Dear Friends of the Kolbe Center,
Christ is risen! Alleluia!
It is a dogma of the Catholic Faith that God created the world to “show forth His goodness.” One of the ways that God shows forth His goodness is through the beauty of creation, one aspect of which is the exquisite design of created things and the incorporation of harmonious patterns and relationships in nature. One of the members of our leadership team was actually converted to the Catholic Faith from atheistic communism in large part by—mathematics!
Kolbe advisor and mathematician Dr. Deborah Arangno has written a short article for the Kolbe website that helps to explain, simply and powerfully, how the mind of our Creator finds expression in the mathematical and numerical patterns that He has embedded in Creation. She writes:
Mathematics surrounds us. And the mathematical reality of the universe permits us – through our reason and intellect – to discover the work of creation and the Creator Himself.
Crystal structure is mesmerizingly mathematical in design. Crystallography can be best studied using the mathematical theory of algebraic geometry, all crystals belonging to one of 230 known spatial symmetry groups, referred to as Federov Groups (see E.S. Federov, “The Symmetry & Structure of Crystals. Fundamental Works”, Moscow, 1949). This includes the mind-boggling fractal patterned symmetry of snowflakes.
The patterns of conic sections – circles, ellipses, parabolas – appear frequently in Nature. Ellipses govern the motion of planetary orbits, tree rings are perfectly circular, parabolas underly the design of the Human eye in focusing light and making sight possible (inspiring us to design lenses and satellite dishes according to the same mathematical principle), as well as describe the trajectory of projectiles in free fall.
Among a vast number of examples, we discover trigonometric functions in sinusoidal systems which are harmonic such as sound or light. The sine function perfectly models all wave motion, and all oscillating or periodic systems, from the behavior of a spring to the motion of a pendulum, as well as vibrational or rotational systems, and the phenomenon of harmonic resonance.
Myriad other regular geometric shapes abound in Nature. Honeycombs are perfectly hexagonal, surface soil erosion causes perfectly tessellated rectangles. The refraction of light into rainbows follows the perfect arc of a circle. And the cycloid, or brachistochrone, provides the path along which an object under the influence of gravity travels fastest between two points.
Countless examples of spheres and other 3-dimensional geometric structure in Nature – fruit, seeds, planets, rocks.
Moreover, the patterns and rhythms of Creation obey mathematical laws in their frequency and regularity, from the night/day cycle of the Sun, to the seasonal changes of the year, and all biological functions of the human body – including everything from gestation, to the circadian rhythms, and the cycle of cell generation and destruction.
Familiar to many is the Fibonacci sequence, discovered by Leonardo di Pisa (aka Fibonacci). This sequence can be generated after an initial terms of zero and 1, by taking the sum of the previous two terms to generate each successive term: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,…
We see the Fibonacci numbers in the structure of the Nautilus shell, the arrangement of seeds in the head of the sunflower, and the electron patterns in the structure of the nucleus of the atom. The Fibonacci sequence corresponds to the pinnation of ferns and the spiral arrangement of leaves around a plant’s stem, which as Fred Willson observes is “a pattern which assures that each leaf will receive its maximum exposure to sunlight and air without shading or crowding other leaves”.
He further points out that “not only do we discover this pattern in leaf arrangements, but it is also commonly found in the arrangement of many flower petals. Examples: a lily has 3 petals, yellow violet 5, delphinium 8, mayweed 13, aster 21, pyrethrum 34, helenium 55, and michaelmas daisy 89. With such a great variety of spiral ratios in leaf and petal arrangement, no one has any reason to get bored with God's creation.”
Moreover, the ratio of each successive pair of terms in the Fibonacci sequence produces a sequence of proportions 3/2, 5/3, 8/5, 13/8, 21/13,… each of which yields a quotient approaching the “golden ratio” phi = 1.61818… This golden ratio is observed in countless examples in Nature in a wide range of structures – from the design of DNA, to the symmetries of pinecones and plants, and even the shape of spiral galaxies such as our own Milky Way.
An excellent visualization of this pattern is given in the video “Nature by the Numbers”.
The golden ratio is crucial to all the best human works of art and engineering, from the Pantheon and the Taj Mahal, and the Great Pyramids, to the masterpieces of da Vinci and Vermeer, to the music of Beethoven, Bach, and Chopin.
Truly these examples – all around us – illustrate that the Universe was created by a Mathematical Genius, indeed a loving and poetic Creator.
The Book of Wisdom teaches that God has “ordered all things in measure and number and weight” (Wisdom 11:20), and we know that He created the world in six days and consecrated the seventh day at the beginning of creation to show us the rhythm that we must live by if we want to live a happy, healthy, holy life. The book “I Have Spoken to You from Heaven”: A Catholic Defense of Creation in Six Days was written to show the overwhelming weight of evidence from Scripture, Tradition, authoritative Magisterial teaching, history and natural science for a literal six-day creation.
The leaders of the two most influential anti-Christian revolutions of modern times—the French Revolution and the Bolshevik Revolution—tried to replace the seven-day week, in France, with a ten-day week, and, in Russia, with a five-day week. Yet, is it not remarkable, that in spite of the global anti-culture of death that now reigns almost everywhere, the whole world still observes the seven-day week, established by God at the beginning of creation?
Beginning in June, Ellen Finnegan who runs the Catholic educational website, “Teach to the Text,” will host a ten-week course on “I Have Spoken to You from Heaven” during which I will give a weekly 30-minute presentation to a class of up to 20 students, followed by a 30-minute discussion. You can learn more about the course at this link.
Yours in Christ through the Holy Theotokos, in union with St. Joseph,
Hugh Owen
P.S. Greg Clovis, the head of Family Life International in the UK, and I will give a series of seminars all over England between April 26 and May 5. You can find the complete schedule at this link. If you live in the UK or have friends or relatives there, please spread the word.
