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Complex Numbers
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.
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When it comes to invention, some of us can be pretty clever. Well, not me. But some of us.
From Cracked, so the usual countdown list and jokes.
An icon of a floppy disk represents saving in Word documents. That’s even though floppies have been almost nonexistent for years, and haven’t been the primary place for saving docs in decades.
And? Some "hang on a sec" computer icons display an hourglass, which is even more obsolete.
“Kids today,” more than one commentator has speculated, “probably don’t even know what a floppy disk is. They just think that’s the ‘save symbol,’ and it doesn’t stand for anything in real life!”
And those ignorant bastards also think # (technically called an octothorpe, which I mention because that's an awesome name) means something other than "number" or "pound."
5. Before Trains, Horses Pulled Goods Through Water
Okay, I can kind of excuse being ignorant about obsolete technology. What I can't excuse is being ignorant about music, and if you weren't exposed to "Low Bridge, Everybody Down" as a kid, your teachers failed you.
In England, people were using these horse barges as far back as Roman times, and the practice came back during the Industrial Revolution, once we finally had a lot to transport. In the 1790s, one single canal eased transport so much that the price of coal halved. The country approved dozens more canals in the years immediately thereafter, and by the middle of the next century, they measured 5,000 miles in length.
The canal system in England is fascinating, and we don't hear much about it here in the US.
4. Before Plastic, We Mixed Sawdust With Blood
Okay, some older technologies won't be missed. Though with current whingeing about plastics, perhaps this one will stage a comeback tour.
Hemacite sounds like some sort of mineral.
Yeah, that's because there is a mineral called hematite.
But as all you vampires and fans of etymology know, hema- means blood.
As does hemo- but not hemi- or homo-.
People manufactured hemacite to deal with a pressing problem: a surplus of blood. Slaughterhouses produced blood in huge quantities, and people had limited success using the sticky stuff in fertilizer.
Apparently, that's not a big an issue anymore. So if there's a resurgence in hemacite, maybe we can use blood from organ donors. Blood's an organ, right?
3. Pre-Satellites, We Used to Bounce Signals Off the Moon
Scientists first used a satellite to relay human communications in 1954. This milestone will raise some eyebrows from most students of space history, who know that Sputnik didn’t launch until three years later.
Saves me from quibbling about how the moon is a satellite.
The military stopped using the “Moon bounce” in the 1960s, now that they had communications satellites. But amateur radio operators can still totally try EME themselves today. It’s not easy, but you can do it. May as well get to practicing now, so you’ll be prepared once a catastrophe knocks out all satellite communications and you need to send a message of hope to all survivors worldwide.
Except the moon needs to be in the sky for this to work, so at best, you'd only catch about half the globe. Unless, of course, the flat-earthers are right [spoiler: they are not].
2. Letterlocking: Envelopes Before Envelopes
This bit is actually pretty cool, and much less gross than hemacite. I'd been seeing various articles about it recently. I don't know why; maybe because it's more secure than Twatter?
The most secure way to send a message is physically. Seal it in an envelope, and the spies who pursue you will not easily be able to open it without leaving some evidence behind.
Because we're all being spied upon, even outside the internet.
1. People Had to Listen Really Closely for Planes
And I can't really do this one justice; you have to see the illustrative photographs.
So, not really a lot of deep meaning in today's article. Just some cool history stuff. |
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