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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

tracker

a day ago
In response to "Revisited: "Housekeeping""

Lol @ 🌕 HuntersMoon My computer files need a thorough house cleaning. My email here too is over half full. I will take the hint and work on cleaning things up. Thanks for the entry.

1 Like

🌕 HuntersMoon

a day ago
In response to "Revisited: "Housekeeping""

Seems like a plan... at the time

Here are some blogging suggestions from Stupid Science:

If we lose net neutrality, will the net become acidic or basic?

If global warming was real, wouldn't the ice wall melt and let the oceans out of the flat earth? So then why is the sea level rising?

Why do meteorites always land in craters?

My pizza says to bake for 18-21 minutes, how do I bake something for -3 minutes?

1 Like

Elisa the Bunny Stik

Jun 8, 2024 at 9:51am
In response to "Terminator"

Interestingly, I've seen the phrase thought-stopping cliché before but not thought terminating cliché. I wonder how that difference came about. Maybe I could ask Laurence, who did cover the titbit/tidbit difference in a video (and explains it's rooted in linguistics and not social factors).

In his book Thought Reform and the Psychology of Totalism, Lifton wrote that these semantic stop signs compress “the most far-reaching and complex of human problems … into brief, highly selective, definitive-sounding phrases, easily memorized and easily expressed. They become the start and finish of any ideological analysis.”

That's a whole lot of words to express what I call "bumper-sticker philosophy," which I suppose is my own thought-terminating cliché.

I now want to make a bumper sticker that asks "Is bumper-sticker philosophy a good thing?" Alternately, it could say "Is your bumper-sticker philosophy a good thing?" The latter might increase your chances of getting shot, but hey. Some people might think it's worth the risk.

And a 2021 study showed that humour is among the qualities that make information more memorable and shareable.

I'd be real curious to see if this person can find a humo(u)rous twist on the violence of late May 2020. There's a lot of disinformation surrounding that, and the truth around it needs to be shared (such as the vast majority of people who engaged in vandalism and arson in Minneapolis were from out of town, and at least a quarter of that crowd came from out of state). I'm not sure humor can really be applied in this situation, though.

“Remember, it’s OK to repeat true information,” says Fazio.

If the comments on Snopes postings are any indication, this is actually starting to annoy people. Snopes has been engaged in this high repetition strategy for a little over a year, and there are notable amounts of complaining about it.

3 Like

🌕 HuntersMoon

Jun 5, 2024 at 11:47am
In response to "Putting the Mental in Experimental"

Wallet? What wallet? Must have fallen off the edge of the earth...

1 Like

Aiva Raine

Jun 4, 2024 at 4:38pm
In response to "Drakes and Pains"

Love your analysis. I highly doubt that in this unfathomably large universe, that humans are the only intelligent and tech-capable species. To assume we are seems the height of human arrogance. But, seeing the mess we continue to make here, if any civilization did somehow make it to level 1 on the Kardashev scale, the chances of them making it to level 2 or 3 is infinitesimally smaller and while we might be of interest to them - they'd be smart enough not to let us figure out they were around.

Personally, I suspect most civilizations implode shortly after they reach nuclear or AI age. That along with the whole "random meteor/comet/supernova/disaster space event" chance to kill the entire planet as a secondary manner of intelligent life control.

If some level 2-3 civ did manage to survive- they'd have their hands full trying to preserve w/o detection any planets like ours from disaster. Provided they actually felt we and others like us deserved to live. I'm on the fence as to whether a species deserves to survive if it's so damned determined to kill itself and the planet off.

1 Like

Lazy Writer est 4/24/2008

Jun 4, 2024 at 1:16pm
In response to "Drakes and Pains"

Their out there,,,in space...waiting patiently...for us to discover them.

Kåre Enga in Montana

Jun 3, 2024 at 8:48pm
In response to "One for Sorrow, Two for Joy..."

The video reminded me how acceptable (or not) adult tantrums are in our society.

As a child I counted 1. 2. 4. Never did like 3.

🌕 HuntersMoon

Jun 3, 2024 at 10:10am
In response to "One for Sorrow, Two for Joy..."

Interesting. No caw-caw here...

1 Like

Elisa the Bunny Stik

Jun 2, 2024 at 11:43am
In response to "Revisited: "Nonbinary""

"We desperately need "accept yourself as you are" messages, but there's no money in that"

Tell that to Psychology Instagram influncer types. They'll be willing to sell services that help you accept you as you are.

Elisa the Bunny Stik

May 29, 2024 at 9:02am
In response to "Ordinary Average Guy"

I think we need to be careful about saying there's no difference in socializing between online and off. I saw the following in response to a comment about discussions of gender online and the stances taken by LGBTQ community members that are chronically online:

"Truth. I had to stop looking for queer spaces online because it was full of this and angry exclusion discourse. I found some queer spaces offline and it reminded me that most people are normal and chill."

This is a topic I will likely be visiting in my journal in July. I figured I'd at least get this response in here first as a warm-up.

1 Like

September 18, 2018 at 1:16am

#941606

The Right Thing

I've been thinking about this story (warning: godsdamned autoplay video):

https://www.cbsnews.com/news/santa-barbara-california-teen-rhami-zeini-finds-pur...

A Santa Barbara, California, high school junior was driving home from school Wednesday when he noticed a black purse in the middle of the street. He rescued the purse from the roadway and was shocked by what he found inside: $10,000.

Okay, cool. Good on the guy. Did the right thing, etc. Also lucky the cops were honest. Could have easily been like "Ma'am, we found your purse. Oh, the money? We didn't see any money. Someone must have lifted it. What's that? Where'd we get the shiny new rims on the police cruisers? Um, DUI fines. Nothing to worry about."

Now, I'd like to think most of us would have done something similar. I don't know what the legal thing to do is; based on the founding legal principle of "finders keepers, losers weepers," it may very well be legal to keep the wad. But what's legal isn't always right and vice versa.

Still, it got me thinking about thresholds. Let's say for the sake of argument that you're the type who would return the money. Pretty easy in this case, given that it was in a purse, and purses tend to also hold IDs. By the Ethical Principle of Least Resistance, you can feel good about your choice with very little effort. Okay.

Now, very likely you've found a penny on the street (assuming you're in a country like the US that still uses pennies). Most of us don't even expend the minor effort it would take to bend over and pick the thing up. Besides, it's probably covered in germs, right? The penny stays. (For the record, I pick up pennies. And shut up about the "heads good luck tails bad luck" or vice-versa or whatever; that's nonsense. Money is always good luck.)

But what if it's a nickel, a dime, a quarter? A dollar? A $20 bill? At what point do you stop saying "hey look, free money" and start looking for the owner? Hell, what are the chances you'd actually find the original owner? That's where ID comes in. What if it's a tiny wad of $1 bills clipped to an ID? Then do you return it? (I would - that might indicate it's a stripper.) At some point between "stack of 100 $100's with ID attached" and "stray penny," we say "fuck it," and the founding legal principle of "finders keepers, losers weepers" takes precedence.

Looking at it from the loser's perspective (something I'm eminently qualified to do), if I lost $10k, I'd be upset, but I wouldn't expect its return. It'd be nice, sure, but I'd consider it's on me for dropping $10K on the street. Not that I'd ever expect to be in a position to do so, but I have, in fact, held that much cash in my hand before. Briefly. It's not as bulky as you'd think. Thinner than most paperbacks. Even thinner than my NaNoWriMo manuscripts, and worth a hell of a lot more.

It's not a simple algorithm, either, not for an individual. Suppose you're in dire straits, just lost a job, buried in debt. Would you still do "the right thing?" About to be evicted or foreclosed upon? In which case "the right thing" starts to get a little murkier. What if you're simply in a bad mood, or - well, if I found that kind of cash lying around and the accompanying ID said "Richard Spencer," I'd probably keep it - though I expect I'd donate it to something left-wing just to piss off that Nazi ass. Except he'd never know about it, which might mute my satisfaction a bit.

Anyway, just got me thinking about it. It's a hypothetical, like the trolley problem - not something you'd expect to encounter in day-to-day life. I will, however, continue to pick up pennies off the street. By the time I die, that'll make my estate about $1.23 richer.

4 Like • Comment • View 5 comments

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