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.
Calculation before we went digital [pdf]
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Re: Calculation before we went digital [pdf]
#12I 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 t…
Its funny how "CC:" has survived into the digital age. I wonder how many 20-somethings or younger realize what it really means?!
Re: Calculation before we went digital [pdf]
#13For 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…
Save the $10 and look at the selection of online virtual slide rules at https://www.sliderules.org/.
Re: Calculation before we went digital [pdf]
#14Yet another conflation of digital and electronic. There have always been "digital" modes of computation.
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."
Re: Calculation before we went digital [pdf]
#15In 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
[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.
Re: Calculation before we went digital [pdf]
#16> 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-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. ;)
Re: Calculation before we went digital [pdf]
#17If 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
Re: Calculation before we went digital [pdf]
#18Yet another conflation of digital and electronic. There have always been "digital" modes of computation.
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'.
Re: Calculation before we went digital [pdf]
#19This is a fantastic resource, actually.
Re: Calculation before we went digital [pdf]
#20For 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…
Save the $10 and look at the selection of online virtual slide rules at https://www.sliderules.org/ .
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.