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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

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Show Recent Comments

10 Most Recent Blog Comments:

Kåre Enga in Udon Thani

about 14 hours ago
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 Udon Thani

about 15 hours ago
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 in Udon Thani

about 15 hours ago
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

a day ago
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

a day ago
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

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

October 7, 2021 at 12:01am

#1018859

Personality

No, I don't get all my information from Cracked. But it's enough so the random numbers occasionally give me two or more in a row.

Why The Myers-Briggs Personality Test Is Nonsense

I see M-B stuff fairly often, though not as often as I used to. I haven't been a fan, but I also lack the background to criticize it in any meaningful way. Fortunately, others have stepped up.

If you use social media or dating apps, you’ve seen Myers-Briggs Type Indicators in profiles. INTJ, ENFP, STFU, and so on.

I see what you did there. But I don't use social media or dating apps.

The 16 different personalities are shorthand for how you view the world. Essentially horoscopes for people who think they’re too smart for horoscopes, they’re often found alongside words like “Believer in Science” or “I’d let Nikola Tesla touch my spheres.”

Basically, this.

It won’t shock you to learn that they’re about as predictive as a quiz on the Denny’s children’s menu, but why? And how did we reach the point where they’re so popular?

Of course, the article goes on to answer its own questions. I'll let you take a look for yourself.

But Myers-Briggs still has plenty of issues, starting with the fact that basing a test on Jungian archetypes is like basing your surgery on bloodletting. Jung himself warned that his archetypes were only rough concepts and, like the MBTI, they’ve since been discredited almost entirely.

I will say this, though: as with archetypes, or horoscopes, the test might have no validity in the real world, but I feel like if people want to use it for writing? Go for it. It's like... I have no belief in the supernatural, and yet I enjoy reading/viewing supernatural fiction. I know it's fiction; I don't try to apply it to The Real World^TM.

And no one is just an extrovert or an introvert like a stock TV character; not only are there too many factors to declare such stark differences, but introversion and extroversion are largely constructs that lack context (you can, for example, be introverted at work around colleagues but extroverted at a party among your friends).

I've described myself as an introvert before, though I've never been diagnosed as such (as if it were some sort of disease, which obviously it isn't). What I mean by being an introvert is that I need my downtime away from other people. Generally, when I am around other people, I can be as open and outgoing as anyone. Some of you have met me, and have probably noticed this. I just have a limited amount of energy for such things. If I had to be around other people for too long -- say a day or so -- it would be utterly exhausting.

But I don't get my self-diagnosis from the MBTI; it's just that after a few years of trying, I got to understand myself better.

Plus, if people take the test twice within a few weeks they often get different results, which doesn’t really make it an ironclad concept to build your personality around.

Confession: I've taken it a few times. What can I say? I'm a curious sort (I think that's on the test too). My results change almost every time. Also, some of the responses can be easily gamed. If you want to come across as an extrovert, for example, you can give a positive response to "I love being around other people." Or something. It's been a long time, so I don't remember how the questions are actually worded.

People say, "Well, you're only supposed to take it once." But if a test purports to measure a person's basic personality, and that personality doesn't change over time, it should give consistent results. If someone's personality does change over time, why bother testing it? It becomes a mood ring instead of a tattoo.

Free idea: use mood ring ink in tattoos. You're welcome.

None of this were a problem if people weren't using MBTI to determine a person's actual fate. It would be like if you went to a job interview and everything was going swimmingly. You're really clicking with the interviewer, and you're nailing the hard parts, like "What do you see as your greatest weakness?" and "If you were a bear, what kind of tree would you scratch your ass on?" Then the interviewer asks, "So, what's your zodiac sign?"

"Pisces," you say with great confidence, as even non-astrologers have their sun signs memorized.

The interviewer gasps through her teeth. "Oh, sorry, we don't hire Pisceses."

And you're done. I mean, okay, such a scenario isn't as bad as racism, sexism, ageism, anti-Semitism, or any of those other isms, but you're still getting banged on out of there for something you can't control.

And yet, even getting passed over for Piscesism can't be so bad; after all, you wouldn't want to work for a company that's that committed to pseudoscience, would you? Such a company would be fishy. But the MBTI has the patina of science, unlike astrology. You've just been kicked out for a completely bullshit reason.

The article goes into this, too; I just wanted to put my own spin on it.

If someone can find guidance from Myers-Briggs without building their whole life around it, well, we all need guidance from somewhere. But there’s something bleak about carving humanity up into immutable categories based on fundamental misconceptions like we’re in a YA dystopia.

Sometimes I get guidance from a die roll or a coin toss. I don't pretend it's fate working in mysterious ways; it's just that sometimes, any decision is better than waffling. I don't think MBTI is any better or worse than a 20-sided die, except that my D&D character never had to try to dodge a fireball using the MBTI.

So anyway, I hope I (and Cracked} didn't burst anyone's bubble here, but basically, MBTI might as well stand for "More Bullshit Testing Ideas." Or something. I suck at acronyms; where's that on the test?

5 Like • Comment • View 4 comments

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