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Sunday, Apr. 28, 2024

12:51pm EDT

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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:

🌕 HuntersMoon

about 2 hours ago
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

a day ago
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

November 30, 2021 at 12:03am

#1022544

Try to November Me

And so it ends.

PROMPT November 30^th

Wow, it's the end of the month! With Thanksgiving behind us (here in the States), and Christmas on the horizon, what, if any, are your Christmas traditions? If you have no holiday traditions, do you have any plans for this month?

As we careen into December, I think it's of the utmost importance to remember the real reason for the season:

Axial tilt.

As the Earth orbits the Sun, the axis stays pointing in the same direction (roughly toward Polaris) (or away from it, depending on your perspective), which changes the apparent path of the Sun across the sky. In summer (assuming a location outside the Tropics), the Sun climbs higher, baking us with more direct rays for a longer stretch of time, while in winter, that bastard can barely get out of bed, and things cool down.

And I'm still not sure which is worse: burning under the pitiless gaze of the accursed daystar, or freezing from its absence.

Okay, I'm going to go with "freezing is worse" because I'd rather be too hot than too cold.

In any case, axial tilt is the reason for the season, and, relative to the Sun, it'll be at its most tilted in about three weeks: The solstice this year (winter for me, summer for the folks hanging upside-down) will occur on December 21 at 10:59 am EST. Why it couldn't wait another minute for a nice, even 11:00 is beyond me. And now I'm tired of coddling the Down Under, so everything else here is going to be presented from an unashamed Northern Hemisphere perspective.

I always celebrate that moment, because it marks the point when days begin to gradually get longer, when the light begins to conquer the dark. Not that there's anything wrong with dark, per se; it's just that, as I noted, less sunlight means lower temperatures, and fuck lower temperatures.

Unfortunately, as weather tends to lag astronomy, the winter solstice isn't usually the coldest day. Obviously that's going to vary from year to year, but on average, around here, that doesn't occur until close to the end of January. Still, I'll take my victories where I can, which in this case means appreciating the solstice.

And then, once I'm done appreciating the solstice, I remember that the next two months are going to be utter hell. The only month I hate worse than January is February. But at least for one moment, I can believe that, as they put it on an episode of Doctor Who, we're halfway out of the dark.

As for other things in December, well, that remains to be seen. Literally. This is the month when I'm supposed to get my eyes worked on. I dread the operation, so I try to focus (pun intended) on the expected result instead. That's hard for me. I've never been one to endure temporary hardship for longer-term benefit. They do one eye, and then a week later, the other eye. Supposedly it has a solid success rate. I'm still absolutely not looking forward (pun also intended) to having them screw around with my eyeballs.

Other things? In the Before Time, I used to go to California every year in December. Travel's a bitch now, though, because a lot of people are infected with weapons-grade ignorance. Perhaps I'll be able to do that again one day, but this year is not that day.

Rather than inflict my presence on those who don't want me around (which as far as I can tell is everybody), a couple of years ago, I began a new tradition for myself on Christmas Day, a day which otherwise holds little significance for me: I walk over to the drafthouse cinema, get drunk, and watch a movie before staggering home. This year, I don't know if I'll be able to do that or not; my second surgery is scheduled for the 23rd. Probably I'll be able to. Unless they botch it, in which case my movie-watching days are over. Hey, it's important to expect the worst, so I can only be pleasantly surprised.

For anyone else who's made it this far through 30DBC, thanks for reading. But I'm on a roll and I don't expect to stop blogging, so tune in next month for a whole lot more of the usual -- and maybe some things unusual.

6 Like • Comment • View 7 comments

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