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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:

Kåre Enga in Montana

about 12 hours ago
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

about 17 hours ago
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

a day ago
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

Kåre Enga in Montana

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 Montana

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.

February 14, 2019 at 12:32am

#951954

Dunning-Krugerrands

https://www.economist.com/finance-and-economics/2019/02/09/what-happens-when-you...

Ah... the frisson of schadenfreude.

BITCOIN WAS introduced to the world in August 2008, in the aftermath of the financial crisis. According to its techno-libertarian fan-base, one of its main attractions was the promise that users could avoid dealing with the hated banks. But after a decade of amateurism, scams and billions of dollars of lost or stolen money, it is clear that many of the ramshackle institutions that play the role of banks in the cryptocurrency world make even their most reckless conventional counterparts look like paragons of good management.

As an aside, there is literally no reason why anyone should be dealing with the Big Banks if they don't want to. While it will take a little work and maybe a little more planning, there are alternatives that don't involve ephemeral blockchain wizardry. Your local credit union, for example. Or national institutions such as USAA or Discover Bank. "But I like having the convenience of ATMs!" Yes, that is why these alternatives usually have deals where you get free withdrawals from any ATM. Most of them even have deposit-by-phone for checks. There are also debit cards available if you must go that route. And if you use credit cards or have/need a mortgage or whatever, there is, as I said, absolutely no reason you should ever have to deal with Wells Fargo and the like. And if people would stop dealing with Wells Fargo, they'd either have to change their ways or go out of business. Or, admittedly, pay off politicians to make the other banks go away, but that strikes me as way too obvious to ever actually work.

Anyway.

The latest example is QuadrigaCX, a Canadian cryptocurrency exchange that was granted protection from its creditors on February 5th. The problem, according to the firm, is not that it has lost its customers’ money, but that it cannot get to it. It says that Gerald Cotten, its boss, died unexpectedly in India in December.

And this is where the schadenfreude comes in. Look, I didn't know the guy, but I'm not celebrating his death; that's not the point. The point is that, unless he was delusional enough to believe in the Singularity or the promise of consciousness uploads - and, to be sure, anyone involved in cryptocurrency could easily be that whacked - he knew he was going to die, just as we all do. So it's not his death that amuses me; it's the fact that...

Mr Cotten was in sole charge of handling deposits and payouts, running everything from an encrypted laptop to which only he knew the password.

Now, to be fair, I don't have my passwords written down anywhere, either. That's just common sense. But then, I don't have (nominally) billions of dollars worth of bits hidden away in my laptop. Some stories and poems, some spreadsheets, some games, some porn, that's about it. Nothing anyone will miss when I inevitably kick it.

I can't say I really understand cryptocurrency. I have a vague understanding of what blockchain is, in a theoretical sense, and why it can underpin cryptocurrency. Thing is, though, I'm sure a lot of people don't understand cryptocurrency. But a lot of those people think they do, hence you get the wild speculation that we saw a couple years ago, culminating in a Dutch tulip-style bubble. That is why I call cryptocurrencies "Dunning-Krugerrands."

And I have a pretty firm rule about speculating in experimental markets: that is, don't speculate in experimental markets. You're better off going to Vegas, and that's not saying much.

Right now if any cryptofans are reading this, they're probably going, "Okay, sure, bitcoin isn't based on anything real, but neither are US dollars. ZING." Well, you have half a point. US dollars - most world currencies - are fiat currencies, meaning their value is pegged to no commodity (most used to be pegged to gold or silver, but that ended years ago). The USD is backed by the US government, which, despite attempts from all sides to bring it to a screeching halt, still keeps chugging along, if only on two cylinders. So, yeah, if the government collapsed, dollars would be worthless, just as bitcoins (or whatever) are worthless in the scenario in the linked article. But there's one important difference: If the US government actually collapsed, we'd have FAR bigger problems than the nominal value of the pieces of paper in our pockets. Contrariwise, if the owner of a cryptocurrency blockchain dies without a succession plan, you're boned - but you're still living in a semi-functioning economy.

Okay, enough of that. Yeah, some people bought bitcoins (or whatever) and got lucky. A lot of other people did not. Point is, a whole lot of people who really didn't understand what they were getting into are now boned. I can't feel sorry for them, though; it was a greed thing and not what anyone with any sense would call a wise investment. Look, you wanna gamble, I'm certainly not one to judge. But if you did, I don't think you knew the actual odds. And that's what's reckless, not the gambling itself.

1 Like • Comment • View 1 comment

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