CHRISTOPHER COLUMBUS

In a post last December, I mentioned in passing the widely held fiction that when Christopher Columbus set off on his first voyage, many if not most Europeans thought he would sail his ship off the edge of a flat earth and into oblivion. I was taught this in elementary school, and I have spoken to many people my age who remember being taught the same thing. More recently, I questioned my college students about this, and many of them said they had the same impression about Columbus.

The fact is that it was common knowledge among Columbus’ contemporaries in Europe that the world was round — a point that Nancy Marie Brown makes in her book, The Abacus and the Cross.

This book is not about Columbus; it’s about Gerbert of Aurillac, a French monk who lived in the 10th century. Gerbert had a thirst for knowledge and he became thoroughly schooled in the humanities and in the sciences.

GERBERT of AURILLAC

His scholarship carried him to Spain, where he came in contact with a thriving Arab Muslim culture which had preserved enormous amounts of philosophical and scientific knowledge that had been lost to Europe. Gerbert seems to have had both the curiosity and the capacity of a Leonardo or Michelangelo, and he devoured as much learning as he could. He was engrossed in both mathematics and in music, for example, and in the relationship between the two disciplines. He scrutinized the properties of organ pipes, and he eventually designed a built a prototypical organ that was not driven by water — the common technique of his time — but by forced air.

He didn’t only strive to satisfy his own curiosity. He was an influential teacher whose students included royalty. In the process of carrying out this vocation he introduced Europe to the place system of arithmetic — vertical rows for the ones, tens, hundreds, and so forth — which was much more efficient than the clumsy Roman system and which the western world has been using ever since. In this connection, he also carried back from Spain numerals that had originated in India and that had been adapted by the Muslims — the forerunners of the so-called Arabic numbers we use today. As the title of the book suggests, he learned in Spain to use an abacus board to calculate, and he later designed his own versions and taught others how to use them.

AN ASTROLABE

Also among Gerbert’s interests was astronomy. He learned all about astrolabes, overlaid disks that were used to trace the positions of the sun and the moon and the stars and the planets — and tell time — and about celestial globes, which were three dimensional representations of the apparent paths of the heavenly bodies. He made his own models of these instruments, too, sometimes taking as much as a year to finish one.

As Brown points out, it is clear not only that Gerber, in the 10th century, knew that the world was round, but that Pythagoras determined that around 530 BC, and Erastosthenes figured out how to calculate the circumference of the globe by 240 BC. Some flat-earthers persisted, but by the time of Columbus the point was moot in western Europe. Columbus knew the world was round; his mistake was in underestimating the circumference.

Being a churchman in that era, and one who enjoyed consorting with powerful people, Gerbert inevitably got drawn into the constant political turmoil in Europe, and his fortunes rose and fell along with those of his patrons.

He almost ended on a high note when he was elected Pope Sylvester II in 999 AD.

SYLVESTER on FRENCH STAMP

Even that didn’t turn out so well, because he had to flee Rome for a while along with his patron of the moment, the Holy Roman Emperor Otto III. Sylvester died in 1003.

During his lifetime and for a long time after his death he was the subject of rumors that he consorted with the devil or engaged in sorcery. Ironically, this was because of his pursuit of knowledge in astronomy and mathematics, which in some ignorant minds were associated with the occult.

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Overall, I don’t think my father was disappointed in me. He didn’t set himself up for disappointment, because he didn’t pressure me to pursue any particular career. When I said I wanted to be a priest, that was all right with him. When I became a newspaper journalist instead, that was all right, too. He was both a practicing Catholic and a newspaper reader, so he was in a good position for success.

There was, however, one thing that he might have found frustrating about the younger of his sons — Tony’s brother, as it were — and that was my inability to learn how to add several columns of figures without carrying numbers.

NACD photo

At slow moments in my family’s grocery store — where adding columns of figures was a frequent chore — Dad would try to show me how to add three or four columns at once, rather than starting with the right-hand column (the pennies column) and carrying the excess to the top of the column to the left. “Put down the two, and carry the four” — that was how I had learned arithmetic. I couldn’t understand the alternate method Dad tried to teach me, which annoyed me, because he could add columns of figures with his technique nearly twice as fast as I could do it with mine.

Many years later, the dawn broke in my clouded mind while I was reading a book on math. There, for Pete’s sake, was Dad’s method — explained just as I remembered Dad explaining it — but somehow I finally understood it and have used it ever since.

Like many people, I suppose, I regarded math at best as a necessary evil in elementary and high school. I didn’t go near the subject in college or graduate school. When I was in my 30s, however, I inexplicably chose to read a book on math written by Bertrand Russell, and was surprised to find that the subject was attractive. As I result, I have read many books about math, the most recent one being “Here’s Looking at Euclid” by the British journalist Alex Bellos.

In fewer than 300 pages, Bellos covers a remarkably wide range of topics. He explains the origins of mathematical concepts that we take for granted — the sixty-minute hour and sixty-second minute, for example — and how mathematical understanding has evolved since some Sumerian in the fourth millennium B.C. first pressed a stylus  into a clay tablet. He writes about pi and infinity and probability (including its role in gambling), and the bell curve.

MUNDURUKU MEN

Bellos begins his book with an account of the Munduruku people of Brazil, who have a number system that goes only from one to five. Moreover, the Munduruku use only the numbers one and two to count precisely, using three, four and five more as estimates. In fact, Bellos explains, the Munduruku are baffled by others’ compulsion to enumerate people or objects and either cannot or will not answer if asked how many children they have. They know who their children are; that’s enough for them. It’s healthy, I think, to be reminded from time to time that everyone doesn’t look at the world through the lens we use.

Ventura College

What I particularly like reading about is the mystery and elegance that many people find in numbers. One example is the “golden proportion” or “golden ratio,” to which Bellos devotes a chapter. The definition of this term, known to mathematicians as phi, might be off-putting at first. Here it is as Bellos explains it: “The golden mean is the number that describes the ratio when a line is cut in two sections in such a way that the proportion of the entire line to the larger section is equal to the proportion of the larger section to the smaller section.” That number begins as 1.61803 and, like pi, goes on forever. It appears in many familiar geometric figures, including the five-pointed star. The 16th century mathematician Luca Pacioli, Bellos reports, “concluded that the number was a message from God, a source of secret knowledge about the inner beauty of things.” That notion may seem remote until Bellos explains how a retired dentist discovered that the golden proportion was the key to designing dentures that give an individual patient a proper smile – now a widely accepted principle in dentistry.

I’m sorry now that I once thought of math only as a nuisance, but books like this one have helped me make up for a misspent youth.

Em cee squared

May 17, 2010

A blackboard with formulas written by Albert Einstein, preserved in the Museum of the History of Science at the University of Oxford.

Several decades ago, I began to make a point of reading several books each year on subjects about which I knew little or nothing — including subjects that I found repulsive. Among those subjects have been mathematics and physics, both of which bedeviled me when I had to study them in high school and college. As I have mentioned here before, at least with respect to mathematics, I have derived a great deal of satisfaction from pondering these subjects when examinations and grades are not at issue, and I have found that those who claim that there  is beauty and wonder in these fields are telling the truth

That background explains why I grabbed the opportunity to review a popular biography entitled “Einstein: The Life of a Genius” by Walter Isaacson. This is a coffee table book that contains a limited amount of text in proportion to the number pages and illustrates its points with many photographs and also with facsimiles of several letters and documents. Among these are Einstein’s letter to Franklin D. Roosevelt in which the scientist advised the president to call together a group of experts to study the possibility of developing an atom bomb — something Nazi Germany was known to be doing at the time. As it happened, Einstein — a pacifist whose work in physics  helped pave the way to such weapons — was considered too great a security risk to work on the project himself, what with him being a native of Germany, a socialist, and a Jew.

Isaacson records that one of Einstein’s early physics instructors described him as “an extremely clever boy,” but added, “You have one great fault: You’ll never let yourself be told anything.”  It wasn’t meant as compliment, but still, this tendency as much as anything else led to Einstein’s achievements in theoretical physics. Einstein — like Isaac Newton before him — would not accept anything as settled just because it was handed on to him by authoritative sources. He wondered and questioned and “experimented” with physical phenomena such as light and motion by forming images in his mind, and he changed the world.

Einstein is a curiosity in a way, because he was one of the most widely known celebrities of his time and his name is part of our language more than 50 years after his death, and yet most of us have little or no idea what he was up to. That doesn’t matter. He deserves his place in our culture if for no other reason than his persistence in questioning even his own conclusions.

ISAAC NEWTON

I was working in the faculty room yesterday when one of the instructors asked the open air, “Does anyone know anything about Newtonian physics?” I told him his question was coincidental, because I had just finished reading a  book about Isaac Newton, the 17th century physicist, mathematician, and natural philosopher.

I think I correctly answered my colleague’s question, which had to do with Newton’s Second Law of Motion: “A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.” But while the book I just read explained the achievements for which Newton is still regarded as one of the greatest of geniuses, its purpose is to recount the work of his later life, when he was warden of the Royal Mint — and particularly the relentless detective work with which he brought to justice Britain’s most brazen counterfeiter.

Statue of Isaac Newton - and the apple - at the Oxford Museum of Natural History

Newton did his signature scientific work at Trinity College in Cambridge, but he lobbied friends for many years to get him a political appointment in London. It finally came in the form of position at the mint, which made the silver coins that were Britain’s only hard currency at the time. When Newton arrived at his office in the Tower of London, the kingdom’s economy was on the verge of collapse, partly because  of expensive military operations undertaken by William of Orange and partly because the royal currency was, in a word, disappearing. An old issue of coins was being degraded by so-called “clippers” who shaved bits of silver from the money to be melted down and sold. Meanwhile British silver was leaving the country altogether because it was worth more in exchange for gold in other countries than it was in exchange for commodities in England. The result was a bull market for counterfeiters, including the audacious and dangerous William Chaloner.

Newton’s predecessors as warden of the mint had not taken the job seriously except as a source of income, and that was expected of Newton, too. But he applied to the mint the same combination of energy and curiosity that had fueled his discoveries in fields like gravity and the behavior of light and his development of the mathematical system known as the calculus.

Isaac Newton's image on a one-pound note

First, Newton took control of a program already underway when he arrived – the recall and replacement of all British coins then in circulation. This project was limping along when Newton took over, and he put the means in place to accelerate it and get the job done in a fraction of the projected time. Then he turned his attention to the counterfeiters, employing a network of spies and informers and counter-agents and double crossers to gather information and pounce on “coiners” – eventually including Chaloner, whose career as a counterfeiter had had its ups and downs.

Isaac Newton investigates the refraction of light.

Like most such scoundrels, Chaloner made his share of mistakes, and one of them was to publicly claim that the heart of the nation’s counterfeiting problem was in the mint itself, and imply that Newton’s incompetence was partly to blame. Don’t knock the Rock. Newton went after Chaloner with a vengeance, spending hundreds of hours personally interrogating people who could help build a case against the fraud. Chaloner had been in and out of prison several times and had dodged the noose that was reserved for counterfeiters, whom British law regarded as traitors. In Newton, he had met his match and – ultimately – his maker.

“Newton and the Counterfeiter,” both informative and entertaining, was written by Thomas Levenson, who is a professor of science writing at MIT.

A topic that Levenson discusses throughout this book – in fact, it’s an important thread that runs through all of Newton’s activities – is Newton’s search for contact with God. In fact, Levenson reports that religious matters became the preoccupation of Newton’s life when he had put most scientific inquiry behind him. I discussed that aspect of the book in a column in the Catholic Spirit, and it’s available at THIS LINK.