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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.
September 15, 2024 at 10:44am September 15, 2024 at 10:44am
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In rooting through the archives at random, I pulled out this entry from early 2020: "Gotta be Aliens"
The linked article, from aeon, is still available as of this post.
The entry was, apparently, one of my earlier attempts to criticize popular coverage of the sciences involved in the search for extraterrestrial life.
Today, I'm going to talk about aliens again.
I checked, and I'd had ET or ET-adjacent entries at least twice before in that month, but it certainly hadn't taken over my blog.
If these topics seem random, that's because they are, in part.
I don't choose articles at random to put into my queue. I add to it when I come across (or someone sends me) something I find interesting or might have something to quibble or laugh about. It's the order in which I draw from the queue which is random.
In this particular case, the linked article plays off the question in its headline: how would we recognise an alien if we saw one?
One of the reasons I do this retrospectives is to see if things have changed, either in the world or with my own opinion. As far as the latter goes, I don't think I've changed my mind, and I'm pretty sure I've done several other blog entries supporting my view that complex life is probably rare in the galaxy.
In the world, things change all the time. One part that didn't age well was the part about someone saying that what would convince them that aliens were out there would be a photograph.
I said:
I'm not sure that would convince me. After all, photographs can be faked, and the technology needed to fake them is widespread and always getting cheaper.
Since then, we have of course seen an explosion in what's commonly called AI, making it way easier and cheaper to fake a photograph of an alien (or anything). Because discovery of any sort of life elsewhere than on Earth would be such a Big Deal, there would need to be multiple kinds of robust evidence for such a discovery to be accepted.
The rest? Like I said, I haven't changed my opinions on the subject. |
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