There are a lot of circles not only in our man-made world but also in the natural world, like the eye of the egret or the ball of the sun. When it’s important to compute the area of the circle, there’s the old Euclidean “Pi” formula, “Circle Area = Pi times the radius of the circle squared.” Pi has a pretty specific mathematical value, 3.14159265359, rounded. For the pure mathematicians, a Google search will provide the calculation of Pi to the nearest million places; however, scientists say that computing Pi to 39 places is accurate enough for most cosmological computations. Pi is represented by the Greek letter π, and is defined as the ratio of a circle’s circumference to its diameter: π = C/d. Archimedes (in 250 B.C.) came up with a Pi formula, long before slide rules and computers, estimating its value at 22/7, which was quite close.
Today, Pi has achieved somewhat of a “celebrity status,” with many schools recognizing “Pi day,” March 14th (3.14), a date surprisingly supported in 2009 by a resolution of the House of Representatives, which hasn’t been able to agree on much else since. “PI Approximation Day” is July 22, recognizing Archimedes Pi formula “approximation,” 22/7.
And August 14, 2012, was a special day for the United States, as reported by Huffington Post:
Shortly after 2:29 p.m. on Tuesday, August 14, 2012, the U.S. population was exactly 314,159,265, or Pi (π) times 100 million, the U.S. Census Bureau reports.
This witty bit of knowledge about Pi came to me from my good friend Denny Smith, a retired math teacher and school principal, in a rather strange way that I think is worth sharing with you. (As you consider the discussion that follows, remember that Pi is an “irrational number,” which means it goes on forever without ever repeating itself.)
I’ve been following the fusion of the political far right with the religious far right and its affects on legislation, particularly K-12 education, and our country’s Getting Our Kids Ready for the Competition. Most of us, I’m sure are aware of the poor standing of our K-12 education system, particularly in literacy, mathematics and science, and parents’ pleas (repeated at least superficially by a number of politicians) to ramp up our “STEM” – science, technology, engineering and mathematics – education so that our kids can compete with the rest of the world, particularly with the 26 advanced countries that are doing a better job than we are.
Recently, I sent Denny Smith an article, Religion Ruins Education Again, for his thoughts. I was particularly concerned about the third clause of a proposed Missouri law, which would give students in public and private schools a new right to refrain from participating in assignments or educational presentations that violate their religious beliefs. The impact of this sort of approach to education, particularly in science and mathematics, warps education far beyond teaching creationism as “science.” I hadn’t realized just how far the impact of this sort of approach to education went until Denny sent me his reply:
This reminds me of a mathematics class I was teaching in the sixties when i told the class that the value of “Pi” in the bible was 3, which is wrong. This disturbed one of my students and he protested because of his religious beliefs. Nevertheless its there.
Now, I think of myself as a pretty good student of the Bible, including Hebrew eschatology. I had always viewed the Bible as a magnificent story of the evolution of human thought and understanding, from worship of Yahweh, a pretty fearful, meddling tribal god, to the New Testament’s God of love and compassion.
But I had never viewed the Bible as a book of science or mathematics, or the message of religion as in conflict with science and its discoveries or the purity of mathematics. Religion is philosophy – about the whys and the oughts of life and our universe. As Will Durant has so ably written in his The Story of Philosophy:
“Every science begins as philosophy and ends as art. … Philosophy is a hypothetical interpretation of the unknown or the inexactly known; it is the front trench in the siege of truth. Science is the captured territory.”
Yes, I’ve written recently about the clashes between Bible literalists and science in Galileo’s Moon, quoting Galileo who said that when there’s an apparent conflict between Scripture and science, it is man’s interpretation of Scripture that errors. Some 200 years after his death, the Catholic Church approved Galileo’s support of Copernicus’s sun-centered solar system and his conclusions about conflicts between science and Scripture. In the Touch of Genius, when discussing Darwin and evolution, I quoted the Pope:
“Currently, I see in Germany, but also in the United States, a somewhat fierce debate raging between so-called “creationism” and evolutionism, presented as though they were mutually exclusive alternatives: those who believe in the Creator would not be able to conceive of evolution, and those who instead support evolution would have to exclude God. This antithesis is absurd because, on the one hand, there are so many scientific proofs in favour of evolution which appears to be a reality we can see and which enriches our knowledge of life and being as such. But on the other, the doctrine of evolution does not answer every query, especially the great philosophical question: where does everything come from? And how did everything start which ultimately led to man? I believe this is of the utmost importance.”
Until the recent fusion of the Tea Party and religion into a stonewall of ultra-conservative political-religious philosophy I had begun to be optimistic that the war between science and religion had simmered down, particularly after deeply religious scientists, like Israeli Gerald Schroeder, wrote about science as “Revealing the Hidden Face of God,” and University of California Professor, Francisco J. Ayla, wrote about evolution as “Darwin’s Gift to Science and Religion.”
But the continuing far right legislative assault on education, insisting that beliefs trump reality, and Denny’s comments about Pi, sent me back to the books. Yes, First Kings, chapter 7, verses 23 and 26 (and a similar quote in Second Chronicles 4, verses 2 through 5) provide:
“And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and…a line of thirty cubits did compass it round about….And it was an hand breadth thick….”
Yes, the Biblical text, if it is considered a mathematical pronouncement, literally makes Pi 3, not 3.14159265359, rounded.
Yes, the First Kings set of calculations, if mathematical, done before Isaac Newton invented Calculus, would stain Calculus, Geometry, Trigonometry, and a host of sciences.
I won’t bore you with the scores of clashing articles by atheists and fundamentalists on this subject that Google provides. Perhaps the most sane discussion appears in the Conservapedia:
Common sense and a rudimentary knowledge of the Bible should cause one to question whether it sets out to define mathematical concepts. The creation of a “sea of cast metal” by human beings in ancient times, without modern construction tools and measuring equipment, does not require nor could it utilize a precise value for pi. An even more fundamental objection is that pi is an irrational number, and therefore has an infinite number of digits. (A “closed form” of pi does exist, but requires mathematical notation that was invented many centuries later.) A decimal expression of pi could not “fit” in the Bible, or in any other finite text.
But any science versus religion debate – today, literally a savage, warlike confrontation – misses the point. And it has for centuries, certainly at least since Saint Thomas Aquinas wrote his Summa Theologiae. Aquinas was a scientist, a naturalist, as well as a theologian. Creation, Saint Thomas Aquinas insightfully saw, was the Artwork of God. Man’s study of creation and nature took up where scripture left off, providing a sacred revelation into the mind, heart, and nature of God, much as Gerald Schroeder concluded in his Hidden Face of God.
Aquinas, too, had his confrontation with religious extremists who objected to the scientific work of Aristotle, a tool for Aquinas’s nature studies, claiming the work of Aristotle could not be valid as Aristotle was an atheist and his conclusions were contrary to sacred scripture. (Aquinas’s biographers are convinced that the unrelenting, hateful challenges to his scientific work led to his early death in 1274.)
But Aquinas would not give up in his search, writing:
“All of us have a desire to know God, and success in the quest should not be limited to the few or to the old. … [E]ven teachers of faith are not bound to believe everything explicitly in every age. For there is gradual progress in faith for the whole human race as there is for individual persons.”
For Aquinas, the evolution of faith, and understanding of God came from his study of nature, of creation, which was sacred. As he wrote:
“Sacred writings are bound in two volumes – that of the Holy Scriptures and that of creation.”
The study of scripture, the first volume, is primarily in the realm of theology and philosophy. But, as Will Durant put it, it is but the beginning. The second volume, the study of nature and creation, is primarily within the province of science, and it takes a clear understanding of both volumes to reach a holistic comprehension of our universe and our place within it. Aquinas wrote, “Every creature participates in some way in the likeness of the Divine essence … . In all creatures there is the footprint of the Trinity.”
When we legislate that religious or other beliefs based on the first volume trump scientific revelations found within the second volume, we deny ourselves a deep understanding of our universe and its requirements for harmonious living.
We have a Constitutional right to religious freedom. That right is meaningless unless it applies equally to our study and understanding of both volumes. Legislating that one volume trumps the other volume, as the Missouri law does, and as laws advocating creationism do as well, blinds us from all the opportunities for understanding and growth that our Creator has provided in the two-volume set.
As far as Getting the Kids Ready for the Competition? If our scientists had used the First Kings set of calculations, there is little chance that the Curiosity would have had it’s flawless landing on Mars a few days ago.
And when it comes to Getting Our Kids Ready for the Competition, ignoring the knowledge of the second volume that can only be provided by science and mathematics will leave our kids far, far behind.
We have been given curious minds and the universe, a wondrous text for us to explore. Let’s not dull the experience!
Pi may be an irrational number, but that doesn’t mean that our approach to unlocking the messages found in the second volume should likewise be irrational.
The “R” we need to square up with is not only the radius of a circle in the Pi formula, but reality itself – the reality of our universe and life revealed in the second volume.