Monday, January 11, 2010

Leonardo’s Temple

(A Mathe-magical Whirligig Axis of Life – From Movie Stars to Spiraling Galaxies)

You could drive by and never notice the essence of this plot of land. There was a tiny shack in the left rear corner of the lot.  It was small with a chimney billowing light gray smoke. The house had a window and a door facing the front and a similar window facing the sides. From those windows the entire field of green and yellow and white was visible. You would miss it because unless you stopped and looked at the grandeur of the entirety, it was a piecemeal disaster. The yellow and white were wild flowers growing as nature would tend to them, interspersed with tall grass. The shack was vintage with wooden rafters weathered and curved straining at the nails that held them in place. The windowpanes were spotless however. A small mound to the right of the house was residence to a swarm of ants that kept their nightly vigil trekking food back and forth snaking tiny paths along the side. There were straight paths cut through this landscape perpendicular to each other. Each subdivision of the tract had a different color based on what grew there. The varnish of asymmetry from near grew dull as the colors of symmetry brightened from afar. The chaos was carefully hidden in the perfection of the whole. A Mandelbrot Fractal!

This was an amazing tract of land. No doubt tended to by man, as the first light glimmered above the high terrain back-drop of the hill. The tops of the fir trees lit up with the golden hue. The elongated shadows traced across the landscape over the wild flowers, the bushes and the one-lane road that bore limit to this nature’s feast.

“What do you want?” The gruff voice from behind the screen-door was startling.
“Your property is so beautiful, I had to mention it.”
“Eh!” he grunted, his face framed by the half-screened door. He was old maybe in his seventies. Thin and tall with long gray hair that came down to his shoulders and a moustache and beard that matched and merged to comport his visage.
“What do you want?” He said again.
“You’re not selling anything?”
“Oh!” He seemed taken aback. The screen door opened with a slight hesitation, “You want to see the field?”
“I’d love to.”

He came out in his pale brown dungarees. He walked around the field carefully winding his way via the partitions crafted to separate smaller tracts from others based on what was being grown. He showed me a beautiful patch of strawberries, another of pineapples. There was a larger patch of sunflowers. In the corner behind his house was a rectangular piece of land with bare earth and on it was an aviary. The bees calmly buzzed in their world of honey entering and exiting as they hunted for nectar. There was even a small patch of cauliflower with purple colored leaves in full blossom.

“Your paradise?”
“I have never seen anything like this.”
“You seem like a man who likes nature. What do you do?”
“Oh!” he said with a mild surprise,  “A doctor?”
“A man of science. Good. Of the ten or so people who have stopped by all have been scientists of one sort or another. Never a doctor has knocked on the door. Come on in. Like some Butternut squash soup? I just made it.”
“Smells delicious.” And it was, heavenly.

The house was a two-room bungalow with a bathroom. The gathering room as he called it was sparsely furnished lending to limited societal interaction. A lone straight back wooden chair and a loveseat. There was a table next to the far end with a stool next to it, presumably for eating. A small stove with a covered pot on the burner heating up the smell of soup that permeated the enclave and an equal size empty sink completed the kitchen. But what caught the eye were the walls. There were photographs of various plants in blossom. Beautiful yellows, reds, violets, blue and magenta colors stared down. There were flowers and bushes and even trees in various shades of blossom.

“My photos. I develop them in the back room.”
“Wow. These are beautiful.”
“Anything catch your eye.”
“Let me share with you an open secret. No one really knows and maybe no one cares to know. This piece of property is subdivided according to the Golden Ratio. You know what that is?”
“Yes a little. It is based on the Fibonacci numbers.”

“Precisely. You see nature has the Golden Ratio in most plants. The Fibonacci numbers have a sequence of 0,1,1,2,3,5,8,13,21,34,55 and so on. Each number is the addition of the previous two. The Golden Ratio is the division between any two sequential numbers. 55 divided by 34 gives you 1.618. Or a line AB with a point C within it and the ratio of the length of the line CB to AC is similar to the ratio of AC to AB. Mathematically it is written as: (1+Square root of 5) /2 = 1.618

“So what I did was to divide my property in the Golden Spiral based on the Ratio. Each tract of land gets progressively bigger and each subdivision grows different vegetable, fruit or flower. Like the nautilus.” His moustache stretched with the smile beneath it. He was pleased with himself.

The Nautilus and the Golden Ratio

The Sea Shell

“Incidentally all the fruits and flowers that grow also have the principle of the Golden Ratio. For example you noted there were the strawberries, cabbage, the sunflowers etc. Their growth pattern is nature’s design of beauty and symmetry, example the bees, their reproduction is based on the Fibonacci numbers. The male bee reproduces without the female while the female needs the male and the breeding results in the Numbers. Fibonacci actually came up with the Numbers by basing it on the rabbits growth rate.”

The Reproduction of Bees.

“I am impressed. What made you do this?”
“I am a mathematician. I worked in the Los Alamos lab in New Mexico and retired a few years ago.”
“All these were grown on this property?”
“Of course, by rotation. Keeps me fed and independent.”
In the middle of the photographs was a lone photo of a woman. It was black and white, faded by age but held in reverence by its position.

“That is my wife. She passed away a few years ago. Since you are a doctor this might interest you too. I found out that each heartbeat has the Golden Ratio in it. The distance between the T wave and the QRS complex is Ratio based. Also the arm and the hand lengths are based on the Fibonacci Numbers and the Golden Ratio. True!” He pulled out some charts to elucidate his point.
“I didn’t know that.”

Electrocardiogram (EKG)

“The ratio of the systolic and diastolic blood pressure falls close to 1.61 and where the ratio is disturbed such that it is 1.7 or 1.5 the life is shortened by disease as happened with my wife.” He grew wistful as the past flooded his mind. The silence was short and abruptly abandoned as if awakened from sleep. He said, “Great works of architecture such as the Parthenon in Greece and the Notre Dam Cathedral were based on the Ratio, as were the Pyramids in Egypt, as well as great works of art like DaVinci's Mona Lisa.”

The Parthenon

Mona Lisa


“To go from the known limits to the limitless space, even the spiral galaxies observe the Ratio. As we peer down from space the hurricanes observe similar laws even down to the waves that crash on the shores observe the 1,1,2,3,5,8 numbers when viewed from their side profile. It is the Golden thread that weaves the fabric of the universe and our lives.

A Hurricane and the M51 Galaxy

“The axioms of mathematics have deciphered some of the nature’s codes. We have a lot more to learn but use them for our benefit is what separated us from animals. Even in music, Mozart’s 5th Symphony is based on the Ratio. It is indeed considered one of the Masterpieces along with Beethoven’s Fifth, also based on the Ratio.”

Mozart's 5th First 9 Notes

The Piano's Musical Octave (2,3,5,8)

“Any other areas of anatomy or physiology that this Ratio appears?”

The Human Hand and the Golden Ratio.

“Now I got your curiosity tweaked. Yes. The branching of the lung tissue and even the neuronal growth and interconnection in the brain seem to have some relationship although that is your field of endeavor. But what is most interesting is that the DNA itself is based on the ratio. The cycle length of the DNA is 34 angstroms and the width is 21 Angstroms. Now here is the kicker, there are 21 microtubules that separate a dividing cell and each microtubule has 5 and 8 rows of right and left moiety. 

The cell dividing Microtubule.

In 1990 Jean Claude Perez while working for IBM discovered a DNA supracode which he termed as “Resonances” controlling the self-organization of the nucleotides Thiamine, Cytosine, Adenine and Guanine (T,C,A,G), which make up the steps in the double helix ladder of DNA.  

The DNA Supracode.

He discovered if you consider 144 contiguous nucleotides it results from 55 T bases and 89 C A G bases, all Fibonacci numbers.

The DNA and the Golden Ratio.

“ A.L. Goldberger from University of California in 1984 reviewed the irregular branching of the human and animal bronchial tree of the lung and found the Fibonacci scaling there too. It appears that Nature in her simplicity and expediency employs the Ratio to create elegance. Just as Leonardo DaVinci did with Mona Lisa and the most beautiful people defined by the present day media  (Audrey Hepburn, George Clooney, the latter data was published in December13 2009 article in the British Medical Journal by Hanno Ulmer

Audrey Hepburn

George Clooney

have faces that show the Ratio between the mouth, the nose and the eyes all bear the beauty of symmetry and the rules of the Ratio. As a mathematician, I don’t know whether the Ratio was waiting to be found or we created it to fit our world. However given the widespread dispersion of it in the universe, I call this Ratio the Fingerprint of God.”

Leonardo of Pisa (Fibonacci)

It is easy to find beauty when one has an open mind. Nature throws colors and architectures of grand beauty waiting for us for our wide-eyed enrapture. But even more we have the tools established by a brilliant mind that of Leonardo Pisano (aka Fibonacci) to explore our world and employ Nature’s own formulae to create a haven. Perfection exists not in the toil but the knowledge. Beauty exists in perfection.


  1. Great stuff on Fibonacci. Love the story at the top of the article? Is that your own writing or is it excerpted from somewhere? How does the story end?

    I'm doing a doc on fibonacci and found this blog through a search on honeybees.

    you can see the site here:

    Keep it Golden,


  2. Thank you Steven for your comments. Yes this is my writing.
    Your question has inspired me to finish the story...soon.
    Wish you success in your movie.