Phi in Nature, Art and Architecture

Way back in the thirteenth century Leonardo Fibonacci wanted to figure out how many offspring a pair of rabbits and their offspring would have if each bred one female rabbit a month. Simple: 144 rabbits after one year, 46,368 after two, and 14,930,352 rabbits after three years. The illustrious mathematician of Pisa had discovered the Fibonacci Sequence.

By dividing each number in his sequence by its previous number, he had detected Phi, and called it the Golden Ratio. Phi can be rounded up to 1.618.

Arab scholars had long known about this sequence, because for ages they had been using Arab numerals, 0, 1, 2, 3, and were far ahead of Europeans, who were still struggling with Roman numerals.  No matter how brilliant a mathematician, the use of II, IV, or CXII is not conducive to doing math. When Fibonacci returned from his travels to Arabia, he vigorously encouraged Europeans to use the Arab system.

Amazingly, Phi happens to be ubiquitous and a fundamental characteristic of nature. It shows up in the patterns of leaves, flowers, pinecones, pineapples and shells, and even in the spiral of the galaxies.

Phi is not only known as the Golden Ratio in nature, it also features in architecture and art. The pyramids and the Parthenon reflect this principle. Le Corbusier carefully calculated a Golden Ratio when he designed the UN Headquarters. Many city halls and theaters are built in the Classical Greek tradition based on Phi.

Even great artists have embraced Phi. Leonardo Da Vinci, Botticelli, Michelangelo and Salvador Mundi are all known for having applied the Golden Ratio to some of their famous works of art, such as The Last Supper, The Annunciation, The Birth of Venus, and The Creation of Adam.

Some people claim that the beauty of a face may depend on its ratio too.

May Phi harmonize your life.

Until next time,

Rosi

Computer Glitches

Computers are simply inanimate devices, right?

Wrong.

Computers are highly delicate and sensitive creatures. At least mine is, and it can be quite stubborn at times.

Have you ever been in a big hurry to print out something? My printer worked fine earlier in the day. But now, when I don’t have a minute to spare, it is not cooperating!

Not only that, but the sentence I changed switched back to the old version. Twice. I’m at my wit’s end. Why do computers do that?

Frustration over technology glitches is becoming so prevalent that yesterday the Wall Street Journal featured a front-page article called "The Tech Fails That Annoy Us Most." Geoffrey Fowler and Joanna Stern write "We love technology, but this week we're shaking our fists at it for all the ways it annoys us." They invite readers to send in their pet peeves.

I suspect that computers want us to be grateful, glad and relaxed when we interact with them. After all, what would we do without them? Computers are everywhere and run everything. They know full well how much we depend on them.

Do you suppose that solar flares might occasionally interfere with our computer? Solar flares are known to cause trouble with satellite signals.

It is useless to talk about a computer’s feelings to an engineer. If he’s polite he will tell you that computers are simply machines—man-made, inanimate objects like shoes. If he’s the more direct type he’ll tell you that you’re nuts, how can computers have feelings?!

But suppose my haste and impatience and my rapidly beating heart are sending out jagged vibrations that interfere with the electronic field of my computer. They affected my grandson when he walked into my office.  Even though we didn’t exchange a single word, he said, “Slow down Grandma, slow down!!” How did he know? Because he felt my haste, just as my computer did. It’s not surprising that my computer is sensitive to my feelings; I spend much of my day with it.

I asked a friend of mine about it. He smiled at the foolish idea and patiently explained that our vibrations are much too weak; they measure in micro-volts and couldn’t possibly interfere with the five or more volts that a computer uses.

Perhaps we need to learn how to accurately measure human feelings and how emotions can interfere with or affect electronic equipment as well as other people.

Or could it truly be just us, hitting the wrong computer buttons causing chaos?

As the Cracker song goes:  I could be wrong, I could be right.

Until next time,

Rosi