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The Wikipedia article Computer (job description) says that before the invention of electronic computers, the term "computer" used to refer to people who worked as "computers".

My question is: what did the "programs" that "human computers" executed look like, and were the "programs" written using a "programming language", and were the "programs" written on a piece of paper?

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    The easiest "programming language" you can give as input to trained mathematicans is, well, a mathematical formula – tofro Jul 25 at 14:45
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    They typically did rather boring calculations. For example, an entire room of "computers" would work on making artillery tables. Simple calculations that had to be repeated over and over for different angles. – NomadMaker Jul 25 at 22:13
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    Why do you presume that they executed "programs"? A computer computes, i.e. does computations, the notion of "computers executing programs" is a modern notion that's not relevant to those times. – Peteris Jul 26 at 8:48
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    "Computing" did not have the same meaning then as it does now, also there was little or no concept of a "program". Then "computing" meant essentially the same as "calculating" does today. – RBarryYoung Jul 26 at 14:56
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    I think you've misunderstood what the job of a computer was, which was not to manually perform the functions of an electronic computer. They were basically calculators, which again, is different from electronic calculators. – CJ Dennis Jul 27 at 1:42
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Partial answer:

This article describes one flavour in more detail:

While the specific tasks a computer did varied according to need and her department, the majority of computing work involved three components: reading film, running calculations, and plotting data. During wind tunnel tests, manometer boards measured pressure changes using liquid-filled tubes. Computers “read” photographic films of the manometer readings, and recorded the data on worksheets. Working one on one for an engineer, or collectively in a computing section, computers then ran different types of calculations to analyze the data, and plotted the results on graph paper. All this work was done by hand, using slide rules, curves, magnifying glasses and basic calculating machines, like the Marchant or the more popular Friedan, which could multiply AND calculate square roots. Once completed, the calculations, graphs and other information were checked for accuracy and sent back to the engineers to design the next tests.

So I'd assume someone explained them what to do, and they had worksheets for the calculations with instructions what to calculate.

And if you look at the first picture in this article, you can see a lot of paper on the desk, some tacked together, so I'd assume these would be the worksheets.

You don't need some "programming language" to tell a human what to do. A human needs reminders about details, but they don't have to be in a specific form.

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    Indeed, human "programming language" is just "language". We're very good at following directions, and aren't terribly particular about the spacing, syntax, or lexicon of written instruction, unlike computers. A good example of one such "program" is filling out tax forms, which is just a series of instructions of how to multiply, add, and subtract numbers to arrive at your tax bill amount for the year. – Nuclear Hoagie Jul 27 at 16:36
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    @NuclearWang: I'm remind of the quadratic formula, IRS style. – dan04 Jul 28 at 15:44
  • Someone had a braino there; Friden was the company that made calculating machines, Friedan was the woman who wrote 'The Feminine Mystique' and co-founded NOW. – dave_thompson_085 Aug 17 at 9:46
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Every ship at sea carried such a human computer, in the person of the navigator. He followed a number of such "programs", properly termed algorithms, taken from Nathaniel Bowditch's seminal work The [American] Practical Navigator. Here is a two-page spread from a 1940 edition of that work:

Bowditch

This is a worksheet, containing labelled spaces as an aid to correctly performing each algorithm, rather than a complete description of the algorithms themselves. The navigator would prepare copies of this worksheet in advance of need, rather than writing in the book itself, and would be familiar enough with the algorithm to be able to follow it using only the worksheet and the various lookup tables that it referenced. Here is part of one such lookup table:

Trigonometry

For an actual algorithm we must look earlier in the book; this describes not only the mathematical operations required, but also the means of taking measurements upon which the calculations are based:

enter image description here

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    As far as I can tell this is the only real answer. – Charles Jul 27 at 13:33
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    @Charles This is the most detailed, and a great example, but the majority of human computers probably worked in accounting, like Bob Cratchit, which may have been a very different process. – Owen Reynolds Jul 27 at 19:08
  • @OwenReynolds Perhaps someone will post an accounting example. – Charles Jul 29 at 3:48
  • @OwenReynolds I imagine that typical accounting algorithms would be much simpler but deal with larger amounts of data. Something like: "Sum these two columns and write the totals at the bottom. If the totals are different from each other, bring that to the attention of Mr. Pinkerton over there. Repeat for each page in this fat ledger." – Chromatix Jul 29 at 4:50
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Here is a brief description of the task carried out by one human computer, Sylvia Asquith:

After joining in 1947, I received instruction on running a tidal machine, stopping at the correct moment and reading off the time showing at the zero point, and noting down high and low waters in succession. Times done first and the high and low to correspond. Also, you need to check the data when taking over from someone else in case they had got it a day out. All the wheels and pulleys are connected by a fine gold wire and represent forces of the moon and sun on the tide http://www.bidstonobservatory.org.uk/asquith-speech/

I had the privilege to meet Sylvia and, on a different occasion, hear her lovely singing voice. She was a computer who worked on an analog tide-predicting machine.

I've also seen one of the actual machines which is still preserved I believe. Here is a picture.

Doodson-Légé machine

enter image description here

https://historicsealevel.wordpress.com/tag/doodson/

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Human computers did execute "programs".

The programs were written (typed up) instructions that included a sequence of steps, such as what numbers to take off which line on a worksheet, what operations to perform, where to put results back on a worksheet, what to do next (including "loops", e.g. repeat n time, or for the number of items in a column on the worksheet.)

The "programs" were written up by the scientists (essentially programmers). The room full of (most often) women would be trained to follow these instructions, and their work was sometimes duplicated by another "computer" for error-checking/fault-tolerance.

Why do I know? My mother claims to have done this as a grad student at U.C. Berkeley during WWII. Also, see the book "When Computers were Human", by D. Grier.

All done on paper, and later after the industrial revolution, on mechanical calculators.

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The human computers did not follow "programs" when carrying out their computations. However, they probably followed established algorithms for deriving results. If they weren't all following consistent algorithms, it would have been next to impossible to aggregate the work of multiple computers together. The human computers would have thought of these algorithms as things that they learned, and not as things that they parsed, compiled, and then executed blindly.
The reason programs were developed when early computers came on the scene is that their machines did not learn the way humans did. They proceeded from one computation to the next in strict obedience to what the program was telling them to do, and not based on an understanding of what they were doing. The idea of learning as an activity that might itself be programmed goes way back to the nineteenth century, and thinkers like Ada Lovelace. But these ideas were not the basis for most of the programs written in the 1950s or 1960s.

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    -1 : Many computers were given instructions while having no clue as to the algorithm. That's because the work was sometimes done in a pipeline, where any computer only calculated a small portion of the actual algorithm. Thus their work was aggregated (on accumulated worksheets, etc.). The algorithms were developed by another party, likely a scientist to busy (ego, etc.) to do all the actual computing work. – hotpaw2 Jul 26 at 19:50
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    Good point. But the piece of an algorithm done by one computer can itself be called an algorithm. – Walter Mitty Jul 26 at 19:56
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    Algorithms are implemented in programs. While this seems facile, early languages like FORTRAN (FORmula TRANslation) and ALGOL (ALGOrithmic Language) make clear how closely linked algorithms and programs were. – RonJohn Jul 27 at 14:48
  • REPEAT PickUpAssignment : Read(Assignment): Compute(getFormula(Assignment)) : Write (Result) : UNTIL Lunchbreak; - Looks like a perfect program to me. – tofro Jul 28 at 15:54
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A chapter in Richard Feynman's autiobiography, "Surely You're Joking Mr. Feynman describes a room full of computers working for the atomic scientists at Los Alamos.

I don't remember all of the details, but part of the "program" involved cards that were passed from station to station, and the person at each station had specific instructions about which numbers from each card they were supposed to combine in which specific ways, and where they were supposed to write the result before passing the card to the person at the next station.

I somewhat vaguely remember that there might have been more than one kind of card, with different instructions for each kind. I definitely remember him saying that there were cards of different colors that got inserted into the process as corrections when mistakes were discovered.

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  • Those would have been IBM punched cards, run through standard mechanical processors. lanl.gov/discover/publications/national-security-science/…, page 37, says that Feynman personally worked with the punch-card machines. I'd imagine the human "computers" were doing roughly the same math, since the machines jammed, were really intended for simple math like payroll or inventory, and the cards had printed values above the punched-out holes for this very purpose. – Owen Reynolds Jul 26 at 15:54
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    I would characterise that episode as "operators of Hollerith tabulating machines" rather than "human computers". Tabulating machines were important for business computing in the early to mid 20th century, until electronic computers replaced them, but they had only limited use in scientific computing, Feynman's anecdote being exceptional. – Chromatix Jul 26 at 19:15
  • Pipelined CPUs! :D – RonJohn Jul 27 at 14:49
  • +1 for Feynman mention. In SYJMF he also says that the human computers worked more quickly when they understood the purpose of their calculations (determining the characteristics of the conventional explosives implosion which triggered the first atomic bombs) and were allowed to make improvements to their algorithms. – gandalf61 Jul 28 at 17:49
  • Feynman is describing an ad-hoc mechanical computer built from a bunch of tabulating machines, not a human computer. – Mark Jul 28 at 22:15

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