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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.
April 30, 2021 at 12:02am April 30, 2021 at 12:02am
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Well, this will probably be the last random article for a while; let's see what we end up with.
Oh joy, panpsychism again.
Well... sort of.
Years before smart homes became a thing, I replaced all the switches in our house with computerized switches. At first, it was just a way to add wall switches without pulling new wire. Over time, I got more ambitious. The system runs a timer routine when it detects no one is home, turns on the basement light when you open the door, and lights up rooms in succession on well-worn paths such as bedroom to kitchen. Other members of the family are less enthusiastic. A light might fail to turn on or might go out for lack of motion, or maybe for lack of any discernible reason. The house seems to have a mind of its own.
I can see the appeal, but the tech just isn't quite up to Star Trek standards yet.
Also, to me, "seems to have a mind of its own" translates to "does stuff at random times because of power fluctuations, cosmic ray events, or loose wires." Never ascribe to consciousness what can better be explained by glitches -- unless, of course, you can get laughs by doing so.
Modern hardware and software have gotten so complicated that they resemble the organic: messy, unpredictable, inscrutable.
On a superficial level, maybe. I'd prefer to say that it's gotten so complicated that there's exponentially more opportunities for things to simply go wrong.
Gradually, we are turning an old philosophical doctrine into a reality. We are creating a panpsychic world.
Sigh. No, we're not.
All the computers with which we surround ourselves are starting to be endowed with a rudimentary sentience.
On the other hand, there might be something to that, after all. The easiest way to shop for something online, these days, is to talk about it near my phone. Within an hour I'll have fifty different ads for the product. Like, I'll say something like, "I'm going to bed now," and I wake up and there's ads for Sealy clogging my screen.
Which is not to say I have a problem with targeted ads in general. I'd rather get ads for beer, movies, and cat food (all relevant to me) than for hemorrhoid cream, tampons, or dog biscuits (all utterly useless to me).
We are placing minds everywhere and instilling seemingly inanimate objects with mental experience.
Are we, though? I'm sure several philosophers would disagree that these devices necessarily have "mental experience."
By dispersing intelligent artifacts, humanity is awakening the material world.
Oh, sure, and because of that, my grass curses my ancestors every time I have it mowed.
Proponents make three main arguments. The first is that there doesn’t seem to be any principled way to draw the line between conscious and non-conscious. If we are conscious, why not a dog? A paramecium? A protein molecule? A proton? These systems lie on a continuum with no obvious break.
Just because there's no obvious break doesn't mean there isn't a line there. Just because we haven't figured out where it is doesn't mean it doesn't exist.
Second, panpsychism would solve the hard problem of consciousness.
And love can be reduced to chemical reactions in the mind. So?
Third, several of today’s leading theories of consciousness imply panpsychism.
Before Einstein, leading theories of cosmology implied that the Universe was contained within a few thousand light-years, and said nothing about being unable to accelerate past the speed of light.
When debating panpsychism, the question is not whether, but when. Either the world already is panpsychic or it will be.
As usual, binary ideas like this are misleading. Even if we end up building gadgets that could be called "conscious," they're not going to imbue the rock I stubbed my toe on yesterday with consciousness. I kinda wish they would, because then the rock might appreciate the words I had for it.
The books paint a fascinating picture of a fully sentient world. People can telepathically communicate not just with friends and family, but with atoms, burbling brooks, and the planet as a whole. If your friends come over for dinner, the group forms a temporary collective mind that you can commune with. Every act becomes a negotiation: You had better apologize to the brook for urinating on its bank and talk nice to your hand tools. Say the right words to the right atoms and you can heal wounds or fly like Superman. On the downside, villains can brainwash atoms, unraveling the fabric of reality.
And you get to hear the screams of everything you eat. Yes, even the plants. Especially the plants. That's more horror than science fiction.
So anyway, despite my snark, the article's a good read; I don't have to agree with something to appreciate the arguments. |
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