The excellent 2016 film Hidden Figures starred Taraji P. Henson and Octavia Spencer, and was based on the women “computers” (that is what they were called) who worked behind the scenes to calculate trajectories for the first U. S. manned rocket flights. What you were seeing written on the chalkboards in that film was mostly the mathematics of differential and integral calculus being done tediously by hand, at a time when digital computers were still not quite up to the task.

For this mathematics, we have to thank two “polymaths” from near the turn of the 18th century, Isaac Newton (1642–1727) from Great Britain and the lesser-known German Gottfried Leibniz (1646–1716). Polymaths in that era wrote without boundaries about science, mathematics, philosophy and religion. Newton and Leibniz knew of each other, and they apparently disliked each other, each accusing the other of stealing their work on the mathematical discipline of calculus.

Calculus is the study of limits, integrals and derivatives so important to the description of things as simple as curved lines or as complex as the originating forces of the universe. Despite Newton getting the lion’s share of credit historically, it is the mathematical notation system of calculus created by Leibniz that survives in common use today.

Newton famously used calculus to demonstrate that the mathematics describing the arc of a rock thrown up and then descending down to Earth by gravity is the same mathematics that describes the path of the Moon traversing around the Earth, and also the path of each planet going around our Sun. Not to mention the future manned rocket ships of the film Hidden Figures, requiring a roomful of bright, underpaid, minority women to process the trajectory math determining the life or death of the first U. S. astronauts. Without yet being able to quite explain gravity, Newton was able to mathematically describe it.

Newton also interspersed his mathematical writing with a lot of “God language,” [1] seeing his mathematics describing a divinely-designed universe as a finely-tuned mechanism. He also dabbled in the occult and alchemy, so even at the time his religious views were seen as suspect by religious authorities.

Gottfried Leibniz took a different tack with this new math of calculus as well in his “God language,” coining the term Theodicy in his classic 1709 book of the same name. [2] Theodicy literally means “the justice of God,” and he mashed his concepts of mathematical calculus into his theological/philosophical explanation for the existence of both good and evil in this world.

Gottfried Wilhelm Leibniz. Source: Wikipedia

Leibniz perceived the net effects trading off from competing good versus evil in the larger universe as forming an arc of “possible worlds,” with a poor mix on either end rising to an “optimal” mix somewhere in the middle. You can’t have “good,” he said, without some standard of “evil” to compare it against, and vice versa. His conjecture of a natural minimum point on a “curved line” for evil competed with a natural maximum point for the countervailing good, pointing to a single optimum point he called “the best of all possible worlds.”

In many ways, this mathematical explanation of justice is anachronistic today. But note that Leibniz opens a language door here. Both Newton and Leibniz were, in their own minds, “doing theology,” but attempting to infuse it with their emerging scientific and mathematical language, though not without resistance from fellow theologians who could not “speak the language” of calculus.

But especially after the publication of the Bible in printed form by Johannes Gutenberg in 1455, “God language” also became increasingly fixed in the culture. Subsequent advances in scientific thought by Charles Darwin, Albert Einstein and others were (and still are) often perceived by religious leaders as heretical, because we already have a printed, unchanging record of “God’s Word.”

The late paleontologist Stephen Jay Gould attempted to bridge this divide in his controversial 2007 book Rocks of Ages. [3] He proposed the model of “Non-overlapping Magisteria,” that is, two separate “authorities,” each with its own questions. Simplifying his argument, he saw the “How?” questions as the domain of science, with the “Why?” questions the domain of theologians and philosophers, and he suggested that the two sides should respect each other’s space. Suffice it to say, neither side particularly liked his argument, so ironically, I still think there is some merit in Gould’s argument. In many ways, science and theology are two different languages trying to explain the same thing. Sometimes one language works better than the other.

But back to Gottfried Leibniz, and taking out the “God language,” there is an odd arching and intertwined “dance” between “good outcomes” and “bad outcomes” with almost every hallmark of human progress. Think the creation of life-saving drugs, bringing hope to billions of people, while at the same time entrapping hundreds of millions of people worldwide into new addictions and even early death.

Albert Einstein certainly saw this dilemma in our knowledge of the awesome power resident in every atom, which he first definitively quantified. The last part of his life is best remembered for his public attempts to rein in the destructive power of nuclear weapons.

Theodicy, yin and yang, good stuff and bad stuff, rolling a “seven” or “snake-eyes.” Choose your preferred language.

Notes:

1. For more discussion of my views on the the mix of “God language” with science and math, check out this earlier post about Albert Einstein.
2. Or more formally, in its English translation, Essays of Theodicy on the Goodness of God, the Freedom of Man and the Origin of Evil. A good reference is Murray, Michael. “Leibniz on the Problem of Evil.” Stanford Encyclopedia of Philosophy. Stanford University, 27 Feb 2013.
3. Gould, Stephen Jay. Rocks of Ages: Science and Religion in the Fullness of Life. International Society for Science and Religion, 2007.

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