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?
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.
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:
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:
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:
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
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.
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.
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.
