.

I don't know about the OP you're replying to, but I rarely divide a recipe up
based on expected portions since portion size is highly variable. Should I
have extra left over, then I deal with that accordingly. If I'm cooking to get
rid of an ingredient, I don't particularly care if I miss the mark by a few
portions provided I have enough in the first place for the objective.

(The other problem is that portioning in this question seems to me to assume
that all guests are equally hungry.)

------
combatentropy
"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,
[https://www.etymonline.com/word/cursor#etymonline_v_494](https://www.etymonline.com/word/cursor#etymonline_v_494).
So its cursor was the precursor to our cursor.

~~~
lurquer
I concur, sir.

------
tr352
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.

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".

[1] [https://en.wikipedia.org/wiki/E6B](https://en.wikipedia.org/wiki/E6B)

~~~
skykooler
I think the E6B contradicts the article's assertion that the last slide rule
in the US was made in 1976; when I was taking flying lessons a few years ago,
I was required to buy a new E6B, and I doubt that was from some massive
overstock in the 70's.

~~~
tr352
True. ASA still makes them but I suppose the only reason they're still made is
that it's been considered standard classroom equipment for the past 70 years,
combined with the well known universal dislike for change in the aviation
world. I don't know anyone who kept using the E6B after getting licensed.

------
dbcurtis
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.

~~~
ghaff
>The transition was nearly instantaneous.

The first pocket scientific calculator was the HP-35 in 1972 (costing about
$2,500 in today's dollars). Within 3 years, at least for most university
engineering programs in the US, slide rules were completely gone. [That's
incredibly fast.]

~~~
7402
In my freshman physics class (1972-73) that price was a brief ethical issue.
The professor said that for a midterm we could use one page of written notes
and a slide rule. One student asked if he could use a calculator instead of a
slide rule. "Are you going to buy calculators for everyone else in the class,
too?" the professor asked. He felt it would be unfair to give such a big
advantage to those few who could afford an HP-35 at that time.

~~~
ghaff
I’m now a bit curious when the switch flipped at the school I attended. There
was no question when I started in 1975 that you needed a calculator. I suspect
that those in the class ahead did as well. But that must have been very new.

------
sam_goody
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,)

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.

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.

[1]:
[https://www.ee.ryerson.ca/~elf/abacus/feynman.html](https://www.ee.ryerson.ca/~elf/abacus/feynman.html)

~~~
dreamcompiler
> My grandfather was an accountant who preferred the slide rule to a
> calculator.

This is hard for me to understand. Slide rules are inherently imprecise, in
the same way floating point calculations are imprecise but much moreso. I'd
expect an accountant to prefer integer (fixed point) math for the same reason
banks do now.

~~~
sizzzzlerz
Yes, they are imprecise. In general, you're limited to just three, maybe four
digits regardless of the actual magnitude of the numbers and you have to keep
the powers of ten in your head. Honestly, though, once you've used it enough,
it isn't that hard to do. Besides, in most calculations, you don't need
precision out to the 12th digit. After all, skyscrapers, bridges, and ocean
liners have been built using slide rules for a long time and they, mostly,
have worked just fine.

~~~
dreamcompiler
Imprecision is fine for engineering and can be compensated for. But this is
not true for managing money, which is why floating point has historically not
been used in accounting applications.

~~~
sizzzzlerz
Yeah, bean counters do like to know their amounts out to the penny. That would
require a pretty big slide rule.

------
sizzzzlerz
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.

------
derekp7
There is a fairly good writeup on various slide rule types and scales, on
[http://www.quadibloc.com/math/slrint.htm](http://www.quadibloc.com/math/slrint.htm)
(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).

------
gshubert17
A nice reference is Clifford Stoll's (author of A Cuckoo's Egg) article in
Scientific American 2006:

[http://www.uvm.edu/pdodds/files/papers/others/2006/stoll2006...](http://www.uvm.edu/pdodds/files/papers/others/2006/stoll2006a.pdf)

And a way to make your own sliderule:

[https://static.scientificamerican.com/sciam/assets/media/pdf...](https://static.scientificamerican.com/sciam/assets/media/pdf/Slide_rule.pdf)

The article has the same IBM ad and says it's from 1953.

------
jhallenworld
People on eBay are selling these Soviet pocket-watch style rotary slide rules:

[https://www.youtube.com/watch?v=Kuzdjy3HpWg](https://www.youtube.com/watch?v=Kuzdjy3HpWg)

I think they were made into the 80s.

------
Sniffnoy
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.

[1]
[https://en.wikipedia.org/wiki/Prosthaphaeresis](https://en.wikipedia.org/wiki/Prosthaphaeresis)

~~~
jacobolus
Angle measure is just the bivector (‘imaginary’) part of the complex
logarithm.

------
thanatropism
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.

What was the name?

~~~
Jtsummers
Possibly this?

[https://en.wikipedia.org/wiki/Nomogram](https://en.wikipedia.org/wiki/Nomogram)

A Python package for it:

[http://pynomo.org/wiki/index.php/Main_Page](http://pynomo.org/wiki/index.php/Main_Page)

~~~
function_seven
This example is one of the coolest things I've seen

[https://upload.wikimedia.org/wikipedia/en/a/a5/Risk_Based_Sa...](https://upload.wikimedia.org/wikipedia/en/a/a5/Risk_Based_Sampling_Nomogram_%283yr%29.png)

I had some fun drawing lines and seeing how each factor influenced the chain
of isopleths.

------
carapace
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.

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 _n_ shows
_nm_ for all _m_. (Actually all _mnEk_ for all _m_ and _k_.)

Some slide rules are circular or tubular.

See also:
[https://en.wikipedia.org/wiki/Nomogram](https://en.wikipedia.org/wiki/Nomogram)

------
abecedarius
The intro about Kepler is inaccurate, so I distrusted the claim about Newton
too. It seems he did use a kind of slide rule:
[http://www.oughtred.org/history.shtml](http://www.oughtred.org/history.shtml)

> In 1675 Sir Isaac Newton solves cubic equations using three parallel
> logarithmic scales and makes the first suggestion toward the use of the
> cursor.

> 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.

~~~
refrigerator
Thanks for raising this — what part of the intro was inaccurate? This was the
source we used for the Kepler info:
[https://www.jstor.org/stable/27838992?seq=1#page_scan_tab_co...](https://www.jstor.org/stable/27838992?seq=1#page_scan_tab_contents)

~~~
abecedarius
> Kepler first formulated his hypothesis: planets had elliptical orbits with
> two foci, and then set out to prove it mathematically.

He didn't start with that hypothesis, he came to it after multiple tries at
fitting other models like an equant (an offset circle with angular speed
controlled from the opposite offset, which is actually a good first-order
approximation to the Kepler-law motion at small eccentricity).

> Only after repeating his procedures 70 times did he offset his computational
> errors. With a little less patience, he wouldn’t have proved his theory, and
> elliptical orbits would have eluded us for longer.

I skimmed the paper, and it seems to be about Kepler fitting an equant instead
of an ellipse. Apparently he used an iterative method, stopping after 70
iterations? And his numerical errors seem to be responsible for it not
converging faster. That makes more sense to me than my misunderstanding that
you were saying he ran through the whole calculation from the start 70 times.
I jumped to a conclusion about that part, and I'm sorry.

Julian Barbour's _The Discovery of Dynamics_ explains what Kepler did in
detail (it's not the whole topic of the book, but a big chunk of it). A great
book -- I didn't really appreciate Kepler before reading it. Both brilliant
and very human.

------
puetzk
> The last slide rule manufactured in the US was produced on July 11, 1976

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.
[https://www.amazon.com/ThinkGeek-Slide-
Rule/dp/B003M5B84C](https://www.amazon.com/ThinkGeek-Slide-Rule/dp/B003M5B84C)
still shows a listing.

~~~
tzs
I have a couple, too. They were not very good though.

I'd be interested if someone made a new good slide rule. And not just slide
rules--there are at least a couple of other older computing devices I'd like a
good quality working replica or reproduction of.

1\. A Curta calculator.
[https://en.wikipedia.org/wiki/Curta](https://en.wikipedia.org/wiki/Curta)

2\. The Antikythera mechanism.
[https://en.wikipedia.org/wiki/Antikythera_mechanism](https://en.wikipedia.org/wiki/Antikythera_mechanism)

~~~
masklinn
> 1\. A Curta calculator.
> [https://en.wikipedia.org/wiki/Curta](https://en.wikipedia.org/wiki/Curta)

The article notes that Marcus Wu has published a printable 3D model of a curta
(at 3:1 size due to printer precision issues, though there are comments about
people attempting 2:1 builds). You can also find actual curtas on ebay, though
they're not cheap ($500~$1500 depending on condition and the like).

------
spreiti
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.

~~~
z2
And most are helpfully marked for unit conversions as well! I have mine set
for restaurant tipping by default (North America).

------
philiplu
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.

------
gepoch
Reading about the usefulness of logs reminded me of another spatial math tool:
The Triangle of Power!

[https://www.youtube.com/watch?v=sULa9Lc4pck](https://www.youtube.com/watch?v=sULa9Lc4pck)

~~~
thunderbong
This one was seriously awesome! Thanks. Most times when people say Math is
hard they are actually talking about this. All the different ways to memorize
stuff which doesn't help them get intuitive in Math.

------
cafard
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.

~~~
ghaff
At one time there were a lot of industry specific tools to calculate various
things (usually made out of cardboard) that were effectively slide rules or
slide rules combined with lookup tables.

------
zokier
> The last slide rule manufactured in the US was produced on July 11, 1976

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.

~~~
asynchronous13
I'm guessing that's a bit of hyperbole, since new sliderules are still
available for purchase today. Obviously manufacture of sliderules dropped
precipitously, but there's still a niche market for them.

~~~
macintux
"manufactured in the US"

I wouldn't be surprised if the quote is accurate.

~~~
ghaff
Missed that. Yes, that makes it plausible as Post and K&E had both ceased
production by then and, presumably, most of the cheaper plastic ones were
either made in Japan or in places like the Soviet Union for domestic use.

------
unethical_ban
First, the positive note: This is an awesome, accessible article.

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?

~~~
roywiggins
I think it's convention, but it would have been good to explain this a bit
more. The previous sentence seems to say "from now on we mean base 2" ("In the
world of 2s, log(x) tells you how many times you have to multiply 2 by itself
to get x.")

Which base gets to be special depends. Log on its own often means base e;
sometimes base 10; and sometimes base 2 (and sometimes 'base whatever, it's
not important')

------
skatanski
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.

