The Library of John Adams

This is not Adams' library. These are from my own.

I believe it was in fourth grade that I first got hooked on biographies. Reading the stories of significant people was both educational and entertaining. Those early bios may not have had the depth that one discovers as the mature, but they were using for forming ideas about our history and human history.  

When I read David McCullough's biography of John Adams (2002) it not only displayed the man himself, but introduced readers to a whole cast of Adams' contemporaries and the major event that threw them together, our American Revolution--the subject of Ken Burns' latest documentary series, currently airing on PBS.

Something that really stood out in that Adams biography was how devoted to writing Adams was. In addition to all his correspondence--he wrote volumes to his wife Abigail when away from her--he wrote legal briefs as a lawyer and legislation as a leader. He also wrote ideas and comments in the margins of his books. One story I recall is that he wrote as many as 5,000 words in the margins of just one of his countless books. 

A voracious reader, he imported hundreds of books from London booksellers like John Stockdale throughout his life. A full collection of his papers, along with his book lists, can be found at the Massachusetts Historical Socety. His personal library (around 3,000 volumes!) is today housed in the Boston Public Library. A review of the titles reveals the scope of his interests: law, history, politics, theology, science, classical literature and poetry. Isaac Newton, David Hume, Adam Smith, Plutarch, Homer, Milton (Paradise Lost) and Edward Gibbon (Rise and Fall of the Roman Empire) reveal the breadth of his interests and thought.

One observation that stands out when I look at his library and copious notes: Leaders are Readers. 

It's been said that Adams’ London imports formed the intellectual backbone of his defense of liberty, law, and balanced government. His library wasn’t just a collection—it was a working arsenal for revolution and nation-building.

As the United States enters its 250th year, there will be much wrangling about whether the Constitution is still valid in the 21st century and whether it's time for an overhaul. We're already hearing the rumblings as some point out its weaknesses and shortcomings. On the other hand, let's be careful here. Though there may be things the founders got wrong, it's still remarkable how much they got right.

A Recycled Blog Post On Rambling

"I have no special gift. I am only passionately curious." ~ Albert Einstein

What was it that made men like Einstein and Newton and Copernicus and Aristotle stand out from the herd? Einstein puts his finger on the nub of it right there. They were inordinately curious. They asked questions. They wanted to understand how the world worked. They didn't just accept things as they were.

For some reason, when we're kids we're taught that "curiosity killed the cat." This is repeated ad nauseaum in our childhood so as to make curiosity something bad, like lying. In reality, curiosity is part of the fabric of who we are. And it is essential to learning.

Making art is a thrill for creative personalities because it employs curiosity in the process of creation. What will happen if I do this? What happens if I do that? There is a sense of being an audience to one's own creations.

By way of contrast, many artists I know hate the way our culture wants "products" which can be reproduced. There's nothing more boring for an artist than mass production. It stunts this natural desire to see what will happen if I color it this way or that. Business people may like mass production for its efficiencies and the revenues generated. But I don't know many artists who want to make 1,000 identical baskets of flowers, teddy bears and ribbons.

According to our friend Merriam-Webster, the word ramble is an intransitive verb of 15th century Middle English origin which means to move aimlessly from place to place or to explore idly. I like the second part of that first definition: "To explore idly."

When we allow our minds to ramble and roam, amazing things happen. We discover gems. We find connections between new ideas and past experiences. There's a therapeutic aspect to it as well.

Every once in a while it's OK for our minds to drift, our thoughts to ramble. I don't know if it's healthy to keep our thoughts tightly coiled all the time. This might be a facet of music's wonder in that as we lose ourselves in the rhythms and harmonies and contours of sounds, whether sweet or discordant, we find a measure of freedom from our inward tyrannies.

Rambling as a lifestyle is also energizing for some. I know a few writers who travel the world, writing articles about what they see here, there and everywhere. I'm sure it's fascinating to meet so many interesting people, become engaged in so many cultures, to see so many scenic wonders.

But books can do a lot for us, too. And you can add surfing the net, idly rambling across an uncharted sea of URLs... There really are marvels out there.

Relax. Enjoy the view. Ramble on.

NOTE: THIS IS A RECYCLED BLOG POST FROM JANUARY 7, 2009

ALL ART AND IMAGES ON THIS BLOG ARE MY OWN CREATIONS UNLESS OTHERWISE NOTED. FEEL FREE TO BORROW WHAT YOU SEE HERE SO LONG AS ATTRIBUTION IS GIVEN. COPYRIGHT ED NEWMAN

Let's Talk Algebra: Ten Minutes with James D Nickel

"I don't know why I should have to learn Algebra... I'm never likely to go there."
~Billy Connolly

My 2009 interview with James D. Nickel explored themes from his book Mathematics: Is God Silent. This past week I read a paper he recently wrote called Algebra: What's It All About, and I had to ask more questions. He answered elaborately and with some keen insights that I find fascinating.

Ennyman: There is a sense in which our understanding of mathematics of today came about by borrowing concepts from various sources. How did these various influences combine to become modern Algebra?

JDN: The development of algebraic syntax and symbolism has a long and complex history. Solving problems using analytical skills (in reality, methods that can be translated into algebraic symbols) is nearly a cultural universal. For example, the ancient Egyptians, Babylonians, and Chinese developed methods (or algorithms) to measure acreage, keep business accounts, assess taxation, and create calendars (by star gazing). Some of the clay Babylonian tablets have problems that require methods of algebra to solve (like completing the square, a method now used to derive the quadratic formula, a formula that almost every high school algebra student dutifully memorizes as a way to find solutions to a quadratic equation).

Today, Algebra is understood in two contexts: (1) Symbolic Algebra or the syntax, symbols, operations, and order by which to find solutions to a wide variety of equations (what we study in high school and what most students must take in college as part of its liberal arts requirement) and (2) the study of mathematical structures. Math majors are required to take courses called Modern or Abstract Algebra. They explore principal framework concepts like fields, groups, and rings. This branch of Algebra is called “Modern” because it was developed in the 19th century. A good book on all of this is Classical Algebra: Its Nature, Origins, and Uses, by Roger Cooke.

Regarding the development of Symbolic Algebra, we can start with the Classical Greeks (600-300 BC). They did not develop good symbolism (their Algebra was rhetorical) partly because of their preference for Geometry. Hence, they understood both arithmetical and algebraic processes in the context of Geometry (e.g., they classified numbers as square, rectangular, or triangular). Not having a positional number system didn’t help them either. In the second century AD, Diophantus of Alexandria, Egypt, did some original work and developed a syncopated form of Algebra (part rhetoric and part symbolic). An algebraic riddle defines his age: “His boyhood lasted 1/6 of his life; his beard began to grow after 1/12 more; after 1/7 more he married; five years later his son was born and the son lived to half his father’s age; the father died four years after his son; how old was Diophantus when he died?” Because of his work, Diophantus is often called “the Father of Algebra.”

Meanwhile, over in India, we see the Hindu development of the base-10 positional number system. For Algebra to really blossom, you need an optimal way to represent numbers.

In a couple of centuries, Islam became a force in world history. In the conquering mode, the warriors of Mohammed eventually reached India and there they recognized the value of the Hindu number system. In the ninth century, at the “House of Wisdom” in Baghdad, the Persian mathematician al-Khwarizmi wrote a book that connected algebraic methods with the new number system, a system we now know as the Hindu-Arabic positional system. Of course, Algebra (al-jabr) is an Arabic word and al-Khwarizmi used that word as a way of naming a foundational method of solving equations, i.e., adding or subtracting a number from both sides of an equation. At its best, al-Khwarizmi’s Algebra was still syncopated.

We have to wait until the sixteenth century for a full-fledged Symbolic Algebra to be developed. Both the French mathematician François Viète and the Flemish mathematician Simon Stevin played key roles. In the 17th century, René Descartes refined their work and then combined algebra with geometry in terms of visualizing algebraic equations, now understood as functions, graphically (i.e., the now familiar x-y coordinate plane). This marriage of Algebra with Geometry is called Analytical Geometry, Coordinate Geometry, or Cartesian Geometry.

It is important to note that Descartes’ invention was not a “bolt from the blue.” A French contemporary, Pierre de Fermat, actually developed this system before Descartes but Descartes was the first to publish. If Fermat had got to the printer earlier, we might now be studying Fermatian Geometry. And, three hundred years earlier, the French medieval scholastic Nicole Oresme had developed the idea of a mathematical function and a way to graph these functions on a “longitude/latitude” coordinate system (and, he borrowed some of his graphing ideas from Arabic mathematicians). What hindered him was the lack of a truly symbolic Algebra. Oresme published his work and both Descartes and Fermat had access to Oresme’s texts (but, like many scholars of the time, both Descartes and Fermat did not “footnote” their sources).

There is much more to this fascinating history, but I think that is enough for a summary.

EN: In what ways has Algebra been essential to our having successfully landed humans on the moon?

JDN: Without Newtonian mechanics, you could not have a successful moon launch. Newton’s seventeenth century publication Principia (or “Mathematical Principles of Natural Philosophy”) relies on the work of medieval scholastics like Oresme and John Buridan (Newton never recognized these “giants” of thinking and innovation), Galileo, Descartes, and Kepler. Newton used algebraic techniques to solve differential equations and thereby calculated the velocity a rocket must attain to escape the gravitational pull of the earth (before such a rocket could even be constructed!). See my paper on Differential Equations and Escape Velocity for how he did that.

NASA scientists also used Newton’s laws of motion, including his Universal Law of Gravitation (written, conveniently, in Algebraic notation), to determine the trajectories necessary to land the lunar module on the “proverbial dime” (if such a coin had been placed on the Moon beforehand!).

TO BE CONTINUED WEDNESDAY

Interview with the Author of Mathematics: Is God Silent?

I met James D. Nickel at Bethany Fellowship in 1976, a Missionary Training Center in Bloomington, MN. We were both amongst the older set of freshman who came in that year, have been through college and a bit more seasoned by life, which added value and perspective to our experience.

In those days we called him Jim. At 6'6" with brillo pad hair he was someone you looked up to. I did, especially, as the shortest member of our Bethany Men's Quartet, which we originally called The Glory Boys, along with 6'5" Jim Towner and my 6'2" room mate Ken. With Jim Nickel's great bass voice (I chimed in at high tenor) we'd sing in the stairwells (the acoustics were terrific), in the dining hall, and eventually at a number of churches around the Twin Cities. Those were fun memories.

A major feature of the school's training was a research paper called the Senior Project. I remember reading a draft of Jim's paper and being impressed with his lucidity on this topic. Eventually the seeds of that research led to his commitment to complete a richly insightful book called Mathematics: Is God Silent?

Rather than break this interview into three segments, I will violate the principle of keeping blog entries brief and dissect the interview in half, the rest to follow tomorrow. Please read it all because James offers a wealth of insight here.

Ennyman: When did you first take an interest in mathematics?
JDN: High school, the result of the influence of my Algebra/Geometry teacher Wilbert Reimer (1965-1967). Unlike most high school math teachers, he was a mathematician and he knew what he was doing. He was tall, thin, reserved (when something excited him, he merely “raised his eyebrows”), and possessed a quiet, yet sparkling wit. He would give extra credit questions on his math tests like, “Who is buried in Grant’s tomb?” and “When was the War of 1812 fought?”

In college, I decided to major in math (simply because of all the subjects, I liked it the most). My freshman Calculus instructor was Larry Walker, a former World War II B17 bombardier. I remember him connecting math to the parabolic flight of bombs as they are released from the bomb bay … unforgettable images!

As the course material advanced beyond differential and integral calculus, it seemed like I had entered into an n dimensional domain of transcendent abstract analysis, aimed not at the Elysian fields of delight, but at the specter of the null and the void. On graduation day, I made an internal vow, “I will never open another math book again as long as I live.” I had the opportunity then to go into graduate school but why study the void? I chose a more practical and financial rewarding route … computer programming (where I spent nearly 25 years of my working life).


After college and entering the work force (1973), my interest in mathematics waned. I was seeing it connected to something tangible, though, because of my work for the United States Navy (I had to write code dealing with three-dimensional coordinate systems tracking F14A Tomcat test flights).

In 1976, I traded work (and its mathematical connections) for missionary training. I never thought I would ever be involved with mathematics again, but, as part of my training (1978-1979), I found myself teaching a year of high school math in Kailua-Kona, Hawaii (with Youth With A Mission). In this tropical paradise, my interest in mathematics was rekindled after meeting, in April of 1979, Dr. Glenn R. Martin (1935-2004), professor of history at Indiana Wesleyan University (then known as Marion College). In a series of profound lectures, he affirmed that all knowledge is understood in terms of presuppositions and that mathematics needed to be studied (and, more importantly, reinterpreted) on that basis. These lectures formed a catalyst that brought mathematics back under my purview, but this time on a foundational and thereby highly motivating level! I began a long and pleasurable journey of rethinking the subject, a study that eventually culminated in the publication (first printing in 1989) of Mathematics: Is God Silent?

Ennyman: What were the most surprising things you discovered as you studied the lives of great mathematicians while working on your first book, Mathematics: Is God Silent?
JDN: I had never known anything about the lives of the great mathematicians, especially the key ones … Galileo, Kepler, Newton, etc. In the early months of 1982, before leaving the States to work as a Christian schoolteacher in Australia, I read Morris Kline’s Mathematics and the Physical World (1959). In it (p. 119), he had this quote by Kepler from The Harmony of the World (1619), “The wisdom of the Lord is infinite; so also are His glory and His power. Ye heavens, sing His praises! Sun, moon, and planets glorify Him in your ineffable language! Celestial harmonies, all ye who comprehend His marvelous works, praise Him. And thou, my soul, praise thy Creator! It is by Him and in Him that all exists. That which we know best is comprised in Him, as well as in our vain science. To Him be praise, honor, and glory throughout eternity.” Astonished, I thought, “I never learned this in school!” Thus, during my years in Australia (1982-1987), I researched the lives of many famous mathematicians and scientists. I spent countless (and highly enjoyable) hours at the library of the University of Adelaide combing through stacks of books, both off the shelves and from its special loan section. The most surprising discovery that I made was reading Kepler. He would write page after page of math equations and then, overwhelmed by what he was seeing in them, pause to write a psalm of praise to God! Then, he would continue with his equations and, a few pages later, stop and compose another paean!

Another fascinating mathematician I learned about is Leonhard Euler (1707-1783), a man whose gift of systematics enabled him to explore and expose a multiplicity of “unities in diversities” within the structure of mathematics. Euler, the mathematician, was also a gifted teacher (you cannot always equate the two). He wrote one of the first textbooks on the Calculus and every succeeding Calculus textbook (approaching “infinity” as a limit!) owes Euler a substantial debt. Everyone should read his fascinating “Letters to a German Princess” (1768-1772). As a committed Christian, Euler often received the vitriolic “wit-wrath” of Voltaire and other French atheists. One of them, Pierre-Simon Laplace (1749-1827), encapsulated Euler’s influence on mathematics, “Read Euler, read Euler, he is the master [i.e., teacher] of us all.”

Kline and a host of other mathematics historians are naturalistic in their presuppositions. To them, the devotion of Kepler (and others like him) to God form an anomaly. Science historian Stanley L. Jaki (1924-2009) amplifies the reason why, “When historians are baffled by ‘the religious convictions that formerly motivated some of the finest research,’ it is because they have never experienced what it means to look at the world as the product of a personal, rational Creator” (The Road of Science and the Ways to God, p. 47).

Not all of the scientists and mathematicians of the 16th to 18th centuries were thorough going and consistent Christians, but all of them, Christian and non-Christian, were doing mathematics in a framework or cultural ambiance built upon Biblical Christian truth: (1) God is a Wise and Rational Creator and (2) His creation reflects His wisdom and rationality. Hence, we can expect to find, via mathematics and science, laws that are “commentaries” on the “language fabric” of creation.

Ennyman: Why is it that so many people seem to be intimidated by math, especially the higher levels like trig and calculus?
JDN: Primarily, the intimidation comes from two sources: (1) the symbology and (2) the disconnect with wonder. Mathematics is a unique language and, in order to appreciate its wonder and power, you must first master its grammar. Many math teachers (and textbooks) do not know how to teach this grammar in a way that engenders mastery. Professor Warren W. Esty of Montana State University has written a wonderful text that attempts to fix the problem: The Language of Mathematics.

In the 1960s, Morris Kline said, in effect, that math teachers know little of how to connect mathematics to the physical world (i.e., science). Since then, nothing much has changed (but there are some splendid exceptions … see the textbooks written by Harold R. Jacobs as an example). My daughter’s College Calculus teacher just taught the “mechanics” of the subject. He never connected any of the concepts to history or physics (where the methods of the Calculus really “shine”). More students would get excited about math if a teacher taught it in a classroom with “walls open to the outside world.” Topics of biography, history, and elementary physics are portals to wonder. For one example of how to do this, see my essay on the rainbow.

CONTINUED

As one who both loved and burned out on mathematics during my school years, I find these thoughts inspirational. Come back tomorrow for the rest of this valuable interview.

By What Measure?

"So far as I can remember, there is not one word in the Gospels in praise of intelligence." ~ Bertrand Russell

It's an interesting comment. On one level it reveals a value system that is common among many intellectuals. Intelligence has high value.

But in the Gospels, there are other values of importance. Being good, for example. Or being compassionate. Or being wise. There are so many educated fools that the very expression has become a byword.

I remember listening to a mean spirited diatribe by Andy Rooney against Mel Gibson and his film Passion of the Christ a few years back on Imus in the Morning. Rooney essentially dissed Gibson and the film because "the smartest man of the last century, Bertrand Russell" was an atheist.

So there you have it. A smart man's ideas are more valid than a holy man's. What do we do, then? Give everyone I.Q. tests to decide who gets to declare what we should all believe? It's nonsense. Newton was a smart man, and a Christian.

Sir Isaac Newton has been near universally ranked as the greatest mathematician of all time. Of Newton, Einstein said, "Nature to him was an open book, whose letters he could read without effort."

So?

This only proves that smarts does not bring us all into agreement. One difference between Newton and Russell, however, might be that Newton was quite humble about his smarts. Before his death he remarked, "I do not know what I may appear to the world; but to myself I seem to have been only a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me." I doubt either claimed to have perfect knowledge. And maybe Russell would have been embarrassed to have Andy Rooney put him on a pedastal like that.

There was a time when I thought being smart was the thing to be. I looked down on people who couldn't spell. Then, in college I met a guy who was valedictorian in his high school and lo, he was an atrocious speller. He wanted to co-write a play with me because I was an excellent speller and he felt I could communicate his message more effectively than he.

This threw a monkey wrench into my notion of smarts. And later when I learned he raped (at the time it was "heavy coercion") a friend of my girl friend, more head spins were occurring for me. Personal character has to be part of the equation.

By what measure, then, should we be measured? I can't recall anyone saying Mother Teresa, St.Francis of Assisi or Gandhi's significance had something to do with I.Q. Where did this strange measure come from?

There are other faulty measures of value, too. But it's getting late, and before too much fog settles in I'm going to pass on that.