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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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| This article is a couple of years old, and I'm sure some additional science has been done since then, but since it presses one of my hot buttons, well, here it is. Does Quantum Mechanics Reveal That Life Is But a Dream?  A radical quantum hypothesis casts doubt on objective reality Every time I see a headline in the form of a yes/no question, I take the default position that the answer is "no." It's not impossible for the actual article (or other evidence) to convince me otherwise, but that's where I start. Further, note the word "hypothesis." The translation of this word for non-scientists is something like "guess." There may be some good reasons to make the guess, but, as I understand things, it hasn't been subjected to rigorous testing, and therefore hasn't really been supported by evidence. My girlfriend, “Emily,” often tells me her dreams, and I, less often, tell her mine, which are usually too murky and disjointed to share. I guess that dynamic works for them. Rare is the occasion when someone's recounting of their dream is actually interesting to the listener(s). Interpreting dreams is an imperfect, highly subjective art, as Sigmund Freud, in his rare moments of humility, would surely have granted. That's a polite way of saying that dream interpretation is bullshit. And yet making sense of dreams, it occurs to me lately, is not wholly dissimilar from making sense of “reality,” whatever that is. Yes, we all live in the same world. We can compare notes on what is happening, and draw inferences, in a way impossible with dreams. If one assumes that solipsism is false, at any rate. And yet your experience of the world is unique to you. So is your interpretation of it, which depends on your prior beliefs, yearnings and aversions, and on what matters to you. This is hardly news. I'm pretty sure there were primitive humans arguing over what to hunt for dinner. Science offers our best hope for achieving consensus about what happens. On that point, at least, I can't disagree. But "best hope" doesn't imply certainty. Scientists accumulate bits of evidence and try to assemble these fragments into a coherent story. After much haggling and second-guessing, scientists converge on a plausible narrative. Remember a few days ago when I wrote about how stories are important and we shouldn't dismiss them as "just a story?" Yeah. But subjectivity is hard to expunge even in physics, the foundation on which science rests. Quantum mechanics, a mathematical model of matter at very small scales, is science’s most rigorously tested theory. Countless experiments have confirmed it, as do computer chips, lasers and other technologies that exploit quantum effects. I agree that physics is the foundational science. Psychology, for example, derives in part from biology, which is really just complicated chemistry, and, in turn, chemistry is, at its core, physics. Also, I have no reason to doubt that QM "is science's most rigorously tested theory." I've seen that assertion in multiple, disconnected places. Unfortunately, quantum mechanics defies common sense. Well, yeah. That's one reason I disparage the idea of "common sense." Saying that QM "defies common sense" is an indictment of the concept of common sense, not science. For more than a century, physicists have tried to interpret the theory, to turn it into a coherent story, in vain. “Every competent physicist can ‘do’ quantum mechanics,” a leading textbook says, “but the stories we tell ourselves about what we are doing are as various as the tales of Scheherazade, and almost as implausible.” I think this is due, in part, to our limited macroscopic experience. A story requires some shared experience; at the very least, the reader must have at least one language in common with the writer for the reader to comprehend the story. And our language, which includes concepts like "something is either a wave or a particle, never both," is incompatible with the language of quantum mechanics. Many physicists ignore the puzzles posed by quantum mechanics. I wouldn't go that far. It's more like they have to decide whether the puzzle is relevant to the outcome. A newish interpretation of quantum mechanics called QBism (pronounced “Cubism,” like the art movement) makes subjective experience the bedrock of knowledge and reality itself. David Mermin, a prominent theorist, says QBism can dispel the “confusion at the foundations of quantum mechanics.” You just have to accept that all knowledge begins with “individual personal experience.” I can accept that assertion. What I don't accept, at least right now, is that it also ends there. But QBism’s core message, science writer Amanda Gefter says, is that the idea of “a single objective reality is an illusion.” A dream, you might say. And here's where I start having Issues. I talked about the importance of stories. But what is a story? It can be passed verbally, but these days, it's transmitted through writing on a screen or in a book. We can each read a book and come away with different impressions of it, like, say, how I think James Joyce wrote dreck while other people worship the guy's stuff and even do entire college courses on it. This difference of opinion and viewpoint doesn't change the objective reality that Joyce wrote books. If you want to get really technical about it, a book is a collection of (usually) formerly-living organic matter, bound with more formerly-living organic matter and containing marks made by matter that reflects light differently. Go another level in, and it's an object made of mostly hydrocarbon chain molecules. Another level beyond that, and it's electrons and quarks and whatnot: all energy of some kind. That may be the base "reality," but it doesn't make our ability to read the book and draw conclusions from it some sort of illusion. It's just a different level of reality. Similarly, our different and varied worldviews aren't evidence of illusion. Proponents bicker over definitions, and physicists and philosophers fond of objectivity reject QBism entirely. All this squabbling, ironically, seems to confirm QBism’s premise that there is no absolute objectivity; there are only subjective, first-person viewpoints. Maybe it's irony that people are arguing over whether disagreement indicates that all this shit around us is an illusion. I don't know. I'm still a little hazy on the concept of irony, despite doing a whole entry about it a while back. Some artists thwart our desire for meaning. T. S. Eliot’s poem The Waste Land is an anti-narrative, a grab bag of images that pop in and out of the void. The poem resembles a dream, or nightmare. Its meaning is that there is no meaning, no master narrative. Some people might find an inherent contradiction in my disdain for Joyce and my appreciation of Eliot. I can only quote Walt Whitman, a poet I'm not generally fond of: I am large; I contain multitudes. If you are a practical person, like one of the finance majors in my freshman humanities class, you might conclude, along with T. S. Eliot, that efforts to comprehend existence are futile. You might urge friends majoring in philosophy to enjoy life rather than fretting over its meaning. I do consider myself a practical person, mostly. But the idea "enjoy life rather than fretting over its meaning" is itself a philosophy. I'd go so far as to say that I consider our different and varied viewpoints to be evidence of reality, not of illusion. If everyone agreed on every detail, then I'd be suspicious that I was living in some holodeck simulation. In the end, the article fails to convince me that "life is but a dream." It may be different things to different people, but we're here, alive at least for now, to argue about it. And unless you're a solipsist, well, there's the foundation of our shared reality. |
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