Tuesday, May 13, 2008

Beauty and Mathematics

"One thing have I desired of the Lord, that will I seek after; that I may
dwell in the house of the Lord all the days of my life, to behold the beauty of
the Lord and to inquire in His temple." Psalm 27:4

One way to behold the beauty of the Lord is to examine His creation mathematically, for the natural world speaks loudly of the Creator's remarkable orderliness. Take for example, the sequence of numbers known as the "Fibonacci Numbers":

1, 1, 2, 3, 5, 8, 13, 21, 34, 55..........

In this sequence, each number in line is the sum of the preceding two numbers. We can trace these numbers in nearly everything that we would call "beautiful" in the world of nature: the spirals on a pineapple, the whorls at the center of a sunflower, the pattern of a pine cone. As you see the predictable pattern in growing things, you begin to surmise that nothing is truly random. That is a comforting thought to me! Foundational structure provides much safety.

Comprehending patterns visually can lead to the next step, which is to apply knowledge of the seen to the unseen. The patterns we can see become a hook onto which we can hang our understanding of things invisible. The workings of the cell, DNA strands, atoms, the concept of aerodynamics-- all of these things we can understand to some extent because we are acquainted with similar, concrete models of the same sort.

"For by Him all things were created....visible and invisible...." Colossians 1:16

The ability to think abstractly is a strictly human attribute and mathematical patterns such as the Fibonacci Numbers give us a starting point onto which we can connect deeper understanding. And it is here that I have only recently made the startling discovery that mathematics is really NOT just about numbers. It is more accurately the science of patterns. How I wish I would have known this years ago!! To have been able to trace the foundational patterns of the universe to the God who made it would have perhaps given me a fresh outlook on all of the math assignments I so dutifully endured but failed to enjoy.

*Music has a definite, mathematical pattern.

*Linguistics involves the study of grammatical pattern.

*Genetics link DNA patterns with physical attributes.

*Chemists understand the orderly pattern of the periodic table of elements.

*Astronomy incorporates the study of orbital patterns of moving objects in space.

*This list could go on endlessly and become a mathematical object lesson for the word "infinity"!

I think that perhaps the most fascinating thing about all of this is that humans recognize beauty within the boundaries of orderly pattern. We perceive only some patterns as beautiful, and those are usually linked to the Fibonacci numbers. Look again at that sequence: take two adjacent numbers and make a ratio; for example 3:5. Now, do the math:
5 divided by 3 = 1.6

The 1.6 quotient has become the famous "golden ratio." Our bodies were designed according to this ratio. The Greeks built the Parthenon in keeping with this pattern. Even the 3x5 inch index card you use for a bookmark is cut to pleasing proportion according to this principle. Whether it is a building a painting, a face, or a song--humans seem innately attracted to anything designed in the 3:5 ratio. Conversely, the things we would dub grotesque or deformed fall outside of the Golden ratio. Beauty has a design, a predetermined orderliness and life becomes endlessly fascinating as we uncover layer after layer of these divinely-conceived patterns.

Here are some beautiful words by a mathematician:

"The mathematician's patterns, like the painter's or the poet's, must be
beautiful, the ideas, like the colors or the words, must fit together in a
harmonious way. Beauty is the first test; there is no permanent place in
the world for ugly mathematics....It may be very hard to define mathematical
beauty, but that is just as true of beauty of any kind--we may not know quite
what we mean by a beautiful poem, but that does not prevent us from recognizing
one when we read it. " --quote by G.H. Hardy from his book, A Mathematician's Apology.


ichthys said...

I came across Fibonacci as a poetic form last year.Here is an example ARACHNIDS from my chapbook of Fibonacci entitled SEQUENCE

riding on the breeze-
ballooning on the world wide web

Poiema said...

That was great! Reminds me of a book my kids recently read: Spiders and Their Web Sites. Catchy title!