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Monday, Apr. 29, 2024

3:22pm 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

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Show Recent Comments

10 Most Recent Blog Comments:

GeminiGem of House Lannister

about an hour 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

a day ago
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

a day ago
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

April 7, 2024 at 12:57am

#1067846

Revisited: "Social Greases"

I'm getting this done early (really early) because I don't know when or if I'll have a chance to get online later today. And the next couple of days' entries might be short and also at weird times, because I'll be traveling.

Today, we're going back in time again, but not very far—February of last year. I have a self-imposed one-year blackout on Revisited entries, and this one makes the cut by less than two months: "Social Greases"

In it, I discussed an article from New York (not The New Yorker). Unsurprisingly, the link

is still valid as of today. I'm not sure I can say the same for a lot of the "rules" they discuss for "living in a polite society" (I'm increasingly unconvinced that we do).

From the article:

We sparked office arguments and made messes and ended up with a guide that we hope will stand the test of at least a bit of time — until the next great exciting social upheaval.

So, a year later, what's held up and what hasn't? You might need to read the article and decide for yourself. Me, I'm just going to rehash some of my own comments.

4. When shopping with a friend, don’t cut them in the rack.

Someone needs to explain this to me. On second thought, no, don't. I never shop with friends.

I still haven't figured out what in the hell this is supposed to mean. I could have looked it up, but it's so far removed from my lifestyle that I simply haven't bothered. Not to mention I promptly forgot it until re-reading it just now.

6. Never wake up your significant other on purpose, ever.

Never wake them up accidentally, either.

You know what's worse than either of those things? Passive-aggressive waking. You're mad that they're still snoozing, so you do the dishes as loudly as you can without breaking them, or run the vacuum, or something equally obnoxious, productive, and designed to make them feel bad that their lazy ass is still in bed.

Their lazy ass is still in bed because they need the sleep. Never mess with that.

Yes, I've been on the receiving end of that.

Another thing sure to make me grumpy? Sleep-shaming. "Oh, look who decided to join the living." Not everyone's a morning person, dammit.

28. Don’t ask people how they got COVID.

29. Or why they’re wearing a mask.

No, please ask me why I'm wearing a mask. Depending on my mood, I might answer with "to mess with facial recognition," "because I get compliments on my cat mask but never on my face," or "to keep you from running away screaming."

This one probably aged less well than most of the others.

30. When casually asked how you are, say “Good!”

Valid only in English-speaking countries. And not even then; if someone asks me that, I assume they really want to know.

Corollary: Don't ask if you don't want to know the truth.

34. Actually, it’s great to talk about the weather.

No. Talking about the weather is just going to start an argument about climate change. It's now a topic more fraught than sex, politics, or religion.

I've had people try to strike up conversations with me by bringing up sports. I'm happy to talk to people, despite what I said in that entry (or others), but the only thing I need to know about sports is that they involve way too many commercials for me to even think about watching them.

38. Always wink.

What the bullshit is this?

Another one I had no idea about then, forgot about until now, and still have no idea.

84-91. There are new rules of tipping.

This might irritate or confuse you, but the reality is there are new social expectations around what deserves a tip.

These have, on the other hand, been on my mind. I've started to follow a simple rule: the more work I have to do, the less I tip. Full-service restaurant? Full tip. Delivery? Same. Pick up at restaurant? If I have to do the driving, I tip less. Uber? Always. (That's kind of a pun.) And if I have to order at a counter, wait, pick up my order, and bus my own table, they get nothing. I despise self-checkout, so I never use it, but I've heard some of them have now added tip begging to the checkout screens. Never. Not in a billion years. If I'm doing all the work, shouldn't I be getting the tip?

I'm considering implementing another one: if the screen suggests something like a 50% tip, they get nothing and I never go back. Already did that for cabs in Vegas. That's when I signed up for Uber.

Some people suggest memorizing who gets lower wages and tip all of them. I guess you can do what you want, but I still think it should be based on actual service, not intricate economic knowledge. I'd prefer a system where people get paid by their actual companies, and not the customers. Raising prices to compensate would make little difference in total amount spent.

Obviously, these tipping tips are only valid in the US.

Enough of that. The "rules" that really raise my hackles? There are some pearls of advice that suggest that one should do the opposite of what you're asked. Like, "Even when a kids’ party says 'no gifts,' you’re supposed to bring a gift." I've lived my entire life in the South, with frequent trips to New York (whose population this article was obviously aimed at). Doing the opposite of what someone says has always been a Southern thing, and I don't like it here, either. In New York, this "I know I asked you to not to being a gift, but what I meant was bring a gift" or similar would be like traveling to Italy and seeing everyone speaking in perfect, unaccented English without moving their hands. It's not right. It breaks my entire conception of how the world works.

Doing as asked is a mark of respect and courtesy. Anything else requires one to memorize a maze of rules, and I don't have the bandwidth for it. On the flip side of that, it's courteous to state your desires plainly. Don't be coy. "Don't bring a bottle of wine" means "don't bring a bottle of wine," not "bring a bottle of wine."

It's not that I try to be discourteous. I'm simply not a mind-reader, and some of society's expectations are opaque to me.

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