I enjoyed all the mathematical biography I read. I’d recommend each and every one of the six books most strongly. And I have to say my favorite children’s book about babies and where they come from is still the first one I read myself when I was a young bunny: Where Did I Come From? The Facts of Life Without Any Nonsense and With Illustrations, written by Peter Mayle, illustrated by Arthur Robins, and designed by Paul Walter.
But that book was published in 1973 and does show its age. So if I were to pick something more recent, I’d go with What Makes A Baby? written by Cory Silverberg and illustrated by Fiona Smyth, or It’s NOT The Stork: A Book About Girls, Boys, Babies, Families, and Friends, written by Robie H. Harris and illustrated by Michael Emberley, for younger bunnies, and I’d pick It’s SO Amazing: A Book About Eggs, Sperm, Birth, Babies, and Families, written by Robie H. Harris and illustrated by Michael Emberley, for older ones.
Caramel: Probably the fourteenth: The Dangerous Gift. But I still read and reread all fifteen of them.
Sprinkles: I know. The books are still all over the house. I think you really like Tui Sutherland and her imaginary worlds. You and I both read and enjoyed Tui Sutherland’s shorter series, The Menagerie, that she wrote with her sister.
Caramel: Yes, that is true. I did not want to read them first, but after you finished them all, you sort of made me. I did not want to get out of the Wings of Fire world at first.
Sprinkles: But you did enjoy them in the end.
Sprinkles: That happens! So Marshmallow, let us talk about the fiction you have read this year.
Today Sprinkles reviews a collection of children’s books that parents can share with little ones to help answer the curious question “Where do babies come from?”
Sprinkles has reviewed several books for the book bunnies blog before. Last October, she reviewed a handful of children’s books on gender identity. Today she once again discusses a selection of books on a topic that is both important and useful but may sometimes be challenging to talk about with little bunnies: Where do babies come from?
As a parent of young and growing children, I have occasionally needed to field curious questions such as “why is the sky blue?” or “why are there only seven colors in the rainbow?” or “why does ice cream taste so much better than cabbage?”. Sometimes these questions lead me to interesting discoveries, as the world is enormous and little ones have no limits to their curiosities but I certainly have a finite amount of knowledge. So often we look things up together online, or check out books, and learn something new together. And these turn out to be quite pleasant learning experiences for all. In fact many grownups I know love to rediscover the world through the questions of the children in their lives.
However there is one question that often challenges grownups: “Where do babies come from?” Some eventually figure out how to give an at least somewhat satisfying answer to this question, or children seem to lose interest eventually, seeing how their grownups are fumbling with words, and move on. But readers of the book bunny blog might want to know if there are smoother ways to talk about this question and the related ones about human sexuality. That is why I decided to read and write about a handful of books that explore these issues and claim to be age-appropriate.
I begin with the first book on this topic that I myself have read (because, yes, I was a curious young bunny once, too): Where Did I Come From? The Facts of Life Without Any Nonsense and With Illustrations. Written by Peter Mayle, illustrated by Arthur Robins, designed by Paul Walter, and published first in 1973, this book might perhaps be the first in this genre. Quite progressive for its time, I think the book holds up relatively well.
Where Did I Come From? The Facts of Life Without Any Nonsense and With Illustrations begins with the natural question almost all curious young bunnies ask their parents at some point. The answer is almost all accurate and illustrated with hilarious and quite anatomically detailed drawings. The explanation starts with a woman and a man wanting to be close to one another and then goes into some of the details of sexual intercourse (called “making love” here). These stages are illustrated with a cute and round mom-to-be and a cute and round dad-to-be. You do not see things in very graphic format, but you do get a full understanding of the mechanics of the process. Then there is a detailed and illustrated description of the uterus and the various stages of pregnancy, and the book ends with a message of love to the child addressed as “you” throughout the whole thing:
You might think it sounds like a lot of hard work for such a little person. But there’s a very good reason why your mother and father went through it all. And if you want to know what that reason is, just take a look in the mirror.
This is where I find that the book is somewhat not completely ready for our times. It assumes that the child asking the titular question is living with a mom and a dad, and that these folks are the child’s biological parents. There is no acknowledgment of other alternatives, such as adopted children or children being raised by people other than their biological parents. Other than this particular shortcoming, the one minor mistake I can find in the book is about baby math. That is, we are told that “one sperm plus one egg makes one baby; two sperm plus two eggs makes two babies, and so on.” This is of course not always true; twins and triplets can come from a single fertilized egg.
But perhaps adults might not want to complicate things, and perhaps theirs is a nuclear family structure made up of a mom and a dad who are the biological parents of the curious child. In that case, I think that Where Did I Come From? The Facts of Life Without Any Nonsense and With Illustrations is still quite capable of doing its job effectively, and all along the way, entertaining everyone involved. Depending on the parents’ level of comfort, the book might be appropriate for bunnies as young as 6 years of age. Readers should know that there are a lot of naked baby illustrations along the way and a few adult naked bodies, too; the inside covers are also full of over a hundred smiling sperm. Visually, the tendency is all on the cute and humorous, and there is absolutely nothing erotic or sexualized, but most characters depicted have no clothes on.
A book, or rather a pair of books, on the same topic where everybody except the unborn is fully clothed is Where Do Babies Come From: A Guide for the Christian Family. This is in fact two separate books, one written for boys aged 6-8 and the other written for girls in the same age range. Folks do not need to be Christian to have some concerns about having images without clothing in a book they are sharing with their young ones. So I thought it might be a good idea to see what this book pair had to offer.
This pair of books does not have a visible author; published by a Christian publisher the author voice is captured by an invisible “we” addressing the parent at the beginning and giving them some ideas about how to share this book with their little ones. Most of the rest of the book is written in the form of a story about a boy named Simon or a girl named Alisa, turning seven and wanting to learn about where babies come from. The Christian nature of the book is very tangible, with Christ being mentioned in the address to the parents; however, the rest of the book mainly focuses on a single God, who creates and loves, so it is possible other religious folks might be able to find it palatable for their context as well.
The books develop content in parallel for most of the time, and they make an effort to mention alternatives to the child living with biological mom and dad setup. There is mention of an adopted neighbor and possibly grandparents living with the child. But the focus seems to be the nuclear, mom and dad setup. The actual making of the baby event is described by mom and dad loving one another and “bringing their bodies together very close and in a special way.” There is not any more anatomical or mechanical details, though words like egg, sperm, uterus, and vagina do come up.
Then comes the part where children are told boys and girls are different and a boy cannot be the mother when playing house (though, thankfully, we are told men can be cooks and women can be firefighters or doctors). Then there is the part about how “sin has ruined God’s perfect plan” so some moms and dads don’t stay together. Furthermore the binary and biological essence of sex is emphasized throughout (boys are like this, girls are like that). These might make it harder for some grownups to choose these books for their little ones.
All in all, I found this pair of books to be an interesting attempt, and I thought that they provided lots of messages which might align with the values of some families. However, I believe they do not provide a concrete answer to the actual question. It was also not clear to me why the authors felt a need to make the two books separate; the only difference I could discern was the main character of the story was a boy for the book meant for boys and a girl for the book meant for girls.
Another book with a similar title is Where Do Babies Come From?, written by Katie Daynes, illustrated by Christine Pym, and designed by Suzie Harrison. Designed as a lift-the-flap book, this book also does not give away too much about the mechanics of how babies are made. We are told only that the father’s sperm and mother’s egg met and became one. It is not clear how or where the meeting happened, but somehow this egg and sperm pair made it into the mother’s body.
The main distinction of this book, in my opinion, other than the flaps that would most effectively engage young bunnies who would likely love to discover what is hidden under each, is that it puts the human process in the context of the larger animal kingdom. The pages of the book are colorful and full of all sorts of animals courting one another, mating, and taking care of their eggs and their young. Each of the animal groupings point to a flap which, when opened, explains a particular animal behavior which leads to the making of offspring (like a bird dancing to attract a mate). And in the middle of each two-page spread is a human mother or a pregnant woman, and a curious child asking her questions.
Where Do Babies Come From? in this way puts human reproduction in the context of natural animal behavior. This might appeal to grownups who know that their little ones like and enjoy books and documentaries about animals. The flappy design of the book makes it accessible to a younger readership; bunnies as young as four years of age might be able to enjoy and learn from the book. And perhaps the lack of information about some of the details of the baby-making process is perfectly fine for this particular audience.
Where Do Babies Come From? Our First Talk About Birth is yet another book with a similar title, aiming for the younger crowd. Written by the child psychologist Jillian Roberts and illustrated by Cindy Revell, this book is part of a new series called “Just Enough: Difficult Topics Made Easy.” As expected, the book does not give too many details, just enough to satisfy a curious five-year-old bunny perhaps. Where do babies come from? The mother’s body has a place named a womb, right under the stomach; that’s where. To make the baby an egg and a sperm need to meet. And how do they meet? “When it’s time to make a baby,” a mommy’s body which has an egg and a daddy’s body which has a sperm fit to one another and get the two pieces of the puzzle together. So again, there is a lot of handwaving and indirection, but the goal is to just say enough so the child is satisfied and not misled, but also does not get confused by the details.
Just like most of the books reviewed earlier in this post, Where Do Babies Come From? Our First Talk About Birth aligns itself more with the attitude that younger bunnies do not need too many details, but they can get to know about the sperm and the egg, and this allows them to think about how two humans came together to make one baby (no matter how vaguely that coming together is described).
For grownups who want their younger ones to have more of the details and who are not worried they will be confused, scared, or inordinately curious (some grownups do prefer less curious bunnies!), I can recommend It’s NOT The Stork: A Book About Girls, Boys, Babies, Families, and Friends. Written by Robie H. Harris and illustrated by Michael Emberley, this book is perhaps the best option for the 4-7 age group. The presenters are a bird and a bee, one curious and wanting to know more and the other a little embarrassed and kind of tentative about things. They start with the stork and other stories children may have heard about where babies come from, and then go into the facts. The illustrations are cute, fully colored, and very helpful.
Unlike any of the earlier books reviewed above, It’s NOT The Stork: A Book About Girls, Boys, Babies, Families, and Friends actually uses the phrase “having sex” and describes in detail the reproductive systems of the biologically male and biologically female human bodies. It also accounts for a range of families including adoptive ones. The binary nature of biological sex is still omnipresent in the book however. The differences and similarities between the body of a boy and a girl are explored in great detail.
One thing I really like about this book was the section on “Okay Touches, Not Okay Touches”. One of the reasons why young bunnies should learn something about their bodies and where babies come from is so that they are aware of the notion of the privacy of certain parts of their bodies. This book takes this concern to the next level and explicitly differentiates between good and natural and healthy ways people can touch them and the not-so-good, and unwanted ways. Reading this book together (maybe a couple sections at a time, as each two-page spread makes a rich section on its own), a grownup bunny and a young one can have some very important conversations.
It’s SO Amazing: A Book About Eggs, Sperm, Birth, Babies, and Families, written by Robie H. Harris and illustrated by Michael Emberley, the same team who produced It’s NOT The Stork, is also a neat book, in the same spirit, providing a lot of useful information in digestible chunks, this time for the 7-and-above age group. In fact It’s SO Amazing! was written first, in 1999, and then came It’s NOT The Stork for the younger crowd, in 2006. Both books are great options, in my opinion, if you want to answer your young bunnies’ questions fully.
If your young one has already read It’s NOT The Stork, they may already recognize the bird and the bee in It’s SO Amazing, who are once again the main narrators of the story. This book also talks about how babies are made, but also, as its intended readership is approaching puberty, there is some mention of the typical changes that a child’s body goes through during this time. The “Okay Touches, Not-Okay Touches” distinction shows up once again.
I was surprised to see that there is a whole section on HIV and AIDS in It’s SO Amazing: A Book About Eggs, Sperm, Birth, Babies, and Families. First I wondered why the section was not more broadly on sexually transmitted diseases. My explanation for myself is that the point was probably not to explain HIV / AIDS as one of many sexually transmitted diseases, but rather to make sure that young readers know and understand the context of HIV / AIDS. Sexually transmitted diseases are not typically discussed in mainstream conversations involving young people, and many may not have heard of them. And perhaps it is okay for a seven-year-old to not learn more details just yet. However, HIV / AIDS is a topic that many will hear about before they turn ten, and some will know people who are living with HIV / AIDS. There are a lot of myths about how the HIV virus is transmitted and the two pages dedicated to it aim to dispel some of these.
The team who created It’s NOT The Stork and It’s SO Amazing! also wrote a book for older children, age 10 and up. I plan on reviewing that book together with a few other books about puberty. Stay tuned for that, coming up in a few more weeks.
Finally, I wanted to share with you some thoughts about a slightly more recent book, What Makes A Baby, written in 2012 by Cory Silverberg and illustrated by Fiona Smyth. Formatted as a picture book, this book, too, seems directed towards the younger crowd. As the most recent book among those I am writing about here, this book is perhaps the most flexible in terms of audience and inclusivity. The subtitle of the book says it explicitly; this is “a book for every kind of family and every kind of kid.”
The book mentions people who have sperms and people who have eggs and people who have uteruses. The words boy, girl, woman, man, mother, father do not appear anywhere. But there is repeated mention of those who wanted you, those who cared for you, those who loved you. There is also a lyrical description of the conception process, involving the stories of the egg joining the stories of the sperm, and being ready to tell a new story together. In other words, a baby is made by love, bringing together stories of multiple people and generations, and is to be loved by the people around them. Anatomy is mentioned to an extent; we hear of the baby coming out of the vagina, we learn how to say the word uterus, but the mechanics of the baby-making process is not included.
I think What Makes A Baby is a neat book which offers grownups the opportunity to share a more inclusive and metaphorical explanation of how babies are made with the young bunnies they love. This will be especially helpful for young ones who themselves do not feel like their identities are captured by words like boy or girl, and those whose families may not fit the traditional biological parents living with their offspring template. However, many young bunnies are ready to love and be loved, and so sharing this version of the story of the beginning of their life when they are not yet ready for the full technical story might be a good idea.
More generally, I think that What Makes A Baby is a good first read for all young bunnies and their grownups. For the ones interested in nature and animals, the flapbook Where Do Babies Come From? might also be very appropriate. For young ones who have a pregnant person close to them and are curious about the process, Where Do Babies Come From? Our First Talk About Birth might also offer a feasible option. If and when the young ones ask for more information, you can move on to some of the more detailed texts, such as Where Did I Come From? The Facts of Life Without Any Nonsense and With Illustrations, or either of the birds-and-bees books (It’s NOT The Stork and It’s SO Amazing!) All in all, I think there are a lot of interesting options out there!
Sprinkles reviews the Mathematical Lives series by Robert Black. From left to right: Pascal and Fermat: The Probability Pen Pals (2019), Florence Nightingale: The Lady with the Diagrams (2019), David Blackwell and the Deadliest Duel (2019), Ada Lovelace: Programming the Future (2020), Benoit Mandelbrot: Reshaping the World (2021), and Edward Lorenz and the Chaotic Butterflies (2022).
Last summer Sprinkles got a hold of a few mathematical biographies, written by Robert Black and published by a small publisher focusing on the homeschooling and educational enrichment market named Royal Fireworks Press. She was planning to at least skim through the books herself before sharing them with the younger bunnies of the household, but once she began reading, she could not put them down. She ended up reading all the books pretty fast, and earlier this year, when she learned that the series had a sixth book, she decided to read that too. In this review, she writes about the whole series, sharing her thoughts on what young bunnies might get out of them (quick hint: a lot!). She also explains why curious adult bunnies might want to read these books, too, whether they like math or not. The quick summary is that the books show us very clearly that people who come up with some of the most fanciful and powerful mathematical theories are all human, with human challenges, human dilemmas, human desires and concerns. And their mathematics is much more interesting in the context of their lives.
Read on for the long version.
Mathematics is a common topic of discussion in the book bunnies household, and the book bunnies have reviewed many mathematical books written for children for the book bunnies blog. I have personally reviewed Women Who Count: Honoring African American Women Mathematicians by Shelly M. Jones as well as several books written about Ada Lovelace. More generally, you can check out all posts we published that are tagged “math“. So when I got a hold of a neat collection of mathematical biographies, written by Robert Black, that are aimed for a young but curious audience, I thought I could write a review of them all for the blog, too. After all, the young bunnies have been complaining nonstop about how I have not reviewed anything for a long time now.
So in this review, I’m talking about Robert Black’s Mathematical Lives series, currently composed of six books: Pascal and Fermat: The Probability Pen Pals (2019), Florence Nightingale: The Lady with the Diagrams (2019), David Blackwell and the Deadliest Duel (2019), Ada Lovelace: Programming the Future (2020), Benoit Mandelbrot: Reshaping the World (2021), and Edward Lorenz and the Chaotic Butterflies (2022). Most of these names are not household names. One might wonder why the author chose these particular people to write about. (I will get to that at the end of this review.) Even though I had heard of all six of them, and reviewed several books written about one of them, in most of the cases, I did not know the specifics of the lives and achievements of these people. And reading these books, I learned a lot. A lot of mathematics as well as a lot of interesting facts about the lives of six fascinating people.
Let me begin with the first book I read from the series: Pascal and Fermat: The Probability Pen Pals (2019). This is the story of Blaise Pascal (1623-1662) and Pierre de Fermat (1607-1665), and how through letters, they developed the foundational concepts of modern probability theory.
The book, like all the others in the series, is divided into ten short chapters. We start with Blaise Pascal, more specifically his family. The author portrays the general setting in which Blaise finds himself, both historically and culturally. Along the way, we learn of the specifics of a question a friend asks Blaise about gambling that gets the ball rolling and leads eventually to the correspondence between Blaise and Pierre de Fermat that in turn leads the two, Blaise and Pierre, to the modern constructs of probability.
The math is sprinkled here and there, always written in an accessible manner, in digestible chunks. The author is writing for a young but curious audience and it seems to me that he knows well how to keep them interested, how to zero in on the crux of the issue at hand, and how to impart significant amount of math accurately all the while keeping things still manageable.
The ten chapters of the book also include a solid narrative on Fermat’s own life story, and the stories of several other mathematicians whose ideas and earlier attempts formed the background to the mathematics the main characters of the book ended up extending, enhancing, and building upon. The author is especially skilled at making connections and finding contexts for the math he is talking about that would be comprehensible to a young bunny, or a curious adult bunny.
Next let me tell you a bit about Florence Nightingale: The Lady with the Diagrams (2019). This is the story of Florence Nightingale (1820-1910), the lady with the lamp, as she was called by many who wanted to remember her role in modernizing the world of nursing (and along with it, updating the whole medical establishment of her times) during and after her service as part of the British corps of nurses in the Crimean War of 1853-1856. In this book we learn about her other (but related) heritage: the statistical work she did to bring attention to the many challenges of hospital care during the war.
After a short prologue that quickly brings the reader up to speed about the general outlines of Nightingale’s life and how her work related to the modernization of nursing (“The Lady with the Lamp”), the book starts with a chapter titled “Misfit in an English Lady’s World”. We learn about Florence as a young girl, her family background, and the general societal expectations from a young woman of her upbringing. We follow Florence as she grows up, learn more about her interests and concerns, and eventually, arrive at the path that takes her to the military hospital in Scutari (today’s Üsküdar, which English-speaking folks might know from this rendition of a classic Turkish song by Eartha Kitt).
Soon math, or more specifically statistics, comes up as Florence looks for a way to help the data tell the right story about the problems she has observed during the war time: how poor sanitary conditions were leading to significant loss of life and how certain standards of care could improve the situation. Florence develops novel and creative visualization methods that finally allow her to tell the whole story clearly to the public as well as the folks in power who can, and eventually do, make the necessary changes.
The math content of this book, just like in all the other books in the series, is distributed among many chapters, showing up in digestible chunks. Some of this content is directly related to what Florence herself did, and some of it is provided as background for the reader to understand how her work fits in with the main history of the development of the field. All in all, the reader gains a solid understanding of the life and times of Florence Nightingale, as well as her significant mathematical contributions, all within about a hundred pages. The book, just like all the other books in the series, concludes with an appendix titled “Doing the Math”, where the author offers some concrete problems for the interested readers to play with and take their understanding further.
The third book from Black’s Mathematical Lives series that I read was David Blackwell and the Deadliest Duel (2019). David Blackwell (1919-2010) was a mathematician who made significant contributions to game theory, probability theory, information theory, and statistics. He was a brilliant theory builder as well as a problem solver, a great communicator as well as an educator.
David Blackwell and the Deadliest Duel (2019) is organized in a way similar to all the other books in the series. The life story of David Blackwell is intertwined organically with some of the most curious problems that Blackwell worked on and the theories he made significant advances in. We learn about the mathematical study of games, and duels in particular, which Blackwell thought deeply and productively about. We also learn about Bayesian probability theory, which approaches the problems of probability in the background context of what we know and what we believe. These topics could get very hairy and pretty incomprehensible very quickly, but the author skillfully manages to give us exactly what we need to get a a general sense of the theories, only focusing on a handful of concrete situations that clearly display the mathematics without making things too complicated.
David Blackwell had an illustrious career, spanning several decades, and today he is remembered as a brilliant mathematician. There is a well-known theorem and an annual award named after him. However, his story also reflects many instances of how things were a lot more difficult for a black person in the United States, no matter how brilliant. Robert Black, the author, does not shy away from this dimension of Blackwell’s life story, and I believe that young bunnies will be able to appreciate Blackwell’s achievements even more, given this background.
All books in the series include a “For Further Reading” section at the end, right after the “Doing the Math” appendix. In David Blackwell and the Deadliest Duel (2019), this section includes a link to a video recording of a special lecture Blackwell gave many years ago titled “Predicting at Random”. The link provided did not work for me, but luckily, I was able to find it at https://www.maa.org/david-blackwell-predicting-at-random. If you are at all interested in seeing this great mathematician in his element, sharing some math he likes with a wider audience and doing a great job with it, check it out. But even if you are not such a math fan, the book is worth reading, as it tells a unique tale, involving math, sure, but also a whole lot of humanity. A crisp snapshot of the whole twentieth century comes along as a bonus.
I approached Ada Lovelace: Programming the Future (2020), Black’s book about Ada Lovelace (1815-1852), the woman who is today recognized as the first computer programmer in the world, with some unease. I read a lot about Ada Lovelace. And as I mentioned above, I have reviewed several books about her written for a younger audience. I have also read a lot of books about her written for a more mature audience. In short, I already knew a lot about her and her work, so I was wary. I was also a bit worried that I would find something I did not agree with in Black’s presentation, something that would not sound right to me, and that would taint my positive opinion of his meticulous work, which so far seemed to me to be not only accessible and engaging but also mathematically accurate to a surprising level (I say “surprising” because it is often really difficult to explain sophisticated technical content to a young audience, and Black has done an outstanding job with it).
Let me quickly say that my concerns were unwarranted. I liked the book a lot. Black does an excellent job telling the story of Ada, as well as the technical work she contributed to. The many mathematical ideas presented in the book are accurately described, and Black does not withhold from his reader the historical debate about exactly what parts of the work credited to her actually belongs t0 Ada. All in all this is a well-written, well-balanced account of Ada Lovelace and her achievements.
Once again Black develops the life story of his main character within the broader historical, cultural, and social context of her time. The mathematical context is presented clearly as well. Black is also an excellent storyteller. Even though I knew almost everything in the book (having already read over thirty books on Lovelace myself), I enjoyed reading it page by page, line by line, eagerly looking forward to seeing how he would tie things up.
The fifth book in Robert Black’s Mathematical Lives series is Benoit Mandelbrot: Reshaping the World (2021). The book tells the story of Benoit Mandelbrot (1924-2010), who is known as the father of fractals. Even if you have not engaged with theoretical mathematics in the past, you must have seen or heard of fractals. Even Elsa mentions them in her famous song “Let It Go”.
Here is the amazing fractal called the Mandelbrot set (named after the guy this particular book is about, because he is the one who discovered its construction and explored some of its complex features):
You can read more about the Mandelbrot set here. But let us get back to the book.
We start with a prologue as always. This one is titled “Clouds Are Not Spheres”, a quote from Mandelbrot himself, whose work offers us an alternative way to think about the world around us, different from the standard one we are taught at school geometry classes, with their emphasis on Euclidean geometry (triangles, circles, spheres, and so on). The prologue whets our appetite, but as usual, the first chapter begins with the childhood of young Benoit and his early life with his family. We travel with the Mandelbrots as they move from one place to another, trying to find a place that is safe for their Jewish family (which, given the time period, was exceptionally difficult to do in Europe). We see Benoit thrive mathematically nonetheless.
The mathematics incorporated into this book, as I expected after having read the previous four books, reflects its main character, and is as eclectic as the person who created said mathematics. One of Mandelbrot’s main strengths seems to have been bringing together seemingly disparate ideas and seeing the connections between them in the form of certain simple rules describing complex systems. And the disparate ideas he brought together are really diverse. The book tells a fascinating story, and shows us some of the connections Mandelbrot does make, and overall, Benoit Mandelbrot: Reshaping the World is a very satisfying read.
The most recent book in Black’s Mathematical Lives series is Edward Lorenz and the Chaotic Butterflies (2022), which is about Edward Lorenz (1917-2008). Some of the adult bunnies reading this review might know that his name is closely associated with that of Benoit Mandelbrot from the previous book. The longer story is told exquisitely in a 1989 book which has now become a classic Chaos: Making a New Science by James Gleick. But the shorter story, as told in the two volumes by Black, is still fascinating.
Lorenz and Mandelbrot did not really work together, but their work complements one another. Lorenz began in the world of meteorology and his explorations to understand and predict weather patterns took him from computer modeling to the more general exploration of dynamical systems which are extremely sensitive to changing initial conditions. He discovered various contexts where simple tweaks on the settings of a given system led to drastically different behavior. This in turn led him to the theory of chaos.
Black once again tells his story within a completely developed context. We read about Edward Lorenz, and his childhood days. We read about how he found his way into meteorology, and how his interest in weather modeling was influenced by the Second World War. We learn about other pioneers of weather modeling and how Lorenz built upon their work. And here and there, we get a good number of glimpses into the actual math involved.
Overall I think that each of the books in the Mathematical Lives series by Robert Black make for excellent reading, both for young bunnies and the adult ones. Young readers should probably already be somewhat curious about math to be able to get much out of the books, but once they are interested enough to pick up a book about “some guy who seems to have done some neat math” or “some lady who apparently did some cool math”, these books will definitely carry them along all the way to the end. They are well written and engaging enough to keep the reader’s attention, for sure.
Now for the adults: I am not sure anyone who is not already somewhat curious about math or mathematicians would be picking up a book of this sort, but I wish they would. These books show that math is not a stuffy subject, that math is alive, and that the people who create it, who live their lives filled with it, are fully human, with human challenges and human concerns. The historical, cultural, and the social contextualization provided in each of the books also allows us to see where we are today and how we got here from where the characters of the book were when they lived. Furthermore, the books make so many concrete connections with the real world that it is almost impossible for anyone to say math is a useless game of pure abstractions.
In some ways, these concrete connections may be a bit disturbing. War plays a significant role in the lives and the mathematics of at least three of the mathematicians in these books: Florence Nightingale in Florence Nightingale: The Lady with the Diagrams (2019), David Blackwell in David Blackwell and the Deadliest Duel (2019), and Edward Lorenz in Edward Lorenz and the Chaotic Butterflies (2022). (Especially in Lorenz’s story, we read about some pretty terrible war acts though Lorenz himself is not directly connected to them in any way whatsoever.) War also shows up in Ada Lovelace: Programming the Future (2020), when Alan Turing and the story of the breaking of the Enigma code come up, and in Benoit Mandelbrot: Reshaping the World (2021), when we see how significantly the Second World War impacted Mandelbrot.
But I still very much appreciated reading each and every one of these books. The war connections did not undermine the achievements of these amazing people for me. The problems they solved, they believed they were solving to help humanity. And for the thrill, the curiosity, the challenge of the problems themselves, which is itself such a human thing! (Of course it should also be acknowledged that mathematicians and others who work in problem-solving oriented disciplines like engineering and technology should always keep in mind to what use their efforts are being put to.)
In the end what is my answer to my original question of why the author might have chosen to focus on these six people? Without actually asking the author himself, my answer would merely be a conjecture, but here it goes: I think the author is writing about people and mathematics that he himself finds interesting and important. I am saying this because while reading these six books, I could distinctly sense the tangible, genuine interest of the author in his characters, as well as his fascination and excitement about the math he was writing about.
Also mathematically there are common themes among the works of the mathematicians in these six books. In each book, the math never stands alone; there are always clear real-world connections, both in the origins and the eventual applications of the problems they involve. And the author’s focus on these connections make the books and the math extremely engaging. The probability theory first developed by Blaise Pascal and Pierre de Fermat described in Pascal and Fermat: The Probability Pen Pals (2019) finds its fruits in some of the statistical work done by Florence Nightingale in Florence Nightingale: The Lady with the Diagrams (2019), and the game theory and probabilistic modeling done by David Blackwell in David Blackwell and the Deadliest Duel (2019). The theories of computation that Ada Lovelace’s work is a natural foundation for as described in Ada Lovelace: Programming the Future (2020) eventually allow Benoit Mandelbrot in Benoit Mandelbrot: Reshaping the World (2021) and Edward Lorenz in Edward Lorenz and the Chaotic Butterflies (2022) to see patterns and emergent phenomena that could not be easily seen without computers.
I recommend these six books to anyone willing to check them out, with no reservations, and with the strongest enthusiasm. You will learn some cool math, you will meet some very interesting people, and you will understand our current world so much better.
This week Sprinkles reviews a few books about gender identity written for children.
Marshmallow and Caramel have been complaining that Sprinkles has not written a post since last Halloween (when she had reviewed a handful of children’s books about zombies). So she decided to write another one before the anniversary of that post came around. This is the post that resulted.
This week Sprinkles reviews a few books about gender identity written for children, with a nod to the International Pronouns Day, which was just this past Wednesday.
There have been a range of children’s books about gender identity written recently. In this post I would like to share some of my thoughts about eight of them: Julián Is A Mermaid by Jessica Love; Red: A Crayon’s Story by Michael Hall; Neither by Airlie Anderson; Pink Is For Boys written by Robb Pearlman and illustrated by Eda Kaban; The Gender Wheel by Maya Gonzalez; Who Are You? The Kid’s Guide to Gender Identity, written by Brook Pessin-Whedbee and illustrated by Naomi Bardoff; It Feels Good To Be Yourself, written by Theresa Thorn and illustrated by Noah Grigni; and They, She, He, Me: Free To Be! by Maya Gonzalez and Matthew Smith-Gonzalez.
I begin with a review of a handful of them that aim to emphasize the point that being different is alright, and there is a place for all of us in this world.
In Julián Is A Mermaid by Jessica Love we meet a little boy named Julián who wants to dress up as a mermaid. He finds acceptance in an unexpected place. The book ends as a celebration of differences. The colors of the book are pastel and lively at the same time, inviting us to Julián’s beautiful world.
In Red: A Crayon’s Story by Michael Hall, we meet a little crayon who is blue but is in a red covering paper. He has a difficult time at the start trying to fit in. But in the end he finds that he can be who he is, and life is good again. The color scheme used is simple and reminded me a bit of the book series about crayons by Drew Daywalt. (Caramel reviewed The Crayons’ Christmas, the third book of that series, for our blog.) The illustrations are not intricate but they do exactly what they are meant to and give us a sense of this crayon’s inner world and the world around him as well.
In Neither by Airlie Anderson, we learn of a land of This or That, where every creature has to be this or that, and when there is an individual who does not fit either, they are mocked and excluded from the two groups formed around being This and being That. Eventually we see our outcast, who sees themself as a Both but is called Neither by the two groups, finds themself in a land where they are accepted, along with everyone else. The colors are bright and cheery, and the little creatures are simply drawn but pretty cute.
All three books remind me a bit of a fascinating little book Caramel reviewed a while ago for this blog: From the Stars in the Sky to the Fish in the Sea by Kai Cheng Thom. That book had a dreamy atmosphere, and the main character was a child though magically different from others. Julián from Julián Is A Mermaid is also a little child, and I can see a little boy being comforted by reading about him and his dream of being a mermaid coming true. In some ways though, Neither and Red: A Crayon’s Story might be easier for parents who want to broach the subject of being different without explicitly bringing up gender identity. It is easy to identify the perceived and assumed boy-girl gender binary underlying the stratification of the land of This and That in Neither, though it is never explicitly stated. Similarly, the Blue Crayon in Red: A Crayon’s Story is also suffering from his peers’ expectations about how he should behave given what he looks like, but there is no explicit discussion of boyhood or girlhood.
On the other hand, Pink Is For Boys, written by Robb Pearlman and illustrated by Eda Kaban, brings up the boy-girl binary right up front. The main point here is that boys can like pink just like girls can like blue. Similarly boys can enjoy bows on dresses and girls can like baseball. The binary is not really questioned here, but instead, children are told that the boundaries of the two categories are porous in many ways, that boys and girls can enjoy all sorts of things and still be themselves.
The first three books I described above were stories and could easily be viewed as fictional, though obviously the authors were writing with a particular goal and an intended moral. The fourth book was more an advice book, a nonfiction text that openly tells the child reading it (or being read to) what to think about the topic.
The next four books fit this mold as well. They are more like an adult talking to a child who is maybe a bit concerned about being different or simply curious about gender identity, even if they may not be asking explicitly to talk about the topic.
Let me start with They, She, He, Me: Free To Be! by Maya Gonzalez and Matthew Smith-Gonzalez. Among the four books explicitly about gender identity, this one is perhaps the simplest though definitely not oversimplified. The book starts with page after page of pronouns and pictures of people, and the pictures are pretty amazing.
The emphasis of the book is on pronouns, but the main text that starts after the pronoun depictions is quite extensive. Though organized under headings of Pronouns, Freeing Pronouns, Claiming Pronouns, Creating Pronouns, Using Pronouns, and Playing With Pronouns, the text touches upon the uniqueness of each individual, the creative possibilities of pronouns, and the freedom to be who you want to be. Creators of this book share a bit about themselves too and then have a few words for the grownups. They summarize the main goal of this book really well in their personal introduction:
As parents we want our kids to feel fully free to blossom into their maximum magnificence.
They, She, He, Me: Free To Be! by Maya Gonzalez and Matthew Smith-Gonzalez
The Gender Wheel is written and illustrated by Maya Gonzalez, too. This book is a bit broader in its coverage of gender identity, and is beautifully illustrated, with lyrical language that explores the implications of thinking of the world and our identities as parts of a circle. I loved how the author kept coming back to the circle as a metaphor and a reflection of the world as well as our own inner lives.
However, the book is very U.S. centric, and explicitly asserts that the boy-girl gender binary was brought to North America by European settlers, who had “linear and rigid” beliefs and so they “boxed people in and kept nature out”. Though I sympathize with the author’s perspective, I see it as quite limited in the global context, as the gender binary is alive and well all around the world, without direct need for any seventeenth-century European influences. And though some native peoples of this continent may have had more fluid perceptions of gender than the ones we are living with these days (according to this Berkeley website for example, “more than 150 different pre-colonial Native American tribes acknowledged third genders in their communities”), this was definitely not always as freeing as some might imagine, and may not have meant what we might think it does. (The same website asserts that “By no means did all pre-colonial Native American communities accept or celebrate gender and sexual orientation diversity.”) So I saw this pass at colonialism as an unnecessary distraction.
The gender wheel in the title of the book is extremely useful as a tool however. It is a beautiful way to visualize and understand the complexities of the construct of gender and it allows the reader to be able to distinguish between physical and biological bodies, how one feels inside their body, and how one chooses or needs to engage with the outside world. While scholars of gender studies dig deep into the nuances of their constructs and appreciate all their complexities, for the rest of us these very same intricacies might be barriers in understanding ourselves and our loved ones. Gonzalez and her wheel make the ideas quite transparent and very much easier to understand (and even discuss with young ones in our lives).
A similar idea is used and offered as a tool in Who Are You? The Kid’s Guide to Gender Identity, written by Brook Pessin-Whedbee and illustrated by Naomi Bardoff. This book, too, explicitly describes gender as made up of three layers; these are called Body, Identity, and Expression. (In The Gender Wheel, Gonzalez labels the layers as the body circle, the inside circle, and the pronoun circle.) Having read the two books together, I now find both sets of labels making a lot more sense to me. Unfortunately it seems that the latter book (Who Are You?) does not acknowledge the source of their own wheel construction, and as a result, it is highly likely that this is a case of plagiarism (see Maya Gonzalez’s blog post about the issue here.)
The illustrations in Who Are You? are in some ways a bit less whimsical than those in The Gender Wheel, which definitely reflects its creator’s particular style (as also seen in her book with Matthew Smith-Gonzalez, They, She, He, Me: Free To Be!). But they are definitely not boring or unattractive. Actually they occasionally reminded me very much of the style of the If You Give … series written by Laura Numeroff and illustrated by Felicia Bond, and could sufficiently capture a young reader’s attention.
Who Are You? also comes with a few pages of advice for the adult reader. I think the author makes the (probably correct) assumption that an adult who shares this book with a young person will likely want to have as much support and ideas for resources as they can. So there are resources about how to use the wheel tool provided, how to engage with particular parts of the book with a young person, and where to find other resources (books and films) that can help support a conversation with a young person exploring these issues.
Finally let me say a few words about It Feels Good To Be Yourself: A Book About Gender Identity, written by Theresa Thorn and illustrated by Noah Grigni.
It Feels Good To Be Yourself introduces the reader to a few different children who have different gender identities and sexual expressions. Terms like “transgender” and “non-binary” are explicitly defined in child-friendly language, and the book depicts all gender identity-related difference positively and ends with the main moral:
No matter what your gender identity is, you are okay exactly the way you are. And you are loved.
It Feels Good To Be Yourself: A Book About Gender Identity, written by Theresa Thorn and illustrated by Noah Grigni.
Having read these eight books, what can I tell the reader who probably already regrets diving into such a long blog post?
First I have to admit I am grateful. I am grateful that our children today have these types of books. I am also grateful that we the parents, too, have access to these types of resources to help support our kids in finding and growing into the people they want to be, despite prejudices and oppressive social models of being a boy / man or a girl / woman in the world. I have found each and every one of the books I mentioned in this post to be helpful, and I think there are little people out there that could very much benefit from reading any of them.
Secondly I think these books would be great conversation starters, with all young people. If your child is not comfortable with the gender binary and its impositions on their life, then pick up one or more of these books and let them read it and then discuss. Or why not curl onto a couch or into a bed together and read them together? Depending on how you usually choose to broach various issues with your little one, there is definitely a book out there that will open the right communication channels for you.
Even if your child is already comfortable in their gender identity, it makes sense to bring these books and topics up for conversation. Sometimes children can be rigid adopters of social assumptions without questioning, and their reactions and comments can be hurtful to other people. If you want to raise children who are open-minded and flexible, and who can respect and love people of all ways of being, then these topics do belong, if not at your dining table (and then again why not there?) then definitely somewhere.
Finally I will add that Caramel told me his two favorites among these were Red: A Crayon’s Story, by Michael Hall, and Neither, by Airlie Anderson. I can see how the less openly didactic texts might be easier to share with young ones. At some point, though, especially for the slightly older crowd, the books with more explicit discussion of gender identity might be more appropriate. These books can easily introduce these growing readers to the correct terms and constructs to think about, understand, and express their own gender identities as well as to learn about other people around them.