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Wednesday, May. 1, 2024

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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:

Elisa the Bunny Stik

about 5 hours ago
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 of House Lannister

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 going to 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 going to 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.

Kåre Enga going to Montana

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

April 18, 2024 at 10:15am

#1069054

Cash Stash

This Guardian article should be uncontroversial.

‘Outdated and misleading’: is it time to reassess the very concept of money?
It’s regularly being created and destroyed – and economic models that don’t reflect that fact are not even slightly useful

...not.

The article itself, which begins with the simplistic concept of banking enunciated in the well-known movie It's a Wonderful Life, isn't as amenable to out-of-context quotations as some of the stuff I post here. I haven't seen that movie in decades, by the way, but I do remember the scene in question: George Bailey (James Stewart) dealing with a potential run on the bank.

When you borrow money and your bank credits your loan account, the account balance is created anew, “from thin air”, not from or in relation to existing deposits or other existing money. And as you repay the loan principal, the money created at the time of the loan gradually disappears, reverting to its previous form of airy nothingness.

I'm no economist money talker person, but to me, that just sounds like someone figured out that negative numbers exist and can be operated upon just like positive numbers.

Your deposit account is a liability for your bank and, as a depositor, you are no more than one among many of the bank’s unsecured creditors.

Leaving aside for the moment the mistaken assumption that everyone has enough unspent money to even have a deposit account, this has been the way it works for at least as long as I've been alive. Which, of course, doesn't mean it's the only way to do things.

In normal times a promise from a private bank is nearly as good as a promise from a government or a central bank. But in a crisis the promise is worth much less, and can be worth as little as nothing at all.

That may be true in the UK, where this source is based (I don't know), but here, we have federal deposit insurance for that sort of thing, as a result of the Great Depression.

If money is as unreal and ephemeral as they claim, though, a run on the bank shouldn't make a difference. The bank, or its insurance agency, could just conjure more out of the same "thin air" that they do when you get a loan. That it does make a difference tells me there's something incomplete about this article's assertions.

Details aside, the US and UK banking and government systems aren't all that different from each other where finance is concerned, so I'm not saying this article is completely useless on my side of the pond.

There's a bit more I can't really quote out of context, then:

Crucially, society as a whole needs to think differently about the nature of money –possibly by first discarding the term itself. “Money” encompasses a range of phenomena that have intrinsically different purposes and risks.

Well, yeah. I've known that for a while. Look up money supply.

Oh, wait, no, I just did that so you don't have to.

The article's conclusion:

A new financial conversation would make the causes of inter-generational inequities more explicit, and it would allow the community to rethink allowing “too big to fail” banks to earn, year in year out, enormous risk-free profits.

There may be ways to accomplish these seemingly-worthy goals without drastically switching to what appears to be a Star Trek economy, which, in truth, would never work without access to near-unlimited free and clean energy. Not that it's ever properly explained in the Star Trek universe, except for maybe holding up the capitalistic Ferengi as counterexamples to it.

The truth that no one seems to acknowledge is that our current system requires an underclass. Okay, that might not be a "truth," but only my opinion, and, like I said, I'm not an expert. The underclass doesn't have to be a particular demographic, though, sadly, it has been. Gotta have people desperate enough to eat and otherwise stay alive, so they'll take the crappy but necessary jobs that almost no one would freely choose.

That's not freedom. That's economic coercion. But any suggestions to improve it are above my pay grade.

Pun intended.

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