Monday, December 26, 2016

Hidden Figures

Yesterday in our tradition of seeing math movies on Christmas, we saw Hidden Figures, the story of African-American women who worked as "computers" at NASA in 1961 Virginia in the last vestiges of "separate but equal". The movie focuses on three women, Katherine Johnson, Dorothy Vaughn and Mary Jackson as they dealt with and crossed racial and gender boundaries. But this isn't just a movie you should see, rather a movie you will enjoy watching and I highly recommend it when it goes into a wide release in the US on January 6. Some minor spoilers ahead.

Beyond the struggle, Hidden Figures does work as a math movie. The major storyline follows the group of mathematicians who compute the trajectories of the Mercury flights with Katherine Johnson playing a main role in figuring out how to pull John Glenn out of an elliptical orbit into a parabolic safe entry back to Earth.

The movie also serves up lessons about computers. The new IBM mainframe comes and threatens the need for human computers, women (here segregated into two groups) who did the tedious manual calculations that NASA relied on. In the movie Dorothy Vaughn recognizes the threat and retrains her team to learn Fortran, perhaps a parable for how technology changes jobs today.

The majority of the audience for the sold-out theater were African-American women and they laughed and cheered as the heroines of the movies succeeded. While we have made much progress in the last 50 years we still have far to go.

11 comments:

  1. I saw the movie yesterday. As a white Southerner I appreciated the struggle that blacks had to endure in the South, which was doubly difficult for black women. That said the only unbelievable part of the movie was the claim that only Katherine Johnson knew anything about the Runge-Kutte Method, or more specific, Euler's Method, which is the reference in the movie. When I heard that in the movie memory bells went off.

    If you have two functions and they intersect somewhere, the iterative Runge-Kutte Method is a simply way of having increasingly accurate ways of determining the coordinates where they intersect. The intersection in the movie would have been the re-entry point for the space capsule which was the intersection of the elliptical orbit with the parabolic descent path. Basically I wrote the same code as an undergraduate Chemistry student in the early 1960s on the vacuum tube IBM computer at Florida State University using Fortran language that was used by the women in the movie. Ironically I was coding it at about the same time as the time frame of the movie. Everyone studying applied mathematics at that time would have known the Runge-Kutte Method.

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    1. In the movie it wasn't that she was the only one that knew about it, she was the one that thought outside the box to use it in this problem. She actually went and got a book off the shelf about it to check herself and help solve the problem. I am sure everyone knew about it, they just didn't think of to calculate the coordinates.

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    2. The engineers in the movie were looking for theoretical solutions rather than iterative numerical approximations - the reference to old math rather than new math. They wanted a human computer who could handle analytic geometry. When she made the suggestion light bulbs went off for the other engineers. She made the intuitive leap. Unlike students who studied Runge-Kutta and wrote programs in the early 60s the IBM 7090 was not online at NASA until 1961 and Fortran programming on the IBM machines was available in 1960. In the time frame of this movie writing Fortran code on IBM machines was not the widespread common practice it would soon become. A year or two makes a big difference in the transition from innovative application to common practice.

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    3. I think you might be confusing Runge-Kutta with Newton's method, which is an iterative method that can be used to approximate function intersections. Runge-Kutta and Euler's method are iterative methods for solving differential equations.

      I think the problem NASA and KLG had to solve was far more complex than computing the intersection of a parabola and ellipse, a pair of simultaneous quadratic equations. And I suspect that the use of Euler's method wasn't to solve a differential equation at all, as of course everyone in the room would have known how to do that. I'm guessing that the ideas behind Euler's method were in fact applied to something else, and that's why identifying Euler's method constituted an insight.

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    4. I agree that the poster was confusing Runge-Kutta with Newton's method (or perhaps some other methods). However, Runge-Kutta and Euler's method are not really iterative, except in the sense of decreasing step size to be sure of convergence. Both method's are forward marching.

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    5. Joseph Breckenridge9:30 PM, May 11, 2017

      Thank you, Mr. Kelsey. You gave me a place to begin in understand her insight that helped move the mission forward. I am not a mathematician but I was curious about exactly what she did and why it was difficult for others to put all the pieces together. I also learned from some of the comments that followed your posting. Again, thank you.

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    6. Is the return path of the space module indeed parabolic? A parabolic orbit results when the object's velocity is EXACTLY escape velocity. They only exist theoretically. If the velocity is infinitesimally larger the orbit is hyperbolic and if less it is elliptical. I believe that the descent of the space module is actually an elliptical orbit which intercepts the earth.

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  2. Are you saying that while it's good for people to know how an African American woman was working for NASA doing math, that if racism or sexism or any number of other things had stood in the way of her having that job that someone else with a math background would have gotten it and also been able to do what she did?

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  3. The issue is simply this: anytime a person of color is attributed with any major contribution, points of diminishing comments follow. Exhibit A: So called Pythagorean Theorem named after a Greek mathematician who learned it from the Egyptians. Start there and go to Benjamin Banneker , an ex slave mathematician who laid out Washington DC from memory after the French surveyor left. What subway station is named after him? "L'Enfant Station" not Banneker..Hmmm Racism is a cancer that America in its Bi polar DNA cant cure.

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  4. The two things that white people can be given credit for are racism and the patent office.

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  5. Is the return path of the space module indeed parabolic? A parabolic orbit results when the object's velocity is EXACTLY escape velocity. They only exist theoretically. If the velocity is infinitesimally larger the orbit is hyperbolic and if less it is elliptical. I believe that the descent of the space module is actually an elliptical orbit which intercepts the earth.

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