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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. |
A couple of weeks ago, in "Hunter's Moon" ![]() Indeed, yesterday was a New Moon, precisely as far as we can get from a Full Moon, so we may not even get to gaze upon the satellite this evening; it's still quite close to the sun, from our perspective, and will set before the end of astronomical twilight. If you're lucky, maybe you'll be able to make out a thin crescent just after sunset. But today's article, from Mental Floss, takes a look at the moon anyway. Why Do People Say the Moon is Made of Cheese? ![]() The moon-cheese nexus may have started with a fable about a hungry wolf and a crafty fox. Everybody knows that Earth’s moon does not, in fact, consist of dairy products. Considering the astounding number of people who insist that the Earth is flat (that is, a nonzero number of people), I would never say "everybody" in this context. So where did the myth that the moon is made of cheese come from? I'm just as interested in folklore as I am in science, and regular readers know I'm a sucker for origin stories. Though the idea that the moon is made of cheese has been around for millennia, it’s doubtful that anyone ever actually believed it, at least not academically. Academics also knew the Earth wasn't flat. That doesn't mean your average farmer, or whatever, didn't believe it. To be fair to those farmers, it's not like it mattered in terms of doing agriculture. The earliest record of this bizarre notion comes from a medieval Slavic fable in which a ravenous wolf chases a seemingly hapless fox, hoping to score an easy meal. Never. Trust. The. Fox. But the best-known early citation dates to 1546, and can be found in The Proverbs of John Heywood. ![]() At last, a time frame for the "a penny for your thoughts" proverb! People nowadays still use that, but they generally offer two pennies (which I suspect is related to "my two cents' worth" because in the US, "cent" and "penny" are interchangeable) "because of inflation." But what would inflation actually do to the value of a 1546 penny? According to this handy website, ![]() So, because I'm not British, how much was £1.14 equivalent to in USD 2017? There's a website ![]() Finally, as you might have heard, inflation has run unusually high these past few years, so we now must convert 2017 USD to 2023 USD. Is there a website for that? Of course there is. ![]() These, are, necessarily, very rough estimates, especially when it comes to the purchasing power of a British pound in a pre-industrial society. And I won't guarantee that I did the math right, because it's too early in the morning. But according to this, today, saying "$1.76 for your thoughts" would buy roughly the same amount of thought (If you need that in 2023 UK pounds, that's on you). But one wonders if thoughts are really that valuable nowadays; maybe I'll just keep saying "a penny." Wow, do I digress. Back to the "greene cheese" article: The scientific community has never supported the claim, yet every children’s program from Tom and Jerry to Wallace and Gromit has made its fair share of moon-cheese references. Well, duh. It's still a fun piece of folklore, and thus great joke fodder. Even NASA couldn’t resist getting in on the joke. On April Fool’s Day 2002, the agency claimed to have “proven” once and for all that the moon was made of cheese by releasing a Photoshopped image with an expiration date printed on one of the moon’s craters. Casein ![]() |