"The Calculus of Friendship" by Steven Strogatz

In The Calculus of Friendship: What a Teacher and a Student Learned about Life While Corresponding about Math, Cornell University math Professor Steven Strogatz shares some of the correspondence he shared over several decades with his high school calculus teacher, Don Joffray.

The book is short, and a quick read if you don’t try to follow too closely the mathematics the two correspondents toss at each other. The two men reverse roles over time — originally Strogatz was the student, but in time he becomes the teacher. Along the way, Strogatz and “Joff” share the joy of being challenged by interesting math problems. But their interaction, while lively, is also frequently sporadic. Neither man (particularly Strogatz) seems comfortable in becoming a friend who shares more than just a love of math and the highlights of day-to-day life. It is only as the two men grow older that they bridge the gap and communicate their more personal feelings. Both men suffered the kinds of personal losses common to most of humankind, but they each failed to share their vulnerability and need for emotional support. One can appreciate the special bond between these two men, even as one can imagine what a deeper relationship might have brought them.

Yes, mathematics is key to this story. But the real theme is friendship, what brings us together, and what we may miss out on by not opening up on a deeper level.

"Elric: The Ruby Throne"

I don’t usually read graphic novels, but I made an exception for Elric: The Ruby Throne, by Julien Blondel et al. Years ago I enjoyed reading Michael Moorcock’s fantasy tales of the albino anti-hero Elric, so when I learned Moorcock himself praised the illustration and story-writing that went into The Ruby Throne, I decided to give it a try.

Because I have so little experience with graphic novels, I can’t judge Elric: The Ruby Throne against others. But I can say that it was interesting, dynamic, and very well conceived. (I must add that this story is really only for adult readers — in showing the decadence of Melnibone’, the kingdom Elric rules, the writers and illustrators present considerable nudity, violence, and horror, as well as dashes of cannibalism and sex.)

Reviews of this book and its sequel on Amazon.com are polarized. In many ways, the Elric portrayed in these books is very different from the one in the original novels by Moorcock. Because Moorcock praised the graphic novels, the evolution of the original Elric to one far more dark suggests Moorcock might have crafted Elric differently from the beginning, if allowed. Or, perhaps his own imagining of Elric has evolved over the fifty years or more since the first Elric story was published.

The fact that I plan on reading the next volume following this one say a lot regarding how well I enjoyed this one.

Swords That Do More Than Kill

The most common weapon found in works of fantasy must surely be the sword. There are people who fight with one, people who carry one just in case they need it, and even some people who simply wear one as a fashion statement. Swordsmanship is often a key skill in many fantasy worlds.

But there are swords that go beyond simple weapons. There are legendary swords, such as Excalibur. There are swords that are legendary within a particular fantasy universe, including several in Tolkien's tales of Middle-earth. Some of my favorite examples of magic swords include the following:

  • Stormbringer. The sword used by Michael Moorcock's albino antihero, Elric of Melnibone', is an example of a sentient weapon. It gives him strength and prowess and frees him from the need for life-sustaining drugs, but it must feast on the souls of humans it cleaves. And sometimes these humans are not enemies, but friends.
  • Changeling. This sword, appearing in the Morgaine stories by C. J. Cherryh, is capable of tapping the power from space-time Gates to send its victims to a place and time they would much rather not be.
  • The Sword of Helsinlae. This sword is obviously a favorite because it appears in my fantasy novel, The Ban of Irsisri. It is pretty much an ordinary sword until its wielder, Visylon, chops down an evergreen growing from the grave of the ancient king Helsinlae. The sword is thus imbued with the power of this king, power that will play a critical role in the vanquishing of the sorcerer Raethir Del.

Though not an example of a magic sword, Terminus Est is a sword used by the executioner Severian in Gene Wolfe's series of science fantasy novels, The Book of the New Sun. This sword plays such an important role in these novels that it is almost a character in its own right.

"Birth of a Theorem" by Cedric Villani

"Beauty is in the eye of the beholder" is a well-known cliche'. And it can be very difficult, if not impossible, to explain to someone who has no knowledge or experience to fall back on why something as abstract and abstruse as mathematics can be said to be beautiful. It would be interesting to conduct an informal survey to test the hypothesis that those who succeed in mathematical studies are those most likely to recognize the beauty of mathematics.

Frenchman Cedric Villani won the Fields Medal (the mathematics equivalent of the Nobel Prize) in 2010 for his work, with former student and colleague Clement Mouhot, on "nonlinear Landau damping and convergence to equilibrium for the Boltzmann equation."

I have no idea what this is, except I do know who Ludwig Boltzmann was, and that this work addressed a problem in mathematical physics.

But I didn't need to understand what this was about in order to follow Birth of a Theorem: A Mathematical Adventure, Villani's story of his work in this area. Yes, there are plenty of equations about as comprehensible as hieroglyphics. But the reader does not need to comprehend the math in order to grasp what life as a mathematician is like, as Villani describes it. Villani describes the joy of discovery, the fear of making a mistake that could negate all his work, the struggle in wrestling a problem to the ground. As many wunderkinds do, he spends long hours absorbed in his work, trying to make sense of a small part of the universe. When he succeeds, the reader breathes a huge sigh of relief with him.

I grasped just the tiniest bit of the mathematics he describes, but it reminded me of the pleasure of seeing something unfold in mathematics. I only understood part of the esoterica presented on these pages, but it left me wanting to dig into old math books to decode and more deeply appreciate the mathematics. As a graduate student taking courses in theoretical statistics. I had glimpsed one example of mathematical beauty when I learned about the close relationship between the concept of moment in mathematics and the concept of moment in physics.

You don't have to be a mathematician to appreciate this book, but I must concede the obvious: only someone with an interest in mathematics may appreciate it.

Bugs Bunny

From 1940 to 1964, Warner Bros. produced 170 cartoons featuring the iconic cartoon character,  Bugs Bunny. I grew up watching Bugs Bunny cartoons as well as many other cartoons produced under the Looney Tunes and Merrie Melodies labels. Thursday nights, when I was little, we watched "The Bugs Bunny Show." My father enjoyed watching Bugs Bunny almost as much as watching the Pink Panther. When the show moved to Saturday mornings, it was the centerpiece of all the morning cartoons.

Bugs Bunny is a culturally-recognized example of the "trickster" archetype. On one hand, he's a friendly character who doesn't go looking for trouble. But on the other hand, once someone brings trouble to him, they better watch out! He is quite adept at devising clever tricks to play on those who have wronged him.

A few years ago, I decided to apply my inherited fondness for making lists, and I constructed a list of all the Bugs Bunny cartoons, drawing on the book, Looney Tunes and Merrie Melodies: A Complete Illustrated Guide to the Warner Bros. Cartoons by Jerry Beck and Will Friedwald. One by one, I checked off the ones I had watched. When I needed a few more to watch to complete the list, I found them on YouTube.

Going back to watching many of the old cartoons was spurred by a trend that concerned me. Many of the old Warner Bros. cartoons, including Bugs Bunny, were being censored before showing on Cartoon Network. A shotgun blast to a character's face would be deleted, for example. I surmised that some group of concerned parents were influencing network executives to edit the cartoons for anything that might - as these parents believed - have a negative influence on their children's behavior. As I looked into this, I discovered that there were some entire cartoons featuring Bugs Bunny that have been banned because they depicted not just violence but racial stereotypes. These cartoons are not shown on TV but can be found on DVDs or on YouTube. The DVDs released as the "Looney Tunes Golden Collection" are compilations that include some of these controversial cartoons. Each DVD shows a message at the beginning explaining that while some cartoons on the disk depict unacceptable behaviors such as racial stereotypes, they are included for historical reasons. But then, cartoons such as "Bugs Bunny Nips the Nips," a World War II-era feature, can now only be found on YouTube. At the time this short originally came out, its treatment of the Japanese as our enemies was dehumanizing, an almost universal sociological factor in wartime. (This cartoon, as well as many others released in wartime, were intended as entertainment for adults, not children.)

And what have I learned by watching cartoons like Bugs Bunny over the years? I learned it's good to have sense of humor and not take oneself too seriously. I learned that being clever is better than being out-and-out mean. I picked up various expressions (like Yosemite Sam's "you durn idgit"), some of which have become so embodied in my day-to-day conversations that I don't even realize I'm quoting a cartoon character. (A recent meme on Facebook claims [tongue-in-cheek] that Bugs Bunny taught us that "revenge on my enemies should be quick, clever, and brutal.")

What did I not learn? I did not learn that shooting someone in the face simply turns their face black with gunpowder. Nor did I learn to think in racist terms. And enjoying the antics of an anthropomorphized rabbit who is said by some to be a "cross-dresser" did not interfere with puberty or my sexual orientation.

Like many others, I miss the "golden years" of animated shorts.

 

 

"The Math Myth" by Andrew Hacker

They say it is a good idea to read things that challenge one's cherished beliefs or values, both to expand one's mind and to test one's beliefs. But, more often than not, this is uncomfortable to do. (And that's why the normal tendency is to avoid doing it.) As in reading The Math Myth: And Other STEM Delusions, by Andrew Hacker. Professor Hacker has a number of arguments against mathematics education in high school and college, not the least of which is that the requirement for taking algebra, let alone classes such as trigonometry or calculus, forces students who have no desire to enter technical fields to endure a painful winnowing as they pursue their education. The acronym "STEM" stands for Science, Technology, Engineering, and Mathematics, and is used in a number of education policy approaches aimed at improving what students know in these subjects, with the objective of improving the competitiveness of the U.S.

As I recall, I was taught the oft-maligned "New Math" in my elementary school. I had no trouble with it, so neither did my parents, because I didn't need to ask them for help with my homework. (Unlike the father in the movie, Incredibles 2, who struggles to help his son with his "new math" homework and exclaims, "I don't know that way! Why would they change Math? Math is Math! MATH IS MATH!")

By seventh grade I was being pulled aside to do more challenging math assignments than the rest of my class was doing. By the time of high school graduation I had taken two years of algebra,  as well as geometry, trigonometry, and calculus, with high scores on standardized tests. I pursued chemistry as a college undergraduate and took calculus and differential equations. I pursued biochemistry in graduate school before moving into a fledgling PhD program in biostatistics and computer modeling. There I continued with coursework in theoretical and applied statistics, operations research, signals and systems analysis, complex systems, and numerical analysis, among others. In my dissertation research I had to apply what I knew about differential equations and numerical analysis to hypotheses in the biochemistry of vision. My first job out of graduate school was in biostatistics for pharmaceutical research.

I have always valued my mathematics education. It was very much aligned to applied mathematics and not theoretical mathematics. I am matho-philic, not matho-phobic, so it is a real challenge for me to put myself in the shoes of those for whom math does not come as easy.

Then along comes Andrew Hacker, with The Math Myth. One by one, Hacker tackles the assumptions that guide everything surrounding math education. As I read this book, I often felt like the subject of Edvard Munch's "The Scream", because I resist his arguments even as I have to grudgingly admit he may be right. Allowing one's beliefs and values to be challenged by reading a book like this is no easy task, especially for someone for whom mathematics and science has dominated their education and career.

I won't attempt to summarize Hacker's arguments. (It would be interesting to read a counterpoint.) But I will touch on one argument, the question of taking coursework that will not likely have practical value for a student. I bristle at this, especially when someone I know tries to tell me that because a knowledge of history has no value in the workplace, history education is a waste. On the other hand, I have been known to argue with one of my friends that there is little or no value in taking classes in Latin. And I do not understand those who put the so-called "classical" education on a pedestal.

What should students be required to learn, and when? This is a really tough question. I could ask how physical education ("P.E." we used to call it) prepared me for supporting myself and my family when I finished school. I could easily grumble over my grades in P.E., grades that were not impressive because I didn't have the athletic "aptitude" that others did. But if I fall back on that argument, was it fair to my fellow students who didn't share my mathematics aptitude for them to be compared against me?

There are no easy answers to many questions in education policy. It may not be comfortable to admit that, but it is a good thing that people like Andrew Hacker challenge our thinking.

Honoring One's Craft

To "honor one's craft" is to treat that craft in a respectful manner. To not take it for granted. To spend the time and effort needed to perfect it. To purchase tools to use that say, "This craft is important to me, and I will show it by the quality of my tools." For some writers, that might be an expensive fountain pen. For other writers, honoring one's craft may mean beginning the day with a small ritual, surrounded by inspiring totems.

I am a sucker for handmade leather goods (that look appropriately masculine!). Several years ago I discovered online a company called Oberon Design. Over time, after purchasing -- and appreciating -- leather covers for iPhones and iPads, I finally decided to spring for a leather cover for my composition notebook. In addition to copious notes I capture on my laptop using Evernote (a future blog topic), I also like to jot down notes in a (retro-looking) composition notebook. I figured purchasing a leather cover for that notebook was an appropriate way to honor my craft as a writer. I chose a pattern called "Celtic hounds" because it seemed like a good fit with my fantasy writing.

Whenever I pick up my notebook, the cover says to me, "There is something very special inside here." That, to me, is what is meant by honoring one's craft.

PS: Nothing can beat a Pentel EnerGel pen for smooth writing!

An Interview with Author Mark E. Lacy

Recently I was interviewed by AC Cobble regarding my fantasy novel, The Ban of Irsisri. Here is a transcript of that interview:

AC:The Ban or Irsisri is in many ways a traditional epic fantasy with an epic quest, lots of action, and powerful sorcery. It’s also packed full of dream sequences, tribal rituals, and mysticism. Why did you decide to add those elements, and do they add to the story?
 
MEL: The mix of traditional elements of epic fantasy with elements of tribalism and mysticism was something that developed over time. I knew I didn't want my main characters to come from privileged backgrounds. Nor did I want them to emerge from serfdom. If you take Robert E. Howard's "Conan", for example, you have a hero who has great disdain for the trappings of "civilization" and who takes great pride in being labeled a "barbarian". I think Conan would enjoy sharing a mug of ale with the tribesmen in The Ban of Irsisri. As far as dreams and mysticism are concerned, I think some of the most profound stories in fantasy and science fiction have supernatural mysteries at their core. Forces we cannot fully comprehend, forces that transcend ordinary experience but nevertheless influence our values, our choices, our sense of destiny.
 
ACI love that you mention Howard’s “Conan”. I was thinking about that character when I read your book. You have a great sequence early in the novel where one of the tribesmen, Enkinor, enters a city and – spoiler! – runs into all kinds of trouble. In fantasy books, it’s always the dark forest that is full of threats. But in real life, it’s usually the cities where people get in trouble. What do you think is so appealing about the idea of a primal man from the wilderness facing off against a modern (well, more modern) world?
 
MEL: I’m pretty sure one could trace back Conan’s barbarism to the concept of the “noble savage.” But I also think “primal man from the wilderness” has an appeal because life in the wilderness, on the frontier, was simpler in many ways than the “modern” world. Not easier, but not as complicated. The threats to your survival in the wilderness are often better known. And perhaps the wilderness could be said to be less-populated by immoral distractions and temptations.
 
AC: The Ban of Irsisri stands out because of its vivid prose, and in some ways it reminds me of NK Jemisin – which is about the biggest compliment I can give a fellow fantasy author. Sorry if this is rude, but, how did a former corporate guy learn to write like that!?! Asking for a friend…
 
MEL: Asking for a friend? (laughs) We might stand your question on its head and ask, how did a fantasy writer survive Corporate America for thirty years? Seriously, I think that, to the extent my writing succeeds, it has a lot to do with reading and revision. Many successful writers have counseled new writers to read a lot and read broadly. And, over time, the more I read, the more I learned how good writers produced their work. And the more I learned, the more I went back to revise. And revise. And revise. I would set my work aside for a while and come back to it later with fresh eyes, only to discover, with chagrin, I had more work to do. 
 
AC: Tell us something no one else knows about Mark E Lacy or The Ban of Irsisri?
 
MEL: Only my junior high school English teacher knows that the fantasy story I wrote in ninth grade, which won first place in the school's literary contest, was a seed that would sprout and influence the scene, early in The Ban of Irsisri, when Enkinor and Strigin escape into the hills beyond the city of Kophid, only to face their pursuers and a forest fire of supernatural origin.
 

Review: The Confessions of Nat Turner

In the process of doing research for an essay touching on racism and Confederate memorials, I was reminded of the novel, The Confessions of Nat Turner, by William Styron. I had heard of the Pulitzer Prize-winning novel but had never read it. I knew it was a fictional tale based on the life and death of a slave who had led a bloody revolt in 1830s Virginia.

Nat Turner was a religious fanatic whose faith led him to commit or facilitate many grisly murders in the name of freedom for the slaves. Styron's book makes clear the indignities and abuse suffered by slaves. The reader is led to believe some kind of action against the white populace is justified, but clearly not the rampage that Turner led. Turner gradually comes to see that a revolt is necessary, and that it is God's will that Turner lead it. I was reminded of how the religious fanaticism of John Brown led him to execute proponents of slavery, believing God was on his side, as well as how both the people of the Union and the Confederacy believing God was on their side in the Civil War.

Turner learned to read and write at an early age, but it is unlikely he was as eloquent as the first-person "confessions" in Styron's novel would suggest (and for which Styron has been criticized). Nevertheless, Styron tells a good story. While the narrative moved back and forth between the events leading up to the revolt and Turner's incarceration, I didn't get confused or lost. I don't always read a famous work and come away with a realization of why that work deserved the praise it received, but I did this book.

Landscapes and World-Building

The English language is rich with terms to describe the outdoor world (many of which have been borrowed from other languages), such as coteau and coulee, jaral and jetty, savanna and sawtooth. The worlds of most fantasy novels use natural settings where the features of the landscape may help or hinder the protagonists, or set the mood for the plot. When an author is creating a fantasy world where she needs to construct these settings, how can she find the best descriptors?

Home Ground: Language for an American Landscape (2006, Barry Lopez, ed.) is essentially an encyclopedia of terms to describe geographical features. The book includes a number of illustrations. I guarantee, if you browse through Home Ground you will find many things you've never heard of before, as well as accurate descriptions to accompany terms you always believed you knew but might not have quite right. (Note, the focus here is on the American countryside; I recently wanted to look up "moors", but since we don't have moors in America, it wasn't listed.)