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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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Sometimes in here I talk about science. Sometimes I talk about philosophy. Other times I talk about booze. Of the three, booze is the most important to me.
But here's an article about science and philosophy anyway. Well, "article" is being generous. It's more like a book promotion.
https://blogs.scientificamerican.com/cross-check/making-sense-of-quantum-mechani...
Making Sense of Quantum Mechanics
Philosopher David Albert thinks there might be a “clear and straightforward” way of thinking about quantum phenomena
Clickbait for nerds! And I bit hard on that hook.
I’ll always be grateful to David Albert. In the early 1990s, when I was struggling to write an article called “Quantum Philosophy,” Albert, a philosopher of physics who specializes in quantum mechanics, took pity on me. He served as my guide through the netherworld of quantum interpretations, elucidating the relative merits of the Copenhagen, Bohmian pilot-wave and many-worlds interpretations.
The problem with popularizations of quantum mechanics is that they too often stray into the territory of New Age nonsense -- something that this article addresses later. So here's somebody who, maybe, has a pretty good grasp on both QT and philosophy.
Horgan: ... What is philosophy’s chief contribution to humanity?
Albert: Clarity. Wonder. A certain kind of anxiety. The obvious and enormous and innumerable consequences for the history of the world that I mentioned above. I don't know.
See? Only an actual scientist is comfortable saying "I don't know." He could have led with that, of course, but "I don't know" doesn't sell books or generate ad revenue.
But I take issue with the "clarity" answer. Philosophy always muddies the water, and discussions thereof always descend into epistemology, and you start to question whether anything -- including yourself -- is real.
I say any philosophy that doesn't start with "I am real" is merely mental gymnastics. Nothing wrong with that, per se; a lot of great discoveries have come out of mental gymnastics. But no amount of wishing away the world around us will make the chair under your ass disappear. Or your ass. That takes diet and exercise.
Here’s my question: Will science ever tell us why there is something rather than nothing?
It already has, in the most basic sense. That is, if there were nothing, then we wouldn't be around to ask the question. Of course, "There is something, rather than nothing, so that we could ask the question," is admittedly unsatisfying and an affront to both philosophy and science.
Horgan: I’ll take that as a no. You’ve spent a lot of time pondering quantum mechanics. Have you figured it out yet?
Albert: Yup. Sort of. I think I understand it much better than I used to, and better than I used to imagine I ever would.
I've always been of the opinion that anyone who claims to have figured out quantum mechanics is lying, at the very least to themself.
And the interpretations of quantum mechanics that I like (although “interpretation” is really the wrong word here - since the various so-called “interpretations” on offer are really different physical theories, which often make different empirical predictions) are the ones that show, by explicit example, that an account like that can still be had - interpretations (that is) like Bohmian Mechanics, and theories of spontaneous localization. And among those I have no favorite. I think all of them are interesting, and promising, and since they make different predictions about the outcomes of certain performable experiments, it will be up to those experiments, and not to philosophers like myself, to decide which of them, if any, are actually true.
So... no. You haven't figured it out. If you had, there'd be only one theory, and you'd have a Nobel Prize. That, or superpowers from having hacked the source code of the universe. Well... I suppose if you have the latter you can always get the former.
It turns out that if you imagine that the fundamental physical space of the world is something other, and larger, and different than the three-dimensional space of our everyday experience, then everything that has always seemed uncanny about quantum mechanics suddenly becomes clear and straightforward and understandable and in some sense to have been expected.
Even I, an utter amateur at this sort of thing, can see how postulating more dimensions can explain a lot of things (the spin of an electron, e.g., or certain features of gravity) But like I said, I know next to nothing, so I leave it to the scientists to figure out exactly how many dimensions and how they relate to each other. "But if there are other dimensions, why can't we perceive them?" Same reason we can't perceive the earth as round without experiments or a change in perspective -- neither of which change the fact that the earth is, indeed, round.
Horgan: Why does quantum mechanics inspire so much New Age nonsense?
Albert: Precisely (I guess) because quantum mechanics had for so long been understood - incorrectly - to have overthrown every hope of understanding the world in an objective and literal and realistic and mechanical way.
Uncertainty is not ineffability.
Horgan: Fair point. What’s your utopia?
Albert: I see that some of your other respondents talked about someplace where they could sit around in bathing suits and have nice conversations with interesting people. I like that too.
While drinking booze. There is no utopia without booze. HA! I got a reference to booze in here.
Anyway, the link is there if you want to read it. I found it interesting but certainly not clear, straightforward, or possessing the ability to help one "make sense" out of anything. Just remember it's basically one person's opinion -- albeit the opinion of someone more knowledgeable about this sort of thing than I am. |
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