Playin' the Numbers

Mathematical number contains in its very essence the notion of a mechanical demarcation, number being in that respect akin to word, which, in the very fact of its comprising and denoting, fences off world-impressions….So also numbers are something that mark off and capture nature-impressions, and it is by means of names and numbers that the human understanding obtains power over the world.  In that last analysis, the number-language of a mathematic and the grammar of a tongue are structurally alike. (Oswald Spengler: The Decline of the West: Vol. 1: 56-57.

            There are two ways to “read” the creation, verbally and digitally.  Traditional Christian theology believed the spiritual and material worlds were in correspondence.  Their metaphor was the analogical union of two Books, the verbum scriptum (which was revealed scripture) and the verbum factum, the Book of Nature.  Adam’s naming of things in Eden is a story of the birth of intellectual knowledge within humanity.  Those same names are written by science in mathematical notation, and indeed all forms of Numerology are systems of this sort.  I am not advocating for Numerology to be on the agenda of the next curriculum development meeting, I am simply pointing out the fact that letters and numbers are, as Spengler states, “structurally alike”, and that each letter and word has its numerical value, as any Scrabble player can tell you.

            For Alfred North Whitehead, “mathematics is concerned with certain forms of process issuing into forms which are components of further process…” a process rather than a structural definition of mathematics, perhaps only meaningful to other mathematicians in that form.  However, if one wanders into the backyard and starts measuring what one finds there, you begin to see what he means.  If you take the mathematician, Fibonacci, out with you he will explain how the simple recursion of the numbers that bear his name appear in such examples as the branching in trees, the arrangement of leaves on a stem, the fruit spouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone.   

            Then, if one looks even more closely at that pine cone, or into the sky, Benoit Mandelbrot will tell you that you are actually looking at examples of fractal geometry.  A fractal is a geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.  This property, called self-similarity, operates by a mathematical equation that undergoes iteration, a form of feedback based on recursion.  Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex.  Natural objects that are fractals include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns.  A fractal says, metaphorically, that all things, being forms of light, are holograms, and, like holograms, you can split them into an infinite number of pieces and the original shape will remain, at least in fuzzy, mathematical outline, in each piece.

            When ‘Abdu’l-Baha explains that: “All beings, whether large or small, were created perfect and complete from the first, but their perfections appear in them by degrees. The organization of God is one: the evolution of existence is one: the divine system is one,” (Baha'i World Faith: 312)  He is not just speaking philosophically of essences and attributes, He is also speaking of words and numbers, words revealing the essence and numbers the appearance of perfections by degrees: structure and process, and the divine iteration of the cosmos.  The American philosopher, Emerson, described the same relation within knowledge as “the proportionate unfolding of the intuition.”    

            I discussed in previous posts how words and letters are runes written upon the world.  The right name releases the power of the thing.  The right number, science calls it its atomic number, puts that release into proper relation with other things.  Learning these two great incantations of human intelligence occurs in the first five years of life.  Words have the resonant power of metaphor that enables multi-variant poetic awareness to develop.  Numbers provide the power of precision to permit exact quantified knowledge of discrete material things and the ratios of their fitting into each other.

            Where does all this “number-ology” start and what are the sources of its development?  As with all “elementary” learning, there is a metaphysical and a physical origin, an inner origin of innate awareness and a manifest start in the visible world; there is the structure of it and the process of its organic unfolding. 

            Organically, numbers start with a vague sense of difference.  The number sense is not the ability to count, but the awareness that some quantity has changed in a small collection. Some animal species are capable of this, as when a mother bird “knows” when one of her young is missing though she can not count them.  It is the number ability that can precisely measure these quantified changes.  The number sense is innate, the number ability is educed by the teaching of mathematics.  Number sense and ability have, too, early associations with music and its distinct and regular vibratory differences of tones, notes, and harmonic scaling, and with astronomy which follows the music of the spheres. The living world is built upon the Pythagorean numbers. So in learning numbers children are not just learning how to count things, but learning how things organically unfold from within.  Pythagoras also “claimed to have heard the whispering sound of the heavens.” (Tablets of Baha'u'llah: 144)   

            Like words, numbers were, first, the essence of things, and the priest classes of ancient civilizations, such as Babylon, used mathematics in their religious rituals and to chart the heavens.  Numerology, the early systematizing of numbers, claimed—and still claims--to know how numbers add up for human destiny, and how numbers mesh to predict events.  Many think Numerology is a lot of hokum, and in that form it may be.  Yet religion has based many prophecies on some magical affinity of numbers, and certain numbers, such as 360, 72, 40, and 9, are of great symbolic and, often, actual importance.  Scientifically, atomic number is the basis of chemistry and physics and changes in number sense create revolutions in perception and technology.  Quantum numbers continue to redefine the basics of many sciences and to fuel the technological revolution.

            For Greeks of Plato’s time numbers were the geometry of things. Some traditions say that over the doorway of his Academy Plato had written: “Let none enter who are ignorant of geometry.”  Arabic numerals really came from India, and Indian thinkers first came up with the idea of zero. Algebra is the way we connect our ideas about geometry with our ideas about numbers. The word Algebra is derived from the Arabic word Al-Jabr, and this comes from the treatise written in 820 by the Muslim mathematician Muhammad ibn Mūsā al-Khwārizmī. 

            The two main tool subjects of language and mathematics are most important to know not just in themselves, but also because the two main knowledge systems of humanity are religion, based on the Word, and science, based on number.  (See: Number: The Language of Science by Tobias Dantzig)  The Baha’i Teachings assert that “science and religion, the two most potent forces in human life, will be reconciled, will cooperate, and will harmoniously develop.” (The World Order of Bahá’u’lláh: 206)   Reconciliation, cooperation, and harmonious development between science and religion is possible because, like words and numbers, religion and science are, as Spengler says, “structurally alike.”  That phrase has two large implications.  First, it implies that science and religion are fractals, each a “reduced-size copy of the whole”, the whole being, for me, Revelation.  Secondly, “structurally alike” is another way of saying self-similarity, which is another term for holographic.  It is also the mathematical principle, if A=B, and B=C, then A=C, which is the structure of metaphor and analogy.  I will explore that topic in the next post. 

            For now, if you need a math lesson go count butterflies.  And take Plato,  al-Khwārizmī, Fibonacci, Whitehead, and Mandelbrot with you for the older kids.