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. |
Part of the whole point of experiments is to falsify a hypothesis. But sometimes, if your hypothesis is precious to you, and your experiment fails to support it, well, really, your only choices are to lie about it or suppress the results. Or you could, you know... own up to being wrong, like some of these folks highlighted in Cracked. 5 Experiments That Proved the Exact Opposite of What They Wanted Turns out Flat Earthers and anti-Semites are no match for science Did you know that visitors to this site are statistically likely to be sexier than people in general? Well, obviously I always suspected it. At least, that’s the hypothesis behind the new study we’re doing. For some reason, I wasn't contacted about the study. Sometimes, a study doesn’t prove what it sets out to. Seriously, though, that's usually a good thing. For starters, it's job security for researchers. 5 The Wallet Experiment You find a wallet someone dropped. Do you seek to return it, or do you keep the cash and toss the rest? Toss a perfectly good wallet containing perfectly good identity theft material? No way! Some wallets contained cash, while others did not. Researchers predicted that people would more likely return wallets that held no money. The researchers also held surveys before the experiment, asking either the general population or hundreds of economists, and all agreed that the cashless wallets would more likely be returned. Well, sure. That's just common sense. The experiment ended up offering all kinds of data about how people vary in honesty, but it showed one consistent trend everywhere: People were always more likely to return a wallet that held money. And this supports my opposition to "common sense." One possible explanation, that people hoped for a larger reward from the money wallets, did not hold water. They seem to have overlooked the most likely explanation: Contrary to common sense, people in general don't suck. Most of them are good, or at least neutral. This ties in with my Lone Asshole Theory, that while the majority of people are decent, all it takes is one bad one to ruin your day. 4 The Attempt to Make Cuddlier Hamsters There's science, and then there's mad science. In 2022, scientists used CRISPR tech to totally remove a type of receptor from the brains of hamsters. These receptors are called Avpr1as, and they respond to a chemical called arginine-vasopressin, which makes males aggressive. By removing the receptors, the scientists figured we’d render the males passive and cuddly. Spoiler: it had the opposite effect. And this is why science fiction should be required reading/viewing for scientists. In this case, specifically, Serenity, from 2005. 3 The German Census of Jewish Shirkers Today's equivalent might be "the fundamentalist Christian census of drag queen pedophiles." So, the government had expected to find evidence of Jewish soldiers shirking duty, but they found the opposite. Bet they didn't like that. Instead, the census really did debunk those theories, the way the government claimed they wanted but really did not. So, authorities responded by refusing to release the results. No, they did not like that at all. Apparently, the other option (flat-out lying about it) didn't occur to them, so... point for prewar Germany? Nah. 2 Zeeman and His Math Sphere And we both just lost half our readers. Not going to quote this one; the article makes it complex enough. 1 The Flat Earthers’ $20,000 Gyroscope Investigation Speaking of dimensional spheres, if you’re seeking evidence that the world is round, you’ll manage that easily. Just watch the sunrise over the horizon, and boom, you’ve seen the curvature of the Earth. Except that flat-earthers find ways to convince themselves that this doesn't mean Earth is roughly spherical. If you’re seeking evidence that the world is flat, however, well, that’s a bit tougher. Yeah, that would require a trip to North Dakota. (People think Kansas is flat, but it's got nothing on ND.) A second experiment used more advanced technology. Host Bob Knodel brought out a $20,000 laser gyroscope, which should keep to the same vertical orientation no matter what goes on with the ground beneath it. At least they came up with an experiment. Most flat-earthers just spout their nonsense on YouTube or whatever. What I find ironic about this is that the idea that Earth is round, and the technology behind $20,000 laser gyroscopes, are both products of science. How a person can accept one without the other is questionable. This, of course, reminded me of "Mad" Mike Hughes, a flat-earther who built a fucking rocket to "prove" his hypothesis. Spoiler: He died in the process. I've written about him before, mostly here: "Bad Advice" Troublesome data must be rejected. When experiments challenge your world view, you must switch to a different experiment you can trust. Well, no. But that's certainly how some people get through life. |