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Wednesday, Apr. 24, 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:

Aiva Raine

about 4 hours 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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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?

Aennaytte: Free & Wild in GoT

a day ago
In response to "Going to the Dogs"

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

May 17, 2021 at 12:07am

#1010284

Connections

PROMPT May 17th

“Nothing of me is original. I am the combined effort of everyone I’ve ever known.” — Chuck Palahniuk

Read this article

and share your thoughts about how the people in your life have had an impact on you.

“They’ve all helped me grow, become more resilient, and many supporting me when I most needed it. I’ve learned, matured, and became wiser thanks to my interactions with them.”

https://medium.com/change-your-mind/we-are-a-mosaic-of-everyone-weve-ever-loved-...

Okay, well, that Palahniuk quote is trivially true. I'm usually quick to side with "nurture" in the "nature vs. nurture" debate -- meaning that our lived experience is far more important than genetics in determining who we are. That's probably because my "lived experience" comes from having been adopted as an infant, so take that for what it's worth.

The article, however, quickly delves into territory that would make it great blog fodder, had I found it first during a time when I'm not doing a blog challenge.

I generally have two main categories of blog fodder: articles I like because they explain things better than I ever could, and articles that I like because I get to snark on them.

This is one of the latter, so buckle up.

Indeed, nothing is original.

For various definitions of original, okay.

We’ve inherited everything that defines us as individuals. Our genetic makeup determines a great deal of who we are; the rest deriving from our interactions with others and our environment. Yet the combination of these traits is what makes each person unique.

I'd turn that around (though probably genetics has a greater impact on appearance). But I see what the author's doing: making a distinction between "original" and "unique." This is, in my view, a distinction without a difference. Each of us is unique. Each of us is original. But each of us is also part of a continuum; a process that started with the Big Bang, proceeded through the formation of the solar system and the first life, and continues in an unbroken chain.

This, too, is profound but trivial.

Your parents (or primary caregivers) had the largest and most significant impact on the person you are today.

Typically, they’re our first encounter with the opposite sex, heavily influencing the romantic partners we unconsciously seek later on.

And? By the time I encountered females other than my mother, I still hadn't internalized what sex differences really were. I suspect most people are the same in that regard. Incidentally, I just saw an article about a monk who died, at a ripe old age, supposedly having never encountered a female person. He was abandoned at the monastery at an early age, and they (officially) didn't let women in. Somehow, this is presented so as to show how holy he was.

A myriad of mental illnesses and personality disorders can also be traced down to how we related to our caregivers during our first years of life.

That sounds Freudian. Almost everything Freud said or believed has been shown to be, at best, misguided.

Today I’m doing the inner work; embracing the positive, cherishing the memories, forgiving what hurt me, and releasing what no longer serves my highest good.

After reading that sentence, my inner work involves swallowing some Pepto-Bismol to counteract the gorge that's starting to rise. This, I think, is one thing that Elisa the Bunny Stik

refers to as "toxic positivity."

Siblings

Siblings play a huge role in our lives. Raised within the same household, they can comprehend our trials and tribulations far more profoundly than others.

And I am eternally grateful that I never had any.

Extended Family

As my genetic background is, by my choice, almost entirely unknown (I mean, it's pretty obvious my genes come from northern Europe, but other than that, who knows), I consider the world my extended family.

My Friends

“Friends are the family we chose for ourselves” — Edna Buchanan

Friends are the family that we're socially allowed to distance ourselves from when they become assholes.

Romantic Partners and Interests

Intimate partners usually mirror plenty of aspects buried deep within us, causing unresolved issues to surface and pushing us to evolve. Thus, romantic relationships are immense learning experiences.

As all of these have ended badly, I no longer pursue such things.

However, we cannot solely blame the other person for how things turned out. It takes two to tango, and we must assume responsibility for our own shortcomings.

I do. That's why I stopped.

Neighbors, Coworkers, Roommates

Believe it or not, for the better or the worse, many of them have somehow marked my life.

Um... DUH. Often these are people we don't choose (with the possible exception of roommates). Some of them become friends. Either way, they're going to have an effect on your life. There's no "believe it or not" involved; they're people we interact with.

Strangers

“No one is sent by accident to anyone” — A Course in Miracles

Oh, man, I wish she'd led with that quote. It would have saved me a lot of time and effort, 45 minutes that I could have spent watching Star Trek, playing a video game, masturbating, or sending internet memes to friends -- all of which are FAR more productive uses of time than even contemplating that stupid fucking book.

But since I'm here anyway, allow me to deconstruct.

"No one is sent..." Passive voice. Sent by whom? Knowing what I know about ACIM, it's "the Universe," or the New Age conception of God. This goes against every fiber of my belief. No one "is sent," period. End of sentence. We may not truly have free will, but nor does some Uber-consciousness direct our actions. More importantly, you are not the purpose of the Universe. Neither am I. I realize other people disagree with this, but it is a big part of why ACIM is anathema to me. (Though I have to admit that one of my great epiphanies in life was triggered by ACIM -- but not in a way the book intended.)

"...by accident..." This is a philosophical distinction, but to me, pretty much everything is an accident at base.

"...to anyone." In a backwards-looking sense, everything that has ever happened to you leads up to the present moment. People have gazed upon this simple truth in wide-eyed wonder. "If I hadn't turned right instead of left, I never would have run over your dog, and we would have never met, and we wouldn't be getting married right now." Big whoop. You'd meet someone else, or learn to live in comfort with yourself, and then you'd contemplate all the accidents that led you to that moment in wide-eyed wonder.

This does not mean we're fated. This means we're adaptable to many different situations.

Anyway, once I encounter a quote from ACIM (or "The Secret,") I Stop Reading Right There. (Exception: when someone is ragging on it, like I'm doing right now.)

So instead I'll expand on the "one of my great epiphanies in life" comment above.

It's my understanding that ACIM boils all human emotion down to two categories: love and fear. Well, I think that's reductionist and oversimplistic, but far be it from me to reject something without at least considering its worth. So I got to thinking: If all emotions are "really" either love or fear, what is fear but an emotional reaction to a real or imagined threat to something that you love? So if you go with the flow, here, you have to follow it to its logical conclusion, which is that the only emotion is love.

But believing so denies us our complexity, thus throwing the entire new-age positivity movement into shadow.

To sum up, yes, I agree with the main premise: that everyone, everything, is interconnected. Again, this is trivial. There's nothing mystical about it. No person is an island, to paraphrase a famous quote. And even if we were, we'd be defined by the ocean around us.

“A certain man once lost a diamond cuff-link in the wide blue sea, and twenty years later, on the exact day, a Friday apparently, he was eating a large fish - but there was no diamond inside. That’s what I like about coincidence.”
― Vladimir Nabokov

Edit:

You know, I was too busy being disgusted by the relentless positivity and New Age gooeyness (and subsequently drinking copious amounts of alcohol to counteract it) that I completely overlooked that the author made a really big, huge, glaring omission in the piece.

I don't see a single word about teachers, who are, after one's parents, the people who... well... teach us the most.

Yeah, this was an oversight on my part, but like I said, it's an enormous gaping void in the article.

Obviously, we have good teachers and bad teachers, but in the end, they all help to make us what we are.

11 Like • Comment • View 5 comments

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