7 ms·

Calculation before we went digital [pdf]

99 points by nostrilwig 3y ago

tempodox 3y ago
A highly interesting collection of machinery, I'm impressed.
userbinator 3y ago
Clearly not written by someone with native English ("subtract is became easy" is particularly memorable), but still not hard to understand, and the content is very interesting although it jumps around a bit --- I like how "physical" these early calculating machines are, as one could easily see the process being carried out.
- red_admiral 3y ago
  Indeed, for learning arithmetic and many other areas of mathematics, being able to do calculations physically is better than (optimistically speaking) 90% of what goes as "ed tech" these days. Cuisenaire rods teach you basic counting and get things like 3+7=10 into your subconscious (or, if you have synaesthesia, also green+black=orange). The abacus, back when it was taught, made place-value and things like "to subtract 8 you subtract 10 then add 2" a physical as well as a mental operation which helps with math learning the way phonics helps with reading. Later on, of course, slide rules do the same for logarithms (as is explained in the linked PDF). I wish we had more of this back in our classrooms.
Mr_Minderbinder 3y ago
Yet another conflation of digital and electronic. There have always been "digital" modes of computation.
- analog31 3y ago
  To be fair, despite the title, the article does describe digital mechanical calculators as "digital." An amusing aside, amongst electronics and audio people, there's an ongoing debate about whether a switchmode power supply or amplifier is "digital." Also, when CD players first came out, I was in a stereo shop, and some speakers were labeled as "digital ready."
- eesmith 3y ago
  Mmmm, that was pretty clear from the text. Top of page 6: 'I wrote "The calculation before we went digital", but the digital age started when the first man has counted some objects with the fingers (digitus in Latin means finger). ... With the digital system the numbers are represented by single units, such as the bead of the abacus or a number: counting the same stones' The author then goes through pages describing pre-computer digital systems, including the pascaline, with 'a digital display of the sixteen century'.
TacticalCoder 3y ago
I still have the Odhner calculator, as seen on page 19 of that PDF, that my grandfather was still using at his SME in the eighties (he owned a little SME making tailor-made clothes)! I think that at some point in the fifties he bought a stock of desks, calculators, typewriters, etc., used, from another company. And then he kept using these old machines for decades. As a teenager I'd go help for a few bucks: I'd use the typewriter to write letters plus actual "carbon copies" (literally putting two or three sheets of paper separated by a carbon sheet). Never understood how that Odhner calculator worked but I still have it (and I had no idea it was from 1920: TIL)! P.S: I also wrote my first program used "for real" back then: I wrote a program on my Commodore 64 that'd compute the discount for his clients (like, say, hotels) according to how many suits they'd buy. And I printed the results on a dot-matrix printer. This saved my grandpa lots of time!
- PopAlongKid 3y ago
  >literally putting two or three sheets of paper separated by a carbon sheet I had to chuckle at your use of "literally", as I too (and probably many others here) would never imagine that there was a figurative way to do this. I should add, carbon paper is not literally made out of carbon. Separately, I noticed the image of the Playboy Magazine cover used in the article. It was customary for them to always include the bunny logo somewhere as part of the image; in this case it is embossed on the leather case for the slide rule.
  - dahart 3y ago
    Why would use of literally imply there’s a figurative way to do it? Literally has been used for emphasis and even sometimes used (correctly) to mean figuratively, for literally hundreds of years. Language is fluid and fun, and words have multiple meanings. Always have, always will. Don’t fight it, enjoy it. https://blogs.illinois.edu/view/25/96439 https://blogs.illinois.edu/view/25/96439 https://www.merriam-webster.com/grammar/misuse-of-literally https://www.merriam-webster.com/grammar/misuse-of-literally
- HarHarVeryFunny 3y ago
  Its funny how "CC:" has survived into the digital age. I wonder how many 20-somethings or younger realize what it really means?!
argiopetech 3y ago
For those who wish to learn more about the slide rule, I recommend Asimov's (yes, that Asimov) book, "An Easy Introduction to the Slide Rule." I was lucky to pick up a physical copy as a young man, but it appears it's available as a PDF online. That, plus any of the $10 vintage slide rules on eBay, opens a while new world of fun. I still use slide rules fairly regularly. I find that I gain better understanding of the equations I use the most when I can reformulate them for easy solving on a slide rule (e.g., so you can solve an equation with two operations with one slide move).
- I_complete_me 3y ago
  Save the $10 and look at the selection of online virtual slide rules at https://www.sliderules.org/ https://www.sliderules.org/.
  - argiopetech 3y ago
    This is an amazing resource, but it just doesn't beat the feel or utility of having a real slide rule in your hands. Part of the appeal is the ability to rapidly compute at the expense of precision (it's the fundamental tradeoff of the slide rule, though larger slide rules and careful use try to minimize it), but the emulated versions encourage precision over speed by design.
    - abecedarius 3y ago
      I've bought a couple of slide rules and feel like I still haven't quite gotten it: - a ThinkGeek one which had an offputting amount of stiction despite not-bad reviews - a used one which was better, but such that I guess I still need to learn how to clean or lubricate it to the standard these things must've been meant for.
      - argiopetech 3y ago
        I clean and lubricate my metal and plastic slide rules occasionally. A good wipe down and petroleum jelly is sufficient. Bamboo slide rules seem to be more slippery, so I just keep them clean. You want it to move freely and without grit, but not so freely that it has a chance of slipping. When necessary, adjustment by loosening the top and bottom scales can be accomplished by using the cursor to fix alignment.
deleted 3y ago
[deleted]
zvr 3y ago
People with interest in calculators might be interested to read Empire of the Sum by Keith Houston, which provides some historical notes on calculating before the electronic and digital revolution. -- A proud owner of a Faber Castell slide rule, inherited from my father, and an Odhner mechanical calculator, from my grandfather.
HarHarVeryFunny 3y ago
The article doesn't mention one of the earliest calculators (an analog computer of sorts) - the "Antikythera mechanism" from c.100 BC. An incredibly intricate device for calculating and indicating the positions of the planets.
tzs 3y ago
In 2015 I took a slide rule with me when I took my US ham radio license exams. I also took an HP-15c [1], which is what I actually used, but I wasn't sure that the calculator would be allowed [2] so brought the slide rule just in case. The exam is multiple choice and usually the choices are far enough apart that you don't need very much accuracy to figure out which one must be the right one, so even rudimentary slide rule skills would be sufficient. You usually just need to get 1 or 2 significant digits and the right order of magnitude. [1] https://en.wikipedia.org/wiki/HP-15C https://en.wikipedia.org/wiki/HP-15C [2] If your calculator has memory or is programmable you have to convince the examiner that you have cleared memory and erased all your programs.
dahart 3y ago
> The slide rules, also known colloquially as “slip sticks”, were the only calculators available before the electronic age, traveled with the Apollo 11 on the Moon and, essentials on board aircraft for the dead reckoning, are still required as a means of emergency. This sentence is funny for several reasons, not least of which is it comes after a long list of pre-electronics calculators. The mention of dead reckoning totally reminded me of one of the coolest math books I ever bought, and I think I first heard about it in a comment here on HN. Maybe I can pass this recommend on to someone else who will appreciate it. “Dead Reckoning: Calculating Without Instruments” by Ronald Doerfler https://www.amazon.com/Dead-Reckoning-Calculating-Without-Instruments/dp/0884150879 https://www.amazon.com/Dead-Reckoning-Calculating-Without-In... It covers how to do lots of calculations very efficiently mentally or manually on paper, not just arithmetic but roots and powers, logarithms and exponents, and trig functions (sin,cos,tan,asin,acos,atan). Lots of interesting number theory, lots of stuff that’s useful in computer science, and a tour de force of the most important analog calculator this article didn’t cover: the human calculator. ;)
- deleted 3y ago
  [deleted]
mooreds 3y ago
If you are interested in this, you might enjoy this Odd Lots episode, about how banks worked before computers: https://www.youtube.com/watch?v=kYpe_K8PzbQ https://www.youtube.com/watch?v=kYpe_K8PzbQ
bvan 3y ago
This is a fantastic resource, actually.
zhrvoj 3y ago
Everything went well then. I graduated without computers help - on computers. Today it's vice versa. Today every new os version - just new clicks or taps, for poor little John to make it with less clicks, and this is always presented as biig advance in computer field. Yes, I mean Microsoft and Apple and .... Everything screwed up for the sake of profit for the shareholders. Every new tech carries the burden of shareholders just thinking of profit.
Jemm 3y ago
Father worked as a calculator. Room full of guys summing columns in their heads. When mechanical calculators came out they ran them in parallel with the human calculators.
KineticLensman 3y ago
I'm currently reading Between Human and Machine: Feedback, Control, and Computing before Cybernetics, which covers the development of analogue computers from 1914 to 1945. It's really interesting to see the development of physical machines which were used to support complex real-time calculations (e.g. from gunfire control on battleships to early radar-driven AA guns) and how these transitioned to electronic (but not yet digital) solutions. What's also interesting is that the development of these machines led to the first published use of terms such as 'systems integration' and the recognition that the feedback control aspects of a system were just as important as the optics, mechanics, etc. Also how cross-domain fertilization occurred, e.g. the realisation that servo motors were in a sense amplifiers, and thus that maths developed to support communications systems could be applied almost directly to physical control systems.

99 points by nostrilwig 3y ago

A highly interesting collection of machinery, I'm impressed.

Clearly not written by someone with native English ("subtract is became easy" is particularly memorable), but still not hard to understand, and the content is very interesting although it jumps around a bit --- I like how "physical" these early calculating machines are, as one could easily see the process being carried out.

red_admiral 3y ago
Indeed, for learning arithmetic and many other areas of mathematics, being able to do calculations physically is better than (optimistically speaking) 90% of what goes as "ed tech" these days. Cuisenaire rods teach you basic counting and get things like 3+7=10 into your subconscious (or, if you have synaesthesia, also green+black=orange). The abacus, back when it was taught, made place-value and things like "to subtract 8 you subtract 10 then add 2" a physical as well as a mental operation which helps with math learning the way phonics helps with reading. Later on, of course, slide rules do the same for logarithms (as is explained in the linked PDF). I wish we had more of this back in our classrooms.

Mr_Minderbinder 3y ago

Yet another conflation of digital and electronic. There have always been "digital" modes of computation.

analog31 3y ago
To be fair, despite the title, the article does describe digital mechanical calculators as "digital." An amusing aside, amongst electronics and audio people, there's an ongoing debate about whether a switchmode power supply or amplifier is "digital." Also, when CD players first came out, I was in a stereo shop, and some speakers were labeled as "digital ready."
eesmith 3y ago
Mmmm, that was pretty clear from the text. Top of page 6: 'I wrote "The calculation before we went digital", but the digital age started when the first man has counted some objects with the fingers (digitus in Latin means finger). ... With the digital system the numbers are represented by single units, such as the bead of the abacus or a number: counting the same stones' The author then goes through pages describing pre-computer digital systems, including the pascaline, with 'a digital display of the sixteen century'.

TacticalCoder 3y ago

I still have the Odhner calculator, as seen on page 19 of that PDF, that my grandfather was still using at his SME in the eighties (he owned a little SME making tailor-made clothes)! I think that at some point in the fifties he bought a stock of desks, calculators, typewriters, etc., used, from another company. And then he kept using these old machines for decades. As a teenager I'd go help for a few bucks: I'd use the typewriter to write letters plus actual "carbon copies" (literally putting two or three sheets of paper separated by a carbon sheet). Never understood how that Odhner calculator worked but I still have it (and I had no idea it was from 1920: TIL)! P.S: I also wrote my first program used "for real" back then: I wrote a program on my Commodore 64 that'd compute the discount for his clients (like, say, hotels) according to how many suits they'd buy. And I printed the results on a dot-matrix printer. This saved my grandpa lots of time!

PopAlongKid 3y ago
>literally putting two or three sheets of paper separated by a carbon sheet I had to chuckle at your use of "literally", as I too (and probably many others here) would never imagine that there was a figurative way to do this. I should add, carbon paper is not literally made out of carbon. Separately, I noticed the image of the Playboy Magazine cover used in the article. It was customary for them to always include the bunny logo somewhere as part of the image; in this case it is embossed on the leather case for the slide rule.
- dahart 3y ago
  Why would use of literally imply there’s a figurative way to do it? Literally has been used for emphasis and even sometimes used (correctly) to mean figuratively, for literally hundreds of years. Language is fluid and fun, and words have multiple meanings. Always have, always will. Don’t fight it, enjoy it. https://blogs.illinois.edu/view/25/96439 https://blogs.illinois.edu/view/25/96439 https://www.merriam-webster.com/grammar/misuse-of-literally https://www.merriam-webster.com/grammar/misuse-of-literally
HarHarVeryFunny 3y ago
Its funny how "CC:" has survived into the digital age. I wonder how many 20-somethings or younger realize what it really means?!

argiopetech 3y ago

For those who wish to learn more about the slide rule, I recommend Asimov's (yes, that Asimov) book, "An Easy Introduction to the Slide Rule." I was lucky to pick up a physical copy as a young man, but it appears it's available as a PDF online. That, plus any of the $10 vintage slide rules on eBay, opens a while new world of fun. I still use slide rules fairly regularly. I find that I gain better understanding of the equations I use the most when I can reformulate them for easy solving on a slide rule (e.g., so you can solve an equation with two operations with one slide move).

I_complete_me 3y ago
Save the $10 and look at the selection of online virtual slide rules at https://www.sliderules.org/ https://www.sliderules.org/.
- argiopetech 3y ago
  This is an amazing resource, but it just doesn't beat the feel or utility of having a real slide rule in your hands. Part of the appeal is the ability to rapidly compute at the expense of precision (it's the fundamental tradeoff of the slide rule, though larger slide rules and careful use try to minimize it), but the emulated versions encourage precision over speed by design.
  - abecedarius 3y ago
    I've bought a couple of slide rules and feel like I still haven't quite gotten it: - a ThinkGeek one which had an offputting amount of stiction despite not-bad reviews - a used one which was better, but such that I guess I still need to learn how to clean or lubricate it to the standard these things must've been meant for.
    - argiopetech 3y ago
      I clean and lubricate my metal and plastic slide rules occasionally. A good wipe down and petroleum jelly is sufficient. Bamboo slide rules seem to be more slippery, so I just keep them clean. You want it to move freely and without grit, but not so freely that it has a chance of slipping. When necessary, adjustment by loosening the top and bottom scales can be accomplished by using the cursor to fix alignment.

deleted 3y ago

[deleted]

zvr 3y ago

People with interest in calculators might be interested to read Empire of the Sum by Keith Houston, which provides some historical notes on calculating before the electronic and digital revolution. -- A proud owner of a Faber Castell slide rule, inherited from my father, and an Odhner mechanical calculator, from my grandfather.

HarHarVeryFunny 3y ago

The article doesn't mention one of the earliest calculators (an analog computer of sorts) - the "Antikythera mechanism" from c.100 BC. An incredibly intricate device for calculating and indicating the positions of the planets.

tzs 3y ago

In 2015 I took a slide rule with me when I took my US ham radio license exams. I also took an HP-15c [1], which is what I actually used, but I wasn't sure that the calculator would be allowed [2] so brought the slide rule just in case. The exam is multiple choice and usually the choices are far enough apart that you don't need very much accuracy to figure out which one must be the right one, so even rudimentary slide rule skills would be sufficient. You usually just need to get 1 or 2 significant digits and the right order of magnitude. [1] https://en.wikipedia.org/wiki/HP-15C https://en.wikipedia.org/wiki/HP-15C [2] If your calculator has memory or is programmable you have to convince the examiner that you have cleared memory and erased all your programs.

dahart 3y ago

> The slide rules, also known colloquially as “slip sticks”, were the only calculators available before the electronic age, traveled with the Apollo 11 on the Moon and, essentials on board aircraft for the dead reckoning, are still required as a means of emergency. This sentence is funny for several reasons, not least of which is it comes after a long list of pre-electronics calculators. The mention of dead reckoning totally reminded me of one of the coolest math books I ever bought, and I think I first heard about it in a comment here on HN. Maybe I can pass this recommend on to someone else who will appreciate it. “Dead Reckoning: Calculating Without Instruments” by Ronald Doerfler https://www.amazon.com/Dead-Reckoning-Calculating-Without-Instruments/dp/0884150879 https://www.amazon.com/Dead-Reckoning-Calculating-Without-In... It covers how to do lots of calculations very efficiently mentally or manually on paper, not just arithmetic but roots and powers, logarithms and exponents, and trig functions (sin,cos,tan,asin,acos,atan). Lots of interesting number theory, lots of stuff that’s useful in computer science, and a tour de force of the most important analog calculator this article didn’t cover: the human calculator. ;)

deleted 3y ago
[deleted]

mooreds 3y ago

If you are interested in this, you might enjoy this Odd Lots episode, about how banks worked before computers: https://www.youtube.com/watch?v=kYpe_K8PzbQ https://www.youtube.com/watch?v=kYpe_K8PzbQ

bvan 3y ago

This is a fantastic resource, actually.

zhrvoj 3y ago

Everything went well then. I graduated without computers help - on computers. Today it's vice versa. Today every new os version - just new clicks or taps, for poor little John to make it with less clicks, and this is always presented as biig advance in computer field. Yes, I mean Microsoft and Apple and .... Everything screwed up for the sake of profit for the shareholders. Every new tech carries the burden of shareholders just thinking of profit.

Jemm 3y ago

Father worked as a calculator. Room full of guys summing columns in their heads. When mechanical calculators came out they ran them in parallel with the human calculators.

KineticLensman 3y ago

I'm currently reading Between Human and Machine: Feedback, Control, and Computing before Cybernetics, which covers the development of analogue computers from 1914 to 1945. It's really interesting to see the development of physical machines which were used to support complex real-time calculations (e.g. from gunfire control on battleships to early radar-driven AA guns) and how these transitioned to electronic (but not yet digital) solutions. What's also interesting is that the development of these machines led to the first published use of terms such as 'systems integration' and the recognition that the feedback control aspects of a system were just as important as the optics, mechanics, etc. Also how cross-domain fertilization occurred, e.g. the realisation that servo motors were in a sense amplifiers, and thus that maths developed to support communications systems could be applied almost directly to physical control systems.