Category Archives: Books

1776 by David McCullough

War ends up being so pivotal in so many developments in history and, yet, the more I read about the most crucial wars in our country’s history, the more I am amazed by how much of the outcome was due to incompetence, bad decisions, or just plain luck.

David McCullough’s 1776 describes the events of that decisive year in the outcome of the Revolutionary War.  Starting with the Siege of Boston, which began in 1775, McCullough takes us through the events that lead to the British abandoning Boston and eventually taking New York.  The year ends with two stunning American victories at Trenton and Princeton, victories that occurred at such a low point in morale in the army that, had they not happened, the war may have gone a completely different way.

McCullough is a master at describing the events on the ground.  Drawing from a huge number of primary sources, especially letters and diaries, he shows us the conditions the average soldier dealt with, including marching in freezing weather with rags covering their feet and hauling cannon through mud and across rivers.  You get a sense for how difficult it was, especially considering that moving the army occurred entirely by foot — there were no transports of course.

In particular, we get great insight into the thinking of the important players, such as Washington, Greene, and Knox, as well as some of the British commanders.  It is amazing that Washington, leading the entire army to determine the future independence of the United States, was only 43 years old in 1775.  I myself, as I write this, am 38.  Jefferson was only 32 and John Hancock, president of the Second Continental Congress, was 38 himself.  Amazing to think how young these leaders were!  Washington is the particular focus, as McCullough tries to uncover the thinking of this most central man.  As the Americans lost battle after battle in New York, due in no small part to the indecisiveness of Washington, and as soldiers left the army as their enlistments ended, Washington begins to fret for the outcome of the war and his reputation as a general.  Even so, he perseveres, keeping up appearances for his soldiers and pushing them to perform.  While Washington may not have been the most brilliant tactical mind of his day, his determination to succeed definitely was the key reason the Revolution itself eventually succeeded.

It is even more astonishing, though, to consider how the weather, how decisions by the British to not pursue the fleeing American army, made such huge outcomes.  More than once, storms masked the movement of the Americans, in a way that had the weather been good, the Americans may not have been able to execute their plans.  The British, on more than one occasion, also stopped in what could have been a complete rout of the Americans, a defeat that would almost assuredly have ended the war with a British victory.  I find it truly astonishing how the outcome of such important events depends on these little details.

I’ve read one other history of the Revolutionary War, The Glorious Cause by Robert Middlekauff.  Middlekauff covers the entire war, including the build up to the war and the aftermath, ending with the writing of the Constitution.  While I remember the book being very good, it’s been a while since I read it, and with my memory like a sieve, I remember very few details, unfortunately.

1776 is a nice, high level overview of the events on the ground.  It is written in a very casual style, with copious footnotes, but those are all relegated to the back (even the numbers are omitted in the text, something which I actually regret).  The reading is fast and easy, but also very vibrant, giving a great sense of the spirit of the times.  I greatly enjoyed this book.

Professor Stewart’s Cabinet of Mathematical Curiosities by Ian Stewart

I picked this up randomly at a bookstore in Santa Fe, intrigued by the thought of delving into a little bit of math.  And that is just what this is.  Professor Stewart’s Cabinet of Mathematical Curiosities, by Ian Stewart naturally, is a tour de force of many of the most interesting corners of math, both historical and modern, covering each just a little bit.  Each topic is never given more than a couple of pages, though some of the topics do join together.  He covers everything from regular polyhedra (Platonic solids) to Fibonacci numbers to the shape of oscillations on a drum head to complexity science.  He gives just enough to tantalize, to intrigue, to whet the appetite.  The history of math is also scattered throughout with brief mentions of many of the important mathematicians.  Finally, there are lots of exercises and puzzles for the interested reader which, I admit, I was not — after so many years of school, I’m hard pressed to do anything that appears like homework.  But, the solutions are in the back of the book and offer further insight into the mathematical topic at hand.

There were two concepts that particularly caught my attention, mostly because I hadn’t heard of them before and they are so interesting.  The first is Benford’s Law.  Imagine you are working at a company and you decide to cook the books a bit, creating false transactions.  You might think that the numbers associated with the transactions should essentially be random, that, for example, the number of transactions starting with 1 (like $10224) should be about the same as starting with 2 ($221) and so forth.  In reality, this isn’t true.  If you look at the distribution of house numbers in a city, or the size of islands in the Bahamas, or the GDP of the nations of the world, numbers starting with 1 are more common than 2 which are more common than 3, and so on.  This fact is Benford’s Law, and it is used today to catch embezzlers and others who don’t realize that the distribution of these numbers isn’t random, but follow this pattern.  Wikipedia, naturally, has a nice article about Benford’s Law.

Ok, the second example I’ve heard about but it is presented in a very nice way.  That example is Penrose tiles (here is the Wikipedia article about those).  If you think about tiling the plane, like say tiling your bathroom floor, there are three shapes you can use that will let you completely tile the floor: (equilateral) triangles, squares, and hexagons.  These, in turn, give you patterns that have 3, 4 or 6-fold symmetry (if you rotate your view direction by 120, 90, or 60 degrees, the pattern will look the same).  It was thought that 5-fold symmetries are impossible:  you can’t tile a floor with pentagons.  However, Roger Penrose showed that if you use two shapes, a kite and a dart, you can tile the floor and get a 5-fold symmetry.  What’s more, the resulting pattern is not completely periodic.  It has short range, but no long range order.  Why does this all matter?  Well, symmetries are crucial for understanding crystal structures:  atoms arrange themselves in patterns that are the three dimensional equivalent of these 2-D patterns.  Again, no one thought that 5-fold symmetry could exist, but on the surface of chemical compounds, “quasi-crystals” can form, which exhibit the same patterns that Penrose tiles do.  Very cool!

This book offered lots of glimpses into many unfamiliar corners of math, and as such was very interesting.  He describes each topic at a level that the basic idea can be gleaned by those who have little or no math background.  I highly recommend this book to anyone who has even a vague interest in math.

One final note: in the previous book I discussed, The Golden Ratio by Mario Livio, he claimed that the nautilus shell followed the logarithmic curve.  Stewart says that isn’t so:  the shell is wound tighter than a logarithmic curve would dictate.

The Golden Ratio and Understanding the Universe

When you stop and think about it, it is truly astonishing how well we can describe the universe around us using mathematics.  That equations as simple as F=ma and E=mc^2 can describe so much of what we observe is really amazing.

The Golden Ratio by Mario Livio is essentially an examination of one of the most remarkable numbers to be discovered as a pretext for ultimately exploring the question why do mathematics work so well.  The golden ratio, known from the time of the ancient Greeks, is a pretty simple concept: take a line (defined by points A and B) and divide it (at point C) such that the length of the entire line over the length of the longer portion of the division is the same as the length of this longer portion over the shorter portion.  That is, if the longer portion is CB and the shorter is AC, then AB/CB=CB/AC.  A pretty simple concept and definition.  It turns out, this has many profound consequences.  This golden ratio, normally dubbed phi by mathematicians, is one of the first irrational numbers discovered and is, in some sense, the most irrational of all.  It shows up in many branches of math, especially geometry, and has been observed in nature in the patterns formed by petals on flowers, the seeds in sunflowers, the shape of certain seashells, and the shape of galaxies.  It is ubiquitous in nature.  Why should that be so?  That is the real point of Livio’s book.

Livio spends a lot of time on the history of phi, how it was discovered, how it was understood, and what it means to math and science.  When he is focusing on the role of phi in science, the book is wonderful.  There were many very interesting insights that I was unaware of that were real gems to discover.  Livio also spends a lot of time on the supposed role the golden ratio played in art, poetry, music, and architecture, including the constrution of the pyramids of Egypt.  His goal is to debunk those who claim that the golden ratio was an instrumental part in many such works, and he does so convincingly.  Unfortunately, I found this a huge distraction and very uninteresting.  I would much rather that he had filled those pages with more discussion of how the golden ratio is found in nature and science.  I understand that he felt a need to determine where the golden ratio is really to be found, but I felt it was over done.

Ultimately, the fact that the golden ratio, and by extension math as a whole, figures in so much of what we see around us leads Livio to examine why that is so.  He describes two alternative views.  First, that the universe is objectively Platonic; that humans are discovering the laws of the universe and those are written in the language of math.  Any civilization in the universe would uncover the same mathematical laws.  The second view is that math is a human language, a human construct, and we are using it to interpret our observations of the universe.  Civilizations with different formulations of mathematics would have a different view of how the universe works.  Livio falls somewhere in the middle, and, to be honest, I did not overly understand his reasoning for his position.

It is an interesting question.  I guess I would tend a bit more towards the Platonic view.  I think that it is just too striking that our math and physics can not only describe but predict what is happening around us so well.  I once had a chat with a fellow grad student at the UW physics department that was about this.  His point, as far as I could understand, is that maybe we create the reality around us via our investigations and our interpretations of our observations.  Essentially, that there is no objective reality, that reality is created by the observer.  Thus, as we develop our math, we view the universe through that math and thus shape it to conform to our math.  This “the observer shapes reality” perspective seems like an extreme view of the Copenhagen interpretation of quantum mechanics.  I definitely wouldn’t go so far as this.  But, it is an interesting question.

Wicked by Gregory Maguire

The idea of taking a familiar story — a fairy tale, a common legend, or a children’s story that all of us know — and turning it on its head appeals to me.  I like the idea of taking the familiar and presenting it from a different point of view.  One of the best examples of this that I’ve encountered is Neil Gaiman’s retelling of Snow White in his Smoke and Mirrors.  Gregory Maguire does it in his own way with Wicked: The Life and Times of the Wicked Witch of the West.

Wicked tells the story of the Wicked Witch of the West, known and feared from the Wizard of Oz stories, form her point of view, giving her a name — Elphaba — and a history.  Is Elphaba really wicked, as described in the original Wizard of Oz, or is she on the losing end of history, her story being told by those who hated her most?

Maguire does a great job of creating a background for Elphaba and her sister, Nessarose, the eventual Wicked Witch of the East.  Especially as a young girl and a young woman, Maguire gives Elphaba a depth and richness that is really captivating.  He creates a setting in which the land of Oz becomes a complex place, full of history and politics.  Elphaba grows up in this land and becomes the woman known as the Wicked Witch of the West as a result of the injustices around her.  That is, her becoming “wicked” is a result of the events happening around her.

Overall, I greatly enjoyed the novel and had a hard time putting it down.  I really felt that Maguire did a good job of creating a character in Elphaba that was both interesting and one that I cared for.  The novel centers on her — other characters come and go as time passes.  There are often big jumps in her life as we move from one major period to another.  All eventually lead to the preordained outcome — Elphaba is killed when Dorothy douses her with water.  But, the events that lead to that eventuallity are still compeling, maybe even more so, because the outcome is known.

There were a couple of things that didn’t quite ring true to me.  For a character that is supposed to be so menacing in the original story, there just didn’t seem to be any real reason for Elphaba to be viewed as overly menacing.  She doesn’t do anything that really threatens the Wizard, for example.  She maybe has an outpost in a backwards part of Oz, but how that matters to the Wizard is never really demonstrated, not in a concrete way.  And the last few acts in which Elphaba engages — creating the flying monkeys and obsessing with the shoes Dorothy got from her dead sister — seem forced, as they had to happen to mesh with the original story but they seem either trivial or of no real importance here.  For example, regarding the monkeys, they play a role in helping get Dorothy to the Witch’s castle, but that is the only time they leap into action.  I felt that these types of details, necessary to make Maguire’s Witch become the Witch of the Wizard of Oz, could have been done in a more meaningful way.

Similarly, the appearance of Glinda, the Good Witch, a character that Elphaba knows well from school days, is brief and anticlimactic.  I expected much more from the encounter, more sparks to fly, as it were.  However, again, Glinda’s appearance late in the novel serves to link this story to the original, and not much more.  I felt the relationship between the two could have been developed more, their mutual antagonisum developed more.

But, maybe this is the point of the novel: why was Elphaba viewed as wicked?  What did she do to deserve this reputation?  In the end, maybe not much.  She certainly wasn’t evil by any definition of the word.  Her sister, who ruled with religious conviction, did more harm in the world and was hated by more than Elphaba ever was.  And Glinda, the “Good” Witch, is a socialite who throws around her money and her status and has no real conviction of doing anything worth while.  Only Elphaba, who fails miserably at most of her undertakings, does what she does out of a sense of justice and right and wrong.  And, as a result, is the one who is perceived as the most evil.

Overall, while the ending maybe wasn’t what I expected, it was still a very engaging novel.  I’m not sure I will immediately delve into the other books Maguire has written set in Oz, but they will be on the bookshelf, waiting for a future day.

Maguire has a website dedicated to Wicked.

The Graveyard Book by Neil Gaiman

Neil Gaiman has become quite a well known author.  With the recent movie Coraline, based on the book of the same name by Mr. Gaiman, he is fast becoming a household name.  I’ve read a few of his previous efforts, including American Gods and his short story collection Smoke and Mirrors, both of which I greatly enjoyed.  His newest book, a children’s book like Coraline, is The Graveyard BookThe Graveyard Book recently won the The John Newbery Medal for “the most outstanding contribution to children’s literature,” an honor which I think it richly deserved.

I don’t want to give away much of the plot, but I’m sure that there might be some spoilers in what follows.  I would rather describe my general thoughts about the story.  The story centers around the childhood of a young boy, Nobody Owens, as he grows up after a tragedy in his family.  I imagine it won’t be much of a spoiler, since the title of the book essentially gives this point away, to say that Bod, as Nobody is nicknamed, grows up in a graveyard.  I’ve read that Gaiman was inspired on this point by The Jungle Book, putting a young boy in a very odd environment in which to grow up.  The plot revolves around Bod growing up and learning about the graveyard and the world around him, as well as the mystery surrounding the events that led him to the graveyard in the first place.

The story is fast paced, with several adventures as Bod discovers new corners of the graveyard.  The reader essentially grows up with Bod, learning about both the world in which Bod lives as well as the greater world beyond the physical world in which most people live.  We learn that Ghouls, Werewolves, and, while never explicitly stated, Vampires exist in this world.  Bod has to learn to navigate both the everyday world as well as this supernatural world in order to survive.

There are three main aspects of the story that I particularly enjoyed.  First, there is a diverse cast of characters and, while we don’t get to know most of them very well, they all add a lot of color to the universe of The Graveyard Book.  Second, the plot is definitely suspenseful, and at the peak I definitely didn’t want to put it down.  It is a real page turner.  Finally, the book is meant for children.  Maybe not the youngest, but maybe preteens or so.  As such, I like that it doesn’t offer a world-view that is all roses.  That is, bad things happen to Bod and, even when he does the right thing, it doesn’t always work out for him.  And the ending is bitter-sweet.  I’ll leave it at that.

I highly recommend this book.  It is full of imagination and I expect that most kids would love the world that Gaiman has created.  I am torn in hoping that Gaiman further explores the world of the graveyard, but, at the same time, it is maybe better to leave those corners too to the imagination.

There is a website dedicated to the book.