You must admit, the Roman Empire was rather impressive. What with the roads, the aqueducts and running water, the bread and circuses, the heated baths, the toga parties. And those spiffy helmets with the shoe brush on top. All very classy. The Roman Empire also had some first-rate engineers, but I wonder what else they could have accomplished were they not impeded by Rome’s appallingly goofy numbering system.
“Goofy? My wristwatch uses Roman numerals!” you object, adjusting your toga indignantly before your VIII o’clock appointment.
Well, the Roman numbering system lacked two essential innovations that we take for granted: the Hindu-Arabic numerals and positional-decimal numbering. With Hindu-Arabic numerals, we’re able to represent ten digits–zero to nine–each with only one symbol and also to represent and perform computations on “nothing” (zero). And with positional-decimal numbering, we can perform computations directly on numbers without having to first represent them in an abacus, since every numeral in a number implicitly indicates something about a power of ten by virtue of its position (e.g., 32 = 2*10^0 + 3*10^1). Arithmetic with positional-decimal numbers is therefore, as one of my math teachers used to say, “Easy-peasy, lemon squeezy.”
Their user-unfriendliness notwithstanding, Roman numerals were still commonly used in Europe well into the Middle Ages. It wasn’t until 1202 that things started to improve. That year, a customs official from Pisa named Leonardo Fibonacci published a book that not only promoted Hindu-Arabic numerals and positional-decimal numbering but also provided handy instruction in how to effectively use these new tools for practical purposes (e.g., how to compute compounding interest, how much toilet paper to take on a long sea voyage, or the odds on the Rockies getting to the postseason). And with one story problem from his book, Fibonacci also inadvertently gave us a glimpse into how The First and Greatest Engineer built His universe.
That story problem involves a rabbit warren that begins with one pair of newborn rabbits, one female and one male. In its third month of life and in every month thereafter, a pair produces another pair of rabbits, always one female and one male. The problem asks how many pairs of rabbits there will be in the warren in twelve months, assuming there are no deaths. The answer is 144 pairs, but unless you’ve got some weird obsession with rabbit reproduction, what’s far more interesting is the number of pairs that occurs in each month: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and 144. In this sequence of numbers, every term (except for the first two terms) is the sum of the two terms that immediately precede it: 144 = 89 + 55; 89 = 55 + 34; 55 = 34 + 21; and so on. Starting with 1 + 1 = 2, you can compute this sequence into infinity, and the further on you go, the closer the ratio of a term and its preceding term is to what’s known as The Golden Ratio ([1+√5]/2 or roughly 1.618).
“What’s so great about this Golden Ratio thingy ?!?” you scoff, probably caressing your abacus defensively.
The Golden Ratio is everywhere in the natural world. It’s the growth factor for the same spiral seen in a chambered nautilus shell, hurricanes, the cochlea of the human ear, the Milky Way galaxy, and growing fern leaves. The ratio of the distance between a man’s feet and navel to the distance between his navel and the top of his head is the Golden Ratio; the same is true for the human face, using the bottom of the chin, nose, and pupils as reference points. The Golden Ratio is also found in the arrangement of branches along plant stems according to their circumference, in the veins of leaves, and in the distribution of seeds in a sunflower. The same ratio is found between the revolutions of planets in our solar system. And it’s found in the ratio of atoms in many chemical compounds.
The Golden Ratio also seems to be innately part of our common aesthetic sensibility. It’s found in musical intervals that are pleasing to our ears. It’s found in great works of visual art: Leonardo da Vinci, Albrecht Dürer, Pierre-Auguste Renoir, and dozens of other artists knew about the Golden Ratio and applied it to their work. It’s found in the structure of the Parthenon and the Great Pyramid at Giza. It’s even found in the length-width ratio of 3×5 and 5×8 index cards, light-switch plates, credit cards, and baseball cards. I don’t remember any big meeting to reach consensus about beauty. So why do we find all these things so pleasing?
The Great Cosmic Engineer seems to have used certain numbers when He made His Universe. The Golden Ratio is one of those numbers. Pi, which is also a ratio, is another. Why do we find these ratios so beautiful when we see them exemplified in the geometry of creation? I suspect it’s because God created us in His image, and just as He looked on His creation “and saw that it was good” (Genesis 1), we can’t help but do the same.
Listen to author Lee Strobel speak about how God speaks to us through His creation: http://bit.ly/2vslRES