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 .
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.
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.
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.
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 .
"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.
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.
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)
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...
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
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'!
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.
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.
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.....
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.
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?
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...
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.
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?
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 RUclips, 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.
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.
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.
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 ????
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).
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 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.
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.
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.
Katherine was my Aunt....and my hero.....thank you for recognizing her accomplishments.
S. Saunders your aunt is one hell of a role model.
Ni bheidh a leitheid ar ais aris- we will never have her equal again, RIP :(
I highly doubt that was your aunt but ok
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 .
Prove it. Show evidences.
Hidden Figures is one of the best movies Hollywood has ever produced.
Wow. At ~6:00 he's talking about my mom. She calculated ballistic trajectories at Aberdeen Proving Ground in Maryland during WWII.
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.
A genious!
probably because he was who wrote the books kkkk
RIP Katherine Johnson, a remarkable lady.
Its sad that until the printing of this book and making of this movie the history of these important women went unknown to the general public.
That’s because it largely didn’t happen. Why should people “know” about things that never happened?
@@peterfireflylundright. Stay in your cave.
@@shelleyking8450 popular movies are not history. Black history month is not history. Don’t be an embarrassment.
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!!!
Ahhh?, is Katherine Johnson your grand-mother? How is she your ancestor??
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. 😂
What the..? Shero? Why not Shestory? Matshematician? 🤦🏻 Idiot.
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.
There's a building with her name on it.
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!
Thank you very much!
Professor Garfinkel teaching and explaining is very good
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.
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!
well said, Robert. Thanks!
No, they had almost zero influence on the success of NASA. That Katherine Johnson was a key figure is basically a huge retcon.
@@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.
@@cjinasia9266 the computing team was very important. She wasn’t, though.
I watched this movie just yesterday. Such powerfull and emotional movie.
Yesterday🙄 where have u been
Crazy, we were doing some of these trajectories in HS. I didnt know people did all this for a living.
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.
Wow. I love hearing truth. This was good to hear.
Must have been an awful movie experience then.
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 .
Thank you for this short but very informative session. Really gives a nice reality supplement to the amazing film
"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.
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.
They must be trumpers...
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......
@@claytonwhitman2611 Did you downvote the video?
@@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.
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)
A great Mathematician. RIP.
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...
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
Contemporaries of Euler said "read Euler, liez Euler" and not for nothing
They are so brilliant.
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'!
I do not believe that a Nobel prize can be given posthumously.
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.
Always watch this movie when it's on now. In my top 20.
It is amazing how a 300 year old formula solved a problem that modern math couldn't
What an excellent lecturer you are. Thank you for sharing your talent of making the complex understandable.
thank you so much!
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.
Thanks so much
Cool video!
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.....
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.
thanks, max. there's a great book called "When Computers were Human" by David Greir that tells the whole story of hand computing.
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.
4:55 They wHeeled it in with cool wHip.
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?
outstanding video.
Thank you very much!
Good old Euler!
She was a genius
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...
before: human computer
now: human tiktoks
Amazing
Great video.
Thanks!
I remember back then, they always talked about "launch windows." That's what she calculated.
Omg. I learned something.
Does consciousness and tiles add up.
Which Euler formula they used?
I mean which order?
1st order, 2nd order etc…
Or the symplectic integrator
Scene wasn't that dramatic. It's just explaining how the different mathematical concepts were joined together using eulers method.
I'm wondering why they wouldn't use splines?
Looks like skeet shooting while doing spins on ice.
🇮🇳 Well, Mathematical Science is to be fastinating subject, simply says Mother of all subjects, while opting her my Major Graduation, I felt her love.
Hi sir can I have personal chat with you for asking a doubt
If this had happened in another other country than the USA, Katherine would probably be on a banknote.
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.
In any other Western country she would at least have to share the credit with the white guys who actually did the work ;)
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?
With all those numbers, isn't it a Riemann sum?
I'm curious, the Soviets must have done those calculations first, do we know who their mathematicians were?
Is it just algorithm
At least I have a better idea of what Euler's method is. The movie didn't explain it.
its a numerical method: ruclips.net/video/X5-ucBtneVM/видео.html this is a great, detailed explanation.
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 RUclips, 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.
6:48
can i ask why 50 000 times?
or was it like a best estimate at that time to do it 50 000 times.
sorry, that's a number I completely made up out of my head to mean "many many times"
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.
@@uclamodelingclass3003 Thank you.
@@uclamodelingclass3003 .
Don’t know why I clicked on this, I barely passed algebra 1.
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.
How did the Soviets solve the same problem?
Remember how dunes change in time due to win
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 ????
I am nat anderstand englısh .but ,katherine jhonson big a human.thank you ,ı am work anderstand.inşallah ı am learn englısh .
Can someone do me a short summary of the video please ?
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).
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.
Well that tells us nothing about Euler's method.
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.
good point. same thing in medicine
They pay men more than women so most of them.find other things to do..
and deservedly so. Good riddance to them. "Get back in the kitchen" should be the rallying cry for all men of the 21st centuryl
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.
Why not use rubber outta. It would be more accurate . RK4 was Developed around 1900 so it was available then.
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.
KATHERINE Johnson.
I zoned out because I wasn't hearing any math being spoken.
LMAO! FUNNIEST NON-MATH STATEMENT EVER!
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.
You're reading into it way too much and misframing it. Racism is literally what's being implied here. It's not that deep lol.
How did the Russians do it ?
Remember how dunes chang due to the wind thats how the russian did it
Nice drawing.... The Moon is bigger than the Earth.
But seriously, when Computers were human women sounds a lot better than AI.
Pass😂
Amazing how she plays her flat-earth part… so convincing!
Sheldon should have thought it.
Nope either we teach our male countwrpats of we go into oblivion
not with that voice
Katherine was an amazing woman and and human being