Is God a Mathematician?

Mario Livio's Is God a Mathematician? is a review of the history of mathematics, the philosophy behind mathematics, and the question of why it is such an accurate description of the universe. He attempts to answer the question of whether mathematics is discovered or invented. Before reading the book, I thought I knew the answer to this question.

Livio first discusses the ancient Greeks Pythagoras, Euclid, and Archimedes. Pythagoras laid down much of the framework of mathematics, and Euclid formalized many theorems of geometry. Archimedes was world-class genius who discovered/invented several major ideas but was tragically killed by an irate soldier. The Greeks, led by Plato, certainly believed that mathematics described an absolute reality, a reflection of the realm of forms.

Galileo was a brilliant mathematician as well as an experimental scientist. He disproved Aristotle's notion that heavier things fall faster than lighter ones, and proved that the Earth moves around the Sun. He even proved that sunspots were really on the Sun and not small planets revolving around it. Descartes formulated a link between mathematics and geometry which opened up whole new avenues of calculations. Descartes still believed that mathematics was a discovery that described a true world.

Livio then discusses Isaac Newton, who invented calculus, and other mathematicians of the Enlightenment. He describes how logic and set theory became formalized and some tried to describe math as a form of logic.

Throughout the book the author describes how math not only describes natural phenomena, but also predicts. Some mathematical constructs have proven useful years after they have been discovered.

While I enjoyed this book, I actually believe it was the first time I came away from a book thinking, I wish there was more math.
I know this was a book for the layperson, but I could have used more concrete examples of the elegance of math myself.

Many modern mathematicians have declared that math is invented, it's a construct of the human mind. Livio makes a convincing argument for both sides of the debate, and declares that math is both invented and discovered. He has convinced me that the math we know is shaped by our brains and our experiences. I think the question can be helped by breaking down the concept of math into: the rules of how the universe works; and our representation of it. Certainly the universe would work according to logic and mathematical formulas even if we weren't here to describe it. But the symbols and concepts we use are a human invention. So I still believe that there is a system of rules that the universe runs by, regardless of whether humans have invented language to describe it. B

Our Magnificent Bastard Tongue

John McWhorter's short book Our Magnificent Bastard Tongue: The Untold Story of English is a treatise on why the English language changed over the centuries to pick up grammar that is far different from any other Germanic language, or even any other language in the world. I found it to be a great complement to the English language history lecture course.

McWhorter questions why our language has some strange features. He names two in particular. The first is what he names the meaningless do: where we say "Do you see that?" instead of "See you that?" The "do" doesn't add anything to the sentence. The other feature is using the -ing suffix to indicate present tense. When we talk about our current actions we say "I am reading" instead of "I read." Both these features are rare in language, and McWhorter expresses dismay that many linguists dismiss them as "just happening." McWhorter points out that Celtic languages like Welsh have similar structures in their grammar, yet linguists consider Celtic influence minimal since English has so few Celtic words. Yet McWhorter makes a convincing case that the Celtic people of the British Isles introduced elements of their grammar when they learned Old English.

The author also argues that English, like all languages, has always been in flux, so one eras grammar mistakes are the next eras standard usage. Another point he brings up is the lack of gender in English, which lost it since Old English. And he points out that our verb conjugations have been wrung down to a simple "s" for the third person singular. These two features he attributes to the Norse and Danes who invaded England and ruled over the north and east for decades. His contention is that English's constant use by non-native speakers has "battered" the language down to simpler components.

McWhorter mentions the Sapir-Whorf hypothesis, the idea that language shapes how different cultures think and perceive reality, and how it has been disproven. And just when I'm thinking, "but there's got to be something to it," he admits that it does . His final theory, only sketched with thin evidence, is that Proto-Germanic, an ancestor of Old English, was influenced by the Phoenicians.

I found this book informative and entertaining. I was impressed by McWhorter's breadth of knowledge and his strong arguments about the influences on English. And I was glad to see him discuss something that I hadn't learned much about: the difference between spoken language and written language. It is fun to learn about other languages and their idiosyncrasies. And it is fun to learn about the language that shapes our thoughts. A-

Foucault's Pendulum

Foucault's Pendulum is a novel by the Italian author Umberto Eco. The material in the novel concerns secret societies such as the Templars and the Rosicrucians, but that is really the background, the threads that are used to weave the story.

The story is narrated by Casaubon, a student of the history of the Knights Templar. He meets a new friend called Belbo who is an editor at a local publisher in Milan. Belbo asks him to consult on a prospective author, Colonel Ardenti. Casaubon determines that Ardenti is another conspiracy theorist full of unsubstantiated rumors, so they send him away. But then a police detective calls to question them on the mysterious circumstances of the colonel's possible murder. Belbo convinces Casaubon to omit certain details, and the matter disappears. The only thing left is a list given to them by Ardenti, who claims it was found in a secret Templar base and is a description of their plan.

Casaubon goes to Brazil where he lives for several years teaching literature. There he meets and old man named Aglie who has knowledge of secret societies. He takes Casaubon and his girlfriend to a pagan ritual where the girlfriend, ever the rationalist, is dismayed to find herself affected by the rhythms and chanting.

Back in Milan, Casaubon finds himself involved with Belbo again, as well as Belbo's colleague Diotallevi. Diotallevi is a Jew obsessed with numerology and the Cabala. When the publisher gets the idea of printing a series of books on secret societies, the three of them run with the idea. They get so involved that they see connections to everything, and they even invent their own Plan, a master history of the world. The Plan tells how the known history has a secret history behind it. Many events were actually caused by things going right or wrong with the Plan.

As the three of them develop the Plan, Aglie, who has moved back to Italy, gets involved as a special consultant. The three don't really trust him due to his secretiveness and his attachment to a woman whom Belbo is involved with. The three start connecting many parts of history and various secret groups. They use the list to show how the Templars planned to meet every hundred and twenty years to put together more pieces of the Plan and wait for the timing to be right after six hundred years. The three men's creation starts to come to life when they notice things from their imagination in real life. Belbo, who ironically has avoided the act of creation by writing, has begun to write in his word processing program and assemble pieces together. This is tied back to the men's discussion of the Demiurge, the creator god who made the universe without permission, which may have been a terrible mistake.

Secret organizations are a rich source for stories. There's something compelling about the idea of knowing the real truth behind historical events, knowing what really happened to an group that supposedly faded from history centuries ago. This drive sucks in the three characters, to the point where they don't know whether Aglie is a knowledgeable older gentleman, a sinister part of a plot to ensnare them, or a figment of their imagination come to life. In a way he is all of these.

It starts to get complicated when Diotallevi gets ill and goes into the hospital. After mentioning too much to Aglie, Belbo becomes implicated in a bomb plot and is pressured into going to Paris. There he is kidnapped by the master secret society, and Casaubon travels there after receiving a frantic call and reading his files. Casaubon hides out in the Conservatoire, the home of Foucault's famous pendulum, and watches a macabre ritual. Aglie tries to force Belbo to reveal the map that will show where the central force of the world is, so that they can use it's powers to control mankind. But Belbo has made up the whole thing, so he is in a quandary: if he admits it is invented, will they kill him, or believe him and let him go? If he makes up something else, would they believe him or continue to demand a satisfying answer? At the pendulum, Belbo becomes fully integrated with his creation.

This novel is very imaginative. Eco takes the legends of the Templars and uses it as a framework, building a complex and involved history. The idea of characters creating history that comes alive and subsumes them is intriguing. In the men's Plan, one secret group is a front for another secret group, and there are secret groups as part of each secret society, creating an interleave network of layers. Supposedly the goal is the ancient Egyptian secret of the telluric currents, which is controlled through a nexus at the focal point of the world, where the pendulum swings.

The Plan comes from the characters, especially Belbo, whose past in part drives the story. His desire for creation, and his hesitation to create, lead to the Plan. He is driven to complete it, regardless of his publisher's urgings.

I enjoyed the many layers of the book, despite the extended histories getting a bit tedious. The history of the Crusades and the Templars is fascinating in its own right. I think at heart this story is about creation, and how it takes so much of one's soul. It's about how a creative work comes to consume one's life. The metaphor of the Demiurge is striking: a god or demon who goes against divine will to create a magnificent creation of its own. A

The Amazing Adventures of Kavalier & Clay

Michael Chabon's book The Amazing Adventures of Kavalier & Clay is a novel mixing fiction and reality. It tells the story of two comic book creators, the stories they create, and how their creations come to affect them.

The story starts with two young cousins. Sam Klayman, who decides to use Sam Clay as his professional name, is a young Jewish Brooklynite living with his mother in 1939. Josef Kavalier, or Joe, is his cousin, who is living in Prague with his family when the Nazis begin to clamp down on travel for Jews. The first section tells about Joe's education as an escape artist by an old master of the art. When Joe's escape from the country is foiled by the latest Nazi restrictions, his teacher comes up with the idea of hiding him in the coffin of the Golem of Prague, which he is trying to smuggle out of the country and into Lithuania. When out of Nazi territory, Joe makes his way across Asia to Japan, San Francisco, and finally Brooklyn.

In the second part, Sam introduces Joe to comic books. Sammy is convinced that with the right artists, he can create great comic book stories. Joe comes up with some sketches and Sammy takes him to see his boss, Mr. Anapol. Sammy says that they can create the next Superman, who is the big sensation. When asked to create a superhero, instead of a tall towering figure he draws a short stocky man, reminiscent of the Golem who helped him escape from Germany. From Sammy's mind comes the Escapist, a superhero who can break out of any situation. The Escapist is not only modeled on Joe--in a sense it is his alter ego. Joe's burning desire is to help his family escape from Nazi occupation. Together, they pour into the comic book the fantasies of justice against the Nazis in a country that is not quite ready to go to war against Germany. The Escapist fights enemies who are thinly veiled Nazis.

In part three, Joe becomes guilty of his and Sammy's success while his family is still stuck in Europe. He starts taking his anger against the Nazis on Germans in New York. When he starts a scuffle with a Nazi sympathizer, his comic book creations seem to come to life as the man creates an identity for himself as the nemesis of the Escapist. He leaves a fake bomb in the offices of the comic books. In this way, Joe becomes entangled with his creations. He also meets Rosa at a party and they fall in love. When Mr. Anapol and his partners try to screw them over, Sammy manages to get them what they deserve.

In part four, the Escapist and other creations grow, and the Escapist gets turned into a radio show. Sammy meets the actor portraying the Escapist, and the two of them start an affair. Joe buys an apartment for himself and Rosa. He gets his brother passage on a ship of children leaving Europe for America. Joe becomes a magician for Bar Mitzvahs. But it all comes crashing down when the ship of children is sunk by a German submarine, and Sammy and his lover are busted at a hotel, just before the attack on Pearl Harbor. Joe runs away to fight Nazis, leaving Sam to marry the pregnant Rosa.

Part five has Joe in Antarctica. When all but one of his team are killed by a leaky furnace, Joe retreats to listening for Nazi signals to deal with the loss of his brother. He becomes determined to kill the last Nazi on the continent as revenge for his brother's death. But when he reaches the man, a scientist, he decides not to succumb, yet is forced to kill him when the man shoots at him.

The last part takes place nearly ten years after the war, and Sammy and Rosa have not seen Joe since he left for the war. Joe realizes that their son Tommy is really his, and starts to make contact with the boy. Tommy sends a prank letter that ends up getting Joe nearly killed on the Empire State Building. He comes home to Rosa and his son, while Sammy decides to stop being an editor of second-rate comics after he is shamed by a Congressional hearing, and goes off to pursue his dreams in Hollywood.

I really enjoyed this book. The elements of magic and escape artistry form a great background, providing a large part of Joe's character. The wonderful part of creating comic book characters is drawn out, with Sammy providing the stories and character elements and Joe providing the illustrations. The comics and real life start to intermingle.

Joe and his struggle to cope with his family's situation is the central theme of the story. It drives his every actions, and if he strays he feels guilty, even for just enjoying himself. He envisions the Escapist as performing liberating feats that he wishes he could do himself. He turns to despair when his brother dies, and nearly allows the continent of ice to consume him. He stays away from his son and the love of his life, fearful of what they would think of him.

The backdrop of World War II is rich ground for the story. Joe's hatred for Nazis and Germans gets him in trouble as well as drives his stories. His family's situations is a huge hole in his life that he can't fill.

The book is scattered with suspense and more laid back sections where the business of making comic books is shown. The partnership of Joe and Sammy, Kavalier and Clay, creates great comic stories, but it's not enough to make them happy in the end. It's a thoroughly enjoyable book. A

The Wine-Dark Sea

Patrick O'Brian's The Wine-Dark Sea is the 16th book in his Aubrey-Maturin series. It has two great naval adventures with an adventure on land in between.

The Surprise is in the Pacific chasing a American privateer. When they catch the Franklin, they taker her owner, Monsieur Dutourd, into custody. Jack warns Dutourd that he will be in dire trouble since he does not have a letter of marque. The Surprise captures a real pirate ship, the Alastor, which had been preying on British ships.

They settle into port in Peru, where Stephen resumes his mission of changing the government to one more friendly to Britain. But his mission is complicated when Dutourd escapes to the mainland and begins spreading rumors that Stephen is a British spy. Stephen is forced to travel through the Andes, where we receive a good dose of travelogue.

With the news of three American trading ships headed for the cape, Jack takes the ship south. They encounter the rough seas of the high southern latitudes, and eventually discover the three American ships. But then another ship, and American frigate, shows up to challenge them. The Surprise loses a mast and her rudder before she manages to escape from the frigate and the dangerous ice. Rudderless, she finally encounters friendly ships at the end of the story.

The great thing about the story is that the characters really come alive. The minister turned surgeon's mate, Martin, becomes ill from clothes soaked in salt water, and comes to believe his illness is divine retribution for his sin with Clarissa Oakes. Stephen Maturin begins to wonder about his wife and the daughter he has never met. Captain Aubrey takes a boat across rough waters in order to warn Stephen that Dutourd has escaped and has changed the strategic situation. As usual, the two of them play music together, with the occasional help of Martin.

The story is always exciting with a sea battle, a sea chase, or intrigue on land. Jack has to use every bit of skill and strategy to capture enemy ships, or even just to survive. This is one of the better books in the series. A-