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72: The Lifestyles of the Mathematical and Famous (an Interview with Author Robert Black)
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Robert Black is an author who has written a six-book series about seven influential mathematicians, their lives, and their work. We interview him and his books, and take a peek into the lives of these influential mathematicians.
Addendum: Hey Breaking Math fans, I just wanted to let y'all know that the second material science podcast is delayed.
[Featuring: Sofía Baca; Robert Black]
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Transcript
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Robert Black's Math Adventure
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Speaker
Robert Black is an author who has written a six-book series about seven influential mathematicians, their lives, and their work. To talk about his latest books and the series itself, we have Robert Black on today. All this and more on this episode of Breaking Math, Episode 72, The Lifestyles of the Mathematical and Famous, an interview with Robert Black.
00:01:24
Speaker
I'm Sophia and this is Breaking Math. With me I have on Robert Black. Welcome. Oh, thank you. I'm very glad to be here.
00:01:32
Speaker
All right, so I guess I'm going to start by asking why you wrote this series. Who's your audience? What do you hope for people to get out of this series? Well, I write. My publisher is Royal Fireworks Press, which is a small press in New York, about an hour and a half outside the city. We market a lot to gifted children programs, homeschool programs, that sort of thing.
00:02:00
Speaker
I've been working for the past 10 years actually or more on using storytelling to communicate math concepts. I kind of have both in my background. I've been writing for
00:02:15
Speaker
35-ish years and I'm an engineer and my parents are math teachers and still keeping up with it even now that they're retired and in their 80s. My dad does FaceTime tutoring sessions with one of my nieces and my mom just took a new tutoring gig to help somebody with geometry. So it goes with me.
00:02:39
Speaker
I started looking for ways to use storytelling to teach math because math does not have the best reputation in education circles and especially in this country. If you watch TV, you know, math is always something that kind of the nerd character does off to the side.
00:02:56
Speaker
So I got the idea that we can use storytelling to show that math is something that real people do for real reasons to solve real problems. And so, of course, my first attempt to do this was a fantasy series about a girl who sees monsters and ghosts and werewolves.
Fantasy Meets Math: Monsters' Fear
00:03:17
Speaker
And it turns out that they're all bad at math.
00:03:19
Speaker
that people are afraid of monsters, but monsters are afraid of math. And this girl, my main character can do math. And so they all come to her for help with their math problems. Yeah, that's, that's really, that's really interesting. And like, kind of like, I mean, just the whole storytelling aspect. I mean, I've often said on this podcast that, you know, if sometimes you've had, if you're struggling to read a concept, I mean, to understand a concept to read the motivation for it, because there's often a story there, you know, a struggle.
00:03:46
Speaker
And I think it's great that your work focuses on that. And it strikes me too that your mission is very similar to Breaking Math's mission, which is to take mathematics, which is taught as a famous paper I can't remember said, like if you had paint by numbers, instead of finger painting in kindergarten, people might grow up to hate painting and art.
00:04:08
Speaker
So it's just one of those things that is really cool to people who often weren't traumatized with math and it's seen often as a traumatic experience even for teachers who have to teach math to their elementary school students and things like that. Absolutely.
00:04:25
Speaker
came to me just in the past couple weeks. They've had this kerfuffle in Florida over banning math textbooks. Once they started to release some of the math textbooks that were supposed to be objectionable, what a lot of them had is this thing called social-emotional
00:04:44
Speaker
learning. And I didn't know what that was. And I still don't know what that is beyond, you know, 30 seconds of reading Wikipedia, which, which contrary to some ideas, some people thinking is just not make you an expert. But just the fact that they see a need to include teaching
00:05:03
Speaker
empathy and feelings with math gives you the idea that most people have the assumption that math isn't a feeling thing, that math isn't a human thing. And so when I started looking into that over the past couple of weeks, it's just like, well, this is what I've been trying to communicate for 10 years is that, yes, math is a feeling thing and math is a thing that human beings do.
Historical Math Projects
00:05:30
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And so now to
00:05:31
Speaker
We've gone way off track from your original question, but now I'm going to circle back to it. The idea of the biographies is that here are some real people in history who made some major breakthroughs
00:05:48
Speaker
in mathematics for all sorts of human reasons, for all sorts of reasons that people can relate to. I mean, the very first book, Blaise Pascal, pretty much came up with probability theory because somebody asked him for gambling advice.
00:06:04
Speaker
So that's the point of the books. And my publisher actually suggested doing the biographies, but then they left it up to me to choose who my subjects are. So it was a very good collaboration, and I think we've come out with a really good result.
00:06:27
Speaker
Oh yeah, definitely. I mean, just looking at the birth dates and death dates of the mathematicians involved, we'll kind of go over each book quickly and the mathematicians within, but it spans about four centuries, just these mathematicians. So I mean, four centuries in mathematical terms, you know, you cover this in quite a bit of detail because I mean, that's really only about five lifetimes. So you've written six books so far, correct? Right. And are you planning to write more?
00:06:57
Speaker
Interesting, you mentioned Four Centuries, because Four Centuries is pretty much about as far back as you can go and get a lot of good, reliable detail about individual people's lives. My publisher wanted something on Euclid, and people don't know what Euclid did in his daily life back in Alexandria.
00:07:19
Speaker
So but the biography series is complete and I am moving on to a new project. But the new project does involve history and mathematics and individuals in history. And it goes back even farther than four centuries, that considerably farther than four centuries. And that's all I'm prepared to say about it at the moment. Awesome, awesome. So without further ado, let's jump in.
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00:09:20
Speaker
So your first book, Pascal and Fermat, The Probability Pen Pals, was written about three years ago, 2019. So tell us about Blaise Pascal and Pierre de Fermat. Pascal was a mathematician, son of a mathematician. Blaise Pascal was the son of a French
00:09:40
Speaker
natural philosopher is what they called it. Pascal's father Etienne was part of Marine Mersenne's salon in Paris. Mersenne corresponded with, again, natural philosophers, mathematicians, scientists all over Europe. And just to clarify, you're saying natural philosopher was the umbrella term for mathematicians and scientists.
00:10:04
Speaker
The first person to be called a scientist actually shows up in one of my books. Her name was Mary Somerville, and that was in Victorian England. But before Mary Somerville, they were called natural philosophers, yes.
00:10:19
Speaker
One thing about Blaise Pascal is he was kind of a child prodigy. He was interested in everything and dove into everything passionately when he discovered it. And his father actually forbade him to study Euclid at first because he knew that once Blaise Pascal got a hold of Euclid, there would be no stopping him. And so Blaise actually studied Euclid in secret.
00:10:51
Speaker
Because, you know, of course, once your father tells you not to do something, that's that's exactly what you want to do. So I'm just imagining him under the covers with the candle. Yeah. Well, we hope not a candle, but yeah. Oh, yeah. Yeah.
00:11:05
Speaker
So he took sticks from the fire and used the charcoal on the end of them to draw geometric figures and things. Pascal later, when his father got involved in some tax collecting work and the workload was so difficult, all this was done by hand. And so Blaise invented a mechanical calculating machine, one of the very first. And it was this thing with
00:11:34
Speaker
cranks and gears and stuff. And you had to know some complicated mathematics to interpret what the machine was telling you. But yeah, he invented this mechanical calculating machine. So by the time he was in his 30s, he had this friend who was a writer. His friend went by the pen name, the Chevalier du Mer. What does that mean in French? Do you know?
00:12:03
Speaker
Chevalier is like a knight and mare, which I'm probably pronouncing wrong, is where he was from. But he was kind of an expert on all things fashionable in France.
00:12:18
Speaker
And one of the fashionable things was gambling. And so he asked Pascal this question called the problem of the points, which is suppose you have two men playing a gambling game where they have to accumulate a certain number of points to win the prize money, and the game has to stop before either side has gotten to the required number of points.
00:12:43
Speaker
What is the fair way to distribute the money? This question had been around for a couple of centuries. Nobody had solved it. And Pascal dove into it. And he didn't quite know how to do it because we were talking about predicting the future. And that was something that you're not supposed to be able to do. And so he ended up, Marine Mersenne, put him in touch with
00:13:08
Speaker
another Frenchman named Pierre de Fermat. Fermat is kind of the greatest of all time, the goat of amateur mathematicians. He was not a natural philosopher. He was a lawyer. He was a government official in his local government and he did math as his hobby.
00:13:27
Speaker
And he wrote letters to people all over Europe with all his mathematical ideas, and he'd pose problems. And Fermat's most famous problem called Fermat's Last Theorem was not proved until 1994. So he knew what he was doing, and he knew how to challenge
00:13:43
Speaker
people with some pretty advanced stuff. And so Pascal and Fermat never met in real life, never met in person, but they wrote letters to each other over several months and together they came up with what we know as probability theory today.
00:13:58
Speaker
So let me ask really quickly, because you see this a lot in this time period where a mathematician, a scientist, whatever, will be sending letters to one another.
Breaking Barriers: Blackwell's Journey
00:14:09
Speaker
Do you happen to know how they got hold of each other's addresses and things like that? Like, how do they know about, I mean, you said they got put in touch with one another. Was it really just that simple, giving each other addresses?
00:14:23
Speaker
Yeah, there were various people who knew people, and one of them was this man I've mentioned a couple times, Marine Mersin. He was- This is the Mersin of the Mersin Primes? That's the guy, the very same. He ran a salon in Paris that eventually became
00:14:45
Speaker
something that his name escapes me right now. The Academy of Paris, a very respected school came out of Mersenne's salons, and it was just people who knew people, and the postal system was pretty rudimentary at the time.
00:15:04
Speaker
But you had these people like Mersenne who were kind of the focal point and they sent letters to other people all over Europe. Interesting. You've mentioned the salons, which were essentially, from what my understanding, social clubs with admission fees. Right. And they got together and they talked about the latest scientific or mathematical studies they'd been working on.
00:15:32
Speaker
I just wanted to bring that up also because the term's been mentioned a few times, but also because one thing that we've talked about on the show before, kind of a difficult aspect of mathematics up to probably like the 1800s and even today in many respects, is something that is done by people who a lot of times are economically privileged. So I just wonder if you would like to speak anything to that in your research.
00:16:00
Speaker
It is something that I have noticed. Pascal was privileged. Vermont was, like I said, Vermont was a lawyer. There are two women in the series, Florence Nightingale and Ada Lovelace, and they were both definitely privileged. But then again, on the other hand, some of my subjects
00:16:22
Speaker
were not. Benoit Mandelbrot was basically, well, he was from a Jewish family, a Polish Jewish family, and spent World War II on the run from Nazis as a teenager in Vichy, France, had a completely disorganized irregular education all the way up until he got into the Grande Coles, the
00:16:50
Speaker
The French system is different. You have high school, but then you have university. And in between, there's the Grande Coles, the big schools. And he got into not one, but the two most prestigious. And he chose the Polytechnic Institute. But before then, he was a refugee. He was poor. His family had no money.
00:17:14
Speaker
His education was sporadic, and a lot of times, for a time, he had a set of old encyclopedias that his father had managed to scrounge up because someone had thrown them out. Mandelbrot started out
00:17:35
Speaker
very, very disadvantaged. Another example, David Blackwell was the son of a railroad worker. David Blackwell's father never made it past the fourth grade. And Blackwell also was African American at a time when this was in the 20s, 30s and 40s, when opportunities for the worst time. Yeah, not very good times.
00:17:59
Speaker
He was fortunate enough to have a geometry teacher in high school who saw his potential and started encouraging him in that direction. But even then, in the 1940s, he was fortunate enough to have a professor, his PhD advisor was asked to join the Institute for Advanced Study at Princeton. And this professor was allowed to bring, you know,
00:18:27
Speaker
three of his recent PhDs along with him. And so Blackwell got to go to Princeton. Princeton didn't want him because visiting scholars at the Institute for Advanced Study are named as honorary members of the Princeton faculty. And Princeton did not want a black man on their faculty. And the people at the Institute for Advanced Study actually got together and threatened to disassociate themselves with Princeton.
00:18:57
Speaker
if Blackwell was not given the same honors that the rest of the visiting scholars were given. After that, he was interviewed for a job at the University of California, which is where he ended up, but not for another 10 years. The guy that would have been his boss and eventually became his boss wanted to hire him, the upper manage, his boss's boss, the deans and everything. They were ready to hire him.
00:19:24
Speaker
the head of the department's wife objected because as the department head, they have all the new professors over for dinner and her objection... Can we waste his time? Yes. Can I say, I'm not going to use the N word, I'm going to use the D word and you can bleat me.
00:19:43
Speaker
Her quote is reported to have been, I'm not going to have any darkies in my house. Which is definitely a rough quote. Yes. Because the dean's wife objected to having a black man in her house, he did not get the job at UC. He ended up at UC 10 years later, but that was after 10 years.
00:20:09
Speaker
And he was always very matter of fact about the racism that he had to contend with. And he had always assumed that he wasn't going to be hired by UC Berkeley. And so he was busy applying to the historically black colleges, which he did get hired by one.
00:20:28
Speaker
There's another story about Blackwell is the first time he was in New Orleans and got on a bus there and saw the little signs that say, you know, coloreds stay here and whites only up here. And he thought that was so fascinating that when he got off the bus, he took one of the signs with him.
00:20:51
Speaker
So I don't know where it ended up, but he just kind of kept on doing his math. And in the 60s, he was at UC Berkeley and he was the first black professor there to receive full tenure. And the black students there made him their faculty advisor for the Black Student Union.
00:21:16
Speaker
until they realized that he was more interested in doing math than in participating in the social activism of the 60s. And so they got rid of him and went with somebody else. That was just his attitude is, hey, I've got this math to work on. So that's my thing. Very Archimedes vibe of don't touch my circles.
00:21:36
Speaker
Right. So, so, yeah, we've talked about Pascal. We've talked about Blackwell and we talked a little bit about Mandelbrot. But what we haven't done yet is we haven't. Well, first, we're going to talk about Florence Nightingale, Adam Lovelace, and then Edward Loran.
Nightingale's Statistical Legacy
00:21:52
Speaker
So tell us about Florence Nightingale. Who was she? What was her deal?
00:21:56
Speaker
Florence Nightingale is known as basically the inventor of the modern nursing profession. Before Florence Nightingale, nurses were basically considered not much better than maids, house servants. Charles Dickens wrote a book in which he had a nurse in there who was an alcoholic, and a lot of them were alcoholics actually because they were
00:22:20
Speaker
They were put on duty, you know, to watch the patients overnight in this grungy, dirty hospital. And a lot of them took to drinking just to get through it. I will say that I have heard that that substance abuse continues to be a major problem for health care providers, but I think different stressors now.
00:22:39
Speaker
Different stressors now. Florence Nightingale developed a passion, wanted to be a nurse very early on. Her family objected to it because it wasn't proper for a woman of her social standing to take on this low menial job.
00:22:55
Speaker
but she had learned through reading and then got to experience some of the professional nurses in Europe. That was really the first place she saw that it could be a serious profession that required education, training,
00:23:14
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experience, that sort of thing. She was also very passionate about mathematics, something else that her family thought was inappropriate for a woman of her social standing to be interested in. She had to study it and not in secret, but she studied it together with her aunt. They got up at like five in the morning, even before the servants were up and studied math together for an hour in the morning.
00:23:40
Speaker
What she's remembered for is during the Crimean War, health care for the wounded and sick soldiers was terrible. The British Army was actually losing more soldiers to disease than to battlefield injuries.
00:23:57
Speaker
This was not new. This had happened in all the wars previous. But what was different about Crimea is that Crimea had journalists who had telegraphs. And so not exactly CNN, but still, this was a revolution in that the British people could read in the newspapers every day that
00:24:16
Speaker
Hey, all our soldiers are dying from from disease from cholera. And so there was this huge outcry to clean up the hospitals. And Florence Nightingale, because of who she knew, was appointed the head of Corps of Nurses to go over to Crimea. Actually, she didn't go to she went to Crimea eventually. But the hospital was in Skutari, which is in Turkey. Today, the town is called Uskudar.
00:24:44
Speaker
and that's where the primary hospital was. I can't wait to talk to school kids. I haven't been able to talk to school kids because of COVID, but I'm looking forward to the time that I'll get to talk to school kids and try to gross them out with all the things that were going on at the hospital in Scutari before Florence Nightingale got there. Why don't you gross out our audience with one story?
00:25:07
Speaker
Well, the toilets in the hospital were all backed up. And so they got these big tubs and put the big tubs in the middle of the room. And that's what all the soldiers used right there. And the orderlies didn't want to empty them because they smelled bad. And eventually they would empty them because Florence would go around and stand there, glowering at them until they emptied the tubs of
00:25:33
Speaker
of what they'd been used for. When they finally flushed out the sewer system to get the sewer system working again, they found dead horses rotting in the sewage lines and things. Basically, the entire hospital was sitting on top of a gigantic cesspit. It's very hard to have people get well under those conditions.
00:25:57
Speaker
Oh, definitely. Also, did somebody flesh a horse down the toilet? No, I don't know how it got there, but there was a dead horse in the sewage line. Somehow it had gotten there. I'm not sure how it did. And one second, I need to let my dogs in, but they're okay.
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00:26:46
Speaker
You know, Florence Nightingale, she's known as the lady with the lamp because at night she would get out her lamp and she would tour the hospital award, which she wasn't supposed to do because it was considered inappropriate for ladies to be on the hospital wards after dark, but she went anyway.
00:27:07
Speaker
And she spent the whole night sitting with the soldiers, talking to them, or if they were dying, she would sit with them. And this was what she became known for. And she's known as the lady with the lamp. And in popular culture, that's where her story ends.
00:27:24
Speaker
right there in Crimea, like she died there herself or something, but that's not the case. She lived another 54 years after Crimea. She lived more than half her life. In that second half of her life, the one that people don't know about, she was a pioneer in statistics. She went back to England.
00:27:41
Speaker
and she wanted to improve the sanitation of the hospitals. She wanted to make her case to the public that, hey, this is something we need to do. Our soldiers are dying over there, and they don't have to. Like I said, she was a very passionate statistician, but at the time,
00:27:59
Speaker
Statistics were pretty much only found in these things called blue books, which were these big blue colored tomes that basically collected dust in government storerooms and that was it. She wanted to communicate with numbers
00:28:15
Speaker
what the British Army was experiencing and what could be gained by making improvements. And so she took her statistics to the general public. And the way she did that was she used diagrams, some of which she invented herself.
00:28:31
Speaker
And so today, we've just come through a pandemic still going on. But in the early days of the pandemic, they talked about flattening the curve and what are the numbers like? And are they going up or are they going down? Any use of that, not just in medicine, but anywhere, any use of diagrams or graphs or anything, you pretty much have Florence Nightingale to thank for that.
00:28:56
Speaker
And people don't know that. People imagine her, you know, she's still marching around Scutari with her lamp. But no, she she did much more after that. That's fascinating. And you know what I'm noticing is a recurring theme amongst all of these is a certain degree of stubbornness.
00:29:13
Speaker
Yes. Well, I also think it's kind of sometimes necessary to make advancements, you know, to have a certain degree of stubbornness, because you have to think of, you know, what we have isn't enough, we have to add to it. And I'm also noticing that access to information, especially sometimes through technology, like, you know, books getting cheaper, like you said, the blue books that, you know, that we're gathering dust, but like, you know, nevertheless, we're
00:29:37
Speaker
probably a lot more accessible than, you know, records back thousands of years earlier. And then into the modern day with like, you know, Mandelbrot and Blackwell and public education. It seems like access to information is really what creates mathematics.
00:29:53
Speaker
Right. Well, it certainly helps. You have to have some place to start and then you build upon that. That's another thing I wanted to point out is that math is collaborative. Math is cumulative. Florence Nightingale did not do all this by herself. She had people she looked up to. There was a Belgian
00:30:12
Speaker
a mathematician named Adolf Kaedle that she idolized. She got help from a statistician in England named William Farr, who had made one of the initial breakthroughs. He was the one that basically statistically discovered that cholera is connected to water. Now, he was wrong about what that connection was, but the fact that he had made that connection to water
00:30:37
Speaker
enabled another person, Jon Snow, to figure out, well, maybe it's something in the water. And so that kind of communication and collaboration is essential for math. And it still is today. Oh, yeah, definitely. And then you I mean, even have, even have other influences, right, like the people who went around collecting the statistics of in the case of Florence Nightingale, you know, just the blue books and stuff like that. But not only that, the the social club set up obviously in France, so
00:31:07
Speaker
And it's much like, I mean, he didn't, he didn't talk about the guy who made the steam engine, whose name escapes me, but, you know, even him, he needed, you know, people to design. Yeah, he, he needed, thank you. He needed people to, you know, solder the metal and, you know, help construct the steam engine. So, and now that's used as a part of this, like the, the, the, the math and science that came out of that.
00:31:33
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are used a lot in modern thermodynamics, obviously. So yeah, I just wanted to agree with you. Okay, round two. Name something that's not boring. Laundry? Ooh, a book club. Computer solitaire, huh? Sorry, we were looking for Chumba Casino.
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Ada Lovelace: Pioneer of Computing
00:32:46
Speaker
Ada Lovelace was a celebrity child of a celebrity. She was the daughter, the only legitimate child of Lord Byron. Lord Byron was a poet and was known as much for his bad behavior as he was for his poetry. Lord Byron and Ada never actually
00:32:57
Speaker
That's the most romantic thing you've said to me all month. We don't make sense. We make chicken.
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Speaker
She never met her father because when she was only a month old, their parents split up. They never divorced because I would have been too scandalous. And there was already enough scandal going around. Lord Byron had been caught up in a scandal involving his
00:33:26
Speaker
half-sister. And that kind of opened the floodgates because other of Lord Byron's former lovers came out with stories of who he was and including the woman who had given him the label, mad, bad, and dangerous to know. And plus Lord Byron was also in debt. So he basically got run out of the country when Ada was only a month or two old. He went off to Europe and he
00:33:55
Speaker
eventually died in the Greek War of Independence from the Ottoman Empire. He didn't die in battle, he died of disease. So here we go back to more people in war die of disease than of battle wounds. So Ada never met him, but she idolized him, and she had some of his wildness about her. And her mother, Lady Byron, was very much afraid that
00:34:24
Speaker
Ada would go off and do all these crazy things, and kind of like the way children of celebrities are today. You have Miley Cyrus and Billy Ray Cyrus, or you have Willow and Jaden Smith, who are the children of Will Smith and Jada Pinkett Smith. You have the child celebrities of this machine would take a problem of computing Bernoulli numbers. I'm not going to get into what those are right now.
00:34:52
Speaker
But it basically takes the problem of calculating Bernoulli numbers and breaks it down into a series of steps that the analytical engine would be able to perform. And that is what she's known for. The other thing that I think is more important is she pointed out what computers could and couldn't do. She wrote, people call the analytical engine a thinking machine.
00:35:17
Speaker
But it doesn't think at all. It only does what we tell it to do. It doesn't come up with any of this by itself. A hundred years later, Alan Turing called this Lady Lovelace's objection. And today, a lot of people think that that Lady Lovelace's objection is actually a more important
00:35:38
Speaker
hurdle for artificial intelligence to get over than the so-called Turing test. And so Turing came up with the name for the hurdle that's even higher than the Turing test. It's this thing that Ada Lovelace has pointed out and in my opinion still hasn't been
00:35:57
Speaker
overcome. I mean, IBM can put the Watson computer on Jeopardy and it can beat the biggest Jeopardy champions ever, but that's only because someone told it to do that. Watson didn't think for itself, hey, I think I'll go on Jeopardy and I'll win the money. It didn't think that. It did what it was told to do, and that's it.
00:36:17
Speaker
Right, and also, where does artificial intelligence end is another question. Not necessarily end, but what if we made a machine with an addictive personality? What are the ethics of that? How about an angry machine or a jerk?
00:36:32
Speaker
Like, not only that, there's so many aspects of thought itself which are sort of specific to the way that human beings, like, you know, like, as evolved, like, you know, from apes kind of thing, well, as another form of ape kind of thing, like, you know, have.
00:36:49
Speaker
like very specific. I can't think of many, well, okay, one example is like, you know, you see children when they first start learning, and they like, you don't have to like, look at their, they like, look at their hands to learn that they open and close what their hands look like, things like that. And that ultimately contributes to probably, to some extent, and probably a great extent, the ways in which we derive inspiration and things like that.
00:37:17
Speaker
So yeah, I just wanted to say, and also there's the issue of like, you know, the first machine to pass the Turing test might not always pass it, right? Because we might learn like, you know, certain patterns, but all this to say, yeah, I do think that's a great point to bring up.
00:37:33
Speaker
And out of Lovelace, she was in the 1800s. And I believe we said that Florence Nightingale was in the 1800s. They actually knew each other in passing.
00:37:49
Speaker
Oh, interesting. Yeah, they did not really, really well, but because because Ada, Ada Lovelace died very young. She was in her 30s and she had cancer. And Florence Nightingale was still in her 20s at the time. So they didn't know each other well, but they, you know, they went through the same social circles. Interesting. You never know who knows each other in his in mathematical history sometimes.
00:38:18
Speaker
And then you got Edward Lorenz and the chaotic butterflies.
Lorenz and the Butterfly Effect
00:38:22
Speaker
You talk about Edward Lorenz. Edward Lorenz was an MIT professor. He was a mathematician at first, and then World War II happened.
00:38:37
Speaker
Lorenz learned meteorology in order to be a weather forecaster in World War II, was sent out to the Pacific to work for 21st Bomber Command under Curtis LeMay. And the big thing at that time was they had the new B-29 bomber, which could go higher up than any other military plane ever had before. And so high up that they ran into the jet stream.
00:39:06
Speaker
And one of the first planes to hit the jet stream was kind of like they suddenly found themselves over the Aleutian Islands instead of Japan. So they brought this information back and Lorenz was part of the team that started to figure out the meteorology of how this worked and how they could use it to make more effective airstrikes during the war.
00:39:32
Speaker
Curtis LeMay came up with some pretty horrendous ideas, and I'm not going to get into that. But Lorenz learned weather forecasting because of World War II, came back and changed his field to meteorology. And by the 1950s, late 1950s, he was very much in the camp of doing numerical weather forecasting. There was this idea that if you just had the right equations,
00:40:02
Speaker
you could calculate, you could predict the weather in advance. And in fact, there was a Walt Disney little 15-minute documentary that Walt Disney put together at some point in the late 1950s.
00:40:19
Speaker
that envisioned this World Weather Bureau with satellites in orbit and the World Weather Bureau would be able to collect so much information and compute it using the new electronic computers that we could forecast the weather weeks and months in advance and so far in advance that we could do things to change the weather and control the weather. This was kind of a dream people had
00:40:45
Speaker
for several decades previously and Lorenz was one of the people that was exploring this idea. By 1960 Lorenz had something that most other college professors or researchers of any kind didn't have yet and that is he had his own computer.
00:41:01
Speaker
MIT had bought him a desk computer. And when I say a desk computer, it's not what you think today that it goes on top of your desk. A desk computer was the size of a desk.
00:41:18
Speaker
is this big gigantic thing. Lorenz described it as sounding like a small airplane flying overhead. The desk computer had its own office. They put it in Lorenz's office, but he didn't want to be in there with it because it was so noisy, so he moved.
00:41:35
Speaker
down the hall and took an extra desk in the room where his assistants were, and the desk computer got its own room. And it did calculations for him. And interestingly, here's another example of who knows who. His very first programming assistant was a young woman who had just graduated college in mathematics and had moved to Boston because her husband was going to Harvard Law School. Her name was Margaret Hamilton.
00:42:05
Speaker
working for Lorenz, taught her a love of computer programming and so she was originally thinking of getting a higher degree in mathematics but she ended up going into computer programming instead and ended up being the lead software engineer for NASA's Apollo moon program and there's a famous picture of her
00:42:28
Speaker
in her very 1960s, 1970s, looking out that standing next to a stack of binders that's as tall as she is. And that's the source code for the Apollo lunar module or the Apollo guidance computer. That's Margaret Hamilton. She got her start doing weather prediction, weather forecasting software for Ed Lorenz. But I digress.
00:42:50
Speaker
So one day, Lorenz is getting ready for a conference where he's going to present some of his ideas, and he's looking at a computer run of some weather forecasting predictions, a weather simulation, and he decides he wants to rerun
00:43:07
Speaker
the calculation from somewhere in the middle so he can recheck his figures. So he looks at the line of numbers. It's like, oh, OK, I'll pick this point right here. And he types in the numbers. And he tells the computer, start at this point. And then he goes, and he gets a cup of coffee. An hour later, he comes back, and the computer is printing out a completely different pattern of results from the one it did before.
00:43:34
Speaker
and it being the early 1960s, the first assumption is that there's something wrong with the computer. He looked into it more and he realized very quickly that it's not a computer problem. What had happened was the computer's memory kept the numbers to six decimal places, but it had only printed them out to three.
00:44:00
Speaker
So when he went back and typed in the results from halfway through and said, here, start here, he wasn't giving the computer exactly the right numbers. One example is the computer had known that the number was 0.506127, but it only printed 0.506. And so that's what he typed in, 0.506.
00:44:24
Speaker
A common assumption at the time would have been that it's numerical work, so it's very close because it's a differential equation. The differences will smooth out was the assumption, but they don't. They don't smooth out. They magnify and they get bigger.
00:44:45
Speaker
And that little difference was enough to throw the whole calculation off. And what Lorenz realized is what that means is that we will never have weather instruments that are precise enough to predict the weather
00:45:06
Speaker
beyond about two weeks. So all this stuff about predicting the weather months and months in advance is never going to happen because we will never have instruments that are precise enough because a slight difference smaller than what the instrument can measure
00:45:24
Speaker
Say your thermometer goes to 0.001 of a degree, there's an error difference of 0.0001. That's enough to throw the whole thing off. The difference will magnify and propagate through the system. And so eventually, about two weeks later, you will have something completely different from what you had predicted.
00:45:49
Speaker
Yeah, and I understand that when he gave his talk, there was a lot of excitement about, well, this means that we can control the weather by using peaceful explosions and this and that for manipulating the atmosphere. But they ignore the second part of the paper, right, that kind of talks about that you can't affect long term statistical behavior.
00:46:10
Speaker
Right. You can't affect the long-term behavior because your instruments aren't precise enough. And yeah, you can use bombs to push the weather off, but how precise is your bomb going to be? Exactly. Your bomb would have to be precise enough to do, you know,
00:46:27
Speaker
things one way or another. It also strikes me that if you had, let's say, some kind of thing out in space, right, that as it has the Schrodinger's box type thing that sends out one part that that either like, you know, that counts the amount of radioactive decay and has a 50%
00:46:47
Speaker
of setting out like an atom, it strikes me that if we follow the multiple world interpretation of physics, that like you're just a tiny little difference that one atom between these two universes, ignoring even quantum fluctuations that you would see different weather patterns, no matter how small the difference was between the two, which is why he talks about obviously the butterfly wings.
00:47:09
Speaker
Butterfly wings, yes. It was originally a seagull. The idea of a seagull flapping its wings in one part of the world can eventually change the weather in another part of the world. Ten years later, in 1972, he was going to give a presentation on this, and it was actually the person who
00:47:29
Speaker
was putting the program together for the conference who came up with the butterfly instead of the seagull. But what we call it today is the butterfly effect, the idea that, yes, the butterfly flapping its wings in Brazil can eventually cause a tornado in Texas. And Lorenz himself was kind of skeptical about this and pointed out that if one butterfly flapping its wings can cause a tornado, then another butterfly flapping its wings can stop a tornado.
00:47:59
Speaker
And what about all the other butterflies and the seagulls and the mosquitoes and everything else? So he was not such a big fan of the butterfly effect. He was a bit too down-to-earth for that, but it did catch on. I like how his range of down-to-earth is a butterfly. The butterfly is far too small. Seagull, that's fine.
00:48:23
Speaker
Yes. So yeah, but the butterfly effect has been very popular. And there is, I guess, I guess I never saw the original Jurassic Park, but there's a scene in the original Jurassic Park where Jeff Goldblum is explaining the butterfly effect. And he does a better job than most. A lot of people don't don't quite get what the butterfly effect means. But if you want to know, I guess you need to watch the original Jurassic Park. Or we could roll that clip. Still not clear on Cass.
00:48:53
Speaker
Oh, oh, it simply deals with predictability and complex systems. The shorthand is the butterfly effect. A butterfly can flap its wings and be king and in Central Park you get rain instead of sunshine. Why?
00:49:11
Speaker
Robert Black's book series covers seven mathematicians over six books spanning four centuries of mathematics and covers mathematicians from all walks of life.
Storytelling to Demystify Math
00:49:21
Speaker
This book is geared towards expanding children's education through bringing mathematicians to life through stories. I'm Sophia and this has been Breaking Math. With me I head on Robert Black. Let me ask you, where can people access these books?
00:49:34
Speaker
My books are available through the Royal Fireworks Press website, rfwp.com, and you can also find my earlier books there. And I just hope that people looking for ways to understand math better and to see it as we've been talking about a human activity, something that regular people do for regular reasons,
00:50:02
Speaker
It's a good opportunity if they want to know more about that and they want to think about how everybody else is, you know, they might think, well, I'm a regular person and I've got regular reasons and wouldn't it be nice if I could do math too? If math has always seemed kind of alien or foreign to them, then maybe reading how other people came to approach it will help them as well. Awesome. So there we go.