Not for the faint of art. |
Complex Numbers 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've certainly heard the cliché, "the greatest thing since sliced bread," which implies that sliced bread was the greatest invention. This is obviously false, as beer was invented before sliced bread. Sometimes it takes a lack of something to truly appreciated it. This was true during Prohibition, and apparently, also true during World War II. Remembering When America Banned Sliced Bread During World War II, the U.S. government turned to drastic rationing measures. The year was 1943, and Americans were in crisis. Across the Atlantic, war with Germany was raging. On the home front, homemakers were facing a very different sort of challenge: a nationwide ban on sliced bread. While it's true that there were far worse things in WWII than a lack of sliced bread, I can see how that would be frustrating. The ban on sliced bread was just one of many resource-conserving campaigns during World War II. In May 1942, Americans received their first ration booklets and, within the year, commodities ranging from rubber tires to sugar were in short supply. These days, of course, such measures would be "government overreach," "tyranny," "an attack on muh freedumbz," and "cause for riots in the streets." So by January 18, 1943, when Claude R. Wickard, the secretary of agriculture and head of the War Foods Administration, declared the selling of sliced bread illegal, patience was already running thin. Since sliced bread required thicker wrapping to stay fresh, Wickard reasoned that the move would save wax paper, not to mention tons of alloyed steel used to make bread-slicing machines. Okay, so I can see the wax paper thing (plastic wasn't much used then), but didn't the slicers already exist? Sliced bread was invented in 1928 , and pretty much everywhere five years later—ten years before the ban. On July 7, 1928, the Chillicothe Baking Company in Missouri first put his invention to use, saying it was “the greatest forward step in the baking industry since bread was wrapped.” So, really, the expression should be "the greatest thing since wrapped bread." As an aside, I'm picky enough to get my bread from a local bakery rather than the supermarket. They'll slice it right there upon request, and slide it into a plastic bag with a twist tie. Since it's fresh bakery bread without preservatives, if it's not wrapped, it becomes a rock within 24 hours. Sliced bread really took off in 1930, when the Continental Baking Company’s pre-sliced Wonder Bread made its way into American homes. Ugh. Foul. Disgusting. After a few years of aggressive marketing, the pillowy, preservative-laced loaves were synonymous with modernity and convenience. They're synonymous with American lack of taste, along with American cheese and light beer. On January 24, less than a week after the ban, the whole thing began to unravel. New York Mayor Fiorello LaGuardia made a public announcement that bakeries that already had bread-slicing machines could carry on using them. See? No wonder he got an airport named after him. One baker by the name of Fink, who also happened to be a member of the New York City Bakers Advisory Committee, publicly advocated for the ban, then was fined $1,000 (more than $14,000 today) for sneakily violating it. Tempting as it may be to claim that his name was the source of the verb "to fink," no, it wasn't. By March 8, the government decided to abandon the wildly unpopular measure. “Housewives who have risked thumbs and tempers slicing bread at home for nearly two months will find sliced loaves back on the grocery store shelves tomorrow in most places,” noted the Associated Press. Government overreach, tyranny, muh freedumbz. In the end, no thumbs were severed and Americans were reunited with the sliced bread they had learned to hold so dear. Once you get used to an invention, especially one that saves time and work, it's very, very hard to do without it. If necessity is the mother of invention, laziness is the milkman. Also, fuck Wonder Bread. |