You have a brilliant aunt that inspires my 3 children’s and i that is African American ,they can achieved anything they want to as long as you put god first the work and have the determination .
A brilliant mathematican. She should have been recognized! May she rest in Power and Arise with the Ancestors! Thank you for your contributions! You are history and a Shero!!!
Cringe. You can say she deserved more recognition, (not that you can name any other mathemarican who worked on this or any other project, you only care cause she was a black woman. You don'tcare about mathematicians getting reicngition, you just care about recognition for people who support your ideological narrative) You can even call her a hero. Great. Save all the cringe political b.s., virtue signaling, made up words and pseudo-philosophical nonsense. 😂
She was honored by both Congress and President Barack Obama. Presidential Medal of Freedom in 2015 and Congressional Gold Medal in 2019. Many years after her valuable service to the US but better late than not at all.
Professor Garfinkel, this video is wonderful! It's well put together. Kudos. Katherine Johnson was a wonderful gal. Euler's method, like sewing - one stitch at a time. I'm glad that you posted this lecture. Best Always!
She wasn’t a “gal”, she was a woman. In the South, the term” Gal” was used in a defamatory manner about Black enslaved women, thus I resent that usage in this context.
Katherine Johnson...I'm sorry, The Great Katherine Johnson even looked and spoke like a math teacher. IDK. Maybe they all looked and talked like her, but she reminds me of every female math teacher I had up till grad school. The way...she spoke...in short phrases...were all very similar to the structure of an equation...and always...seemed like...it followed the rhythm of how her mind was working at the time. Mathematics and music are twins.
This video and movie , got me through a lot of my early calculus classes as it was so Inspiring. It came out when I was taking calculus 2 in the summer and inspired me to push through . NASA is a dream job to this day because of those women , the book , and film I watched . Fun fact Dorothy ( Octavia Spencer’s character ) - her sons also became engineers ! I’d be an awe if ever meet any one of these women .
At 6:05 when Prof Garfinkel mentions 'Hand Calculators' he is not talking about a TI 89, but an adding machine, slide rule, and log tables. Great work.
When I taught Technology Education classes for Middle school, I had been given some of these machines by my uncle who was a retired engineer. I made spot for them and called it the history of calculations. I couldn't keep the students away from them. I even taught lessons where they had to use the old machines. I even had them re-ink a typewriter ribbon.
Disagree with that statement! Back then she would have not been recognized at all in ANY other country other than the USA. You should not cloud your mind with present day rhetoric. Also you should not limit her greatness to her skills as a mathematician. She was a Great woman in many ways throughout her life.
HUH? This is talking about greeting from the Earth to the Moon, which was computed by a friend (Dan P) with the use of machine computers in 1965-1969, while working in Wernher Von Braun's group. The movie was about sending Alan Shepard up and down and John Glenn into orbit year s before this. I have to raise the BS flag on this one.
The professor who taught us differential equations in about 1976 started his working life as a human computer in our university. He was an amazing man, he taught us two differential equations courses without referring to notes or to a book in class. He was in his 70’s at that time.
Actually the book in the movie was on one computer language, FORTRAN, which is literally short for FORmula TRANslation. It was the first computer language I learned in Engineering School. These women made the success of the NASA Space program possible. Unfortunately for humanity, we have lost the real women the main characters were portraying. May we never forget their incredible achievements. On a lighter note, I truly love that line when Costner says "For you it is". That one line elevates her above everyone else in that scene. Stellar!
@@peterfireflylund She may have had little effect on the NASA program but she and the rest of the computing team had a massive impact on the success of the missions.
As of the date that I watched this video, there were actually 2 people that gave this a “thumbs down”. This basically proves the premise that you can’t get 100% of the people to approve of anything.
you sort of wonder. there was definitely some fictionalizing in the movie. KJ didn't compute the trajectory from the Earth to the Moon, another part of her group did that. She calculated the paths of the lunar module and the lunar command module, according to Wikipedia. But is that a reason to give 'thumbs down'? I wonder
@@amramjose really? wow, and you must be woke. who gives a rat's ass about politics, we are talking about mathematics, and the amazing roles that The Great Katherine Johnson and many many other great women played at NASA ( and other agencies and companies) in making the "impossible", POSSIBLE!!! By the way, don't believe everything you hear or read on social media or the internet, about anyone or anything. Some of us have brains, and think for ourselves, and refuse to be put into pigeon holes by moronic leftist racist politicians and their sycophant followers. I bet you are one to tear down our police, and fire, and EMS, and other first responders, as well as all of our service men and women from the Air Force, the Navy, the Marines, the Coast Guard, and the Merchant Marine, oh and not to forget the Customs and Border Patrol. Here's a Pro Tip: if you will not stand behind them, then feel free to stand in front of them when they are in combat. NEVER forget that the Rights and Freedoms that you take for granted, to abuse others with, including the Freedom of Speech, is bought and paid for in Blood. I am betting that you would never choose to SERVE anyone or anything other than yourself. Those men and women who have fought for our country, did not fight for the government. They fought for our PEOPLE. ALL OF THEM. Including you......
@@amramjose Dumocrats don't believe in facts and truth, but feelings. That's why you can't have a good honest debate, because they start yelling when over whelmed with facts and truth.
8:00 Stating that she couldn't get the book from the library because she was African American is perpetuating the problem by blaming the victim. Ethnicity is not her fault. The color of her skin is not her fault. The library policy was racist and and we should all try to frame it properly when we speak on racist policies. They wouldn't lend it to her because they had racist policies specifically against African Americans.
"Computing machines" Yep. I was using those in the early 1970s while going to school at Control Data Institute in Miami. The IBM 360 (which means it had a storage capability of 360K or 360,000 bytes (you're cell phone has about 140 GB) was about the size of a car and had to be in a room that was around 60-50 degrees F. We froze in there when using the machine. Had to use punch cards to program the machine in COBOL, FORTRAN or Assembler (in essence, binary code). What a difference with today's computers!
@GoodnightRain In a very basic way u can think of the punch cards as a blind person reading blind script on cards. Becouse computers only reads 1 and 0 u can think of the little bumps on the cards as a 1 and the space betwinn a 0. The way it worked then was that u hade a code printed onto a card and then inserted that into the computer kinda like very old school floppy discs. The computer then read that code and executed that command. The computers back then was pretty mutch just a processor and all the programs u wanted it to run was on the punch cards u inserted.
Very wrong. The S/360 was named after “360 degrees” because it could handle ALL computing problems: both “business computing” which was basically simple decimal arithmetic (addition, subtraction, multiplication, and division) and simple text and “numerical computing” which was floating-point computation with logarithms, powers, trigonometric functions, etc. The name had zero to do with the memory capacity! Some of the early machines had very little memory (16kB), others had maybe half a megabyte. Later machines had more. The family could originally handle up to 16MB but was later extended several times and can now handle many, many, many gigabytes.
I learned Euler's Method when I went back to school, took math for non-majors and feel in love with it. I actually like math especially algebra but hated "word problems". Euler's Method freed something in me to get them. I literally jumped when Taraji said Euler's Method in the movie cuz I knew what she was talking about and everyone looked at me - this little Black woman. How could she/me know what that was? LOL! I really appreciate this perspective and how he broke things down both scientifically/mathematically while related it back to what happened historically as portrayed in the movie. Hated that squeaky marker on the glass board. Had me all cringed up. LOL!!!
Henson herself is no slouch, and might have seen Euler's method when she was an electrical engineering student at the world-historical North Carolina A&T (She later transferred to Howard to study acting, according to Wikipedia)
Thx Prof. Those who appreciate Eulers ( Katherine Johnson & OTHERS as such ) DO NOT Regret his Aquaintance & Methodic later on. I blieve He was & STILL is ( up to now ) the best 😘 among our Mathematicians untill the Next One comes!!🍻
Mehrdad, I'm with you about Euler. He isn't given enough credit, for example, as the person who invented partial differential equations, which are what allow us to model spatial and spatio-temporal phenomena
the scene in the movie about Glenn and Garfinkel's description don't match -- in the movie the computer tech results were off and Katherine corrected them.
The other thing that astonishes me as that these human "computers" were *all women*. Nowadays the computer industry is dominated by *men* and *women* are usually shunted aside. Once again, women do a great job and then men come in and push the women out of that industry.
Haven't had my mind blown on math (concepts: I'm not trying to UNDERSTAND this stuff, I'll just catch the edge) since looking into the basic math of Alternating Current. Had an excellent math teacher (several, really) but even if they couldn't teach me to do all, they at least taught me to appreciate the application. I could probably learn now, 20+ years out of school, but I'll just take things slow.....
Thanks a.lot for the video, I just watch the movie for the 3rd time, and decided to check on the accuracy on the Euler's method scene... I am far from being a Math perso, did it ok at school... Still was impressed by all the problems and situations described in the movie... Thanks again...
Amazing and inspiring woman! She was more than a mathematician! She deserves a Nobel prize for advancing humanity's space cause! She has contributed to our hopes of being an interplanetary species. Besides, everything about going to space is physics! Smart black woman AKA 'human computer'!
thanks, John, that's a great link. But I think what Abigail meant was that the movie "Hidden Figures" didn't explain what Euler's method is. Our videos 5.1-5.3 do explain Euler's method in detail.
Since I was recommended this video by RU-vid, I was unaware of the whole playlist. Thanks for pointing it out,@@uclamodelingclass3003 ! I’ll take a look
Euler's method simply relies on the fact, that for short distances, the tangent line of a curve approximates the curve itself. So you calculate the derivative and tangent line of the curve, calculate the next position as a short distance from the initial point along the tangent line, then you repeat using the new point as your new initial point. Repeat as necessary until you reach your destination point. The real trick is figuring out the error so that you know how small of a distance to use to achieve the necessary accuracy.
My thanks for the detailed explanation, that looks remarkably like an Archimedes Spiral. I was under the impression that the actual flight path looked more like a figure 8, if you considered the flight out and back You can do such a Spiral, but the propulsion type is more useful in terms of long-term low thrust like an ion drive. For those that are interested; see the Kindle/Amazon book, 'Traveling Through Space Without Rockets --- The Shorter Version,' by Jim Parsons, for the full progression of the cumulative ideas and techniques, see the longer book by a similar name by James G. Parsons. Ain't math elegant?
Probably already been mentioned….but this problem can also be applied to the discovery of Quasars. Pulsing Radio signals from quasars had been “received” before, but were not “visible” because astronomers were integrating too long. It was perceived as noise. When they started running the charts faster, the quasar pulses began to be visible as a valid signal as opposed to noise.
At the beginning of this video he says....."So that's the assignment. 5000 steps by hand or write a computer program that will do it in a minute or two."....but at 6:43 he says....."And you just have to apply Euler's Method, ehh, 50 000 times.".... Does he talks about different calculations here or did they apply Euler's Method 10 times to calculate 1 step?
Hi Fornax- those are 2 different calculations. The first one was an assignment to my class. They had done 2 steps of Euler by hand, and then I wanted them to see that what the computer does was no magic, just doing the same thing 5000 times. The second ref was to the actual NASA calculation of the moonshot. It was off the top of my head, and it's probably way too low. If you figure a delta-t of 0.1 sec, that's a little under a million steps for a 24-hour trajectory.
Makes sense ,a woman's mind calculates from the time of conception of a child ,time steps to body change to deliver life from herself ,much like early men producing food from dirt , just not so calculated on a molecular point of view ????
you for got the conversion she built for the change in data values between the two different orbital position... that conversion must be done on the finishing orbit and the commensing orbit.... the equation she made was similar to using tensor calculus in unlike data types and normalize.... was fields of variations of data in frames or manifolds. she mentions euclidian, euclidian analysis has rules to concider in the calculus...
Thee is Euler's method, improved Euler's method but I would have used Runge-Kutta. It was known back then. It is easy to get RK4 to work on a computer. The problem with using a lot of small steps is that round off error accumulates. So I wonder what was the precision of the computers they had back then and did it even have floating point? Probably not so the floating point was probably programmed in a custom way so it would have enough precision.
I have to confess that I know absolutely nothing about the actual history of those computations. I doubt that there was a specific aha moment when Johnson exclaimed "Euler's method". They were probably doing RK4 in real life. But the Hollywood story is wonderful, isn't it?
OK-they were trying to find a mathematical way to transition from an orbit to a reentry-going from a circular trajectory to a parabolic one. The problem is there's no formula for that. She used a method developed by an 18th-century mathematician (Euler) to get around that by breaking the problem into a whole lot of little, solvable problems. (and by "a whole lot", I mean thousands of them).
By hand? Hardly. Mechanical calculators existed (I have an antique Othner, for example). Some were even motorized so they could do finite differences automatically. Feynman mentions some of them when he writes about the Manhattan project. And Euler’s method was not at all forgotten and did not at all require any great flash of insight from Kathleen Johnson.
In the movie, they were all using Friden "Comptometers" - which I know about because Southern Bell (part of AT&T) used them in their accounting offices. My mom was a supervisor there and I would play with them now and then if she had to go in for something on a weekend.
yes, when I said "by hand" I should have qualified that by allowing for mechanical calculators like the Friden and the Brunschviga that Hodgkin and Huxley used to compute the neuron.
yes, RK4 is what we use scientifically in our lab today. Much more accurate than Euler. I honestly don't know what numerical integration method they used in the Apollo program. Of course, RK4 is a much more expensive computation at each time step, so there's a trade-off. And to respond to many of the other comments here, the movie Hidden Figures is not accurate *in detail*. Katherine Johnson was not the first person to suggest numerical methods. The key scene that I talk about ("Euler's Method") was a dramatic license that was taken by the writers. It didn't happen that way historically. The thing is, in my field, which is differential equations applied to biology, it's super-important that the subject is moving beyond linear equations that can be solved by paper-and-pencil methods, and embracing--Euler's method! So the scene is perfect for my class, even if it did not historically happen that way at NASA.
I wonder if you gain a higher precision in fewer steps in the calculations of the trajectory if you do 2 separate calculations, one with the earth as the starting point and one with the moon as starting point, and chose the same end point for both those calculation located half way the distance between the earth and the moon?
that might be a way to reduce what is called "round-off error". but nowadays, computers are so fast that people use very sophisticated integration methods that are more accurate than Euler and they use super-short time steps
i don't know... Is shooting a person on a plane from the ground the same problem as a person on a plane shooting someone on the ground, but in reverse? I think it would require a lot of adjustments.
