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Thursday, May. 9, 2024

9:49am 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:

Lazy Writer est 4/24/2008

about 19 hours ago
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

about 23 hours ago
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
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

May 4, 2024 at 5:42pm
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.

February 17, 2024 at 9:04am

#1064327

Inside Voice

Bit out of the ordinary for me today—a link sent by a friend:

Some People of Color Don't Like the Outdoors and That's Okay

As I, too, shun the not-so-great outdoors, I found great wisdom in these words.

The outdoor industry has spent hundreds of millions in marketing dollars to convince you that everyone belongs outside.

To be fair, lots of industries spend lots of money trying to convince us that everyone needs their products.

That simply isn’t true. Some People of Color aren’t outside for very valid reasons.

As far as I'm concerned, every reason is a valid reason, but I can only imagine how much worse it must be when you have to be concerned that racist rednecks love to be outdoors. With guns.

Some don’t like the outdoors and that’s okay.

"I don't like it" is a valid reason. So is "I don't want to."

They don’t need you to convert them. Unless, maybe, you’ve found the perfect beginner-friendly hike that ends in a waterfall and free universal healthcare.

Okay, that bit made me laugh.

But failing that, here are eight reasons why you should leave your friends and family alone.

Oddly, like Cracked (which this isn't from), it's a countdown list. I won't be covering everything.

Some of us occupy entirely different realities from our parents. For us, sleeping on the ground is an adventure. For them, sleeping on the ground is elective poverty and strange (or a bad memory). Why would they pay to do that?

I've gone on about this sort of thing before. You live in a nice house, and you want to experience two weeks of homelessness? With bears and snakes? Okay, you do you, but count me out.

Some of your friends aren’t interested in hiking or climbing because they can’t afford to get hurt and miss work. They also can’t afford medical care.

Laaaaand... of the... freeeeeee!

And yes, you can get hurt at home, too. But I'm pretty sure the chances of that go up in areas of uncertain footing, wild animals, and stinging insects.

4. They don’t want to get their hair wet

This section turned out to be important for me to read, because I was mostly unaware of this aspect of culture.

3. They don’t have the money

We like to pretend that being outside doesn’t cost a thing. And it’s weird. Stop that.

While poverty looks different for different people, this point is something to remember when considering a trip to the not-inside. Proper gear (which I'm sure would help reduce the chance of injury, as above) can get expensive. Even those not experiencing poverty might have better (to them) things to spend money on.

Why do we pretend that the outdoors costs nothing—that you are required to bring nothing but yourself? Then in the next breath we shame hikers who don’t bring reusable water bottles, moisture wicking technical clothing, wool base layers, wind and water resistant shells, puffers, GPS, a trail map subscription with downloaded maps, a paper map and compass, etc.

I read an article about someone who died on Mount Washington in New Hampshire last month. The article described him as an "experienced hiker." Now, I certainly don't claim to be an expert on mountaineering, though, yes, I've hiked mountains, and experienced firsthand how quickly the weather can turn on you there. And I've read that Mount Washington is the worst of the bunch, being well-known for having logged the highest recorded non-cyclonic wind speed of any point on Earth. So my first thought was "Funny; I thought 'experienced hikers' don't mess with Mount Washington in fucking January."

It’s winter now and social media is full of photos and videos of happy people skiing, snowshoeing, tubing and snowboarding.

One of those things is not like the others...

Anyway, while a lot of the cultural reasoning doesn't apply to me, and to be fair, I was privileged enough to spend a lot of time outdoors as a child and young adult before deciding I just didn't like it, I appreciate the article's perspective. And to be clear, it's not "being outside" that I dislike; it's being farther than a short walk from civilization.

Now watch, some marketing guru is going to try to take all the stuff in that article into account the next time they need to market a line of rugged-yet-fashionable outdoor wear that'll be lucky to last for a year.

3 Like • Comment • View 5 comments

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