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 |    Not for the faint of art. |
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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. ![Merit Badge in Quill Award
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I've written about the Trolley Problem before. At length. I even wrote a very short story featuring it: "The Trolley Problem"  [18+]. This is very likely to be the last time I feature an article about it; this blog is steadily approaching its end.The article itself is a few years old, but I'm not aware of any progress in Trolleyproblemology since it came out in 2018. It's also from Slate, so no surprise they got it wrong. Does the Trolley Problem Have a Problem? What if your answer to an absurd hypothetical question had no bearing on how you behaved in real life? It was never meant to have bearing on how you behaved in real life. Consider this article from Philosophy Now (limited free articles), which concludes: The answer, in my view, is that there is no definitive solution. Like most philosophical problems, the Trolley Problem is not designed to have a solution. It is, rather, intended to provoke thought, and create an intellectual discourse in which the difficulty of resolving moral dilemmas is appreciated, and our limitations as moral agents are recognized... I do not believe there will ever be a perfect solution to the Trolley Problem, nor a consensus as to the best possible solution. All we can hope for – and should hope for, as I have argued – is to utilize the tools of philosophy as well as the scientific method to continue this discourse. The Trolley Problem does not have to be resolved; it merely needs to be contemplated, and to be the topic of our conversations from time to time. That is, of course, the opinion of one philosopher, but it rings true to me. Philosophers, however, aren't known for having a sense of humor. They're all Very Serious Thinkers. We have a different name for philosophers with senses of humor: we call them "comedians." And comedians have been having a field day with various permutations of the Trolley Problem, many of which are legitimately hilarious. Which is, as the Very Serious Philosopher notes, the point—even if he'd be appalled at the humor elements. So, back to the Slate article: I ask because the trolley-problem thought experiment described above—and its standard culminating question, Would it be morally permissible for you to hit the switch?—has in recent years become a mainstay of research in a subfield of psychology. And there's the "problem," right there: It's not psychology. It's philosophy. In November 2016, though, Dries Bostyn, a graduate student in social psychology at the University of Ghent, ran what may have been the first-ever real-life version of a trolley-problem study in the lab. In place of railroad tracks and human victims, he used an electroschock machine and a colony of mice—and the question was no longer hypothetical: Would students press a button to zap a living, breathing mouse, so as to spare five other living, breathing mice from feeling pain? Right, because our moral calculus involving mice is obviously exactly the same as it would be with fellow humans. I'm not saying people don't feel sorry for mice. I always feel sorry for the ones that Edgar Allan Purr leaves on the doorstep. But I'd be horrified if he brought us a dead human for a present, instead. Not that he could, but, you know, as long as we're talking hypothetically. It’s a discomfiting result, and one that seems—at least at first—to throw a boulder into the path of this research. Scientists have been using a set of cheap-and-easy mental probes (Would you hit the railroad switch?) to capture moral judgment. But if the answers to those questions don’t connect to real behavior, then where, exactly, have these trolley problems taken us? I suppose the answer to that depends on whether you ask a philosopher, a psychologist, a lawyer, or a comedian. It also seemed a little off that trolley problems were often posed in funny, entertaining ways, while real-life moral dilemmas are unfunny as a rule. Except that it's the comedian's job to make things funny when they're not. There's a lot more at the link, of course, but I've banged on long enough. In short, I disagree with the basic premise that it's a psychology issue instead of a philosophy one. Still, as I've noted in here before, it's not completely hypothetical: there are real-life situations where exercising agency can make a difference, one way or the other. So it's worth thinking about. And it's worth making jokes about, because comedians can often do philosophy better than philosophers. |
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