B What Replaced Mechanical Calculators Before Modern Calculators Were Invented?

[etotheipi]

Not very modern, but straightforward to understand. He actually does the experiment and analyses the results right in front of you.

Digression, but what on Earth is that ruler thing he's using to calculate products at 14:10 and 15:40?

Edit: I found it, it's called a "slide rule":
https://www.math.utah.edu/~alfeld/sliderules/

 

[robphy]

Digression, but what on Earth is that ruler thing he's using to calculate products at 14:10 and 15:40?

Edit: I found it, it's called a "slide rule":
https://www.math.utah.edu/~alfeld/sliderules/

possibly useful: https://www.sliderules.org/ virtual slide rules

possibly interesting:
https://www.physicsforums.com/threads/relativator-the-circular-slide-rule-for-physicists.767964/ (original posted in 2006)

updated link to the article on Symmetry:
https://www.symmetrymagazine.org/article/december-2005january-2006/artifact-relativator

 

[andresB]

Digression, but what on Earth is that ruler thing he's using to calculate products at 14:10 and 15:40?

Edit: I found it, it's called a "slide rule":
https://www.math.utah.edu/~alfeld/sliderules/

Pretty ingenious, but thank gods for computers.

 

[robphy]

https://www.sliderulemuseum.com/Circular.htm

https://www.si.edu/spotlight/slide-rules/circular-slide-rules

(I’ve been working on and off
on making a virtual version of that relativator.)

 

[Sagittarius A-Star]

Not as clumsy or random as a computer
... an elegant instrument for a more civilized age ...

(Obi-Wan Kenobi)​

​

Source:
https://www.sliderules.org/

The last line may be helpful for relativity ($\sqrt{1-x^2}$, see on the right side):
https://www.sliderules.org/react/aristo_0906_bischolar.html

 

[DaveE]

Seriously, there is one great thing about slide rules. They only give you the mantissa, and just a few significant digits at best. This forces people to actually think about the calculation; built in error checking. An electronic calculator is quite capable of giving erroneous answers if you make a mistake (so will a slide rule), but people don't always do a sanity check. There is some value in using your brain to get a rough answer, before the machines give you a more exact solution.

BTW, my circular slide rule got me through High School Chemistry class and was then permanently retired, it now sits in a box of mementos.

 

[jedishrfu]

Hold on to your slide rules folks when the EMP comes you'll need them to rebuild civilization. :-)

 

[gmax137]

http://www.oughtred.org/

More than you ever wanted to know about sliderules and the people who love them.

 

[Janus]

Not a slide rule, but an old style "flight computer".

 

[Sagittarius A-Star]

Slide Rule vs Calculator Showdown: Decilon & HP-35​

 

[Keith_McClary]

Hold on to your slide rules folks when the EMP comes you'll need them to rebuild civilization. :-)

I'll just get some bamboo and make one.

 

[Gordianus]

I'm old and I've used slide rules. I remember the cheap, small models (5" long and a few lines). The "monsters" were about 12" long, 3" wide and had lots of lines. Quite useful (50 years ago). Perhaps, the last great survivor of the "analog" era is the Smith chart.

 

[jedishrfu]

I'll just get some bamboo and make one.
View attachment 281499

Easier said than done.

 

[Mark44]

I've got about six slide rules here at the house. Back when I first started college, there were no pocket calculators, so calculations were done using slide rules exclusively. About 10 years later, HP came out with the HP-35, which cost about USD300, and they still go for close to that.

They only give you the mantissa, and just a few significant digits at best. This forces people to actually think about the calculation; built in error checking. An electronic calculator is quite capable of giving erroneous answers if you make a mistake (so will a slide rule), but people don't always do a sanity check. There is some value in using your brain to get a rough answer, before the machines give you a more exact solution.

Or an "exacter" solution. Forcing people to actually think about the calculation is a good thing; otherwise it's garbage in, garbage out.

 

[jedishrfu]

I did my physics lab with a combination of sliderule math and adding machine math.

In some cases, i converted my data to logs, added things up and converted back to get a few more digits of accutacy.

 

[hilbert2]

Then there's this mechanical calculator first made by someone when being a prisoner in a nazi concentration camp:

https://en.wikipedia.org/wiki/Curta

Too bad that nowadays senior high school students are not even shown how to calculate approximations for irrational square roots by hand without a calculator. Except in some East European countries where there's more advanced math at that level of schooling.

 

[jedishrfu]

Scientific American did an article on these incredible devices.

https://www.scientificamerican.com/article/the-curious-history-of-th/

I recall someone saying you could never repair them because once you opened it the springs would escape and there was no chance of putting it back together.

i always wanted to own one but they were always way out of my budget even now.

They were also known as a pepper grinder because of their shape and the need to spin a handle.

 

[Keith_McClary]

I did my physics lab with a combination of sliderule math and adding machine math.

In some cases, i converted my data to logs, added things up and converted back to get a few more digits of accutacy.

That's nothing. I had to use an abacus and record intermediate results on a clay tablet with a stylus.

 

[Gordianus]

Does someone remember nomograms?

 

[gmax137]

That's nothing. I had to use an abacus and record intermediate results on a clay tablet with a stylus.

Lucky bastid! We could only dream of having a stylus

 

[Baluncore]

i always wanted to own one but they were always way out of my budget even now.

I find the details of computational instruments fascinating.

I keep a Curta on my desk, to remind me of that tragic past. My slide rules are in the draw, where their batteries won't go flat. There is a box of retired HP RPN calculators somewhere in the store. I keep a HP 48G under my pillow.

My Original Odhner LuSiD is good for 10 digits. I gave it a full service and taught myself to calculate square roots on it when it was over 80 years old. I now take it to "show and tell" events where I get to demonstrate what very few people have seen.
http://www.vintagecalculators.com/html/odhner_lusid.html

 

[anorlunda]

Very nostalgic.

Does someone remember nomograms?

Ah yes. In my M.E. courses, we learned to make our own nomograms. Some of the homework assignments were difficult. You can be very creative about the position, and angles of the scales, and even use curved scales.

It might be fun to do that today. I wouldn't be surprised to see an online calculator that could do it for you. Young people might be fooled into thinking that it was a new invention.

Hold on to your slide rules folks when the EMP comes you'll need them to rebuild civilization. :-)

My Post slide rule came with a high quality leather sheath that could be worn on the belt. I still have it. Back then, there was a big social stigma about wearing it on your belt; very nerdy. Wearing it today might get you shot by police who think it must be a weapon, but at least you would have it with you when the EMP comes.

I also remember raging debates among engineering students about which was best, Pickett (metal) or Post (bamboo). My boss owned a one meter long Pickett slide rule. He claimed to be able to get one more significant digit in his results.

 

[Baluncore]

The most accurate slide rules gave 4 or 5 significant digits. They were cylindrical, with 40 foot long helical scales.
https://americanhistory.si.edu/collections/search/object/nmah_694148

 

[Keith_McClary]

... slide rule came with a high quality leather sheath that could be worn on the belt.

In the campus lost-and-found they had a big bin of those, much better than my little bamboo model in the tattered cardboard box.

 

[jedishrfu]

In case of EMP and no sliderule, there's always the Trachtenberg system of arithmetic to get you through those dark days:

https://en.wikipedia.org/wiki/Trachtenberg_system

 

[anorlunda]

In case of EMP and no sliderule, there's always the Trachtenberg system of arithmetic to get you through those dark days:

https://en.wikipedia.org/wiki/Trachtenberg_system

Don't forget a backup method to make your PF posts.

 

[Sagittarius A-Star]

Don't forget a backup method to make your PF posts.

That should be possible with a Z1 computer.

 

[jedishrfu]

Except the Z1 is electro-mechanical and an EMP might still knock it offline.

https://en.wikipedia.org/wiki/Z1_(computer)

It was a great computer though and ahead of its time.

 

[Sagittarius A-Star]

Except the Z1 is electro-mechanical and an EMP might still knock it offline.

In 1962, the USA carried out a nuclear EMP experiment in high altitude near Hawaii:

Starfish Prime caused an electromagnetic pulse (EMP) that was far larger than expected, so much larger that it drove much of the instrumentation off scale, causing great difficulty in getting accurate measurements. The Starfish Prime electromagnetic pulse also made those effects known to the public by causing electrical damage in Hawaii, about 900 miles (1,450 km) away from the detonation point, knocking out about 300 streetlights,[1](p5) setting off numerous burglar alarms, and damaging a telephone company microwave link.[6] The EMP damage to the microwave link shut down telephone calls from Kauai to the other Hawaiian islands.

Source:
https://en.wikipedia.org/wiki/Starfish_Prime

I think, that electro-mechanical relais are more robust against EMP than transistors or integrated circuits, because their wires have a larger diameter, and so the current density is lower. Solid state equipment has a problem:

Older, vacuum tube (valve) based equipment is generally much less vulnerable to nuclear EMP than solid state equipment, which is much more susceptible to damage by large, brief voltage and current surges. Soviet Cold War-era military aircraft often had avionics based on vacuum tubes because solid-state capabilities were limited and vacuum-tube gear was believed to be more likely to survive.

Source:
https://en.wikipedia.org/wiki/Nuclear_electromagnetic_pulse#Vacuum_tube_vs._solid_state_electronics

On the other hand, computers with smaller size collect less voltage from a certain electric field. So smartphones may work:

An EMP has a smaller effect the shorter the length of an electrical conductor; though other factors affect the vulnerability of electronics as well, so no cutoff length determines whether some piece of equipment will survive. However, small electronic devices, such as wristwatches and cell phones, would most likely withstand an EMP.

Source:
https://en.wikipedia.org/wiki/Nuclear_electromagnetic_pulse#On_small_electronics

 

[emmawarner96]

The slide rule is often used for multiplication and division, but it can also be used for functions like exponents, roots, logarithms, and trigonometry. It is rarely used for addition or subtraction.

The introduction of the inexpensive, fast, and versatile electronic pocket calculator led to the slide rule's demise.
The owner's slide rule used to have a special status, but that was happily replaced by the equally special status of the dazzling HP-35.

 

[Baluncore]

The “General Report On Tunny With Emphasis On Statistical Methods” (1945) from Bletchly Park, GCCS, includes the following inventory item and comment;

“Section 57. Simple Machines.
(a) Slide-rules.
The operations required are multiplication, division, squaring, extracting square roots, and taking logarithms to base 10. Many of the slide-rules used lack logarithms, and have elaborate useless scales.”

Obviously the scales A, B, C & D had no meaning to the author, while the L scale on the rear was not Log because it was Linear !

 

[anorlunda]

Obviously the scales A, B, C & D had no meaning to the author, while the L scale on the rear was not Log because it was Linear !

Ah the nostalgia. You motivated me to take down my old Post from the wall to see what scales it had. When I used it actively, I knew the purpose of all those scales and I found productive uses for them.

Here are the scale labels:

e^x LL0 0.001→0.01
e^-x LL/0 -0.001→-0.01
K
DF
CF
CIF
CI
C
D
R₁
R₂
L
e^-x LL/1
e^-x LL/2
e^-x LL/3
T T
sec T ST
Cos S
e^-x LL/1 -0.01→-0.1
e^-x LL/2 -0.1→-1.0
e^-x LL/3 - 1.0→-10.0
C
X D
e^x LL1 1.0→10.0
e^x LL2 0.1→1.0
e^x LL3 0.01→0.1

 

[Mark44]

That's nothing. I had to use an abacus and record intermediate results on a clay tablet with a stylus.

Lucky bastid! We could only dream of having a stylus

Luxury! We could only count on our fingers...

 

[Vanadium 50]

Luxury! We could only count on our fingers...

Fingers? You had fingers? Why, when I was a lad we hadn't yer evolved fingers...

 

[Baluncore]

There are a couple of good historical references here;
“From webbed fingers to the World Wide web” and “From dactylonomy to binary arithmetic”. Both by the scientist and author; Sly Drool.

 

[jedishrfu]

Not a slide rule, but an old style "flight computer"

Your post inspire me to look on eBay where I found a Concise Circular sliderule that I bought. Concise still has a website and still sells circulars. This one is a model 300 with a 4” diameter which makes it have the roughly same resolution as a 12” stick sliderule.

There are two kinds of circulars that I have found. The first a Post uses two connected cursors. Place one on the index’s point of the scale and the other on the number then use them together preserving the angle to find the second number and at the other end you’ll find the answer.

The concise uses two rotating discs where you move one the smaller disk index point to the first number and then line the cursor on the second number on the smaller disk and read the answer on the larger disk under the cursor.

 

[anorlunda]

Your post inspire me to look on eBay where I found a Concise Circular sliderule that I bought.

Cool. Post a picture.

 

[jedishrfu]

https://www.sliderule.tokyo/products/detail.php?product_id=8

 

[anorlunda]

Very nice. You can challenge your students with that.

Keep it clean and treat it gently so that the markings don't erode.

 

[Ibix]

View attachment 282470
https://www.sliderule.tokyo/products/detail.php?product_id=8

$3200!

 

[anorlunda]

$3200!

3200 JPY = $29.34

 

[YoungPhysicist]

The fact that Concise is still in business is remarkable. From what I know they have no real market, as with every other kinds of slide rule, and only serve as collectibles nowadays. Even Hemmi(a major Japanese slide rule manufacturer alongside Concise, many of it's products known as POST in the west)has turned into a small enterprise selling PCBs, with almost no evidence of its former glory besides its company name.

https://www.hemmi-inc.co.jp/english/

So either Concise made too many of them and had to get rid of them for decades or maybe there is actually someone buying them for genuine calculation purposes, I think.

 

[Mark44]

My slide rule collection, plus an HP 11-C that my brother gave me, and that uses RPN (reverse Polish notation).
The yellow one is a Pickett that I've had since the early 60s. The third one down is also a Pickett that someone gave me. Besides the L scale, which I remember using, it also has LL0, LL00, LL1, LL2, and LL3 scales that I'm not familiar with. The one at the bottom belonged to my wife's father.

 

[hutchphd]

Keep it clean and treat it gently so that the markings don't erode.

I always used to put a little talcum powder on my linear rule (probably give me lung cancer!).

 

[hutchphd]

The third one down is also a Pickett that someone gave me.

Yeah I spent many anguished hours on that machine. As I recall the HP 35 Calculator was around $400 ...too rich for my sophomore self.

 

[jedishrfu]

Here’s a insturctable on making your own primitive rule in case of EMP

https://www.instructables.com/Making-Your-Own-Slide-Rule/

Print before EMP strikes.

 

[jedishrfu]

@Mark44 here’s a discussion on the slide scale functions including the LL series.

https://www.math.utah.edu/~alfeld/sliderules/

In high school, a chemistry teacher taught me those after school. I used them in Ph calculations but don’t remember much beyond that.

I also remember using them in an approximation scheme starting with the answer and twiddling the slide to find when the two operands were the same. As an example, the trick could be used to find square roots using the C and D scales that were slightly more accurate but I remember using them on other scales too.

 

[anorlunda]

The one at the bottom belonged to my wife's father.

The one on the bottom was a Post rule. That's the kind I had. (see #22 in this thread.) Post was made of bamboo, compared to metal for Pickets or plastic for other brands. Undergrads took great delight arguing which was best.

Bamboo would shrink or swell with the humidity, so the screws holding it tight had to be adjusted often. If I remember, the surface of the metal Pickett was more vulnerable to scratches and abuse.

I too bought a HP-35 on the first day they came out, and I took it with me to Finland on a business trip that same day. I was the envy of every engineer in all of Finland that day.

Does anybody have a fond memory of the mechanical calculators the HP-35 replaced? I hated them, and I hated the noise they made. Slide rules were far superior unless you needed many more digits of precision.