Complex Numbers (Book)

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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.

http://www.ddewey.net/mandelbrot/

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June 7, 2022 at 12:22am

#1033462

Let's Freeze More Peaches

Here's a thing that I can only vaguely relate to, but it seemed interesting enough from a philosophical point of view.

Elon Musk's Perspective on Free Speech is Likely Different to Your Own, Which is Important to Note

The purpose of my linking this is not to spark a fruitless discussion about the billionaire. I've largely stayed out of that fray and will continue to do so. No, I wanted to highlight what "free speech" means. The background, for anyone who's been hiding under a rock, is that there's been talk about Musk taking over Twatter; I don't know the current state of that process because I don't follow it that closely.

If anyone's interested, my earlier comments on free speech, from way back in January, are here: "Freeze Peach"

And something else I found from the truly ancient days of 2010: "On a serious note..."

And stretching even further back into the murky past: "Quick civics lesson"

So what is Elon Musk’s definition of free speech, exactly, and how does that relate to what you can and can’t say in your tweets?

"Given that Twitter serves as the de facto public town square, failing to adhere to free speech principles fundamentally undermines democracy." -Musk

First of all, here's my perspective, for whatever it's worth.

Before DikDok, Twatter, Bookface, etc., even before WDC, there was IRC and newsgroups.

The internet wasn't as populated back then, and a lot of people accessed it through the filter of AOL. In many ways, this was superior, as in order to connect with people then, everyone had to have some minimum level of understanding of how shit worked. Kind of like how there's a filter here keeping out casuals who can't or won't learn simple formatting tools.

Superior, yes, but by no means utopia. Newsgroups were largely unmoderated, and they mostly trusted people to keep discussions on the topics listed (and boy, were there a lot of topics, some of which were definitely in XGC territory). This lack of moderation meant that, over time, most newsgroups got choked by spam ads and porn. I'm not knocking porn, but there were specific newsgroups for the various categories of porn; I mean that adult material got into things like alt.rec.teletubbies or whatever. The result was a low signal to noise ratio, creating a positive feedback loop as ordinary people left newsgroups alone. I think the last time I checked on them, 20 years ago or so, it was nothing but spam. I have no idea of newsgroups are still around in any way, and I'm not going to bother to check.

IRC (Internet Relay Chat) was also a kind of Wild-West thing. Anyone with moderate knowledge could create a channel. Whether anyone came to the channel or not was another story, but most channels were, as a result, moderated. Channels, incidentally, were prepended with the pound sign #. Yes, that is a pound sign, or perhaps a number sign. It is not, and never will be, a hashtag in my universe.

All of which is to say that it's clear to me that absolute, unfettered free speech may sound like a good idea in theory, but in practice, you end up with nothing but spam, porn and porn spam as people seeking meaningful content abandon ship.

And yet I believe that if that's what people are looking for, there should be access to it. Just labeled correctly, kind of like genres and Content Ratings here on WDC.

Speaking of, one thing that attracted me to this site in the first place is that we do have freedom of speech here. Yes, we require things to be rated appropriately, but as I said, that's a bare minimum so that people have some idea what they're in for. Still, I've seen people write about things I find completely appalling, and that's okay because I can choose whether to read it or not. I've written stuff that other people find completely appalling. And yet, things like advertising are restricted, and images are another subject altogether.

Point is, no practical interpretation of freedom of speech guarantees a speaker (or writer) the right to an audience.

I chose to abandon Failbook, and I never did get a Twister account. The first I heard of Twutter was a friend of my then-wife told me that some engineer she worked with had rigged his office chair to tweet every time he farted, and I decided right then and there that I wanted nothing to do with the platform. Nothing I've seen since then has convinced me that the level of bumper-sticker discourse on the site has been raised since then, and when I see a transcript of multiple tweets because the story's too long for whatever character limit, I get enraged. Just write a damn blog and link to it already.

Discussing shit on Twitter is like arguing with bumper stickers.

I am aware of the irony of me distilling my idea to a less-than-140-character bumper sticker slogan, there.

I'm not quoting any more from the article, as I wanted this to be more about my own thoughts on the subject matter. Go read it if you care. Don't if you don't. No one's forcing you either way.

And isn't that really the point?

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