Symbols and Ciphers: Toward a Theology of …Math?
The universe and the scientific laws that govern its meaning and all the various movements and motions within it can be seen as one interrelated whole. For the mystic, this is also true, but the language differs as they are more likely to express this truth in words like “the universe is governed by holy laws, divine principles, and cosmic connections that can supersede mere logic or commonly held scientific theories.”
However one chooses to express or describe it, these rules and laws that govern the universe teach us about the universe that exists as an interconnected unity, covering mind expanding distances, and linked to incredible elegant designs. As the frontiers of science have become settled(?), and what was once too mysterious becomes more mundane, we can readily approach the conclusion, at least in the areas of cosmology, that it appears as if science and mysticism seem to agree: That a series of definitive rules that are emerging, and Nature and the Cosmos correspond to concise, even harmonic patterns.
Everything that has a natural origin, can be observed and will eventually reveal that it has a relationship or a connection to other life forms, energy events, or participates in some sort of chain action and reaction. Each blade of grass, each drop of rain, every bird and every child, is a part of the Cosmos, the Greek word that means holy order or grand design. As a rainbow is connected to its colors, all of life can be seen as connected to the eternal laws of order, balance, harmony, beauty and form.
In short, there is an all-inclusive syntony, an empathetic yet expansive correspondence that governs all the worlds of life. Today, I will begin to explore these unifying laws by examining how there can be theological connections and implications derived from a deeper study of mathematics.
Before I begin, a little disclaimer… I realize that some of you already know many of these interconnecting principles. No doubt that you have been blessed with a fine, discriminating, and logical mind that easily grasps and perceives these designs.
Please consider what I say to be a helpful review. But for the new, uncharted explorers like myself, who could be known
as a desperate refugee from math anxiety, someone who assiduously avoids those cute but exasperating geometric coffee table puzzles, allow me to calm your fears, and join me in explore new connections.
First, let me explain that I always hated math! (My apologies to all you scientists and mathematical pros… I just never got it!) I do not remember getting over a C in 24 years of school.
I can even remember my high school guidance counselor… Poor fellow! After getting my SAT scores back, I went into his office all excited and full of positive anticipation. He was faced with the task of letting me down gently. I went over my good scores in English and advanced biology and everything seemed to be great… then I expressed my happiness over getting 300 on my math score, exclaiming that I never thought I could do so well!
Looking at me compassionately as he could, in an almost
inaudible voice, he said,” Peter… (wondering how he could tell me this… “they give you 200 for just signing your name” AHHHHH! The truth be told, I was asked to leave Algebra II, and geometry, well, it was all so hopeless! From my junior year on, anything that smacked of being parabolic, was to me simply diabolic!
Actually, its only been the last twenty years or so,
that I have been able to have a truce or make any connections to the world of mathematics. What moved me toward a respectful appreciation was, ironically enough, my study of theology…
Particularly, philosophy and metaphysics, and how fascinating esoteric principles related to certain mathematical truths.
I guess you could say that for me, the study of mysticism was the back door to understanding math’s hidden treasures. Just think of it, through knowing about the great mystic Pythagoras, now even geometry makes more sense! (My geometry teacher was a UU-When I was ordained, he sent me an irenic and amusing note saying how glad he was for me, that math’s loss was surely ministry’s gain)
When I look back on how I was introduced to math, I can readily understand why it did not appeal to me, and as it got more complex, it baffled me more and more. It was presented to me in a drab, cut and dry manner- almost devoid of any creative application or expressiveness. There was little reference to how math reveals the beauty of the natural world, the harmonies of music, art, and the rhythms of life.
It was always “how many apples did it take… or a
train is going through a tunnel… remember those? They
were problems all right, ones I just could not get interested in, much less develop the desire to solve! When I look back, I can only wonder if it were explained differently, maybe the Harmony of the Spheres, the mystical values and esoteric meaning of numbers, or that all of life corresponds to divine proportions … I am sure I would have responded better. (well, chances are, with my dismal record, I could not have done much worse!)
Classically, mathematics was one of the training
disciplines for the development of reason and greater awareness. However, when the “hard science” outlook began to dominate, scientific reductionism, or a more objective, exclusive results oriented approach were ensconced, math was pulled away from its more philosophical and mystical origins. Then, it took on more of a formal, abstract and exacting approach that only accepted scientific proofs and formulas as applied to rational questions
and worldly concerns. People who did not have such a logical mind or a gift for abstract reasoning, were made to feel inferior, as science and math began to define excellence in our Western academic awards and our educational esteem.
This partial understanding of math was made to be colorless and lifeless- shorn of its natural elegance and beauty, math no longer was a tool for developing spiritual awareness, maturity and insight.
As an example, how many of you were told about the
Pythagorean Theorem? Most likely all of you. No, I won’t
ask you to repeat it, so don’t panic! Now, how many of you
were also informed that Pythagoras was considered a great
spiritual teacher, a mystical adept, and founder of mystery schools in Italy and Asia Minor? That he educated his students to carefully observe the mathematical and spiritual connections in our Cosmos, especially between music and math, or that his theorems were also alchemical equations and demonstrated occult mysteries from Egypt, India and beyond? I would venture that very few of us ever received the whole story behind all those angles, bases, and hypotenuses!
Another example, Were you ever told that what is taught in math class corresponds to what the mystics call Holy Law, Divine Order, God’s Will, or what the Chinese call the Tao? Most likely those chapters were skipped, if they were ever written in any textbook. By the way, the same is true for the other sciences as well: Astronomy, Medicine, Physics, all suffer from a lack of complete understanding of how knowledge can become wisdom, and how science and spirituality are both close encounters with
the same truth, approached from different paths.
Pythagoras taught some 500 years BCE or before the Christian Era. He believed that all that exists conforms or belongs to certain definite and distinct rations and proportions…
The chief among these ratios was the golden ratio or the Divine Proportion of 1:1.6 which he called Phi. These ratios form the basis for all the great buildings in the ancient world. He also stated that music and its harmonies are truly celestial; all the planets, stars in the heavens combine in a chorus to sing and orchestrate “the Harmony of the Spheres.”
In our greater Judeo-Christian heritage, the Holy Bible contains many symbolic references to numbers and formulas that mystics in the Western world have utilized as teaching tools for personal and spiritual transformation. Numbers such as 1,3,7,9,12,24,40 when employed as teaching symbols by a Jewish tzaddick, a Sufi sheik or Christian master, they are transformed to become patterns and metaphors that describe ideals such as unity, balance, testing, completion. Numbers are also used to chart the human psyche, and discern the “face of God” in mystical disciplines such as numerology, astrology, tarot, and the Kabbala. Freemasonry has carried on these symbols, they are a part of our American heritage as well, right down to the design of our dollar bill!
One of the most intriguing and enlightening discoveries that I found was the connection between natural design and mathematical sequences as formulated by the famous Leonardo Fibbonaci of Pisa. Who was he? (a long lost relative? During coffee hour, his books will be on the back table for only $5.95!) Seriously, Fibbonaci was famous for two things; one which is quite obvious, one quite hidden from ordinary knowledge.
The obvious contribution to Western culture and the advancement of science and math was that he was the one responsible for adopting the Arabic numbers, 0-9, into Western culture replacing the awkward Roman numerals for everyday use. The second discovery was the Fibbonaci series- a postulate that links numbers to what proceeded them in a logical and orderly sequence. His theorem
states that from a sequence of numbers where you add the preceding number to the previous sum, you arrive at a totally consistent answer… a sequence that also parallels Nature in its creative designs. Examples of this are: 2+3=5; 3+5=8; 5+8=13; 8+13=21 and so on… But so what??? This ratio, along with Pythagoras and his gold proportion, are the mathematical clues to many of the greatest works of music and art, and the most wondrous designs in nature. We find this ratio or design within the masterpieces of architecture such as the Great Pyramid, and the Parthenon, paintings such as Da Vinci’s “The Last Supper” and Raphael’s “The School of Athens”.
In the natural world, we find this same series and design in the hydrogen atom, the spiral of DNA, which are the essentials for all organic life. Those of you who are into gardening and natural design can note this: Beans and peas grow upward along the same ratio; all the petals of every round flower, from asters to zinnias; pineapples (8-13) and pine cones (5-8) sea shells and nautilus all develop by adhering to this formula or design in their growth cycle called Phylotaxis.
So, in math as in many things, what precedes the present also prepares us for the future. In math as in everyday existence, both can be seen as building for expansion based on continued balance and cohesion. In this way, the progression of numbers becomes the slide rule for life. The past determines the present, the present shapes the future … What we are now is a result of what we were, and where we are now, will shape the future and our possibilities. (growth of a church or a spiritual community?)
All of you who are creative, (and I feel that everyone
is whether they are aware of it or even if believe it or not) are the potential makers or designers of such beauty in your lives. Your successes are as certain as the great artists, builders and composers IF you align yourselves to these golden ratios and
these same divine proportions, or holy laws of balance and harmony, elegance and equilibrium.
Every creative concept, every creative act corresponds to a mathematical beauty in line, form, or symmetry, which then can be seen as a principle that corresponds to timeless truth in heart and soul. Believe it or not, there is a sensuous elegance to be found in studying math, for more than the dull and dry academic precision of notes and numbers, it can reveal the sheer ecstasy of life!
Regardless if your attention is on honeycombs or snowflakes, both perfect, harmonious hexagons by the way, or how the endless spirals of a seashell’s shape carries with it a deeper meaning, a cosmic purpose behind and within it, we can come to know that each equation of life has a beauty of its own. And it is with this wider view, that merges the spiritual with the scientific, we can appreciate more of the everyday miracles of life.
My hope is that if any of you were like me, either fearing or disdaining math, that you can benefit from this more right brain, inclusive approach to numbers. Maybe someday, you can join Johannes Kepler, famous mathematician and mystic when he declared,” The study of mathematics, as in music, art, and in all creation is the process whereby we, as humans, can begin to think God’s thoughts [and by following Divine reasoning, come to a greater appreciation of the grace and beauty found in our world.]
May you walk and act in proportion to this beauty…. So Be It!
The famous anthropologist, Jacob Bronowski looked at the beauty of nature and the beauty of science in this way:
[“When the poet Coleridge tried to define beauty, he returned always to one deep thought: Beauty, he said was unity in variety! Science is nothing else than the search to discover unity in the wild variety of nature, and mathematics is a way to express the laws and proportions of that beautiful variety.”]
From the physicist and philosopher Paul Dirac:
It is more important to have beauty in our life’s equations than for them to simply fit the problems. Stick with any theory only as long as it remains beautiful.
Benediction: From the poet Wordsworth:
Sweet is the lore that Nature brings- we murder when
we dissect. Enough of dry Science and arid Art- Close up
those barren leaves.
Come forth and bring with you a heart that watches and receives. AMEN
Selected Readings: Collected thoughts on Mathematics
from The Divine Proportion
Thomas Hardy once wrote these reflections on math and the
need for beautiful patterns:
” A mathematician, like a painter, or a poet, is a
maker of patterns. If his patterns are more permanent than
theirs, it is because they are made with ideas… The
mathematical patterns, like the painter’s or the poet’s
must be beautiful; the ideas like the colours or the
words, must fit together in a harmonious way…”
” Perhaps the best reason for regarding mathematics as
an art is not so much that it affords an outlet for
creative activity as that it provides spiritual values. It
puts a [person] in touch with the highest aspirations and
loftiest goals. it offers intellectual delight and the
exaltation of resolving the mysteries of the universe”
Pastoral Reflections: On Wordsworth and Nature
(“Lines written Above Tintern Abbey”)
… that Nature never did betray the heart that loved
her; tis her privilege through all the years of this our
life, to lead From joy to joy : for she can so inform the
mind that is within us, so impress with quietness and
beauty, and so feed with lofty thoughts that neither evil
tongues, rash judgments, nor the sneers of selfish men,
… could disturb our cheerful faith, that all which we
behold is full of blessings.”
In my teenage years and early adulthood, I used to
feel separate or alienated from Nature- removed from the
Earth, animals and plants. Being outside meant one of two
things: work or play, but never that I was a part of a
greater life, that I participated in larger world that was
blessed and beautiful. Consequently, I became “lost in my
head” because maturity meant, I had to lose my childlike,
playful connection to snow, wind, water, and dirt. I had lost my intuitive regard for beauty, harmony, and balance that Nature daily displays and blesses us with each day.
What broke the spell was learning about spiritual approaches to gardening and metaphysical ideas of connections and cycles, through Rudoph Steiner, the Waldorf Schools, and Bio-Dynamics-
They teach how life grows and is infused with spiritual principles. If any of you are more like me, less than logical, or more “right brain” maybe looking spiritually at the whole of Nature will give you a greater appreciation of its parts.