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Sunday, Apr. 28, 2024

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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 20, 2021 at 12:01am

#1021994

People Eating Tasty Animals

Don't we have enough crazy conspiracy "theories" in the world already?

PROMPT November 20^th

In your blog tonight/today, write about a story you've been told, or use a newscast story and CREATE a conspiracy theory. Tell us why you chose this subject, and of course, provide 'evidence' that your theory could be rooted in truth.

Earth is flat, the moon landing never happened, JFK was assassinated so Johnson could take office, 9/11 was an inside job, the Holocaust never happened, aliens built the pyramids, and Santa Claus isn't real.

While planning for the 2017 solar eclipse trip, I noticed that the path of totality crossed Yellowstone, so I got an idea. Other people start crazy just-barely-plausible rumors that get repeated as fact (such as the one where you can only balance an egg on its small end on the equinoxes -- sorry if you bought that one, but it's utter tripe), why not start one of my own?

So I started putting out there that during the eclipse, the combined gravity of the sun and moon would be just enough to trigger the Yellowstone Supervolcano. I felt dirty doing it, though. It's complete nonsense couched in semi-plausible astronomical language. True, an eclipse can only happen during a conjunction, and during conjunctions (eclipse or not) ocean tides are measurably higher. But there's no way it could be strong enough to trigger a supervolcano, at least not particularly during an eclipse. The gravitational effect isn't significantly different than during any new moon (or full moon for that matter).

Unfortunately (actually, fortunately), I don't have nearly enough influence online for that to catch on, and it didn't "go viral."

But... that's not really a conspiracy theory; that's just more spreading bullshit, and I've since sworn off that particular method of trolling.

So. This is one I've been knocking around in my head for a while:

Consider PETA.

Buncha loonies, trying to move the center by being so extreme that "middle ground" gives more rights to animals. But what if, at the top, they're not actually animal rights activists, but instead have a more honest motive?

Like money.

See, everything about PETA starts to make perfect sense if you accept that it's being directed by business interests -- specifically, companies such as soybean growers and fake fur manufacturers. If they can push veganism more into the mainstream, we'll need more soybeans, right? For tofu and other disgusting concoctions. And the fake fur thing is obvious; I mean, hardly anyone wears fur anymore anyway, but they still need to grow their business, right?

I'm sure you can think of other business interests that would be aided by such a shift.

Why do I choose this subject? Well, I like animals -- some of them are delicious. And PETA is, shamefully, based here in Virginia. Also it was simply the first thing that came to mind after my failed attempt at eclipse fearmongering.

As for more evidence, well, consider that PETA operates an animal shelter with an abnormally high kill rate.

Does that sound like an organization that truly believes animals have the same rights as humans? So there must be another agenda at work. We don't eat dogs or cats (usually), so they're not competing with the tofu industry; therefore, it doesn't matter to the organization if they're alive or not.

Still, I have to admit I miss their naked protests. Those always made me hungry, and I'd have to go out and get a big thick juicy steak whenever I saw one.

Anyway, I should note that I have not one single shred of evidence that business interests are behind their craziness. But it wouldn't surprise me in the least if I turned out to be right.

7 Like • Comment • View 5 comments

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