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Monday, May. 6, 2024

3:41am 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 19 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

a day 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 19, 2022 at 12:01am

#1030967

Save Game

Today's link will probably only make sense to people in the US. Or, more accurately, some people in the US.

401(k) Plans No Longer Make Much Sense for Savers
The inherent extra return participants enjoyed for many years has almost disappeared because of changes in tax laws and high fees.

So if you don't know what the hell this is all about, congratulations.

The tax advantage of a 401(k) depends on four factors, all of which have changed dramatically since 1980 to the detriment of 401(k)s.

I'm certainly not going to argue the numbers here; they seem right. I do wonder if one can truly extrapolate the average situation here, as the author does, to give advice to everyone.

Nevertheless, the reason I'm sharing this article isn't to nitpick it, but to point out something that I should formalize into a Law of Life, though I'm not quite sure yet how to boil it down to bumper-sticker philosophy (or even if I should)

That observation is this:

Any advantage the ordinary person might enjoy will promptly be socially engineered out of existence.

There's also this bit from the article:

Reducing taxes on 401(k)s will cost the government money, but it could be a good investment if it results in retirement security for more middle-income households.

Except that it would be an even better investment for the government to ensure that people don't retire, so they can continue to pay higher taxes until death.

When I was a kid, saving was considered a virtue. Not that I was any good at practicing that or any other virtue, but at some point, most likely coinciding with the 1980s, we collectively decided that saving was for suckers, and to keep the economy going, we should spend, spend, and spend some more. And then borrowing money became easier for most people, so the economy retooled itself again. Can't afford something? No problem, just go into debt. We offer easy finance terms!

Younger people today don't expect to ever retire anyway, so why bother saving anything?

This, of course, plays right into the hands of our economic overlords.

So how do you get ahead? Well, I don't know. Some people never will, though it's important to hold out a carrot of hope to them, usually in the form of a lottery. Even without state-sponsored gambling, though, a lot of it comes down to luck.

The whole deal with any kind of retirement account, at least here in the US, is a trade-off: do I pay taxes now, or defer them until later? Deferring them until later requires that you make some assumptions about "later." What will inflation look like? How will tax brackets be handled, and where do I expect to be in them? Will the government cave in to short-sighted efforts to increase the capital gains tax rate? Will all of this effort be in vain because we're going to get nuked anyway?

If you asked these questions in 1982 about 2022, you'd have gotten the answers wrong. Back then, we all figured we'd either be radioactive craters by now, or populating a Mars colony. Or maybe even both.

The reality, as always, turned out to be way worse.

5 Like • Comment • View 4 comments

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