The Golden Ratio by Mario Livio (science, math)

The number phi (Greek Φ, pronounced ‘fee’) has been known for millennia  Aside from it's direct use in mathematics, it is often called ‘the golden ratio’ that defines the most perfect esthetic proportions. That might sound pretty breathless (and it is), but it's also pretty accurate. In The Golden Ratio: The Story of Phi, the World's Most Astonishing Number Mario Livio addresses both the mathematical and esthetic features of phi, exploding historical myths and finding it in a number of less-than-obvious places. It's a fine little book and a very pleasant excursion after the disappointment of Kline's Mathematics and the Loss of Certainty.

This is a book about a number and about mathematics, but it is not a mathematics text. Livio writes for a  general reader, never getting into more mathematics or geometry than you got in high school (or at least, what you should have gotten in high school). His explanations are simple and clear, with good references for those who wish to go further into the topic. I could wish for a few more illustrations and appendices, but their lack didn't keep me from enjoying or finishing the book.

It's difficult to talk about the book without talking about the number, and that's to Livio's credit. He writes clearly enough that you focus on the topic rather than struggling to understand. Phi is the star, and it's place in history and mathematics is what you remember coming out of the book. Phi is found in  the logarithmic spiral and the chambered nautilus, in ferns and the Fibonacci sequence, in the corners of the dodecahedron and in the placement of branches on trees. Its use is as ancient as the early Greeks and as recent as Penrose tilings, with both beauty and math seen at every step of the way. In many ways Livio combines the two, with beauty in the math and mathematics in the beauty.

This was almost everything I want in a math or science book. It made me think, it educated me on both the science and the history, and it made me want to find more on this and similar topics. Recommended for both laymen and professionals.

The Last Lion: Winston Spencer Churchill: Defender of the Realm by William Manchester and Paul Reid (biography)

In 1984 The Last Lion: Winston Spencer Churchill: Visions of Glory was published, the first volume of William Manchester's biography of Winston Churchill. Volume 2 (Alone) followed in 1989. Manchester stepped aside from Churchill to write A World Lit Only By Fire, then intended to return to and finish Churchill. But his health began to decline and it became clear he was not going to be able to finish. Fortunately he turned the project over to Paul Reid before his death, and Reid has completed the work. While it doesn't quite live up to two decades of anticipation, it's nonetheless a fine book.

These volumes are both history and biography, and it would be fair to call them a history of the British Empire as lived by Winston Churchill. It covers the Empire from its peak to its essential dissolution, focusing on how Churchill lived through and influenced huge swathes of it. In the first two volumes Churchill grows up, aims high, stumbles and falls, and recovers admirably. Volume 2 closes with Churchill returning from the political wilderness to become Prime Minister just as Hitler begins to move against Britain.

Defender of the Realm shows Churchill to be the right man at the right time. His public face inspired Britain to hang on during the years they held the western front alone. His private one was more pragmatic and realistic, but we come to understand there was less difference between them than it seemed at first. Churchill knew instinctively that to hold out would require convincing the population that the war could and would be won, but that doing so would be a horribly difficult, painful and prolonged task. Once one see the forces arrayed against them, his classic "I have nothing to offer but blood, toil, tears and sweat" becomes almost an understatement. The common man would have to bear the brunt of suffering and fighting, and Churchill understood that. In spite of being an aristocrat to the bone, he managed to cross the class divide and make a direct connection with the working-class public. The authors present him heroically in this, and that's as it should be.

The book is not a paean to Churchill. He was often rude, sometimes treated staff and family with casual cruelty or volcanic anger, and never apologized. He bubbled over with ideas, most of them impractical. He wasted huge amounts of his and his staffs time with details that should have been left to others. He was at his worst after a success, flying off on new projects that would prevent the consolidation of a success. One of his aides later published a quite damning memoir of his dealings with Churchill. That publication (which the authors quote from frequently) included both an apology to and an appreciation of Churchill obtained in retrospect. The assessment of Churchill at the time is accurate, as is the appreciation in retrospect. Churchill was a flawed and complex man, and the biography reflects that honestly.

One particularly enjoyable point is the wit. Churchill was famous for some of his comments, and they were broadly displayed in the first two volumes. They are not as prominent here, but that's largely because there was less time for repartee and fewer British opponents to spend it on. In volume three the authors spend more time on the words of others, and they manage to slip in a few of their own. A couple of my favorites:

• The authors on Averell Harriman, US Ambassador to England: “. . . [Churchill's daughter-in-law] was certainly taken with him, and within a few weeks, taken by him.”
• Evelyn Waugh on Randolph Churchill having a biopsy for suspected lung cancer: “It was a typical triumph of modern science to find the one part of Randolph which was not malignant and remove it.”

There are plenty more, but I'll leave them for your enjoyment.

On a personal level, I wanted deeply to love this book. The first two volumes were wonderful, and by comparison this one seems a bit flat to me. There are two reasons for this, neither of which is the fault of the authors.

The first is Churchill himself. By 1940, Churchill is in his 60s and fully formed in both his virtues and his flaws. Both are fully displayed here, but we don't see the growth that was so interesting in the first two volumes. This is to be expected, but it makes him a bit less interesting as a person.

The other is the reader (me). All three of these volumes are both history and biography. The first two covered periods I wasn't particularly familiar with, and as such were of interest on both fronts. By the time Defender of the Realm was published I was already very familiar with World War II in Europe, and didn't learn much from the book that I didn't already know. Fortunately, seeing the war by looking over Churchill's shoulder was a fine new viewpoint, and it gave me a better appreciation of the whys of the political and military events. I read the 1050+ pages in about a week, and it wasn't an effort.

Overall I recommend this book, but with warnings. You should definitely read the first two volumes before this one. And if you're already up to speed on World War II in Europe, be prepared for a lot of material you're already familiar with, but presented from a different and interesting point of view. Still, though, strongly recommended -- especially if you start from the beginning.

Mathematics and the Loss of Certainty by Morris Kline (science)

When setting out the goal of reading and reviewing 52 books this year, I had to deal with the problem of bad books. I'm no longer one for killer reviews, reviews in which a book is eviscerated for the entertainment of those reading the reviews. Conversely, it's not fair to simply say "this book is bad" without saying why. So please, bear with me as I attempt to describe this most disappointing book without devolving into rant. Please do give me feedback, as I've recent encountered another book which is likely to get a bad review.

Morris Kline's Mathematics: The Loss of Certainty is a failure. It attempts to describe how the belief that mathematics and mathematical reasoning were complete and correct fell apart and why. Instead it is a disorganized history of mathematics, geometry, and proof across the ages. Kline never adequately describes the nature of geometric proof, nor the alternate geometries which shattered it. He dwells to no particular purpose on 1,500 years of irrelevancy during which algebra et. al. were developed and used without proof and without quest for proof. When he reached the 18th through 20th centuries, he jumps backwards and forwards discussing the changed feeling about proof and provability of mathematics, but leaves the causes of those changes for later chapters. In short, what should have been a fascinating history of mathematics and treatise about the nature of mathematical proof is a rambling mess. He focuses on nits, glides over critical but admittedly difficult items, and winds up leaving even this educated reader frustrated and uniformed.

In summary: not recommended.

1861: CIVIL WAR AWAKENING by Adam Goodheart (history)

Last year I heard a fascinating interview with Adam Goodheart about this book. He and the interviewer discussed an incident very early in the war when three slaves building fortifications for the army of Virginia fled to the nearby Union fort, Fortress Monroe, arriving Thursday May 23. The commander at Monroe was Major General Benjamin Butler, a lawyer with little military experience. When a representative of the owner came on Saturday to claim the slaves, he had to make a tough decision. Under Union law, he was obliged to return them. This went against his grain for a number of reasons, and with the help of a little military law he found a middle course. Since the slaves were being used to construct Confederate fortifications, they were lawfully seizable as military supplies. He declared the escaped slaves contraband of war and declined their return. Thus he avoided returning the slaves, damaged the Confederate war effort, and stayed on the correct side of all Union laws and most Virginia law. The owner did not press his claim further, Butler informed Washington of his actions, and it all seemed to be over. On the next day, a Sunday, more slaves fled to Fortress Monroe. By Wednesday, one soldier wrote home "Slaves are brought in here hourly." By the end of May, it was happening all across the Union/Confederate border. The South was in a serious conundrum - lose your slaves on the front, or take more men from home and leave homes undefended against the slaves. The impact on the war was profound.

This anecdote, with far more detail and breadth than I've provided here, is Chapter 8 of 1861. Each chapter follows the same general mode. It focuses on a few people, some well-known, some not, and how their actions during the first half of that year shaped the war and the politics of the time. The reader comes away with an understanding of how everyone's thinking and actions affected the national sentiment for and against the war, for and against slavery, for and against equality. In particular, it made me understand how the Great Compromise that preserved the Union for so long led both sides into a trap of double-think about slavery and equality. The thought of breaking up the Union was anathema to many, and many subverted their own thinking rather than consider the long-term result of either action or inaction. After reading it, I have a much better understanding of how the issues could simmer for so long in the face of what seem obvious final outcomes.

This book is about people. The events are important, but they are both the result of the actions of people and the framework that impels people to the next events. With this presentation, it shows how people thought during that time and how that thinking changed. Each event narrowed the path and made the war more likely. But when choices were removed, things that could not have been considered before became thinkable, then possible and then real. Butler's decision above is a fine example, but the book is full of them. There are nine chapters covering nine groups; Butler and the Fortress Monroe contraband are only one. All were interesting, most were moving, all were an education about the time, the events, and the country of 1961. Recommended.