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Tuesday, Apr. 30, 2024

2:14pm 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:

GeminiGem of House Lannister

a day ago
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

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

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
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

September 17, 2021 at 12:02am

#1017585

...iiiiiiiin Spaaaaaace!

Another one from Cracked today. The Random Number Generator moves in mysterious ways, its wonders to behold.

5 Harsh Reminders That Living In Space Will Be Absolutely Terrible

I've been a science fiction fan for as long as I can remember. This doesn't mean I like all of it. I can even put up with playing fast and loose with science for the sake of plot. But when I started watching The Expanse, I almost stopped at the first episode (which would have been a mistake, as it turned out, because the story is very good.)

What was it that almost stopped me?

Sex.

No, I'm not a prude. Nor is there any truth to the rumor that nerds never get laid. It's just that one of the opening scenes features zero-gravity sex (I don't consider it a spoiler if it's at the damn beginning). I have heard a lot of people, SF authors included, gush effervescently at the thought of being able to bone in free fall.

Now, if any astronauts have gotten it on in orbit -- and I can't believe they haven't -- they've kept mum about it so far. So I don't have any actual data or even anecdotes about the practice. But if you've ever had sex, and also possess the ability to think critically about it while thinking about it (admittedly, a quality sadly lacking in humans in general), a moment's thought would make the entire idea of how great it must be flare and burn up in re-entry.

Basically, unless there's a custom-made harness (which, given that space travel is now opening up to the wealthy portion of the general public, I really should design), sex in microgravity would be a -- I can't help this pun; sue me -- real pain in the ass. All it takes to understand this is a basic comprehension of Newton's Laws of Motion. I won't go into detail because I like keeping this blog 18+, but it simply won't work the way you think it'll work.

So when that scene was up there setting the tone for the rest of the series, I almost switched to something more realistic, like Stargate or Lost in Space. Because I'll believe instant travel to distant planets, and sentient robots, before I'll believe that ZG sex without physical aid is even possible, let alone satisfying.

Anyway, the point of all this rant is not to get you thinking about sex (which I know you are anyway), but to segué into other things that will suck about space, and for that, there's Cracked.

5. To Put It Plainly, The Radiation In Space Will Mess You Up

Space looks empty and serene, but it's a chaotic hellscape of radiation. In addition to cancer-causing solar ejaculations, astronauts are bombarded by cosmic rays, produced by the cataclysmic deaths of stars that dwarf the Sun -- stars so big and mean they play keep-away with the Sun's Ninja Turtles lunch pail. When they explode, they launch protons and nuclei from heavy elements, like iron, at nearly the speed of light. These microscopic cannonballs obliterate any atom in their way, which spells bad news for astronauts, who are made of atoms.

Incidentally, I'm not fact-checking all of this. What's written there that's also in my prior knowledge base, though, is entirely factual, if phrased for humorous effect.

So you might be thinking, "But what about all the people on the ISS? They're not in the atmosphere; wouldn't they be affected by this?" Well, they've still got most of the magnetic field protecting them. The astronauts that went to the Moon were outside its protection for days or weeks at most, so their dosage wasn't all that bad. But a trip to Mars, for example, will take nine months with current technology.

And while they're actually on Mars, the article points out:

Researchers calculated that an 8-inch-thick layer of fungus could negate an entire annual radiation dose on Mars, which is 66-times greater than on Earth, where we're protected by an atmosphere and magnetic field.

Alternatively, just go underground.

4. Space Life Constantly Introduces New Medical Problems

A study used ultrasound to track astronauts' circulation as it passed through the left jugular vein in the neck, which collects blood from the brain. Six of the eleven astronauts displayed stagnant blood flow, which sloshed back and forth, or reverse blood flow, which traveled (the wrong way) up toward the brain faster than those "return this nickel to feed a child" letters travel to the trash.

All of our systems are "designed" (that is, they evolved) to work in approximately one G. We're clever, and we can usually find workarounds, but when a whole lot of systems - skeletal, circulatory, muscular, etc. - start failing all at once, you get chaos. Not the mystical version, but the physical one, where tipping one thing a tiny bit could have massive repercussions.

The gravity on Mars is about 0.4G, and as far as I know, we don't know if that's enough to mitigate some of this. But they're talking about putting a colony on the Moon now, which sounds awesome, but the gravity there is about 0.17G. I'm sure the guinea pigsbrave pioneers who first join that colony will provide reams of scientific data about surviving (or not) in a low-G environment.

3. Spacefarers May Be Eating Subpar Urine Tomatoes

Pretty sure that's what they sell at the local Food Lion anyway.

Popular science-fiction gets one thing (partially) correct: colonists on the Moon and Mars will have to grow their food. Not in expansive Martian greenhouses or lush hydroponic gardens, but in tanks are full of piss that could provide an essential food source to sustain cosmic exploration. Unlike astronauts aboard the ISS, colonists can't rely on terrestrial supply lines. So the German space agency, DLR, hopes to solve two problems at once by turning urine into fertilizer.

All of this sounds gross, I know, but just remember: everything you drink or eat contains molecules that were once in somebody's excretions. Nature recycles all that. All we're doing is streamlining the process. Chances are, it won't be as good as an ecosystem, but pretty soon we won't have one of those anyway, so, so what?

2. Colonists Will Be Weak-Boned And Kidney-Stoned

According to mainstream science fiction, colonists will need to be hard and hearty for all sorts of strenuous space activities, be it farming, building shelters, or engaging in high-speed, low-gravity rover chases. But when space colonists arrive on other worlds, their bones may be too brittle to outrun and outgun space pirates and Martian sandworms. That's because the stresses of gravity are essential for maintaining bone strength.

This goes back to what I said before: we evolved on a one-G world.

1. Space Colonists' Living Accommodations Will Be Less Than Luxurious

Life on other planets is going to be sah-weet! We'll live in giant domed cities with tree-lined pavilions, drive flying cars, and attend soda fountain socials like back in the '50s! Or that's what we've been promised.

Yeah, maybe, eventually. But for now, I'm content to read about other people drinking their own piss, tunneling underground, and not having satisfying sex in space.

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