Descarte’s Secret Notebook by Amir D. Aczel

Aczel, Amir D. Descartes’ Secret Notebook. New York: Broadway, 2005.

A famous mathematician with suspected ties to a secretive cabal of global reformers dies from possible poisoning at the hand of a doctor employed by a European power. A French official surveys his papers, including a coded notebook, and has them quietly sent to the safekeeping of a relative. Years later, another brilliant mathematician, suffering from attacks on his reputation, seeks out the notebook to uncover its secrets.

It sounds like the plot of a thriller. Amir Aczel uses it to frame his biography of philosopher and mathematician René Descartes.

Descartes’ greatest hit as a philosopher was, “Cogito, ergo sum” (I think, therefore I am). He was a leader in rationalism, a philosophy that emphasizes the discovery of truth by use of reason. His method focused on methodical doubt by which he aimed to find truth (to him, all knowledge was connected, not discreet, unrelated truths) by reasoning out those things that could not be doubted. Thusly he reasoned his existence because he couldn’t very well doubt it when he was sitting there thinking about it. His method set him against the prevailing philosophy of the day, scholasticism, which focused on learning from authoritative figures and sources, particularly Aristotle.

High school algebra students will immediately recognize Descartes’ contribution to math. From today’s perspective, it may be hard to understand why it was such a big deal in the 17th Century. Descartes created analytic geometry, which uses algebraic equations to describe and understand geometric shapes. Before this, geometry and algebra were distinct fields, not parts of a unified mathematics. As part of this, he gave us Cartesian coordinates, the familiar x,y graph that has makes so many high school kids cross-eyed. Despite complaints that they’ll never use it, behind the scenes Cartesian coordinates are ubiquitous.


Descartes was not part of a secret society. He was a devout Catholic and was careful not to publish anything that would put him in direct conflict with the church. Even so, the writings of the Rosicrucians, a group of philosophers who sought political and religious reform and the advancement of science, influenced him. He even knew one of the brotherhood, though he may have been unaware of it. Despite his efforts to distance himself from the Rosy Cross, his books used terms that made some believe he was a Rosicrucian and his notebook included alchemical symbols that the group used.

Gottfried Leibniz, co-creator of calculus, was under attack from proponents of Isaac Newton, who independently created calculus contemporaneously with Leibniz. Other accused Leibniz of deriving his work from Descartes, which is why he diligently tracked down the Frenchman’s papers.

What did Descartes’ secret notebook contain? Leibniz handily decoded it. Descartes discovered Euler’s theorem. For polyhedrons, the sum of the number of faces (F) and the number of vertices (V) minus the number of edges (E) is 2 (F + V – E = 2). Descartes kept his discovery secret because some may have construed it as supporting a theory of Johann Kepler that used regular polyhedrons to describe planetary orbits in a Copernican model of the solar system. This was contrary to the teaching of the church, which Descartes wanted to avoid because of his personal devotion and because conflict with the Inquisition could be a career-ending (and life-ending) move.

Amir D. Aczel also wrote Chance.

If you’re interested in this book, you may also be interested in
1089 and All That by David Acheson
Fortune’s Formula by William Poundstone
The Numbers behind NUMB3RS by Keith Devlin & Gary Lorden
The Unfinished Game by Keith Devlin

Enchantress of Numbers by Jennifer Chiaverini

I usually don’t write reviews of fiction books, but occasionally I find a novel so enjoyable, or its subject so interesting or important that I want to write about it. That is the case with Enchantress of Numbers, a novel by Jennifer Chiaverini.

The subject is Ada Lovelace, who I think is interesting and important. She is credited as the author of the first published computer program in 1843. The only thing resembling a computer at the time was in the drawings and notes of mathematician and inventor Charles Babbage, a friend of Lovelace. He called the device, which was never built, an analytical engine.

Lovelace’s contribution has been debated, but it seems likely that she saw more capability in the analytical engine than even its inventor. As she described in her notes on her translation of a scientific paper on Babbage’s invention, originally printed in French and shorter than her notes were, she imagined the device being able to handle all manner of symbolic and logical functions in addition to solving mathematical equations. Even Babbage himself seemed mainly to see it as an improvement on his difference engine, a programmable calculating machine that was partly built, but never finished.

If she had been a man, her accomplishment would very likely have received much more accolades than it did at the time, or even for more than a century afterward. It was unusual for a woman to be even permitted to study math or science in those days. Her mother encouraged her to take on these fields to discourage her from following in the footsteps of her father, the poet Lord Byron.

Lovelace lived in a period of great change in society and science. She was a contemporary of Charles Darwin. She was a friend of Charles Dickens and Michael Faraday. When Queen Victoria was coronated, her husband was elevated to an earl and the new monarch called her forward to take her hand as the couple, newly made Count and Countess Lovelace, were took their bows. She attended the Great Exhibition of 1851, housed in the Crystal Palace, where the exhibits included the still relatively new telegraph.

I wasn’t sure I would care for a novelization of Lovelace’s life. I was not especially impressed with Arthur and George, Julian Barnes’ novel based on events from the life of Arthur Conan Doyle; I thought I would have preferred a straight nonfiction book on the subject. I found Chiaverini’s novel more compelling, perhaps because it is written as if by Ada Lovelace herself. As with any such fictionalization, there are parts that Chiaverini made up, though she draws on sources I enjoyed such as Benjamin Woolley’s excellent biography Bride of Science and James Essinger’s defense of the countess, Ada’s Algorithm. I realize that there are people who will pick up a novel who would not be attracted to a biography, and if it takes that to get more people to now about Ada Lovelace an her contributions, then Chiaverini’s effort was worthy.

If you’re interested in this book, you may also be interested in

Ada's Algorithm by James Essinger

Empires of Light by Jill Jonnes

How We Got to Now by Steven Johnson

On a Grander Scale by Lisa Jardine

Rust by Jonathan Waldman

Chiaverini, Jennifer. Enchantress of Numbers. New York: Dutton, 2017.

Interesting Stuff March 18, 2011

Another Real-Life Costumed Hero (or Two) Joins the Fray
-Britain Gets Its Own Kick-Ass: Banker Turns into Superhero The Statesman at Night to Fight Crime
-Britain’s Real Life Superhero The Statesman Battles Evil with the Power of Incredible Facial Hair
-Masked Environmental Vigilante “Super Tri” Put on French City’s Payroll
-Phoenix Jones Protects Seattle

Awesome Artist: Dustin Nguyen
Huckabee Toys with Whitehouse Run
I don’t like everything about Batwoman, but I like the art of J. H. Williams III
Jack Kirby My Little Pony

Jane Russell Passes
-“Gentlemen Prefer Blondes” Beauty Jane Russell Dies at 89
-Jane Russell
-Jane Russell Dies
-Jane Russell, RIP
-In Memoriam: Jane Russell
-Rants and Raves: Jane Russell

Interesting Stuff Feb. 17, 2011

Practice Babies
-Arthur Explores Lives of Practice Babies Once Raised on College Campuses
-Practice Babies: An Outdated Practice Discovered

Waterworks Museum Opens In Boston
Why my wife doesn’t leave me in charge of decorating
Working Conditions Drive Women from Engineering

Defining Noah Webster by K. Alan Snyder

Snyder, K. Alan. Defining Noah Webster: A Spiritual Biography. Washington, DC: Allegiance Press, 2002.

Noah Webster was in interesting man in interesting times. A young man during the American Revolution, he became interested in politics and went on to know many of the statesmen of that era, especially amongst his fellow Federalists . He was published the first magazine of original material in America and edited a Federalist newspaper, sometimes drawing fire from his own party for his evenhanded reporting. He is best known for writing educational materials, readers, texts, and especially his dictionary.



K. Alan Snyder covers this biographical fare in Defining Noah Webster. He is more interested in the philosophical and religious arc of Webster’s life and how his views changed, especially after his conversion to Christianity.

Webster was raised in the Congregational church of his family in Connecticut and attended Yale, which was still ostensibly a religious college at the time. (Incidentally, later in life he would help to establish Amerherst because, among other things, he found Harvard, itself originally a seminary, to be too liberal.) As he reached adulthood and had to fend for himself, he turned away from the faith and sought guidance in literature and philosophy. He is hardly the only Enlightenment-era youth to seek to perfect himself through reason .

Snyder sees Webster falling under the influence of Scottish Common Sense philosophy. After reading his book, I can’t tell you much about Common Sense philosophy, though Snyder provides just enough to follow how it appears in Webster’s activities and writings in the early part of his career. The major themes are that reason must be guided by conscience, and that as a person matures and develops reason, reason should take the drivers seat and direct his other faculties. Thus, Webster’s educational views include inculcating moral values. Common Sense also viewed political philosophy as part of moral philosophy. Webster valued character in politicians and thought foolish put public trust in people whose private morals were questionable.

While Webster’s views were not opposed to Christianity, his real faith through much of his career as an educator, author, politician, and public figure was in reason, not in Christ. As he saw his country grow and become factious and reported the horrors that developed during the French Revolution, he became disillusioned with the idea that reason, even if guided by a trained conscience, could cure people of moral shortcomings.

Webster converted to Christianity at the age of about 50, to the delight of his wife and daughters. He did not make a disillusioned retreat to religion. He was born again and the experience changed his perspective on everything. The final chapters are the meat of the book. Snyder writes about how this conversion changed Webster’s views on politics and education and influenced his dictionary.

Webster remained a staunch Federalist. However, the reasoning behind his political views changed. He found the roots of republican government in the Bible-base wisdom of America’s Christian settlers. Solid character, especially Christ-like character, became an even more important requirement for elected officials.

Before his conversion, Webster steered clear of what he saw as the overuse of the Bible in readers. Afterward, he no longer trusted natural conscience and reason. People were too prone to error and selfishness. They needed revelation from God’s Word as a reliable to guide to what is right.

These Christian views are prominent in Webster’s dictionary, though largely removed from its successors. Webster traced etymologies with the notion of finding the true meaning of a word in its origins in an Adamic tongue. His illustrations of meanings frequently reflected his Christian views.

If you’re interested in this book, you may also be interested in
His Excellency by Joseph J. Ellis
The Invention of Air by Steven Johnson
The Politically Incorrect Guide to Western Civilization by Anthony Esolen
Triumvirate by Bruce Chadwick

Planck by Brandon R. Brown

German physicist Max Planck was one of the most famous and well-respected scientists of his day. His work formed the foundation of quantum mechanics and is still relevant to physics today. He lived through both world wars, and these resulted in tragedy for his family.

Planck is a brief biography of the man by another physicist, Brandon R. Brown. Brown focuses his book on the last years of World War II, but from there reaches far back to his subject’s birth in 1858 and forward a little to his death in 1947. It is interesting that Brown did not choose to take a chronological approach given that entropy and the irreversibility of time were subjects of great interest to Planck. Perhaps he wants to readers to be somewhat unsettled, no doubt the way Planck must have been unsettled by events of his lifetime and the conclusions younger scientists drew from his own theories.

Brown presents Planck and as a flexible thinker who contributed to physics and accepted new theories at an age when most of his contemporaries were ready to shut the books on what could be learned. Apparently what most of us like to think of as middle-aged (at worst) is ancient for a physicist. His own work on thermal radiation established fundamental concepts of quantum theory, though he didn’t use the term “quanta.” When a young Albert Einstein proposed his special theory of relativity, Planck quick promote and build on it. He was slower to come around to general relativity (as wild as it is to us, it was insane to many in that time), and both men suffered philosophical heartburn from the quantum mechanics served up by the generation that came up under them.

Planck was very loyal to his country. His brother Hermann died in the Franco-Prussian War, and the family became intensely patriotic. At the start of World War I, he was hopeful that the war might strengthen and unify Germany. His oldest son, Karl, died at Verdun, and Germany fell on hard times.

Things were more complex when the Nazis took power. At times, his reputation as the nation’s most prominent scientist gave him leeway to resist anti-Semitic policies. At other times he acquiesced, hoping that the excesses of Nazi policies would be smoothed out or even reversed by the necessities of governing and the needs of the nation. He was so hopeful he even encouraged Jewish colleagues to stay. The Nazis saw no need for moderation, so Planck’s influence quickly waned. His son, Erwin, became involved in a resistance movement that hoped to topple the Nazis. He was implicated in a plot to assassinate Adolf Hitler. Though the Planck family appealed to every ear in and around the Nazi regime that might have sympathy, Erwin was convicted and eventually hanged. (Planck survived his first wife and four of his five children).

Brown doesn’t judge Planck too harshly, though some might. He had no love for the Nazis, but perhaps too much love for Germany, its scientific achievement, and its international standing, may have made him reluctant to boldly oppose them. This led to a break in his relationship with Einstein, though the younger eminence spoke very kindly of Planck even many years later. Because of he refused to embrace the Nazis, and he was well-liked by many foreign scientists, the Allies gave him a place in rebuilding the German scientific establishment after the war. The British, French, and Americans reorganized scientific institutes into the Max Planck Society, which is still active in supporting all manner of scientific endeavor.

I think the book is approachable for most adult readers who may have an interest in Planck or his times. Brown does not get so deep so deep into the science that he loses readers; he tries to explain it in a way that will make sense to a general audience. The structure of the book may make it difficult for a young reader to follow.

If you’re interested in this book, you may also be interested in

Einstein’s Clocks, Poincare’s Maps: Empires of Time by Peter Galison 

Newton and the Counterfeiter by Thomas Levenson

The Physics of Superheroes by James Kakalios

Brandon R. Brown. Planck: Driven by Vision, Broken by War. New York: Oxford University Press, 2015.

The Instinct to Heal by David Servan-Schreiber

Depression and anxiety seem to be the new defining diseases of our age, especially in the West. These disorders, and even severe stress, can affect our health as much as smoking or obesity.

 French psychiatrist David Servan-Schreiber notes that drugs and talk therapy are not especially effective, though the side-effects can be serious. The operating theory behind antidepressant drugs may simply be wrong.

 Dr. Servan-Schreiber suggests we look elsewhere for solutions to depression. The roots of depression are in the emotional brain, rather than the thinking brain, the body and the interaction between them.

 Our brain is layered, an as you go deeper inward, you get to older structures similar to other life forms: first those similar to other primates, then to mammals and finally to reptiles. The wordy, analytical, thinking part of the brain is the newest outer layer, the neocortex. Anxiety and depression are more strongly linked to the inner parts of the brain, which is emotional, image-oriented and much more closely linked to the operations of the body.

 One aspect of the brain-body connection is the heart. The heart has a bundle of nerves associated with it that are practically a simple brain itself, and this heart-brain has a direct connection to the emotional brain in the head. Our emotional and physical states are closely tied this way. Servan-Schreiber discusses techniques related to heart coherence, the variation of heart rate in a regular patter, that can be calming to the heart and brain and put is in a relaxed, restorative mode. His book includes instructions on a type of meditation for increasing heart coherence.

 He also talks about a technique that uses eye movements similar to those that occur while we dream to help the emotional brain process trauma, called eye movement desensitization and reprocessing (EMDR). This therapy will require a trip to a psychiatrist or psychologist, but for the right patients it can provide quick results.

 There is the suggestion that some cases of depression can be a symptom of disease or other issues in the body, especially inflammation. One of the things one can do deal with this type of depression is to get more Omega-3 fatty acids. These can help improve the function of the brain by improving the coating on brain cells. Depression seems to be more prevalent in countries where the typical diet is lower in Omega-3. Exercise can also improve depression and anxiety, especially when it is done regularly; three times a week for 20 minutes is enough to see a benefit.

 In addition, relationships and community are important to mental health and a sense of wellbeing. The quality of ones relationships can have a great impact on physical and mental health. Over the last few decades, people have come to have fewer and shallower relationships and less connections to community and purpose. Servan-Schreiber’s advice on this particularly focuses on ways to communicate that resolve conflicts and build empathy.

 Depression and anxiety are complex. Servan-Schreiber provides a suite of options for treating it. One of these may be helpful along, and some may need to use various ones in combination. In any case, there are things you can do, especially with the aid of a physician or psychologist, to make things better.

 If you’re interested in this book, you may also be interested in

Anxious for Nothing by Max Lucado

The Beethoven Factor by Paul Pearsall

Change Your Brain Change Your Body by Daniel G. Amen

The Last Self-Help Book You'll Ever Need by Paul Pearsall

The Mindful Way through Depression by Mark Williams, John Teasdale, Zindal Segal & Joh Kabat-Zinn

Overwhelmed by Brigid Schulte

The Relaxation Response by Herbert Benson with Miriam Z. Klipper

Rewire Your Anxious Brain by Catherine M. Pittman & Elizabeth M. Karle

The Solution by Lucinda Bassett

Switch on Your Brain by Caroline Leaf

Timeless Healing by Herbert Benson with Marg Stark

 Servan-Schreiber, David. The Instinct to Heal: Curing Depression, Anxiety, and Stress Without Drugs and Without Talk Therapy. New York: Rodale, 2003.

Pascal's Wager by James A. Connor

Blaise Pascal had a great impact on mathematics. He laid the foundations of our mathematical understanding of probability. A computer programming language was named for him.

Pascal was also a deeply religious man and philosopher. His book Pensées is read as a devotional by many Christians. His argument that the belief in God is rational is widely known.

James A. Connor takes the name of that argument for the name of his biography of the man, Pascal’s Wager. Connor considers both Pascal’s life in science and math and his religious convictions.

For many, there is no conflict in scientific study and religious devotion, but there was for Pascal. He was a Jansenist, though somewhat at odds with the leaders of the movement because of his interests in science and philosophy. The Jansenists were deeply concerned with sin and living a life of penitence; to pursue anything else was to embrace worldliness. Pascal loved the discoveries he made by reason and experiment, but he also longed for a life of purity and closeness to God.

Pascal was seen as a bit of a mathematical prodigy, especially in his youth when his father led a secular life by the standards of the day. He published a pamphlet on conic sections when he was 16 years old. He invented a calculating machine, the Pascaline, when he was 19. He was still fairly young by modern standards when he developed a theory of probability in a series of letter he exchanged with Pierre Fermat.

He had a mystical experience in 1654 that changed his focus in life. He told know one about it, but wrote a note about it that he kept pinned in his coat to carry with him the rest of his life. The note was discovered by his nephew shortly after his death.

After his experience, he devoted more of his time to supporting Jansenism, which his entire family had come to follow, especially his sister, Jacqueline, a nun. Jansenists were in conflict with other Catholics over their views on original sin and election, especially with the Jesuits. Pascal became an apologist for Jansenism, and especially mocked the Jesuits in The Provincial Letters.

Politics and religion were deeply linked in 17^th Century France, and the conflict between Pascal’s sect and the wider French Catholic church became a conflict with Louis XIV. He felt that the Jansenist leaders capitulated to the king and the Jesuits, which brought him into conflict with them as well.

Though religious debates had been part of his entire life, this heating up of the conflict to such a level occurred toward the end of his life. He expressed his devotion to God in self-imposed poverty and care for the poor; which in one case took the form of establishing the first public transportation system. He did not abandon math, though, and published a paper on the cycloid as well. He had been sick most of his life and passed away in 1662 at the age of 39.

Connor’s book is approachable for most readers. Though Pascal’s fame today probably rests more on his accomplishments as a mathematician, Connor shows how his life was shaped by his religion and both the religious and secular traditions of his time (Connor is a former Jesuit priest).

If you’re interested in this book, you may also be interested in

Chance by Amir Aczel

The Drunkard’s Walk by Leonard Mlodinow

How Not to Be Wrong by Jordan Ellenberg

The Language of God by Francis S. Collins

On a Grander Scale by Lisa Jardine

The Unfinished Game by Keith Devlin

Connor, James A. Pascal’s Wager: The Man Who Played Dice with God. San Francisco: HarperSanFrancisco, 2006.