by Robert Waltz
Not for the faint of art.
A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.
The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.
Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.
Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.
|You'd think that, as a long-time beer snob, I'd like Guinness.
You'd be wrong.
I mean, it's not bad, and it's certainly an important beer for many reasons. I'm sure I'd like it better if I were to go to Ireland and drink it from the tap there. And given a choice between Guinness and that watered-down rice water that passes for "beer" that's mass-produced in the US, I'll take Guinness every time.
But I made the mistake once of drinking a pint at a concert. The mistake was, before the concert, I'd gone to a taphouse and had a really good stout. By comparison, the Guinness just didn't measure up.
Like I said, though, it's a culturally important beer for many different reasons, one of them being just how long it's been brewed.
Beer drinkers are used to seeing eye-catching beer labels — some good, some not so good. But stroll past a beer fridge and you might see a label that’s simple, nostalgic, and a throwback to the 1930s: the Guinness toucan.
Beer art is flourishing right now. Graphic artists are probably having a field day with all the logos and labels and tap handle designs, to say nothing of posters and taphouse decorations.
“The Guinness family did not want an advertising campaign that equated with beer,” the UK History House writes. “They thought it would be vulgar. They also wanted to stress the brew’s strength and goodness. Somehow it led to animals.”
At least they didn't pick an elephant.
There was the pelican that stole everyone’s beers with the copy, “My goodness — my Guinness!” Also the sea lion that had a habit of stealing Guinness. And the turtle that steals Guinness on its back. A lot of thirsty animals, basically. None earned as much fame as the toucan, however.
I don't think I was ever aware of these other mascots.
The toucan’s brightly colored beak contrasts nicely with two dark glasses of Guinness (almost always two glasses, playing off of the similar sounds of “too can” and “toucan”).
As I'm only aware of the ones with draft pints, I never would have made the "two can" connection. No cans, no pun.
The toucan and its gang of animal friends graced Guinness ads for decades. Then, in 1982, Guinness stopped working with S.H. Benson and dropped the animals. In recent days the toucan has made some appearances, including a limited-edition can released in 2016. But it primarily lives on in the memories of Guinness lovers and collectors.
They're more than happy to sell toucan merchandise in dedicated Guinness stores (yes, these exist), along with the famed bar towels.
So yeah, even with the proliferation of beer choice nowadays, there will always be a place for Guinness. But that's as much a testament to the power of marketing than to the beer itself.