originally published January 27, 2012
If one is truly the loneliest number – and in my experience, you should believe anything you hear in a classic rock song – then without a doubt the least loneliest number would be 1.6180339887.
This number is the golden mean, the medial section, the divine proportion, the mean of Phidias… and for the purposes of Miss Wiki’s supernatural wheel-spinnery today, it is the Golden Ratio.
To put it algebraically:
To put it in terms that normal humans can understand, it is the ratio that is considered the most aesthetically pleasing in the world. This ratio can create the perfect rectangle, the perfect face, probably the perfect raisin muffins if only someone would figure out how to apply it.
I’m not kidding though (well, maybe about the muffins); this isn’t just a math thing. This ratio has been studied by artists, historians, musicians, biologists and mystics. Even guys with two beards have studied it.
The first notable use of the Golden Ratio can be found in the Parthenon. The structure makes use of what’s called a Golden Rectangle (which I think you can find in knock-off brand Lucky Charms). With a golden rectangle, if you remove a square piece you’re left with another rectangle whose sides have the same length ratio. Confused? Does this help?
No? Forget it, let’s move the hell on. Math makes my brain hurt. I hope I get a softball topic tomorrow, like another kind of stacking chair.
The Golden Ratio comes up in novel The Da Vinci Code, and possibly the film, I don’t remember. Robert Langdon recalls a lecture he gave where he discussed the Ratio with his students, discussing how it relates to the Fibonacci sequence of numbers, how often it comes up in nature, and how Zoltar can use the Golden Ratio to make you big, then get you a job working for Robert Loggia.
The point is, Da Vinci was all about this ratio. It shows up all over the Vitruvian Man drawing, that four-armed, four-legged guy showing off a rather modest 15th-century penis. Beautiful people have been picked apart by Ratio enthusiasts (or, more accurately, psychologists) for years, finding the ratio in eyes, lips, and all sorts of body parts of our most gorgeous specimens.
Apart from the Greeks, architects all over the world have made use of the Golden Ratio in their work. The Great Mosque of Kairouan (located in Kairouan… I want to say Idaho?) uses the Golden Ratio all over the place. Swiss architect Le Corbusier, who was a pioneer of the modernist style, was so fascinated by the perfection of the Golden Ratio, he couldn’t stop talking about it. Eventually people weren’t inviting him to parties, weddings, bar mitzvahs, cheese hole-punching ceremonies, whatever else they do in Switzerland.
Salvador Dali used the Ratio in his Sacrament of the Last Supper. Apart from the Golden Rectangle dimensions of the canvas, the giant dodecahedron behind Jesus is a geometrical expression of the Ratio. Also, the whole thing looks like it should be sold on a pillow through the Bradford Exchange.
The majority of books printed between 1550 and 1770 had pages that had dimensions of a Golden Rectangle (not counting centerfolds).
The Golden Ratio shows up in music, though it would take a pretty well-trained ear to find it. Bartok’s music makes use of it, so does some of Satie’s. Debussy’s “Reflets dans l’eau” builds on the Ratio. I can’t find any musical examples from music’s most honest era (as mentioned earlier, classic rock), but it’s interesting to note that Pearl, one of the world’s leading drum kit manufacturers, positions the air vents on its Masters Premium kits based on the Golden Ratio. The company has been quoted as saying that this exact placement is ideal for producing “scrote-crunching grooves.”
Some sources claim – and that’s Wikipedia’s vague and indeterminate paragraph-starter here, not mine – that you can find the Golden Ratio all over every day things, like widescreen TVs, playing cards, posters, post cards and light switch plates. Is your mind blown yet? No? Oh. Then it probably won’t be.
How about some nature? Adolf Zeising found the Ratio all over the arrangement of branches along plant stems, or the veins in leaves. The way our own nerves and veins branch out often conforms to the ratio. You can find the ratio in crystal faces. If you don’t believe me, check out the magnetic resonance of spins in cobalt niobate crystals. No seriously, have a look at the niobate crystals you no doubt have in your home.
The Golden Ratio is used in the world of finance as well: trading algorithms, applications and strategies make use of it somehow. I have no idea how, but it’s in the article and I don’t feel like fact-checking.
There’s such thing as a Golden Triangle, though if I try to explain it my fingers might melt. The pentagon’s angles can be calculated using the length of its sides and the Golden Ratio. To put that in real-world, architectural terms, the Pentagon’s angles can be calculated using the length of its walls and the Golden Ratio.
Alright, let’s turn back briefly to Tom Hanks in The DaVinci Code. Remember the Fibonacci sequence that I glossed over before? That’s a sequence of numbers in which the next number in the sequence is equal to the total when you add up the previous two numbers. So you get 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. Well, if you divide a Fibonacci number by the number right before it in the series, you get a number pretty damn close to the Golden Ratio.
That’s it. That is as much as a completely non-math guy can write about math and sound as though he can successfully pretend to understand most of it. I’ll grant that it’s an impressive little number, and I am in awe of the folks who spent years studying it and figuring it out, double-beard guy included. But complicated math is better left to minds that function much differently than my own, minds that haven’t been battered and flayed by numerous recreational substances and an intense desire not to give a crap about math. As a wise man once said:
Smoke on the water.
Fire in the sky.