Book Review: The Manga Guide to Linear Algebra

Vectors, matrices, and eigenvalues, oh my! The Manga Guide series’ triumphant return to the fertile and abstract realms of mathematics is, to this reader, most welcome and not a little overdue. This is not to say that previous forays into the physical-, life-, and computer sciences were at all unsuccessful. But even on their worst day, these real-world subjects are not nearly so difficult to penetrate as, say, set theory or integral calculus. And this is coming from a card-carrying math geek.

The wonderful and beautiful thing about this series is in its ability to come at complex and foreign topics from a sideways angle. I’m still amazed at the unusual points of reference the book authors find to bring the reader into some notoriously difficult topics – explaining onto and one-to-one functions in terms of restaurant orders, for example. The highly visual nature of the comic medium also serves as an anchor in what might otherwise be a text-heavy topic.

The manga scenario wrapped around all this math draws on a number of classic tropes, and not only from the realm of manga. Reiji is working hard as the newest student in his university karate club, a membership he paid for by agreeing to tutour his sensei’s sister in linear algebra. He’s the proverbial 98-pound weakling with a good heart, and it’s as good a reason as any to have two young people flirt and talk about matrix multiplication.

Of eight chapters, the first six are laid out as groundwork before the “real” linear algebra topics in the last two. The fundamentals in chapter two include reiviews of (or introductions to) set theory, some basic mathematical logic, and functional relationships. Following this are two chapters covering matrices, and two more on vectors (in a matrix interpretation). Only then are we able to tackle the true topics of the book title, linear transformations, eigenvectors, and eigenvalues.

It may sound like a hodgepodge, but it’s not. Each chapter builds carefully on the previous one. No calculus and only some basic algebra, trigonometry, and co-ordinate geometry are needed before reading this book. But the topics are tough for a newbie. This is university-level mathematics and requires a lot of practice problems before it will sink in for most readers.

The example problems in the text are great, but there are only a few. As with all books in the series, The Manga Guide to Linear Algebra is best utilized in conjunction with a thick textbook, chock-full of additional practice exercises. Much like earning a black belt, the road to mathematical mastery requires many hours of practice and perhaps more than a few forehead smacks on nearby slabs of wood.

(No Starch Press, 2012)

Reprinted with permission from The Sleeping Hedgehog
Copyright (2012) The Sleeping Hedgehog

Book Review: The Manga Guide to Biochemistry

I was looking forward to No Starch Press’ latest Manga Guide release for months before it actually came out. I quite enjoyed The Manga Guide to Molecular Biology, and thought this would make for an excellent companion piece. Obviously I wasn’t the first person to think so, the author of that previous book, Masaharu Takemura, must have felt the same or he wouldn’t have agreed to write this one as well.

Biochemistry and molecular biology are like solid state physics and physical chemistry or, if you like, psychology and sociology. Both disciplines find themselves interested in many of the same phenomena, but consider slightly different aspects of each one.

Molecular biology is interested in how the body works as a system on the sub-cellular level. The basic processes of life are considered with respect to how they manage to maintain all the functions of a cell. Biochemistry is interested in all the chemical behaviour involved in life, which ultimately is responsible for all those same cellular functions.

Both books discuss many of the same ideas, therefore, but there’s virtually no overlap in content. In Molecular Biology, enzymes were considered as helpers in chemical processes. In Biochemistry, more time was spent on the specific reactions they catalyzed, and the actual chemical structures of reactants and products. Both books discuss the way DNA information is read and translated into specific proteins, but biochemistry goes into the chemical detail of DNA, RNA, and the amino acids that make up a protein and determine its folding.

The storyline is cute: Kumi is a teenage girl constantly worried about her weight. She decides to study biochemistry so she has a better understanding of her metabolism and its relationship to weight gain. This is not just an entertaining framing device; Takemura is intentionally using a non-traditional approach to the topic, introducing major chemical characters into the narrative in an organic way as they become relevant to particular chemical processes.

Proteins, fats (lipids), and carbohydrates (saccharides or sugars) are each discussed in different chapters. The chapter on carbs isn’t really just about carbs, it’s about how sugars are used to create ATP which in turn provides energy for the cell (amongst many other things). The chapter on proteins isn’t just about the Atkins diet, it’s also about how enzymes are created and how they function as biological catalysts.

This isn’t the first Manga Guide to take a non-traditional approach to a topic. Calculus took a much more intuitive, less mechanical approach to derivatives and integrals, though not a less rigourous one. Universe followed a historical sequence in discussing the heavens, steadily overturning pre-conceptions as contradictions were discovered. And all of the books in this series have emphasized real-life examples and applications, whatever the topic. The chemical reactions discussed in the book are used to explain everything from the ripening of fruit to the springiness of mochi-style rice.

And it works. There are a number of topics in science that are frequently taught a certain way because it makes it easier to organize a textbook, or faster to “cover” in class, even though it’s not the most efficient approach to actual learning. I appreciate this series’ willingness to eschew traditional learning sequences in favour of intuition, learning in context, and developing ideas organically from previous knowledge. Another enjoyable entry to the series.

(No Starch Press, 2011)

Reprinted with permission from The Sleeping Hedgehog
Copyright (2012) The Sleeping Hedgehog

Book Review: The Manga Guide to Electricity

This is a story about how Rereko, a fairly ordinary high school student from the advanced world of Electopia, gets sent to Earth for remedial courses in the science of electricity. Her society expects absolutely everyone to know a little something about how electricity behaves, and its more important applications. Since she’s a little bit slow in this subject, a tutour from our own, more primitive planet, may be just her speed. A Tokyo graduate student in electrical engineering, Hikaru, seems like the perfect fit.

Like the other books in this series, The Manga Guide to Electricity aims to break down potentially difficult subject matter into bite-sized, comic book chunks, all wrapped up in an engaging story. While the target audience is individuals interested in the subject matter rather than manga fans only after a fun read, the story provides a natural vehicle for the book to give lots of real-life examples of the subject in question, an endless litany of answers to the unasked question: why does this stuff matter, anyway? As usual, the book features a tutour and a (sometimes reluctant) student.

The dialogue-based format is not only an effective way of unpacking concepts, but also makes it easy to build up a book-length political argument simultaneously: that this information is important and worthwhile even for an average citizen. Plato made Socratic dialogue famous in his philosophical treatises, Galileo appropriated it for the use of scientific education, and Ohmsha and No Starch Press did both of them one better by adding pretty pictures. You almost can’t go wrong.

The focus of this book is on applications. It’s at least as much about basic electrical engineering as it is about electrostatics and electrodynamics. The abstract concepts of electric forces and fields are not really touched on. Point charges don’t come into it. Instead, we jump directly into circuits, explicitly using the analogy of electricity as flowing water: voltage is pressure; current is rate of flow. This is a very useful picture, although there are times it could have been used to greater effect.

The only weakness in this book, from my perspective, is failing to take a little more time to fully flesh out some of the basics. Voltage, current, and resistance are all explained very well. The reader is not simply given a definition, but aided in visualizing the real physical meaning of the concepts. However, the relationship between them is not as well explained. The current is equal to the voltage over the resistance. Why does a higher voltage result in a higher currrent? It’s analogous to increasing the water pressure, forcing it through even faster. Why does an increased resistance lower the current? It’s analogous to constraining or restricting the path, slowing each individual drop of water down.

This and a few other concepts were not sufficiently spelled out, though the formula was introduced. On the other hand, a tremendous number of applications were discussed, although many of them were only roughly sketched out: transformers, generators, semiconductors, diodes, and transistors of many kinds. These thumbnail sketches were appropriately short, and a writer with less of an engineering background may even have left some of them out, but a writer with a pure physics background probably would have spent a little more time on some of the basic concepts, and this is my own background, so I admit my bias.

Still, a solid overview of the topic. I really like the practical, real-life examples that are a hallmark of this series. The very first chapter started by looking at the labels on kitchen appliances, and this was a brilliant way of introducing the topic. And I was quite surprised, I didn’t expect to learn something new in this book, but actually a good chunk of the material was unfamiliar territory for me. I didn’t know that much about the basic physical operations of diodes, transistors, or some of the other types of electrical technologies discussed. It makes me want to learn more about electrical engineering. After all, who isn’t crazy about all the electronic gadgets that make our modern world go round?

(No Starch Press, 2009)

Reprinted with permission from The Sleeping Hedgehog
Copyright (2011) The Sleeping Hedgehog

Book Review: The Manga Guide to Physics

Having read and enjoyed nearly all of the entries in the Manga Guide series by Ohmsha/No Starch Press, I’ve been going back to read those ones I missed the first time around. The Manga Guide to Physics is pretty much what it sounds like, covering what most people think of when they hear the word physics: mechanics, which is the physics of motion, force, and energy. Other areas of physics, like electricity, thermodynamics, and quantum mechanics, are left to future titles.

The book covers its material in four chapters: Law of Action and Reaction, Force and Motion, Momentum, and Energy. The subject matter is explained via a series of private tutoring sessions between the two main characters, high school students Megumi and Ryota. In the prologue, Megumi, an all-star athlete, has a bad day, losing a tennis match to her arch-rival while she is distracted by thoughts of her poor test performance in physics class. She enlists Ryota, the star science student of the school, to get her back on track academically. It may even turn out that a better understanding of physics could improve her game.

The storyline is simple but good, and the tennis angle provides a good vehicle for illustrating and applying physical concepts. Many people think physics is just a series of formulae, but a mathematical formula is just one way of expressing the behaviour of, and relationships between, objects in the physical world. Visual and graphical representations are also very effective ways of conveying concepts in physics, and The Manga Guide to Physics expertly applies these approaches.

Although the author, Professor Nitta of Tokyo Gakugei University, does not shy away from the relevant equations, even including some (completely optional) calculus-based sections, this book’s focus is firmly centred on conceptual understanding rather than calculation. Typical of this series, the main ideas are introduced via the story, which is illustrated in graphic novel form, while deeper explanations are left to a few pages of text at the end of each chapter. However, while some of the other books in the series include end of chapter practice questions (Manga Guides to Calculus, Molecular Biology, and Statistics, for example), the text-heavy pages in Physics are reserved for derivations and more complicated calculations.

This book does an excellent job of explaining these concepts, however, and showing where the equations come from, even if it doesn’t provide the reader with practice using those equations. Unusually, Nitta starts out with forces, specifically, Newton’s Third Law, discussing details of motion (velocity, acceleration, displacement) later. This approach works well, because it allows the first chapter to be qualitative, rather than jumping straight into the math.

He only touches briefly on force diagrams, but gets the main idea of action-reaction pairs across via thought experiments and Socratic questioning. The use of both equations and different types of motion graphs in the next chapter are explained well through examples in the main body, and would be well-paired with a more traditional textbook’s practice questions. Momentum and energy are also well done, explained first qualitatively, then with numbers.

The Manga Guide to Physics has the potential to be a great resource for the independently-minded student, and its non-traditional topic sequence is an effective alternative to the usual way of doing things. The series’ book on calculus also takes an uncommon, but much superior approach to its topic that I found most helpful in refreshing my memory, and this alternative approach to the physics may also be just the ticket for some students. Sound pedagogy, a fun story, and the natural pairing of a visual medium with a visual topic make for another home run from this consistently strong series.

(No Starch Press, 2009)

Reprinted with permission from The Sleeping Hedgehog
Copyright (2011) The Sleeping Hedgehog

Book Review: The Manga Guide to the Universe

The Manga Guide series began modestly with a single title near the end of 2008, The Manga Guide to Statistics, and it was a surprise hit. Now here we are on book eight of the series, with book nine just around the corner. We’ve had Manga Guides to Databases, Calculus, and Molecular Biology. It seems there is no scientific topic that can’t be improved by adorable comic illustrations. Now we see if that even applies to the universe itself.

The premise is quite brilliant. Japanese high school students Yamane and Kanna are the only members of their struggling drama club. They’ve committed to putting on a show at an upcoming arts festival to justify their existence, but are at a loss as to what they will do. Just then, an American exchange student, Gloria, walks in, eager to join the club and displaying a deep enthusiasm for Japanese culture. The three of them put their heads together and settle on doing an adaptation of “The Tale of the Bamboo Cutter”, wherein a tiny girl is discovered inside a stalk of bamboo, only later to be discovered a princess of the moon.

There’s only one problem, this tenth-century tale needs some updating, today’s post-Apollo program audience won’t buy the idea of a kingdom on the moon. Yamane needs to update the story with a more distant, mysterious location. But knowing little about the heavens, more research is needed. Fortunately, Kanna’s brother is an astronomy major at the university, and his favourite professor is more than willing to share the wonders of the universe with an interested audience. But just how far will they need to go to find a home for their princess?

An introductory astronomy course or textbook normally surveys such a wide array of different disciplines and reasoning techniques that most of them can be covered only qualitatively. The hodge-podge nature of the topic thus provides a less obvious intellectual progression than something like molecular biology, calculus, or chemistry, wherein each new topic builds on a previous one. Ishikawa’s chosen narrative arc is both historical and natural to new students of astronomy, first focusing on the skies as seen from the Earth (especially our own moon), then expanding to the rest of the Solar System, our Milky Way Galaxy, other galaxies, and then the overall shape, history, and future of the universe as a whole. The final chapter discusses a number of open problems in astronomy, including the theory of other universes, and the mysteries of dark matter and energy.

Although I wasn’t expecting to learn about Japanese literature in this book, it was really a nice fit, and in retrospect, it’s quite natural to discuss how cultural views of celestial objects and the universe as a whole have changed over time. Ishikawa also ties the birth of new universes back to the original story in the final chapter in a brilliant and very satisfying way.

Throughout the book, we get a good view of why astronomers believed the universe was a particular way, as well as why they were proven wrong, from discarding the Earth-centered model, to recognizing the vastly greater distances of the stars compared to the relatively nearby objects of our Solar System. The text engages the reader with leading questions and logical implications, and the data and thought experiments are well served by the visual illustrations. Ishikawa uses both some classic analogies and some fresh, unique ones to get some difficult concepts across.

I was delighted that he also took time to cover some hot-button topics that a traditional textbook may have left out: Kanna discovers a UFO and by the end of a chapter, she has learned enough astronomy basics to figure out what it really was and why it seemed to be following her; the possibility of life either in our Solar System or elsewhere in the galaxy is discussed, including the specific details of our best nearby candidates, and the more general statistical argument made famous by Frank Drake.

The Manga Guide to the Universe is a perfect blend of lucidly argued basics and unfettered, cutting-edge possibility. One of the best yet in the series (which is saying a lot).

(No Starch Press, 2011)

Article first published as Manga Review: The Manga Guide to the Universe by Kenji Ishikawa on Blogcritics.