Tag Archives: Euler

Portraits of Christians – Leonhard Euler

Leonhard_Euler - portrait by Jakob Emanuel Handmann, 1753.
Leonhard_Euler – portrait by Jakob Emanuel Handmann, 1753.

In a time when our culture wants to denigrate Christians as stupid, backwards, anti-intellectual cretins opposed to science, I’d like to refresh our culture’s  memory with some portraits of some of the phenomenal, ground-breaking people who helped our science – and our society – advance. Not only did these people happen to be Christians, their beliefs were quite often foundational to their achievements.

The name Leonhard Euler (pronounced “oiler”) may not be a household name, but it is one familiar to many engineers. The Euler-Bernoulli Beam theory he developed with his friend Daniel Bernoulli became a cornerstone of structural engineering, and we still use the “Euler buckling stress” in column compression calculations 2 centuries after he died.  But his contributions to engineering were only a small part of his amazing résumé. Besides being considered one of the greatest mathematicians of all time and the top mathematician of the 1700’s, he also advanced the fields of physics, astronomy, and logic. If you’ve ever seen the symbol “e” (the base of the natural logarithm) on a calculator, you’ve seen one of 2 mathematical constants named after him (the only mathematician with that distinction). In math, he contributed to the fields of calculus, geometry, algebra, graph theory, and number theory. Science historian Carl Boyer compared the impact of his book on mathematical functions to Euclid’s Elements; Euclid’s being the foremost textbook of ancient times, and Euler’s the foremost of modern times. He won the Paris Academy’s Prize Problem (an international problem-solving competition of the 1700’s) 12 times. He extended Newton’s laws of particle motion to include rigid bodies. In logic, he came up with the graphical representation of a syllogism now known as an Euler diagram. Much of our math notation (such as the Greek letter Σ for summation) is due to him. If you’ve taken a math class anywhere between junior high and grad school, any general physics class, or any of several different engineering courses, you’ve been helped by (or, depending on your perspective, been tortured by) Euler’s analytical brilliance. Although the term isn’t used much anymore, Euler was a true “polymath” – one with expertise in a wide variety of subjects.

His credentials as a genius are unquestionable. And yet, he was also a devout Christian. He pushed the boundaries of math and science, and yet never felt that science had led him away from God.  In fact, he wrote an impassioned “Defense of the Revelation Against the Objections of Freethinkers”, a treatise against the atheists of his day. This is a roughly 14 page work laid out in 53 paragraph-length points to build a case that true happiness is only achieved through knowing and obeying God, and that the Bible is God’s gift to us to show us how to achieve that. He postulates that the human soul is exemplified by the exercise of understanding and will; that happiness consists in the “perfection”, or betterment, of a situation; that for humans,  the complete happiness of their soul depends on perfecting these two faculties of the soul – understanding and will. With regard to the first, Euler proposes, “The perfection of understanding consists of the knowledge of truth, from which is simultaneously born the knowledge of good.  The principal aim of this knowledge is God and His works, since all other truths to which reflection can lead mankind end with the Supreme Being and His works.” Regarding the second, he says that “the will of man should submit to the will of God in all respects and with the greatest exactitude.  Since God is the source of all good, it is obvious that the man who wishes to bend his will in this way must necessarily be in the happiest state.”[1] He goes on to (briefly) answer a wide range of objections to why the Bible is God’s road map to lead us to Himself.

After being asked to tutor Frederick the Great’s niece, he wrote 200 letters to her explaining physics and philosophy, but also delving into his Christian knowledge as foundational premises to his understanding of the world. Note, these are not compartmentalized statements of personal faith separate from his science and philosophy lessons. For instance, in explaining about the marvels of the eye to her, which was only then just beginning to be studied in detail, he wrote, “Though we are very far short of a perfect knowledge of the subject, the little we do know of it is more than sufficient to convince us of the power and wisdom of the Creator. We discover in the structure of the eye perfections which the most exalted genius could never have imagined.”[2] This coming from a genuine genius! Ironically, two centuries after Euler recognized it, we are still learning more about the complexity and amazing design demonstrated in the human eye (see my previous post on that topic here). I could go on with several other examples of the faith of this intellectual giant, but I’ll stop here and just say that Euler was one of many great scientists through the centuries who delighted in the study of God’s creation, and clearly recognized it as such. Do you?

[1]Leonhard Euler, “Defense of the Revelation Against the Objections of Freethinkers”, c.1740’s.
[2] Leonhard Euler, Letters to a German Princess on Diverse Subjects of Natural Philosophy, “Letter XLI”, written 1768-1772.

The Engineer’s Faith

Leonhard_Euler - portrait by Jakob Emanuel Handmann, 1753.
Leonhard_Euler – portrait by Jakob Emanuel Handmann, 1753.

Engineering and faith might not be two words you normally associate, but faith is nevertheless an integral part of our profession. What tends to obscure this relationship for many today is the rather antagonistic definition of faith promoted by atheists as “belief in spite of the evidence.” Certainly, that is the last characteristic you’d want in the engineer designing your new home/office/hospital/school/etc. But as I’ve written extensively on this site (here especially), that is not the biblical definition of faith. Biblical faith is rather a warranted trust, or looking at the Greek root for the word, a divine persuasion. Let’s look at a scenario that exemplifies the correlation between biblical faith and “engineering faith”.

Suppose I told a client that an existing column in a building being renovated would need to be reinforced or replaced, at significant cost, or else it would fail under the new loads the owner wanted to add. Now suppose the owner didn’t like this and wanted to argue about whether this was really necessary (yes, this does happen). He could ask whether I’d ever actually seen a column that big fail. Or, supposing that part of the issue was tied to increased seismic loads on the existing structure caused by this new addition, he might ask if I’d ever experienced an earthquake, because he had, and it wasn’t that bad… In both cases, I’d have to answer “no”. So what is my basis for saying he needs to perhaps double the cost of his renovation? My trusted engineering books. Here’s why:

  • I trust the authors. While I’ve never personally seen a large column fail, I don’t have to have personally seen it to know it can truly happen. Various people over the years have performed tests, witnessed the results, and applied reason and logic to sift through the noise and ascertain the essence of different phenomena. Then they distilled all of that down into some of the elegantly simple theories we still use today. They have demonstrated themselves to be trustworthy with their meticulous attention to detail, their investigative diligence, and their relentless pursuit of the truth about how structures behave.
  • I trust their records. These early pioneers and those coming after them have written down very detailed accounts of these tests, their results, and their reasoning for how far their theories can be expected to be applicable to similar conditions. These have been preserved (or at least copies have been) for future generations of inquisitive engineers like myself. Names like Euler and Timoshenko still cast their shadows on much of our work long after they died.
  • I trust the transmittal of their works. Our engineering textbooks and reference books faithfully transmit these principles to my generation of engineers, even though we are far removed from the original authors, and may not have the resources to reproduce their findings. Their theories are also reproduced in a variety of books. If one publisher made an error in Euler’s column buckling formula, for instance, it could be readily verified by comparing it against other reference books on the same topic.

So then, even though I have never personally witnessed a W14x90 column fail in an earthquake, I can trust that my various books have reliably passed down to me the true results of research by trustworthy men indicating that would be the outcome in my example. The end result being that I can put some amount of faith – or trust – in what I’ve learned and apply it to the current project. Of course, men are still fallible, and their theories might be mistaken, but these basic principles are have stood the test of time sufficiently to persuade me to trust them.

Now, how does that relate to my Christian faith?

  • I can trust the biblical authors. God used a unique mix of people to write the Bible. Just looking at the New Testament, the first apostles were simple fishermen, who brought a simple, down-to-earth, eyewitness testimony to their records. Theirs was a record that said, “whether you believe me or not, I cannot tell otherwise, for this is what I saw, and heard, and felt – no more, no less.” Luke was a doctor who sought to record “a more orderly account” of the life of Christ. His account is an extremely detailed, first-rate history that has proven itself accurate over and over again. Paul was a Pharisee, a teacher of the Jewish religious law, himself taught by one of the leading teachers of his day. He explained the deep richness of the simple gospel message, connecting it to the whole backstory of the Old Testament. But in each case, these men have shown themselves to be trustworthy instruments of the infallible God.
  • I can trust their findings. Luke’s geography and description of various cultures of the time are born out by archeology. When Paul describes the fallen nature of mankind, he describes the world I observe; the results of his examination match reality. But moreover, he holds up a mirror to my own heart. I need look no further than my own life to recognize the soundness of his words.
  • I can trust the transmission of their records to me. They wrote early after the events they described, these writings were copied carefully, and on a massive scale far exceeding any other historical manuscripts, such that the integrity of their writings are adequately preserved by comparison of the variances between dispersed copies.

We all place our faith (or trust) in people and things that may prove all too fallible: the pilot of the plane you’re about to board, the engineer who designed the school you send your kids to, the political leader that promised you the moon, or objects as simple as the new tires on your car that you trust to not have a blowout.  But there’s really only One who warrants our complete trust. Have you studied His textbook, the Bible?