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Tuesday, May. 7, 2024

12:42pm 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

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.

🌕 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

September 3, 2020 at 12:07am

#992214

Everyone's a Critic

Does getting a failing grade on an elementary school art project count?

PROMPT September 3rd

Describe a time when your work was criticized. How did you react?

Well, of course my work gets criticized on a regular basis. I'm a writer on a peer review website. We all are, and it's part of the deal here. In fact, sometimes I wish for more criticism. "I love this!" is great to hear, yes, tell me that, don't stop, oh! But the only part of me that grows from it is my... ego. (What were you expecting me to say?)

But oodles of reviewing articles abound on this site, including one in my own port, so there's no need to belabor the point. I'm going to talk about my previous life as a professional.

Don't worry. I'm not going to go into details. The details of civil engineering, especially on the small scale that I practiced it, are incredibly boring. (That's a civil engineering pun. Boring? Because we sometimes bore to install.. oh, never mind.) So I'll write in broad generalities.

I worked on the design of a subdivision. Roads, lots, sewer, water and -- the important part for this discussion -- storm drainage.

Used to be you could design a subdivision and put in a pond downstream that caught all the runoff and released it slowly. But then there came issues with wetlands disturbance, and that sort of thing was frowned upon. So instead of one big pond that disturbed a natural stream, I needed to put in dozens of little ones to catch the runoff before it got to the existing streams. Again, I'm oversimplifying here, but I can already sense you nodding off. Bear with me just a little longer.

Well, this method was not only time- and math- intensive, but it was new to me and, more importantly, it was new to the people whose job it was to review the plans for compliance with local, state, and federal regulations.

Said reviewers tore me a new one for overcomplicating things.

How did I react? Well, my first reaction -- a private one -- was anger. What the hell was I supposed to do? I had to put in stormwater management, and couldn't do it in the traditional way, so I basically invented a new paradigm. Don't give me too much credit for that, though; I found out later that other people were already doing similar stuff, and I didn't know about it because, honestly, civil engineering advances on that small a scale aren't exactly fast-paced, so we didn't keep up with the literature like, say, computer scientists are supposed to.

So yeah, anger -- but it was short lived and, like I said, private. After taking a few deep breaths, I arranged a meeting with the reviewers and we hashed it all out like the professionals we all were.

Sorry there's no big denouement here; like I said, the details are ennui-inducing, and far in the past now. Hell, I don't know if the subdivision ever got built. The developer handled things after the plans were eventually approved, and this was just before the Bush recession.

I guess the point is that this is not the sort of thing I take personally -- provided it's not a personal attack in the first place. Getting back to writing, if I get a review that essentially says "this story sucks and here's why," I take it seriously. If I read, "you suck and here's why," well, that's another issue entirely. Fortunately, I don't recall any of that on this site.

On a related note, I went to see Tenet yesterday; Alamo had early access screenings. Once again, it turned out to be a private viewing. I was the only one in the theater. Great for avoiding the 'rona, probably not so great for Alamo's bottom line. Anyway, the movie was not nearly as clever as its makers thought it was. Now, I can't say "Christopher Nolan is a hack," because I've seen his other stuff and a lot of it is very good. But I, personally, would hate to put that much work, that much of my heart and soul into a movie, only to have someone (like me) with absolutely no talent for moviemaking say that it sucked. I suppose you have to develop a thick skin, like a politician.

I'm not sure I could do that, which is one reason I haven't aggressively pursued publishing. I mean, what if I succeed and some idiot calls me a no-talent hack?

I guess that ties into yesterday's entry, too.

Speaking of which, thanks for all the comments. I appreciate all of them, even the ones that disagree with me... because I can accept other points of view besides my own. I'm going to give today's MB to Charlie ~

, though, because of the math thing:

Math is probably one of the best examples of not people not believing in themselves. I don't know how many times in school I heard people say that math "just wasn't their thing" or "better you than me" when they found out my majors. I'll concede that some people have a natural aptitude for math, but it's absolutely learnable, just like any other language.

I think a lot of that falls on teachers though because the teachers in my formative years did not instill a lot of self confidence in us when it came to learning math. I do think you have to have a special understanding of mathematics to actually be able to present it in an understandable way. It seemed like my teachers gave up pretty quickly on students and allowed them to just go with the "I don't do math" mentality.

I mean, after all, math is the central metaphor for this blog. But also it got me thinking: the way other people are about math is the same way I am about art and music. I've tried both, with lousy results... but I love to look at art and listen to music. It's very frustrating to me that I can't create them the way other people seem to do so effortlessly.

Perhaps I just haven't tried hard enough. Or maybe I've just had it instilled in me from a very early age that I just don't have the aptitude for these things. So even though I (and Charlie) spoke about math blockage, I understand because I'm blocked in other areas.

Please keep the comments coming; I'll award another one of my free Birthday Week Merit Badges tomorrow, but mostly I just like feedback - positive or otherwise.

6 Like • Comment • View 7 comments

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