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Sunday, May. 5, 2024

5:35pm 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 9 hours ago
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

about 24 hours ago
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
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

April 5, 2021 at 12:01am

#1007766

Procrasti-later

Here's another one for all my fellow procrastinators out there. I keep meaning to get a procrastinators' convention together, but can't ever seem to get around to it.

'Why Do I Spend Weeks Avoiding Tasks That Will Take Me 10 Minutes to Do?'
Procrastinating has less to do with time management and more to do with mood management.

The article is dated from mid-January and I'm just now posting it.

Sometimes we just can’t make ourselves do stuff! Last month, when I asked people to talk about times they’d opted to not do something that they could also simply… do… my mentions were flooded.

Example: taxes. Here in the US, the Federal income tax deadline is usually April 15, though it's been extended this year due to... you know. Individual states, the ones that have state taxes, have different deadlines. Either way, it needs to be done soon. My accountant has been bugging me, and I've collected most of what I need. The rest? Well. I'll get to it eventually.

I can't tell you how many times I've mentally prodded myself to Just Do The Thing and yet fail to do that very thing. Until it's the last minute. Or after. Blogging every day has helped a little bit with that, but the underlying problem (me) remains.

Whether it’s watching your plants wither for weeks before repotting them (total time to complete: six minutes) or waiting until you get pulled over to replace the registration sticker that’s been expired for a year (that was me, I did this), a lot of folks are procrastinating on alllll kinds of little things.

How about procrastinating on getting someone to edit your article?

Why, exactly? When it’s relatively simple to Do The Thing, and when the consequences of Not Doing The Thing can be serious or fairly unpleasant, why do so many of us look the other way?

Of course the article goes on to answer that question. It's a Vice article, not clickbait. Oh, wait...

“We get punished for being late in our culture,” Ferrari said. “We don’t get rewarded for being early.” And when you internalize the message that there’s no point in being early, you can apply that to any task that needs doing.

Well, that's just a matter of point of view, isn't it? If you're a procrastinator, things are often late and you suffer negative consequences. These consequences comprise your default. So anything better than the default is a reward, such as not suffering negative consequences. That's the same thing as a reward in my book.

“Procrastination is an avoidant way of coping,” Sirois said. “How do I manage uncomfortable feelings around that paperwork I have to do? I know, I’ll put the task aside and feel better about it. Ah, I feel better already. You just managed your mood by procrastinating.”

This makes sense. To go back to the taxes thing, I always end up owing money. I do not want to pay money. So I put it off. Which sometimes means I owe more money.

That fear of fucking up can keep you from starting in the first place—even if it’s a little thing like taking five seconds to write a text or answer an email. And on the other hand, if you do a good job... well, what if you can’t maintain it? What if you can’t do it as well the next time?

Which may explain at least one reason I haven't really pursued story publication.

Procrastination tends to be a solitary struggle, but literally everyone does it!

I know people who don't. Stop misusing "literally."

And if this behavior has become a regular occurrence—the kind of thing that’s paralyzing you in your personal and professional life or preventing you from reaching your goals—it might be time to talk to a professional. Chronic procrastination can be a symptom of anxiety disorders, depression, and ADHD; a mental health expert will be able to tell you more.

I've had a shrink's number pasted on my board since December. Have I called them yet? What do you think?

2 Like • Comment • View 4 comments

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