The movie Hidden Figures is out in theaters. We’re planning on going to the theater as soon as our presence is not required in the house every single evening, i.e., in 2033. I looked at the book on which the movie is based last night. This title is Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race. I.e., it contains the word “mathematicians.”
I majored in math in college due to a mistaken belief that I was intelligent. So I was eager to see some equations. Yet the book is solid prose. The only numbers are page numbers, basically. Certainly there are no equations. Instead of the festival of LaTeX that I expected, the book could have been authored via text message.
So… what did the NASA employees chronicled in this book actually do?
[Note that I was myself a NASA employee in 1978(!), developing a database management system for Pioneer Venus Orbiter data to support physicists writing analysis code. The PDP-11/70 that I used has disappeared because hardware engineers have made so many advances since the mid-1970s. The computer language that we used, however, which was developed by John Backus in 1957, is alive and well today. What does the survival of Fortran tell us about progress in computer software and computer science?]
Related:
Katherine Johnson, Dorothy Vaughan, and Mary Jackson, who were part of NASA’s team of human “computers.” This was a group made up of mostly women who calculated by hand the complex equations that allowed space heroes like Neil Armstrong, Alan Shepard, and Glenn to travel safely to space.
While they did the same work as their white counterparts, African-American computers were paid less and relegated to the segregated west section of the Langley campus, where they had to use separate dining and bathroom facilities. They became known as the “West Computers.” Despite having the same education, they had to retake college courses they had already passed and were often never considered for promotions or other jobs within NACA. Hidden Figures depicts this in a scene in which “computer” Mary Jackson is asked if she’s want to be an engineer if she were a white man. Jackson responds, “I wouldn’t have too. I would already be one.”
http://www.popularmechanics.com/space/rockets/a24429/hidden-figures-real-story-nasa-women-computers/
Later, when a machine computer from IBM was available, many learned Fortran.
I only used FORTRAN (now Fortran, I guess) for some trivial student projects in the 70s, and I couldn’t see myself using it today. But I found this article interesting, and it suggests that Fortran’s legacy may be greater than I had realized.
http://canonical.org/~kragen/memory-models/
Only tangentially related: this TED radio hour show includes the fascinating story of “Steve” Shirley, a woman who built a huge business by recruiting women to program in their own homes with a remarkable amount of flexibility. http://www.npr.org/programs/ted-radio-hour/443411154/the-meaning-of-work
Bruce: Thanks for the link. Maybe due to the fact that it is targeted to an American audience, the magazine article contains not a single equation. So my original question remains; What did these people actually do? A numerical approximation of a solution to a differential equation? Something else? And why? To figure out when to burn a rocket and for how long?
Links to NASA biographical sketches of the women depicted in the movie:
https://www.nasa.gov/modernfigures/overview
And a link to a NASA technical report co-authored by Katherine Johnson titled “Determination of Azimuth Angle at Burnout for Placing a Satellite Over a Selected Earth Position”
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980227091.pdf
A quick search of the NASA Technical Reports Server found 13 documents co-authored by Katherine G. Johnson.
http://go.nasa.gov/2iJ8pa8
Thanks, Liam! That tech report is awesome. Look at all of the cool stuff they were able to do before academia got ruined by LaTeX! Anyway, this is certainly a lot more interesting than anything I could find (quickly) in the book.
“Boundary-Layer Transition on a Group of Blunt Nose Shapes at a Mach Number of 2.20” by Mary W. Jackson
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980227788.pdf
Okay.. now let’s start a new discussion. These reports are free on the Web. Liam found them presumably with less effort than it took to write a whole book and get it published. Why aren’t excerpts from these reports in the book? Is it possible that American readers are so uninterested in and hostile towards equations that they wouldn’t at least want to see a sample?
philg: “Is it possible that American readers are so uninterested in and hostile towards equations that they wouldn’t at least want to see a sample?”
Yes, it’s possible. Also obvious is that these things are targeting a broad audience. What percentage of that audience would understand the math?
Liam showed that it isn’t too hard to find out more details about what they did.
The “Determination of Azimuth Angle” paper was interesting but it appeared to be mostly at the level of high school trigonometry and Johnson had 2nd position. This doesn’t appear to make her a mathematical genius and the hidden linchpin of the American space program as the publicity for the film seems to imply.
We owe the American space program to Nazis, not to American black women. A really interesting movie would show how and why we allowed actual war criminals to run our space program. I don’t mean just in the sense that they sent rockets at civilian population centers (itself a major war crime) but that these rockets were assembled, with their full knowledge and participation, by concentration camp slave labor under brutal conditions.
The main job of human “computers” was to do repeated mathematical CALCULATIONS – to take the equations that you see in the paper and to plug in all the numbers and come up with an actual solution. This of course is what digital computer also do, except must faster and with fewer errors. I have a TI-82 programmable graphing calculator which I think, with a few hours of programming, could be programmed to spit out the solutions ( that must have taken these women days for each one) in a few seconds.
According to the Popular Mechanics article, Johnson’s main job in the lead-up and during the [John Glenn] mission was to double-check and reverse engineer the newly-installed IBM 7090s trajectory calculations. In other words they didn’t yet trust the programmers and so had her redo the same calculations by hand. Normally a job like this would be considered (and was considered) drudgery and not something that would cover you in glory.
The key qualification for a job like this is the willingness to undergo tedium. You need someone who is bright enough to do the math but not so bright that they would go completely nuts. If you put someone like Phil in this job then he would go nuts out of boredom in a week. (By the 2nd week he would figure out a way to convince his bosses to trust the computer).
Regarding Fortran, is is still “alive” (and it will always “live” in the sense that it always will be possible to write programs in Fortran and to execute them by emulating Fortran in another computer language – I think most Fortran compilers are now written in C) but I would not call it “well”. The vast majority of job openings for programmers are for coding SQL, Java, C, Python, etc. with Fortran waaay down the list. There may be certain niches where Fortran continues (such as weather forecasting models) – possibly because it would be a major expense to throw out the existing code base and start fresh.
Jackie: That the paper can be appreciated by someone with a basic math/physics background makes my follow-up question more interesting, I think! If the book is “About people who did Job X,” why not stick in a few excerpts to show concretely what Job X was? People who truly hated trig in high school could skip over the excerpts and be no worse off than readers of the book in its present formula-free form.
Stephen Hawking (on A Brief History of Time): “Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein’s famous equation, E=mc^2. I hope that this will not scare off half of my potential readers.”
I think the bottom line is economics (book sales). The target audience for this book was not you. It was written with a liberal (which often means liberal arts) female audience of book buyers in mind. Not so much blacks as goodwhites – white women (and a few men) who may not have any actual black friends but would LOVE to be friends with smart sassy black female mathematicians if they knew any (as long as such imaginary friend didn’t bore her by talking about equations all the time). If said target buyer picked up the book and started flipping thru it and in the back (or dispersed among the text) were a bunch of equations with sin and cos and greek letters and such, this might bring back bad memories of high school math and would make them LESS likely to buy the book.
I just saw the movie about Ramanujan – The Man Who Knew Infinity. Again for a film about mathematicians, there is very little math. There are a few scenes where there are blackboards full of equations but no real attempt made to explain them. Very briefly they discuss partitions in laymen’s terms – Jeremy Irons (Hardy) literally attempts to explain partitions to his valet. But the soap opera aspects (evil mother in law, evil white people, Ramanujan coughing blood, etc. predominate. If you want to see 90 minutes of someone talking about equations, then you can always pull up OpenCourseWare.
We owe the American space program to Nazis, not to American black women. A really interesting movie would show how and why we allowed actual war criminals to run our space program.
The answer to that question could be answered in a few sentences. Many Americans thought that we were in a life and death struggle with the USSR. Thus we had to develop better rockets and missiles as quickly as possible. So former Nazis were hired because they had relevant skills and experience.
A movie with a few minutes of a talking head explaining that wouldn’t be very interesting. It’s possible that a talented filmmaker could make it more interesting by going back and forth between death camps during the war and fawning American journalists in the 1960s.
Speaking of Fortran, it’s currently used in power grid simulation and analysis for production power grid control.
I think a von Braun biopic would be fascinating. How many people met with Hitler AND JFK? Himmler AND Disney?