book review

Astronomy, 1777

A number of years ago I was helping a friend clean out his father’s house when I came across, among stacks and stacks of old books, a book that was falling apart, with pages tan with age. It was obviously old, but it was hard to tell how old it was. It was missing the title page, and the book was written in German. To make matters worse, it was printed using the difficult-to-decipher Gothic characters known as “Fraktur.” Here was a puzzle!

But was it a puzzle worth spending time against? In the back of the book are a number of star charts. They are "tipped in,” meaning, they are fold-out charts that are bound with the regular pages. Twelve of the charts show the constellations in the sky for each month of the year. The illustration of each constellation is a fanciful pen-and-ink drawing of how that constellation is represented. A larger chart shows the solar system (as it was known at the time) with the position of the planets at various times of the year. A final chart shows the surface of the moon.

So, it is an astronomy book. But how old is it? The answer comes at the end of the foreword to the book: “Berlin, den 25ten Marz, 1777.” The book was published in Berlin in 1777!

After the table of contents, the first page is titled “Anleitung zur Kenntniss des gestirnten Himmels.” (Translated: “Instruction for the Knowledge of the Starry Heavens.”) This was written by the eminent German astronomer Johann Elert Bode. The 1777 printing was the third edition of this work, a work of sufficient importance to be released in several more editions into the early 1800s.

Bode was known for his reformulation and popularization of a mathematical model, originally proposed by Johann Daniel Titius, that purported to predict the distance of then-unknown planets from the sun. This law, known as the Titius-Bode Law, originally met with success but as further knowledge of the outer planets was gained, the predictions of the law broke down. Nevertheless, Bode played a part in the discovery and naming of the planet Uranus.

Scientific genealogies relate scientists to their graduate school advisors, and their advisors’ advisors, as well as their students, and their students’ students. Bode is not as well known as his “grand-student,” the eminent mathematician Carl Friedrich Gauss, or his “great-grand-student,” the famous mathematician Bernhard Riemann.

Book collectors would describe my copy of Bode’s Anleitung as having bumped corners, chipped boards, worn ribs on the spine, and a deteriorating binding (not to mention the missing title page). Judging by prices asked for this book by dealers of antiquarian books in Germany, a complete restoration of the book would not be worth the expense. I opted to have the book professionally rebound. It now sits on my shelf, smug in its old age, taunting me, challenging me to renew my limited understanding of German from college language classes and translate it. Alas, I suspect that disassembling the book and removing the charts so they can be framed and displayed would make the book more valuable, but I don’t think I can bring myself to do surgery on the old man.

Layers of Secrets: Joseph Kanon's "Los Alamos"

New Mexico. Ancient ruins of vanished Native Americans. Desolate spaces and tumbleweeds crossing the highway. Snow-capped mountains. Little bars with menus listing hundreds of different brands of tequila. And two of our country’s national laboratories, Los Alamos and Sandia. Los Alamos was established as a secret center of research for atomic weapons during World War II. In the years following the end of the war, Sandia was established for further weapons testing, but its mission is now focused on developing and testing non-nuclear components of nuclear weapons. The mission of Los Alamos is now one of supporting a broad range of interdisciplinary research covering national security, nuclear fusion, supercomputing, and other areas.

Secrets permeate these facilities as easily as unshielded radioactivity, and are just as invisible to the naked eye. And they can be just as dangerous. In Joseph Kanon’s literary thriller Los Alamos, set in the final months of World War II, the secrets are not all military. There are clandestine meetings with Communist sympathizers, lover’s trysts in the desert, and personal histories that many would like to keep from the watchful eyes of government security. I was drawn to the book, and willing to give it a go, because I’ve visited New Mexico’s national labs. I’m familiar with the countryside, from the urban sprawl of Albuquerque to the views from Sandia Peak, from the historic Plaza of Santa Fe to the Anasazi ruins at Bandelier National Monument (the location of an unpublished story of mine). Sure, it’s fun for a fantasy reader to be plopped down in the middle of an invented landscape, but sometimes reading a story where you know the locale well can be even more fun.

Kanon gives us a murder mystery based largely in Los Alamos during the final stages of the development of the bombs that would destroy Hiroshima and Nagasaki and bring World War II to an end. Needless to say, neither the scientists nor the military involved in developing the atomic bomb were pleased to know that one of their own could be murdered. The story of how this mystery is solved spans many pages but kept me glued to the page - not a requirement for me to give a book my blessing, but certainly an indication of how much I enjoyed reading it.

Highly recommended.

When We All Get to Heaven: John Eldredge's "All Things New"

I am a very self-conscious person. There are exceptions to every rule, but in general I don't like to draw attention to myself. Hence, reluctance to step out on the dance floor with my wife. Or perform a karate kata in front of my class. Growing up in the Baptist church, no one raised their hands to God in praise as they stood with closed eyes and swayed gently back and forth with the music. (I'm guessing that would've been considered too showy, maybe even irreverent.)

My friend Mark Adams thought it was funny, when he and I went to see KISS and Def Leppard in concert, that I stood there in the crowd with my arms folded across my chest while he shouted and fist-pumped with excitement. Vicki Dudash thought the same thing while she was rocking out to the sounds of Elevation Worship. Nevertheless, in both cases I was enjoying the music and focusing on how the guitarists were playing. (My crossed-arms body language frequently confuses my wife.)

In the old hymn, "When We All Get to Heaven," we sing, "When we all get to heaven, what a day of rejoicing that will be! When we all see Jesus, we'll sing and shout the jubilee!" I'm thinking when I get there I'll be in the back (where all Baptists and former Baptists like me tend to sit in church), kneeling, relieved and just thanking God for his promise of eternal life - while glancing at St. Peter and whispering my thanks for letting me slip through the Pearly Gates.

Don't get me wrong ... there are lots of things I hope to do when I get to heaven. Reunite with friends and relatives. Discover the true fate of my great-great-grandfather who disappeared in the middle of the Civil War. Have God show me how he came up with the fabric of reality and set things in motion so his Creation would evolve over time. Explore the universe. Discover who really shot JFK.

In his book, All Things New: Heaven, Earth, and the Restoration of Everything You Love, John Eldredge tells us that too much of our imaginings of heaven don't do it justice. It will not only be a glorious place -- it will be somewhere where we are rewarded for having striven all our lives to be good Christians, for the sacrifices we made in the name of doing what's right, for persevering when it might've been easier to give up and give in to temptation.

I'm not sure I quite agree with all of John's theology. After all, the way I was raised, since we only receive eternal life through faith in Jesus Christ, who redeemed us through his sacrifice on the cross, and that this is a gift we don't deserve but receive because of God's mercy, it seems like what we ought to do when we get to heaven is spend all our time thanking God for his mercy and worshiping him. It's as if we should just be grateful that we even got to heaven, period. But John Eldredge says there is more to it than that. There will be rewards we receive for having fought the good fight (2 Timothy 4:7). The Bible is clear that we can't earn our way into heaven (Ephesians 2:8-9), but it is also clear that there will be rewards beyond simply the joy of being in God's presence. 

Another old hymn (by the same person who wrote "When We All Get to Heaven") says "Will there be any stars, any stars in my crown?" When I get to heaven, will I have earned any rewards? Some of those who we see in heaven will have done more for the Kingdom of God than others. Some will have given up more than others, in order to follow Jesus. Each will be rewarded in kind.

"Jesus teaches that his people [will] receive rewards in heaven based on their faithfulness ... Our reward in heaven is based not on the amount of work we do, but our faithfulness in doing what we are called to do."

Patricia McKillip, Fantasy Author and Prose "Sorceress"

I can always tell when a book speaks to me and I need to hang onto it (and not give it away) by the number of times I highlight passages in the book. The more lines and paragraphs that catch my eye, the more I feel engaged with the writing. This usually occurs when I’m reading non-fiction, but it will sometimes happen with fiction too. I highlight passages that I want to come back to.

Recently I picked up an abused copy of Patricia A. McKillip’s Alphabet of Thorn. She is well-known for her “Riddle-Master” trilogy (The Riddle Master of Hed, Heir of Sea and Fire, and Harpist in the Wind) as well as many other works. Many years ago I read the Riddle-Master trilogy and enjoyed it very much. I’ve even gone so far as to re-collect these books after letting them go years ago. (I seldom reread books - not because they aren’t worth rereading but because I have a Pile of Unread Books Waiting that grows week by week.) I began reading Alphabet of Thorn and realized very quickly there were examples of beautiful writing that struck me. So much so, in fact, that I purchased a new copy of the book so I could begin highlighting these examples. Here are just a few:

  • (page 2) “He carried a manuscript wrapped in leather that he laid upon the librarian’s desk as gently as a newborn. As he unswaddled the manuscript …”

  • (page 7) “[As a toddler in the library] Nepenthe had drooled on words, talked at them, and tried to eat them until she learned to take them into her eyes instead of her mouth.”

  • (page 9) “The world was so still that it might have vanished, swallowed by its own past or future.”

  • (page 13) “Dawn mists were shredding above the water, tatters and plumes of purple and gray.”

While “plagiarism is the sincerest form of flattery,” writers are often advised to study the writing of authors they admire. If I could only do sorcery with prose like Patricia McKillip does, I would be thrilled.

"Treehouse Living" and Experimental Fiction

Once in a while I decide to be daring and pick up a work of experimental fiction. You’ll know experimental fiction when you see it—it may use multiple fonts, eschew ordinary chapter structure, or perhaps take the form of something unusual for fiction, such as a dictionary. I’ve enjoyed experimental fiction by Italo Calvino, particularly If on a winter’s night a traveler and Invisible Cities. I’ve considered reading but have not yet summoned the courage to read Mark Z. Danielewski’s House of Leaves, but only because of its structure and length, not because it’s a work of horror.

Many years ago I read the “male” version of Dictionary of the Khazars, by Milorad Pavic. The fact that there are both “male” and “female” versions of this book is a dead giveaway that it is a work of experimental fiction—along with the fact that it is structured like a dictionary. The two versions of the book differ in only sixteen or seventeen different lines. I can no longer remember whether those lines are highlighted or the reader is expected to buy both versions of the book and compare them line-by-line to find what’s different. I see on Amazon there is also an “androgynous” edition of this book, but it’s not clear how it differs from the “gendered” versions.

Like Pavic’s Khazars, Elliot Reed’s A Key to Treehouse Living is arranged as a dictionary. The entries are written by the narrator, an orphaned boy who struggles to make sense of the world. This boy’s tidbits of “wisdom” give us insight into his life. The question with any book like this, of course, is, what is the plot? How do pieces that are not chronologically arranged function when structured in an interconnected alphabetical arrangement? The Kindle version makes it easy to follow hyperlinked cross-references, but the text is not nearly as hyperlinked as it could be.

I found A Key to Treehouse Living mildly interesting but frustrating to follow. One can’t help but finish reading a book like this and wonder what you have missed. Did the author explain everything needing explanation? Why did he cover this topic before this one? Which entries are important and which are whimsical digressions by the narrator? While the narrator’s nuggets of wisdom are arranged alphabetically by their defining concepts, early on the narrator explains to the reader that he couldn’t always adhere to strict alphabetical order.

Experimental fiction can be very hard to understand. We are used to following the course of a story in a linear, time-based fashion. But if the story is nonlinear, jumping between past and future and present, is it still a story? What was the author intending to do by making the reader encounter a story in this way? How does one follow a “character arc” when there is no chronological order? I would suggest experimental fiction to anyone wanting to experience something unique in their reading, but it is not likely to appeal to everyone.

Poul Anderson's "The Broken Sword"

Readers of my blog are aware of my respect for fantasy author Michael Moorcock and his tales of the albino anti-hero Elric. In his book Wizardry and Wild Romance, Moorcock points out a book that he holds in high regard: The Broken Sword, by Poul Anderson. Anderson is a well-known scifi/fantasy author, but The Broken Sword, published in 1954, is not so well known.

The Broken Sword, set in a supernatural and mythological Scandinavian past, tells the story of a man, living among elves, and the troll-born changeling with which he was exchanged at birth. Each man struggles to fit into the world in which he lives. Once their paths inevitably cross, these struggles only grow more fierce. The story overflows with sorcery, Vikings, epic battles, Norse gods, and sadness. The eponymous Sword, Moorcock admits, influenced his own creation of Elric’s sentient sword, Stormbringer.

As Moorcock points out, The Broken Sword is a true tragedy, something not often seen in modern fantasy. It echoes of Shakespeare, with its somewhat (intentional) archaic style. This style works well, even if it does make for slower reading. It is also reminiscent of Greek tragedy - particularly when a pair of lovers discover they are actually brother and sister.

Moorcock calls The Broken Sword “Anderson’s finest dramatic achievement.” After reading this high praise, I had to read the book. It was a great read; I highly recommend it.

"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.

"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.

"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.